refs.bib

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@Article{Gromos_2012,
  author   = {Schmid, Nathan and Christ, Clara D. and Christen, Markus and Eichenberger, Andreas P. and Gunsteren, Wilfred F. van},
  title    = {{Architecture, implementation and parallelisation of the GROMOS software for biomolecular simulation}},
  doi      = {10.1016/j.cpc.2011.12.014},
  issn     = {0010-4655},
  number   = {4},
  pages    = {890--903},
  volume   = {183},
  abstract = {{In this work the design of the latest version of the GROMOS software for biomolecular simulation, GROMOS11 is discussed. Detailed organisation and class descriptions of the MD++ simulation program and the GROMOS++ analysis package are given. It is shown how the code was documented, how it can be easily modified and extended, how debugging of it is carried out. Additional efficiency and parallelisation concepts are presented and benchmarked.}},
  journal  = {Comput. Phys. Commun.},
  year     = {2012},
}

@Software{kulhanek2011pmflib,
  author = {Kulh{\'a}nek, Petr and Mones, Letif and St{\v{r}}elcov{\'a}, Zora and Simon, Istvan and Fuxreiter, Monika and Ko{\v{c}}a, Jaroslav and others},
  title  = {PMFLib--A Toolkit for Free Energy Calculations},
  url    = {https://pmflib.ncbr.muni.cz},
  year   = {2011},
}

@Article{doi:10.1021/jp013346k,
  author  = {VandeVondele, Joost and Rothlisberger, Ursula},
  title   = {Canonical Adiabatic Free Energy Sampling (CAFES): A Novel Method for the Exploration of Free Energy Surfaces},
  doi     = {10.1021/jp013346k},
  eprint  = {https://doi.org/10.1021/jp013346k},
  number  = {1},
  pages   = {203-208},
  url     = {https://doi.org/10.1021/jp013346k},
  volume  = {106},
  journal = {J. Phys. Chem. B},
  year    = {2002},
}

@Article{Comer2014mwABF,
  author    = {Comer, Jeffrey and Phillips, James C and Schulten, Klaus and Chipot, Christophe},
  title     = {Multiple-replica strategies for free-energy calculations in NAMD: multiple-walker adaptive biasing force and walker selection rules},
  doi       = {10.1021/ct500874p},
  number    = {12},
  pages     = {5276--5285},
  volume    = {10},
  journal   = {J. Chem. Theory Comput.},
  publisher = {ACS Publications},
  year      = {2014},
}

@Article{Autieri_MetaD-US-2_JCP2010,
  author   = {Autieri, E. and Sega, M. and Pederiva, F. and Guella, G.},
  title    = {{Puckering free energy of pyranoses: A NMR and metadynamics-umbrella sampling investigation}},
  doi      = {10.1063/1.3476466},
  eprint   = {1006.2515},
  issn     = {0021-9606},
  number   = {9},
  pages    = {095104},
  volume   = {133},
  abstract = {{We present the results of a combined metadynamics-umbrella sampling investigation of the puckered conformers of pyranoses described using the GROMOS 45a4 force field. The free energy landscape of Cremer–Pople puckering coordinates has been calculated for the whole series of α and β aldohexoses, showing that the current force field parameters fail in reproducing proper puckering free energy differences between chair conformers. We suggest a modification to the GROMOS 45a4 parameter set which improves considerably the agreement of simulation results with theoretical and experimental estimates of puckering free energies. We also report on the experimental measurement of altrose conformer populations by means of NMR spectroscopy, which show good agreement with the predictions of current theoretical models.}},
  journal  = {J. Chem. Phys.},
  pmid     = {20831339},
  year     = {2010},
}

@Article{jourdain-lelievre-zitt-21,
  author  = {Jourdain, B. and Leli\`evre, T. and Zitt, P.A.},
  title   = {Convergence of metadynamics: discussion of the adiabatic hypothesis},
  doi     = {10.1214/20-AAP1652},
  volume = {31},
  number = {5},
  pages = {2441 -- 2477},
  journal = {Ann Appl Probab},
  year    = {2021},
}

@Article{wl_convergence,
  author  = {Yves F. Atchad{\'e} and Jun S. Liu},
  title   = {The Wang-Landau Algorithm in General State Spaces: Applications and Convergence Analysis},
  number  = {11},
  pages   = {209--233},
  volume  = {20},
  journal = {Stat Sinica},
  year    = {2010},
}

@Article{Pfaendtner2015_pbmetad,
  author   = {Pfaendtner, Jim and Bonomi, Massimiliano},
  title    = {{Efficient Sampling of High-Dimensional Free-Energy Landscapes with Parallel Bias Metadynamics}},
  doi      = {10.1021/acs.jctc.5b00846},
  issn     = {1549-9618},
  number   = {11},
  pages    = {5062--5067},
  volume   = {11},
  abstract = {{Metadynamics accelerates sampling of molecular dynamics while reconstructing thermodynamic properties of selected descriptors of the system. Its main practical difficulty originates from the compromise between keeping the number of descriptors small for efficiently exploring their multidimensional free-energy landscape and biasing all of the slow motions of a process. Here we illustrate on a model system and on the tryptophan-cage miniprotein parallel bias metadynamics, a method that overcomes this issue by simultaneously applying multiple low-dimensional bias potentials.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {26574304},
  year     = {2015},
}

@Article{10.1021/acs.jctc.5b00907,
  author   = {Dama, James F and Hocky, Glen M and Sun, Rui and Voth, Gregory A},
  title    = {{Exploring Valleys without Climbing Every Peak: More Efficient and Forgiving Metabasin Metadynamics via Robust On-the-Fly Bias Domain Restriction}},
  doi      = {10.1021/acs.jctc.5b00907},
  issn     = {1549-9618},
  number   = {12},
  pages    = {5638--5650},
  volume   = {11},
  abstract = {{Metadynamics is an enhanced sampling method designed to flatten free energy surfaces uniformly. However, the highest-energy regions are often irrelevant to study and dangerous to explore because systems often change irreversibly in unforeseen ways in response to driving forces in these regions, spoiling the sampling. Introducing an on-the-fly domain restriction allows metadynamics to flatten only up to a specified energy level and no further, improving efficiency and safety while decreasing the pressure on practitioners to design collective variables that are robust to otherwise irrelevant high energy driving. This paper describes a new method that achieves this using sequential on-the-fly estimation of energy wells and redefinition of the metadynamics hill shape, termed metabasin metadynamics. The energy level may be defined a priori or relative to unknown barrier energies estimated on-the-fly. Altering only the hill ensures that the method is compatible with many other advances in metadynamics methodology. The hill shape has a natural interpretation in terms of multiscale dynamics, and the computational overhead in simulation is minimal when studying systems of any reasonable size, for instance proteins or other macromolecules. Three example applications show that the formula is accurate and robust to complex dynamics, making metadynamics significantly more forgiving with respect to CV quality and thus more feasible to apply to the most challenging biomolecular systems.}},
  journal  = {J. Chem. Theory Comput.},
  keywords = {Journal Club},
  pmid     = {26587809},
  year     = {2015},
}

@Article{REST2_Wang_2011,
  author   = {Wang, Lingle and Friesner, Richard A and Berne, B J},
  title    = {{Replica Exchange with Solute Scaling: A More Efficient Version of Replica Exchange with Solute Tempering (REST2)}},
  doi      = {10.1021/jp204407d},
  issn     = {1520-6106},
  number   = {30},
  pages    = {9431--9438},
  volume   = {115},
  abstract = {{A small change in the Hamiltonian scaling in Replica Exchange with Solute Tempering (REST) is found to improve its sampling efficiency greatly, especially for the sampling of aqueous protein solutions in which there are large-scale solute conformation changes. Like the original REST (REST1), the new version (which we call REST2) also bypasses the poor scaling with system size of the standard Temperature Replica Exchange Method (TREM), reducing the number of replicas (parallel processes) from what must be used in TREM. This reduction is accomplished by deforming the Hamiltonian function for each replica in such a way that the acceptance probability for the exchange of replica configurations does not depend on the number of explicit water molecules in the system. For proof of concept, REST2 is compared with TREM and with REST1 for the folding of the trpcage and β-hairpin in water. The comparisons confirm that REST2 greatly reduces the number of CPUs required by regular replica exchange and greatly increases the sampling efficiency over REST1. This method reduces the CPU time required for calculating thermodynamic averages and for the ab initio folding of proteins in explicit water.}},
  journal  = {J. Phys. Chem. B},
  pmcid    = {PMC3172817},
  pmid     = {21714551},
  year     = {2011},
}

@Article{REST1_Liu_2007,
  author    = {Liu, P. and Kim, B. and Friesner, R. A. and Berne, B. J.},
  title     = {Replica exchange with solute tempering: A method for sampling biological systems in explicit water},
  doi       = {10.1073/pnas.0506346102},
  issn      = {1091-6490},
  number    = {39},
  pages     = {13749–13754},
  url       = {http://dx.doi.org/10.1073/pnas.0506346102},
  volume    = {102},
  journal   = {Proc. Natl. Acad. Sci.},
  month     = {Sep},
  publisher = {Proc. Natl. Acad. Sci. U.S.A.},
  year      = {2005},
}

@Article{Henin2022dashboard,
  author        = {H\'enin, J\'er\^ome and Lopes, Laura J. S. and Fiorin, Giacomo},
  journaltitle  = {J. Chem. Theory Comput.},
  title         = {Human learning for molecular simulations: the Collective Variables Dashboard in VMD},
  eprint        = {2110.08758},
  url           = {https://pubs.acs.org/doi/10.1021/acs.jctc.1c01081},
  archiveprefix = {arXiv},
  journal       = {J. Chem. Theory Comput.},
  primaryclass  = {physics.comp-ph},
  year          = {2022},
}

@Article{denOtter2000,
  author    = {den Otter, W. K.},
  title     = {Thermodynamic integration of the free energy along a reaction coordinate in Cartesian coordinates},
  pages     = {7283-7292},
  volume    = {112},
  journal   = {J. Chem. Phys.},
  owner     = {jhenin},
  timestamp = {2006.09.15},
  year      = {2000},
  doi = {10.1063/1.481329},
}


@Article{Lelievre2007,
  author      = {Tony Leli{\`e}vre and Mathias Rousset and Gabriel Stoltz},
  title       = {Computation of free energy profiles with parallel adaptive dynamics},
  doi         = {10.1063/1.2711185},
  number      = {13},
  pages       = {134111},
  url         = {http://dx.doi.org/10.1063/1.2711185},
  volume      = {126},
  abstract    = {We propose a formulation of an adaptive computation of free energy differences, in the adaptive biasing force or nonequilibrium metadynamics spirit, using conditional distributions of samples of configurations which evolve in time. This allows us to present a truly unifying framework for these methods, and to prove convergence results for certain classes of algorithms. From a numerical viewpoint, a parallel implementation of these methods is very natural, the replicas interacting through the reconstructed free energy. We demonstrate how to improve this parallel implementation by resorting to some selection mechanism on the replicas. This is illustrated by computations on a model system of conformational changes.},
  institution = {CERMICS, Ecole Nationale des Ponts et Chaussées (ParisTech), 6 and 8 Avenue Blaise Pascal, 77455 Marne-la-Vallée, France. lelievre@cermics.enpc.fr},
  journal     = {J. Chem. Phys.},
  owner       = {jhenin},
  pmid        = {17430020},
  timestamp   = {2009.06.29},
  year        = {2007},
}

@Article{doi:10.1021/acs.jctc.8b00500,
  author  = {Zimmerman, Maxwell I. and Porter, Justin R. and Sun, Xianqiang and Silva, Roseane R. and Bowman, Gregory R.},
  title   = {Choice of Adaptive Sampling Strategy Impacts State Discovery, Transition Probabilities, and the Apparent Mechanism of Conformational Changes},
  doi     = {10.1021/acs.jctc.8b00500},
  eprint  = {https://doi.org/10.1021/acs.jctc.8b00500},
  number  = {11},
  pages   = {5459-5475},
  url     = {https://doi.org/10.1021/acs.jctc.8b00500},
  volume  = {14},
  journal = {J. Chem. Theory Comput.},
  pmid    = {30240203},
  year    = {2018},
}

@Article{Andersen1983,
  author    = {Hans C. Andersen},
  title     = {Rattle: A ``velocity'' version of the {Shake} algorithm for molecular dynamics calculations},
  doi       = {10.1016/0021-9991(83)90014-1},
  number    = {1},
  pages     = {24--34},
  volume    = {52},
  journal   = {J. Comput. Phys.},
  month     = {oct},
  publisher = {Elsevier {BV}},
  year      = {1983},
}

@Article{WANG2020139,
  author   = {Yihang Wang and João Marcelo {Lamim Ribeiro} and Pratyush Tiwary},
  title    = {Machine learning approaches for analyzing and enhancing molecular dynamics simulations},
  doi      = {10.1016/j.sbi.2019.12.016},
  issn     = {0959-440X},
  pages    = {139-145},
  url      = {https://www.sciencedirect.com/science/article/pii/S0959440X19301551},
  volume   = {61},
  abstract = {Molecular dynamics (MD) has become a powerful tool for studying biophysical systems, due to increasing computational power and availability of software. Although MD has made many contributions to better understanding these complex biophysical systems, there remain methodological difficulties to be surmounted. First, how to make the deluge of data generated in running even a microsecond long MD simulation human comprehensible. Second, how to efficiently sample the underlying free energy surface and kinetics. In this short perspective, we summarize machine learning based ideas that are solving both of these limitations, with a focus on their key theoretical underpinnings and remaining challenges.},
  journal  = {Curr. Opin. Struct. Biol.},
  year     = {2020},
}

@Article{10.1021/acs.biochem.8b00977,
  author   = {Ribeiro, João Marcelo Lamim and Tsai, Sun-Ting and Pramanik, Debabrata and Wang, Yihang and Tiwary, Pratyush},
  title    = {{Kinetics of Ligand–Protein Dissociation from All-Atom Simulations: Are We There Yet?}},
  doi      = {10.1021/acs.biochem.8b00977},
  issn     = {0006-2960},
  number   = {3},
  pages    = {156--165},
  volume   = {58},
  abstract = {{Large parallel gains in the development of both computational resources as well as sampling methods have now made it possible to simulate dissociation events in ligand-protein complexes with all--atom resolution. Such encouraging progress, together with the inherent spatiotemporal resolution associated with molecular simulations, has left their use for investigating dissociation processes brimming with potential, both in rational drug design, where it can be an invaluable tool for determining the mechanistic driving forces behind dissociation rate constants, as well as in force-field development, where it can provide a catalog of transient molecular structures on which to refine force-fields. Although much progress has been made in making force-fields more accurate, reducing their error for transient structures along a transition path could yet prove to be a critical development helping to make kinetic predictions much more accurate. In what follows we will provide a state-of-the-art compilation of the enhanced sampling methods based on molecular dynamics (MD) simulations used to investigate the kinetics and mechanisms of ligand-protein dissociation processes. Due to the timescales of such processes being slower than what is accessible using straightforward MD simulations, several ingenious schemes are being devised at a rapid rate to overcome this obstacle. Here we provide an up-to-date compendium of such methods and their achievements/shortcomings in extracting mechanistic insight into ligand-protein dissociation. We conclude with a critical and provocative appraisal attempting to answer the title of this review.}},
  journal  = {Biochemistry},
  pmid     = {30547565},
  year     = {2018},
}

@Article{Hamelberg2004,
  author    = {Donald Hamelberg and John Mongan and J. Andrew McCammon},
  title     = {Accelerated molecular dynamics: A promising and efficient simulation method for biomolecules},
  doi       = {10.1063/1.1755656},
  number    = {24},
  pages     = {11919-11929},
  url       = {http://link.aip.org/link/?JCP/120/11919/1},
  volume    = {120},
  journal   = {J. Chem. Phy},
  keywords  = {molecular biophysics; potential energy functions; molecular dynamics method; free energy; potential energy surfaces},
  owner     = {jhenin},
  publisher = {AIP},
  timestamp = {2012.06.12},
  year      = {2004},
}

@Article{Singh-JCTC-2012,
  author        = {Singh, Sadanand and Chiu, Chi-cheng and de Pablo, Juan J.},
  title         = {Efficient Free Energy Calculation of Biomolecules from Diffusion-Biased Molecular Dynamics},
  doi           = {10.1021/ct3003755},
  issn          = {1549-9626},
  number        = {11},
  pages         = {4657--4662},
  url           = {http://dx.doi.org/10.1021/ct3003755},
  volume        = {8},
  bdsk-url-1    = {http://dx.doi.org/10.1021/ct3003755},
  date-added    = {2015-01-28 10:11:26 +0000},
  date-modified = {2015-07-28 14:38:13 +0000},
  journal       = {J. Chem. Theory Comput.},
  month         = {Nov},
  publisher     = {American Chemical Society (ACS)},
  year          = {2012},
}

@InCollection{Miao2017,
  author    = {Yinglong Miao and J. Andrew McCammon},
  booktitle = {Annual Reports in Computational Chemistry},
  title     = {Gaussian Accelerated Molecular Dynamics: Theory, Implementation, and Applications},
  doi       = {10.1016/bs.arcc.2017.06.005},
  pages     = {231--278},
  publisher = {Elsevier},
  year      = {2017},
}

@Article{Invernizzi-PNAS-2017,
  author        = {Invernizzi, Michele and Valsson, Omar and Parrinello, Michele},
  title         = {Coarse graining from variationally enhanced sampling applied to the Ginzburg--Landau model},
  doi           = {10.1073/pnas.1618455114},
  issn          = {1091-6490},
  number        = {13},
  pages         = {3370--3374},
  url           = {http://dx.doi.org/10.1073/pnas.1618455114},
  volume        = {114},
  bdsk-url-1    = {http://dx.doi.org/10.1073/pnas.1618455114},
  date-added    = {2018-04-22 23:01:45 +0000},
  date-modified = {2018-04-22 23:02:19 +0000},
  journal       = {Proc. Natl. Acad. Sci.},
  month         = {Mar},
  publisher     = {Proc. Natl. Acad. Sci. U.S.A.},
  year          = {2017},
}

@InProceedings{6114444,
  author    = {Pronk, Sander and Bowman, Gregory R. and Hess, Berk and Larsson, Per and Haque, Imran S. and Pande, Vijay S. and Pouya, Iman and Beauchamp, Kyle and Kasson, Peter M. and Lindahl, Erik},
  booktitle = {SC '11: Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis},
  title     = {Copernicus: A new paradigm for parallel adaptive molecular dynamics},
  doi       = {10.1145/2063384.2063465},
  pages     = {1-10},
  year      = {2011},
}

@Article{doi:10.1063/1.5127780,
  author  = {Hussain,Sarwar and Haji-Akbari,Amir},
  title   = {Studying rare events using forward-flux sampling: Recent breakthroughs and future outlook},
  doi     = {10.1063/1.5127780},
  eprint  = {https://doi.org/10.1063/1.5127780},
  number  = {6},
  pages   = {060901},
  url     = {https://doi.org/10.1063/1.5127780},
  volume  = {152},
  journal = {J. Chem. Phys.},
  year    = {2020},
}

@Article{cerou-guyader-lelievre-pommier-11,
  author  = {C\'{e}rou, F. and Guyader, A. and Leli\`{e}vre, T. and Pommier, D.},
  title   = {A multiple replica approach to simulate reactive trajectories},
  doi     = {10.1063/1.3518708},
  pages   = {054108},
  volume  = {134},
  journal = {J. Chem. Phys.},
  year    = {2011},
}

@Article{Yang_MetaD-ITS_2_2018,
  author   = {Yang, Yi Isaac and Niu, Haiyang and Parrinello, Michele},
  title    = {{Combining Metadynamics and Integrated Tempering Sampling}},
  doi      = {10.1021/acs.jpclett.8b03005},
  eprint   = {1807.10486},
  issn     = {1948-7185},
  number   = {22},
  pages    = {6426--6430},
  volume   = {9},
  abstract = {{The simulation of rare events is one of the key problems in atomistic simulations. Toward its solution, a plethora of methods have been proposed. Here we combine two such methods: metadynamics and integrated tempering sampling. In metadynamics, the fluctuations of a carefully chosen collective variable are amplified, while in integrated tempering sampling the system is pushed to visit an approximately uniform interval of energies and allows exploring a range of temperatures in a single run. We describe our approach and apply it to the two prototypical systems a SN2 chemical reaction and to the freezing of silica. The combination of metadynamics and integrated tempering sampling leads to a powerful method. In particular in the case of silica we have measured more than 1 order of magnitude acceleration.}},
  journal  = {J. Phys. Chem. Lett.},
  pmid     = {30354148},
  year     = {2018},
}

@Article{10.1371/journal.pcbi.1005659,
  author    = {Eastman, Peter AND Swails, Jason AND Chodera, John D. AND McGibbon, Robert T. AND Zhao, Yutong AND Beauchamp, Kyle A. AND Wang, Lee-Ping AND Simmonett, Andrew C. AND Harrigan, Matthew P. AND Stern, Chaya D. AND Wiewiora, Rafal P. AND Brooks, Bernard R. AND Pande, Vijay S.},
  title     = {OpenMM 7: Rapid development of high performance algorithms for molecular dynamics},
  doi       = {10.1371/journal.pcbi.1005659},
  number    = {7},
  pages     = {1-17},
  url       = {https://doi.org/10.1371/journal.pcbi.1005659},
  volume    = {13},
  abstract  = {OpenMM is a molecular dynamics simulation toolkit with a unique focus on extensibility. It allows users to easily add new features, including forces with novel functional forms, new integration algorithms, and new simulation protocols. Those features automatically work on all supported hardware types (including both CPUs and GPUs) and perform well on all of them. In many cases they require minimal coding, just a mathematical description of the desired function. They also require no modification to OpenMM itself and can be distributed independently of OpenMM. This makes it an ideal tool for researchers developing new simulation methods, and also allows those new methods to be immediately available to the larger community.},
  journal   = {PLOS Comput. Biol.},
  month     = {07},
  publisher = {Public Library of Science},
  year      = {2017},
}

@Article{Min_OSRW-3_JCTC2010,
  author   = {Min, Donghong and Zheng, Lianqing and Harris, William and Chen, Mengen and Lv, Chao and Yang, Wei},
  title    = {{Practically Efficient QM/MM Alchemical Free Energy Simulations: The Orthogonal Space Random Walk Strategy}},
  doi      = {10.1021/ct100033s},
  issn     = {1549-9618},
  number   = {8},
  pages    = {2253--2266},
  volume   = {6},
  abstract = {{The difference between free energy changes occurring at two chemical states can be rigorously estimated via alchemical free energy (AFE) simulations. Traditionally, most AFE simulations are carried out under the classical energy potential treatment; then, accuracy and applicability of AFE simulations are limited. In the present work, we integrate a recent second-order generalized ensemble strategy, the orthogonal space random walk (OSRW) method, into the combined quantum mechanical/molecular mechanical (QM/MM) potential based AFE simulation scheme. Thereby, within a commonly affordable simulation length, accurate QM/MM alchemical free energy simulations can be achieved. As revealed by the model study on the equilibrium of a tautomerization process of hydrated 3-hydroxypyrazole and by the model calculations of the redox potentials of two flavin derivatives, lumichrome (LC) and riboflavin (RF) in aqueous solution, the present OSRW-based scheme could be a viable path toward the realization of practically efficient QM/MM AFE simulations.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {26613484},
  year     = {2010},
}

@Article{Guo2018,
  author    = {Ashley Z. Guo and Emre Sevgen and Hythem Sidky and Jonathan K. Whitmer and Jeffrey A. Hubbell and Juan J. de Pablo},
  title     = {Adaptive enhanced sampling by force-biasing using neural networks},
  doi       = {10.1063/1.5020733},
  number    = {13},
  pages     = {134108},
  volume    = {148},
  journal   = {J. Chem. Phys.},
  month     = {apr},
  publisher = {{AIP} Publishing},
  year      = {2018},
}

@Article{doi:10.1063/1.4733389,
  author  = {Chen,Ming and Cuendet,Michel A. and Tuckerman,Mark E.},
  title   = {Heating and flooding: A unified approach for rapid generation of free energy surfaces},
  doi     = {10.1063/1.4733389},
  eprint  = {https://doi.org/10.1063/1.4733389},
  number  = {2},
  pages   = {024102},
  url     = {https://doi.org/10.1063/1.4733389},
  volume  = {137},
  journal = {J. Chem. Phys.},
  year    = {2012},
}

@Article{Gil-Ley_JCTC-2015,
  author        = {Gil-Ley, Alejandro and Bussi, Giovanni},
  title         = {Enhanced Conformational Sampling Using Replica Exchange with Collective-Variable Tempering},
  doi           = {10.1021/ct5009087},
  issn          = {1549-9626},
  number        = {3},
  pages         = {1077--1085},
  url           = {http://dx.doi.org/10.1021/ct5009087},
  volume        = {11},
  bdsk-url-1    = {http://dx.doi.org/10.1021/ct5009087},
  date-added    = {2015-03-25 11:08:58 +0000},
  date-modified = {2015-03-25 11:09:12 +0000},
  journal       = {J. Chem. Theory Comput.},
  month         = {Mar},
  publisher     = {American Chemical Society (ACS)},
  year          = {2015},
}

@Article{tiwary_rewt,
  author        = {Tiwary, Pratyush and Parrinello, Michele},
  title         = {A Time-Independent Free Energy Estimator for Metadynamics},
  doi           = {10.1021/jp504920s},
  eprint        = {http://dx.doi.org/10.1021/jp504920s},
  number        = {3},
  pages         = {736-742},
  url           = {http://dx.doi.org/10.1021/jp504920s},
  volume        = {119},
  bdsk-url-1    = {http://dx.doi.org/10.1021/jp504920s},
  date-modified = {2015-06-02 10:33:24 +0000},
  journal       = {J. Phys. Chem. B},
  year          = {2015},
}
,

@Article{woodard_sufficient_2009,
  author   = {Dawn B. Woodard and Scott C. Schmidler and Mark Huber},
  title    = {Sufficient conditions for torpid mixing of parallel and simulated tempering},
  doi      = {10.1214/ejp.v14-638},
  pages    = {780--804},
  volume   = {14},
  abstract = {We obtain upper bounds on the spectral gap of Markov chains constructed by parallel and simulated tempering, and provide a set of sufficient conditions for torpid mixing of both techniques. Combined with the results of Woodard, Schmidler and Huber (2009), these results yield a two-sided bound on the spectral gap of these algorithms. We identify a persistence property of the target distribution, and show that it can lead unexpectedly to slow mixing that commonly used convergence diagnostics will fail to detect. For a multimodal distribution, the persistence is a measure of how ``spiky'', or tall and narrow, one peak is relative to the other peaks of the distribution. We show that this persistence phenomenon can be used to explain the torpid mixing of parallel and simulated tempering on the ferromagnetic mean-field Potts model shown previously. We also illustrate how it causes torpid mixing of tempering on a mixture of normal distributions with unequal covariances in {R{\textasciicircum}M,} a previously unknown result with relevance to statistical inference problems. More generally, anytime a multimodal distribution includes both very narrow and very wide peaks of comparable probability mass, parallel and simulated tempering are shown to mix slowly.},
  journal  = {Elect. J. Prob.},
  month    = mar,
  year     = {2009},
}

@Article{CHONG201788,
  author   = {Lillian T Chong and Ali S Saglam and Daniel M Zuckerman},
  title    = {Path-sampling strategies for simulating rare events in biomolecular systems},
  doi      = {10.1016/j.sbi.2016.11.019},
  issn     = {0959-440X},
  pages    = {88-94},
  url      = {https://www.sciencedirect.com/science/article/pii/S0959440X16302068},
  volume   = {43},
  abstract = {Despite more than three decades of effort with molecular dynamics simulations, long-timescale (ms and beyond) biologically relevant phenomena remain out of reach in most systems of interest. This is largely because important transitions, such as conformational changes and (un)binding events, tend to be rare for conventional simulations (<10μs). That is, conventional simulations will predominantly dwell in metastable states instead of making large transitions in complex biomolecular energy landscapes. In contrast, path sampling approaches focus computing effort specifically on transitions of interest. Such approaches have been in use for nearly 20 years in biomolecular systems and enabled the generation of pathways and calculation of rate constants for ms processes, including large protein conformational changes, protein folding, and protein (un)binding.},
  journal  = {Curr. Opin. Struct. Biol.},
  year     = {2017},
}

@Article{10.1016/j.cplett.2020.137384,
  author   = {Ono, Junichi and Nakai, Hiromi},
  title    = {{Weighted histogram analysis method for multiple short-time metadynamics simulations}},
  doi      = {10.1016/j.cplett.2020.137384},
  issn     = {0009-2614},
  pages    = {137384},
  volume   = {751},
  abstract = {{ An efficient calculation scheme for obtaining free energy surfaces (FESs) in chemical or biological systems from multiple metadynamics (metaD) simulations was developed. In this study, the biased probability distributions of the collective variables and other degrees of freedom were separately calculated, in multiple short-time metaD simulations using the reweighting method. The corresponding equilibrium probability distribution was finally constructed using the weighted histogram analysis method (WHAM). This method was applied for the conformational transitions of alanine dipeptide in the gas phase as an illustrative application. The results confirmed that this method was feasible for efficiently generating the converged FES.}},
  journal  = {Chem. Phys. Lett.},
  year     = {2020},
}

@Article{McGovern-JCP-2013,
  author        = {McGovern, Michael and de Pablo, Juan},
  title         = {A boundary correction algorithm for metadynamics in multiple dimensions},
  doi           = {10.1063/1.4818153},
  issn          = {0021-9606},
  number        = {8},
  pages         = {084102},
  url           = {http://dx.doi.org/10.1063/1.4818153},
  volume        = {139},
  bdsk-url-1    = {http://dx.doi.org/10.1063/1.4818153},
  date-added    = {2015-07-17 10:55:44 +0000},
  date-modified = {2015-07-17 10:55:52 +0000},
  journal       = {J. Chem. Phys.},
  publisher     = {AIP Publishing},
  year          = {2013},
}

@Article{White_EDS_JCTC2014,
  author   = {White, Andrew D. and Voth, Gregory A.},
  title    = {{Efficient and Minimal Method to Bias Molecular Simulations with Experimental Data}},
  doi      = {10.1021/ct500320c},
  issn     = {1549-9618},
  number   = {8},
  pages    = {3023--3030},
  volume   = {10},
  abstract = {{  A primary goal in molecular simulations is to modify the potential energy of a system so that properties of the simulation match experimental data. This is traditionally done through iterative cycles of simulation and reparameterization. An alternative approach is to bias the potential energy so that the system matches experimental data. This can be done while minimally changing the underlying free energy of the molecular simulation. Current minimal biasing methods require replicas, which can lead to unphysical dynamics and introduces new complexity: the choice of replica number and their properties. Here, we describe a new method, called experiment directed simulation that does not require replicas, converges rapidly, can match many data simultaneously, and minimally modifies the potential. The experiment directed simulation method is demonstrated on model systems and a three-component electrolyte simulation. The theory used to derive the method also provides insight into how changing a molecular force-field impacts the expected value of observables in simulation.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {26588273},
  year     = {2014},
}

@Software{lindahl_2021,
  author    = {Lindahl and Abraham and Hess and van der Spoel},
  title     = {GROMACS 2021.2 Source code},
  doi       = {10.5281/zenodo.4723562},
  url       = {https://doi.org/10.5281/zenodo.4723562},
  version   = {2021.2},
  month     = may,
  publisher = {Zenodo},
  year      = {2021},
}

@Article{jang-shin-pak:prl:2003:hamiltonian-exchange,
  author  = {Jang, Soonmin and Shin, Seokmin and Pak, Youngshang},
  title   = {{Replica-exchange method using the generalized effective potential}},
  doi     = {10.1103/physrevlett.91.058305},
  pages   = {58305},
  volume  = {91},
  journal = {Phys. Rev. Lett.},
  year    = {2003},
}

@Article{BRUCE20181,
  author   = {Neil J Bruce and Gaurav K Ganotra and Daria B Kokh and S Kashif Sadiq and Rebecca C Wade},
  title    = {New approaches for computing ligand–receptor binding kinetics},
  doi      = {10.1016/j.sbi.2017.10.001},
  issn     = {0959-440X},
  note     = {Theory and simulation • Macromolecular assemblies},
  pages    = {1-10},
  url      = {https://www.sciencedirect.com/science/article/pii/S0959440X17301094},
  volume   = {49},
  abstract = {The recent and growing evidence that the efficacy of a drug can be correlated to target binding kinetics has seeded the development of a multitude of novel methods aimed at computing rate constants for receptor–ligand binding processes, as well as gaining an understanding of the binding and unbinding pathways and the determinants of structure–kinetic relationships. These new approaches include various types of enhanced sampling molecular dynamics simulations and the combination of energy-based models with chemometric analysis. We assess these approaches in the light of the varying levels of complexity of protein–ligand binding processes.},
  journal  = {Curr. Opin. Struct. Biol.},
  year     = {2018},
}

@Article{doi:10.1021/ct400919u,
  author  = {Doerr, S. and De Fabritiis, G.},
  title   = {On-the-Fly Learning and Sampling of Ligand Binding by High-Throughput Molecular Simulations},
  doi     = {10.1021/ct400919u},
  eprint  = {https://doi.org/10.1021/ct400919u},
  number  = {5},
  pages   = {2064-2069},
  url     = {https://doi.org/10.1021/ct400919u},
  volume  = {10},
  journal = {J. Chem. Theory Comput.},
  pmid    = {26580533},
  year    = {2014},
}

@Article{Zhang_SIAM-JSC-2014,
  author        = {Zhang, Wei and Wang, Han and Hartmann, Carsten and Weber, Marcus and Sch{\"u}tte, Christof},
  title         = {Applications of the Cross-Entropy Method to Importance Sampling and Optimal Control of Diffusions},
  doi           = {10.1137/14096493x},
  issn          = {1095-7197},
  number        = {6},
  pages         = {A2654--A2672},
  url           = {http://dx.doi.org/10.1137/14096493X},
  volume        = {36},
  bdsk-url-1    = {http://dx.doi.org/10.1137/14096493X},
  bdsk-url-2    = {http://dx.doi.org/10.1137/14096493x},
  date-added    = {2018-04-23 00:18:59 +0000},
  date-modified = {2018-04-23 00:20:00 +0000},
  journal       = {SIAM J. Sci. Comput.},
  month         = {Jan},
  publisher     = {Society for Industrial & Applied Mathematics (SIAM)},
  year          = {2014},
}

@Article{sindhikara-meng-roitberg:jcp:2008:exchange-frequency,
  author  = {Sindhikara, Daniel and Meng, Yilin and Roitberg, Adrian E},
  title   = {{Exchange frequency in replica exchange molecular dynamics}},
  doi     = {10.1063/1.2816560},
  pages   = {24103},
  volume  = {128},
  journal = {J. Chem. Phys.},
  year    = {2008},
}

@Article{doi:10.1080/00268976.2020.1737742,
  author    = {Hythem Sidky and Wei Chen and Andrew L. Ferguson},
  title     = {Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation},
  doi       = {10.1080/00268976.2020.1737742},
  eprint    = {https://doi.org/10.1080/00268976.2020.1737742},
  number    = {5},
  pages     = {e1737742},
  url       = {https://doi.org/10.1080/00268976.2020.1737742},
  volume    = {118},
  journal   = {Mol. Phys.},
  publisher = {Taylor & Francis},
  year      = {2020},
}

@Article{Bonomi-PRL-2010,
  author        = {Bonomi, M. and Parrinello, M.},
  title         = {Enhanced Sampling in the Well-Tempered Ensemble},
  doi           = {10.1103/physrevlett.104.190601},
  number        = {19},
  pages         = {190601},
  volume        = {104},
  bdsk-url-1    = {http://dx.doi.org/10.1103/PhysRevLett.104.190601},
  date-added    = {2014-10-10 10:10:47 +0000},
  date-modified = {2015-03-25 10:49:44 +0000},
  journal       = {Phys. Rev. Lett.},
  month         = {May},
  publisher     = {American Physical Society},
  year          = {2010},
}

@InCollection{hummer-07,
  author    = {G. Hummer},
  booktitle = {Free energy calculations},
  title     = {Nonequilibrium methods for equilibrium free-energy calculations},
  doi       = {10.1007/978-3-540-38448-9_5},
  editor    = {C. Chipot and A. Pohorille},
  pages     = {171--198},
  publisher = {Springer},
  year      = {2007},
}

@Article{Junghans2014wte-wl,
  author    = {Junghans, Christoph and Perez, Danny and Vogel, Thomas},
  title     = {Molecular Dynamics in the Multicanonical Ensemble: Equivalence of Wang–Landau Sampling, Statistical Temperature Molecular Dynamics, and Metadynamics},
  doi       = {10.1021/ct500077d},
  issn      = {1549-9626},
  number    = {5},
  pages     = {1843–1847},
  url       = {http://dx.doi.org/10.1021/ct500077d},
  volume    = {10},
  journal   = {J. Chem. Theory Comput.},
  month     = {Apr},
  publisher = {American Chemical Society (ACS)},
  year      = {2014},
}

@Article{doi:10.1021/ct500827g,
  author  = {Voelz, Vincent A. and Elman, Brandon and Razavi, Asghar M. and Zhou, Guangfeng},
  title   = {Surprisal Metrics for Quantifying Perturbed Conformational Dynamics in Markov State Models},
  doi     = {10.1021/ct500827g},
  eprint  = {https://doi.org/10.1021/ct500827g},
  number  = {12},
  pages   = {5716-5728},
  url     = {https://doi.org/10.1021/ct500827g},
  volume  = {10},
  journal = {J. Chem. Theory Comput.},
  pmid    = {26583253},
  year    = {2014},
}

@InBook{DellagoBolhuis,
  author    = {Dellago, Christoph and Bolhuis, Peter G.},
  booktitle = {Advanced Computer Simulation Approaches for Soft Matter Sciences III},
  title     = {Transition Path Sampling and Other Advanced Simulation Techniques for Rare Events},
  doi       = {10.1007/978-3-540-87706-6_3},
  editor    = {Holm, Christian and Kremer, Kurt},
  isbn      = {978-3-540-87706-6},
  pages     = {167--233},
  publisher = {Springer Berlin Heidelberg},
  url       = {https://doi.org/10.1007/978-3-540-87706-6_3},
  abstract  = {Computer simulations of molecular processes such as nucleation in first-order phase transitions or the folding of a protein are often complicated by widely disparate time scales related to important but rare events. Here, we will review sev eral recently developed computational methods designed to address the rare-events problem. In doing so, we will focus on the transition path sampling methodology.},
  address   = {Berlin, Heidelberg},
  year      = {2009},
}

@Article{hansmann:physica-a:2010:replica-exchange,
  author  = {Ulrich H. E. Hansmann},
  title   = {Temperature random walk sampling of protein configurations},
  doi     = {10.1016/j.physa.2009.12.027},
  pages   = {1400},
  volume  = {389},
  journal = {Phys. A},
  year    = {2010},
}

@Article{Babin2008,
  author    = {Volodymyr Babin and Christopher Roland and Celeste Sagui},
  title     = {Adaptively biased molecular dynamics for free energy calculations},
  doi       = {10.1063/1.2844595},
  number    = {13},
  pages     = {134101},
  volume    = {128},
  journal   = {J. Chem. Phys.},
  month     = {apr},
  publisher = {{AIP} Publishing},
  year      = {2008},
}

@Misc{plumed_masterclass,
title = {PLUMED Masterclass Tutorials},
howpublished = {\url{https://www.plumed.org/masterclass}},
note = {Accessed: May 26, 2022}
}

@Misc{plumed_nest_url,
title = {PLUMED-NEST},
howpublished = {\url{https://www.plumed-nest.org}},
note = {Accessed: June 30, 2022}
}

@Article{10.1073/pnas.1303186110,
  author   = {Limongelli, Vittorio and Bonomi, Massimiliano and Parrinello, Michele},
  title    = {{Funnel metadynamics as accurate binding free-energy method}},
  doi      = {10.1073/pnas.1303186110},
  issn     = {0027-8424},
  number   = {16},
  pages    = {6358--6363},
  volume   = {110},
  abstract = {{A detailed description of the events ruling ligand/protein interaction and an accurate estimation of the drug affinity to its target is of great help in speeding drug discovery strategies. We have developed a metadynamics-based approach, named funnel metadynamics, that allows the ligand to enhance the sampling of the target binding sites and its solvated states. This method leads to an efficient characterization of the binding free-energy surface and an accurate calculation of the absolute protein–ligand binding free energy. We illustrate our protocol in two systems, benzamidine/trypsin and SC-558/cyclooxygenase 2. In both cases, the X-ray conformation has been found as the lowest free-energy pose, and the computed protein–ligand binding free energy in good agreement with experiments. Furthermore, funnel metadynamics unveils important information about the binding process, such as the presence of alternative binding modes and the role of waters. The results achieved at an affordable computational cost make funnel metadynamics a valuable method for drug discovery and for dealing with a variety of problems in chemistry, physics, and material science.}},
  journal  = {Proc. Natl. Acad. Sci.},
  pmcid    = {PMC3631651},
  pmid     = {23553839},
  year     = {2013},
}

@Article{Tribello2014,
  author    = {Gareth A. Tribello and Massimiliano Bonomi and Davide Branduardi and Carlo Camilloni and Giovanni Bussi},
  title     = {{PLUMED} 2: New feathers for an old bird},
  doi       = {10.1016/j.cpc.2013.09.018},
  number    = {2},
  pages     = {604--613},
  volume    = {185},
  journal   = {Comput. Phys. Commun.},
  month     = {feb},
  publisher = {Elsevier {BV}},
  year      = {2014},
}

@Article{Henin2010a,
  author  = {H\'enin, J. and Fiorin, G. and Chipot, C. and Klein, M. L.},
  title   = {Exploring multidimensional free energy landscapes using time-dependent biases on collective variables},
  number  = {1},
  pages   = {35-47},
  volume  = {6},
  journal = {J. Chem. Theory Comput.},
  year    = {2010},
  doi     = {10.1021/ct9004432},
}

@Article{Dickson2010,
  author               = {Dickson, Bradley M and Legoll, Frédéric and Lelièvre, Tony and Stoltz, Gabriel and Fleurat-Lessard, Paul},
  title                = {Free energy calculations: an efficient adaptive biasing potential method.},
  doi                  = {10.1021/jp100926h},
  issn                 = {1520-5207},
  issue                = {17},
  pages                = {5823--5830},
  volume               = {114},
  abstract             = {We develop an efficient sampling and free energy calculation technique within the adaptive biasing potential (ABP) framework. By mollifying the density of states we obtain an approximate free energy and an adaptive bias potential that is computed directly from the population along the coordinates of the free energy. Because of the mollifier, the bias potential is "nonlocal", and its gradient admits a simple analytic expression. A single observation of the reaction coordinate can thus be used to update the approximate free energy at every point within a neighborhood of the observation. This greatly reduces the equilibration time of the adaptive bias potential. This approximation introduces two parameters: strength of mollification and the zero of energy of the bias potential. While we observe that the approximate free energy is a very good estimate of the actual free energy for a large range of mollification strength, we demonstrate that the errors associated with the mollification may be removed via deconvolution. The zero of energy of the bias potential, which is easy to choose, influences the speed of convergence but not the limiting accuracy. This method is simple to apply to free energy or mean force computation in multiple dimensions and does not involve second derivatives of the reaction coordinates, matrix manipulations nor on-the-fly adaptation of parameters. For the alanine dipeptide test case, the new method is found to gain as much as a factor of 10 in efficiency as compared to two basic implementations of the adaptive biasing force methods, and it is shown to be as efficient as well-tempered metadynamics with the postprocess deconvolution giving a clear advantage to the mollified density of states method.},
  completed            = {2010-07-21},
  country              = {United States},
  created              = {2010-04-29},
  issn-linking         = {1520-5207},
  journal              = {J . Phys. Chem. B},
  journal-abbreviation = {J Phys Chem B},
  month                = {May},
  nlm-id               = {101157530},
  owner                = {NLM},
  pmid                 = {20380408},
  pubmodel             = {Print},
  status               = {PubMed-not-MEDLINE},
  year                 = {2010},
}

@Article{bennett:jcp:1976:fe-estimate,
  author  = {Bennett, C H},
  title   = {{Efficient estimation of free energy differences from Monte Carlo data}},
  number  = {2},
  pages   = {245--268},
  volume  = {22},
  journal = {J. Comput. Phys.},
  year    = {1976},
  doi = {10.1016/0021-9991(76)90078-4}
}

@Article{Shell_MultiTP_2002,
  author   = {Shell, M. Scott and Debenedetti, Pablo G. and Panagiotopoulos, Athanassios Z.},
  title    = {{Generalization of the Wang-Landau method for off-lattice simulations}},
  doi      = {10.1103/physreve.66.056703},
  eprint   = {cond-mat/0206461},
  issn     = {1539-3755},
  number   = {5},
  pages    = {056703},
  volume   = {66},
  abstract = {{We present a rigorous derivation for off-lattice implementations of the so-called “random-walk” algorithm recently introduced by Wang and Landau [Phys. Rev. Lett. 86, 2050 (2001)]. Originally developed for discrete systems, the algorithm samples configurations according to their inverse density of states using Monte Carlo moves; the estimate for the density of states is refined at each simulation step and is ultimately used to calculate thermodynamic properties. We present an implementation for atomic systems based on a rigorous separation of kinetic and configurational contributions to the density of states. By constructing a “uniform” ensemble for configurational degrees of freedom—in which all potential energies, volumes, and numbers of particles are equally probable—we establish a framework for the correct implementation of simulation acceptance criteria and calculation of thermodynamic averages in the continuum case. To demonstrate the generality of our approach, we perform sample calculations for the Lennard-Jones fluid using two implementation variants and in both cases find good agreement with established literature values for the vapor-liquid coexistence locus.}},
  journal  = {Phys. Rev. E},
  pmid     = {12513633},
  year     = {2002},
}

@Article{PhysRevLett.94.018104,
  author    = {Allen, Rosalind J. and Warren, Patrick B. and ten Wolde, Pieter Rein},
  title     = {Sampling Rare Switching Events in Biochemical Networks},
  doi       = {10.1103/PhysRevLett.94.018104},
  issue     = {1},
  pages     = {018104},
  url       = {https://link.aps.org/doi/10.1103/PhysRevLett.94.018104},
  volume    = {94},
  journal   = {Phys. Rev. Lett.},
  month     = {Jan},
  numpages  = {4},
  publisher = {American Physical Society},
  year      = {2005},
}

@Article{hukushima-nemoto:j-phys-soc-jpn:1996:parallel-tempering,
  author  = {Koji Hukushima and Koji Nemoto},
  title   = {Exchange {Monte Carlo} and application to spin glass simulations},
  pages   = {1604--1608},
  volume  = {65},
  journal = {J. Phys. Soc. Jpn.},
  year    = {1996},
  doi = {10.1143/JPSJ.65.1604}
}

@Article{Grubmuller-PRE-1995,
  author        = {Grubm{\"u}ller, Helmut},
  title         = {Predicting slow structural transitions in macromolecular systems: Conformational flooding},
  doi           = {10.1103/physreve.52.2893},
  issn          = {1095-3787},
  number        = {3},
  pages         = {2893--2906},
  url           = {http://dx.doi.org/10.1103/PhysRevE.52.2893},
  volume        = {52},
  bdsk-url-1    = {http://dx.doi.org/10.1103/PhysRevE.52.2893},
  bdsk-url-2    = {http://dx.doi.org/10.1103/physreve.52.2893},
  date-added    = {2015-04-14 10:08:44 +0000},
  date-modified = {2015-04-14 10:08:57 +0000},
  journal       = {Phys. Rev. E},
  month         = {Sep},
  publisher     = {American Physical Society (APS)},
  year          = {1995},
}

@Article{Zheng2012,
  author    = {Zheng, L. and Yang, W.},
  title     = {Practically efficient and robust free energy calculations: Double-integration orthogonal space tempering},
  doi       = {10.1021/ct200726v},
  number    = {3},
  pages     = {810-823},
  volume    = {8},
  journal   = {J. Chem. Theory Comput.},
  owner     = {jhenin},
  timestamp = {2012.08.16},
  year      = {2012},
}

@Article{Bonomi-CPC-2009,
  author        = {Bonomi, Massimiliano and Branduardi, Davide and Bussi, Giovanni and Camilloni, Carlo and Provasi, Davide and Raiteri, Paolo and Donadio, Davide and Marinelli, Fabrizio and Pietrucci, Fabio and Broglia, Ricardo A. and et al.},
  title         = {PLUMED: A portable plugin for free-energy calculations with molecular dynamics},
  doi           = {10.1016/j.cpc.2009.05.011},
  issn          = {0010-4655},
  number        = {10},
  pages         = {1961--1972},
  url           = {http://dx.doi.org/10.1016/j.cpc.2009.05.011},
  volume        = {180},
  bdsk-url-1    = {http://dx.doi.org/10.1016/j.cpc.2009.05.011},
  date-added    = {2015-07-24 12:51:17 +0000},
  date-modified = {2015-07-24 12:51:26 +0000},
  journal       = {Comput. Phys. Commun.},
  month         = {Oct},
  publisher     = {Elsevier BV},
  year          = {2009},
}

@Book{cchipot07:molsim,
  title     = {Free Energy Calculations: Theory and Applications in Chemistry and Biology},
  doi       = {10.1007/978-3-540-38448-9},
  editor    = {Chipot, {\mbox{Ch}}ristophe and Pohorille, Andrew},
  publisher = {Springer-Verlag},
  series    = {Springer Series in Chemical Physics},
  volume    = {86},
  abstract  = {This volume sets out to present a coherent and comprehensive
                  account of the concepts that underlie different approaches
                  devised for the determination of free energies. The reader
                  will gain the necessary insight into the theoretical and
                  computational foundations of the subject and will be presented
                  with relevant applications from molecular-level modelling and
                  simulations of chemical and biological systems. Both formally
                  accurate and approximate methods are covered using both
                  classical and quantum mechanical descriptions. A central theme
                  of the book is that the wide variety of free energy
                  calculation techniques available today can be understood as
                  different implementations of a few basic principles.},
  added-at  = {2013-03-23T15:55:46.000+0100},
  address   = {Berlin},
  annote    = {First printing. Series editors: A. W. Castleman, Jr., J. P. Toennies, K. Yamanouchi, and W. Zinth.},
  biburl    = {https://www.bibsonomy.org/bibtex/2c4ed41b0f057a1e4f3886a6791c6e420/drmatusek},
  interhash = {ef620ffc115d6f197d0413e6cb9a79b1},
  intrahash = {c4ed41b0f057a1e4f3886a6791c6e420},
  keywords  = {Carlo Monte chemistry dynamics mechanics molecular physics review statistical},
  timestamp = {2013-03-23T16:20:00.000+0100},
  year      = {2007},
}

@Book{Lelievre2010,
  author    = {Tony Leli{\`e}vre and Mathias Rousset and Gabriel Stoltz},
  title     = {Free Energy Computations: A Mathematical Perspective},
  doi       = {10.1142/p579},
  publisher = {Imperial College Press},
  owner     = {jhenin},
  timestamp = {2011.05.13},
  year      = {2010},
}

@Article{Pitera_MaxEnt_JCTC2012,
  author   = {Pitera, Jed W. and Chodera, John D.},
  title    = {{On the Use of Experimental Observations to Bias Simulated Ensembles}},
  doi      = {10.1021/ct300112v},
  issn     = {1549-9618},
  number   = {10},
  pages    = {3445--3451},
  volume   = {8},
  abstract = {{Historically, experimental measurements have been used to bias biomolecular simulations toward structures compatible with those observations via the addition of ad hoc restraint terms. We show how the maximum entropy formalism provides a principled approach to enforce concordance with these measurements in a minimally biased way, yielding restraints that are linear functions of the target observables and specifying a straightforward scheme to determine the biasing weights. These restraints are compared with instantaneous and ensemble-averaged harmonic restraint schemes, illustrating their similarities and limitations.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {26592995},
  year     = {2012},
}

@Article{Tiwary_RAVE_2018,
  author   = {Ribeiro, João Marcelo Lamim and Bravo, Pablo and Wang, Yihang and Tiwary, Pratyush},
  title    = {{Reweighted autoencoded variational Bayes for enhanced sampling (RAVE)}},
  doi      = {10.1063/1.5025487},
  issn     = {0021-9606},
  number   = {7},
  pages    = {072301},
  volume   = {149},
  abstract = {{Here we propose the reweighted autoencoded variational Bayes for enhanced sampling (RAVE) method, a new iterative scheme that uses the deep learning framework of variational autoencoders to enhance sampling in molecular simulations. RAVE involves iterations between molecular simulations and deep learning in order to produce an increasingly accurate probability distribution along a low-dimensional latent space that captures the key features of the molecular simulation trajectory. Using the Kullback-Leibler divergence between this latent space distribution and the distribution of various trial reaction coordinates sampled from the molecular simulation, RAVE determines an optimum, yet nonetheless physically interpretable, reaction coordinate and optimum probability distribution. Both then directly serve as the biasing protocol for a new biased simulation, which is once again fed into the deep learning module with appropriate weights accounting for the bias, the procedure continuing until estimates of desirable thermodynamic observables are converged. Unlike recent methods using deep learning for enhanced sampling purposes, RAVE stands out in that (a) it naturally produces a physically interpretable reaction coordinate, (b) is independent of existing enhanced sampling protocols to enhance the fluctuations along the latent space identified via deep learning, and (c) it provides the ability to easily filter out spurious solutions learned by the deep learning procedure. The usefulness and reliability of RAVE is demonstrated by applying it to model potentials of increasing complexity, including computation of the binding free energy profile for a hydrophobic ligand-substrate system in explicit water with dissociation time of more than 3 min, in computer time at least twenty times less than that needed for umbrella sampling or metadynamics.}},
  journal  = {J. Chem. Phys.},
  pmid     = {30134694},
  year     = {2018},
}

@Article{Lindner_ASQPM-MetaD_2019,
  author   = {Lindner, Joachim O. and Röhr, Merle I. S.},
  title    = {{Metadynamics for automatic sampling of quantum property manifolds: exploration of molecular biradicality landscapes}},
  doi      = {10.1039/c9cp05182a},
  eprint   = {1909.09005},
  issn     = {1463-9076},
  number   = {44},
  pages    = {24716--24722},
  volume   = {21},
  abstract = {{We present a general extension of the metadynamics allowing for an automatic sampling of quantum property manifolds (ASQPM) giving rise to functional landscapes that are analogous to the potential energy surfaces in the frame of the Born–Oppenheimer approximation. For this purpose, we employ generalized electronic collective variables to carry out biased molecular dynamics simulations in the framework of quantum chemical methods that explore the desired property manifold. We illustrate our method on the example of the “biradicality landscapes”, which we explore by introducing the natural orbital occupation numbers (NOONs) as the electronic collective variable driving the dynamics. We demonstrate the applicability of the method on the simulation of p-xylylene and [8]annulene allowing to automatically extract the biradical geometries. In the case of [8]annulene the ASQPM metadynamics leads to the prediction of biradical scaffolds that can be stabilized by a suitable chemical substitution, leading to the design of novel functional molecules exhibiting biradical functionality.}},
  journal  = {Phys. Chem. Chem. Phys.},
  pmid     = {31675023},
  year     = {2019},
}

@Article{LAMMPS_2022,
  author   = {Thompson, Aidan P. and Aktulga, H. Metin and Berger, Richard and Bolintineanu, Dan S. and Brown, W. Michael and Crozier, Paul S. and Veld, Pieter J. in 't and Kohlmeyer, Axel and Moore, Stan G. and Nguyen, Trung Dac and Shan, Ray and Stevens, Mark J. and Tranchida, Julien and Trott, Christian and Plimpton, Steven J.},
  title    = {{LAMMPS - a flexible simulation tool for particle-based materials modeling at the atomic, meso, and continuum scales}},
  doi      = {10.1016/j.cpc.2021.108171},
  issn     = {0010-4655},
  pages    = {108171},
  volume   = {271},
  abstract = {{Since the classical molecular dynamics simulator LAMMPS was released as an open source code in 2004, it has become a widely-used tool for particle-based modeling of materials at length scales ranging from atomic to mesoscale to continuum. Reasons for its popularity are that it provides a wide variety of particle interaction models for different materials, that it runs on any platform from a single CPU core to the largest supercomputers with accelerators, and that it gives users control over simulation details, either via the input script or by adding code for new interatomic potentials, constraints, diagnostics, or other features needed for their models. As a result, hundreds of people have contributed new capabilities to LAMMPS and it has grown from fifty thousand lines of code in 2004 to a million lines today. In this paper several of the fundamental algorithms used in LAMMPS are described along with the design strategies which have made it flexible for both users and developers. We also highlight some capabilities recently added to the code which were enabled by this flexibility, including dynamic load balancing, on-the-fly visualization, magnetic spin dynamics models, and quantum-accuracy machine learning interatomic potentials. Program Program Title: Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) CPC Library link to program files: https://doi.org/10.17632/cxbxs9btsv.1 Developer's repository link: https://github.com/lammps/lammps Licensing provisions: GPLv2 Programming language: C++, Python, C, Fortran Supplementary material: https://www.lammps.org Nature of problem: Many science applications in physics, chemistry, materials science, and related fields require parallel, scalable, and efficient generation of long, stable classical particle dynamics trajectories. Within this common problem definition, there lies a great diversity of use cases, distinguished by different particle interaction models, external constraints, as well as timescales and lengthscales ranging from atomic to mesoscale to macroscopic. Solution method: The LAMMPS code uses parallel spatial decomposition, distributed neighbor lists, and parallel FFTs for long-range Coulombic interactions [1]. The time integration algorithm is based on the Størmer-Verlet symplectic integrator [2], which provides better stability than higher-order non-symplectic methods. In addition, LAMMPS supports a wide range of interatomic potentials, constraints, diagnostics, software interfaces, and pre- and post-processing features. Additional comments including restrictions and unusual features: This paper serves as the definitive reference for the LAMMPS code. References [1] S. Plimpton, Fast parallel algorithms for short-range molecular dynamics. J. Comp. Phys. 117 (1995) 1–19. [2] L. Verlet, Computer experiments on classical fluids: I. Thermodynamical properties of Lennard–Jones molecules, Phys. Rev. 159 (1967) 98–103.}},
  journal  = {Comput. Phys. Commun.},
  year     = {2022},
}

@Article{Awasthi_TASS_JCP2017,
  author   = {Awasthi, Shalini and Nair, Nisanth N},
  title    = {{Exploring high dimensional free energy landscapes: Temperature accelerated sliced sampling}},
  doi      = {10.1063/1.4977704},
  eprint   = {1612.08240},
  issn     = {0021-9606},
  number   = {9},
  pages    = {094108},
  volume   = {146},
  abstract = {{Biased sampling of collective variables is widely used to accelerate rare events in molecular simulations and to explore free energy surfaces. However, computational efficiency of these methods decreases with increasing number of collective variables, which severely limits the predictive power of the enhanced sampling approaches. Here we propose a method called Temperature Accelerated Sliced Sampling (TASS) that combines temperature accelerated molecular dynamics with umbrella sampling and metadynamics to sample the collective variable space in an efficient manner. The presented method can sample a large number of collective variables and is advantageous for controlled exploration of broad and unbound free energy basins. TASS is also shown to achieve quick free energy convergence and is practically usable with ab initio molecular dynamics techniques.}},
  journal  = {J. Chem. Phys.},
  year     = {2017},
}

@Article{Huber1994,
  author    = {Huber, T. and Torda, A.~E. and van Gunsteren, W.~F.},
  title     = {{Local elevation: A method for improving the searching properties of molecular dynamics simulation}},
  doi       = {10.1007/BF00124016},
  pages     = {695-708},
  volume    = {8},
  journal   = {J. Comput. Aided Mol. Des.},
  owner     = {jhenin},
  timestamp = {2012.06.12},
  year      = {1994},
}


% * G. Fort, B. Jourdain, E. Kuhn, TL and G. Stoltz, Efficiency of the
% Wang-Landau algorithm: a simple test case, AMRX, 2, 275-311, (2014).

@Article{fort-jourdain-kuhn-lelievre-stoltz-14,
  author  = {Fort, G. and Jourdain, B. and Kuhn, E. and Leli\`evre, T. and Stoltz, G.},
  title   = {Efficiency of the Wang-Landau algorithm: a simple test case},
  doi     = {10.1093/amrx/abu003},
  pages   = {275-311},
  volume  = {2},
  journal = {Appl. Math. Res. Express},
  year    = {2014},
}

@Article{Zhao2017,
  author    = {Tanfeng Zhao and Haohao Fu and Tony Leli{\`{e}}vre and Xueguang Shao and Christophe Chipot and Wensheng Cai},
  title     = {The Extended Generalized Adaptive Biasing Force Algorithm for Multidimensional Free-Energy Calculations},
  doi       = {10.1021/acs.jctc.7b00032},
  number    = {4},
  pages     = {1566--1576},
  volume    = {13},
  journal   = {J. Chem. Theory Comput.},
  month     = {mar},
  publisher = {American Chemical Society ({ACS})},
  year      = {2017},
}

@Article{tavan:cpl:2008:pseudoconvergence,
  author  = {Robert Denschlag and Martin Lingenheil and Paul Tavan},
  title   = {Efficiency reduction and pseudo-convergence in replica exchange sampling of peptide folding-unfolding equilibria},
  doi     = {10.1016/j.cplett.2008.04.114},
  pages   = {244--248},
  volume  = {458},
  journal = {Chem. Phys. Lett.},
  year    = {2008},
}

@Article{10.1107/s2052252514027626,
  author   = {Giberti, F. and Salvalaglio, M. and Parrinello, M.},
  title    = {{Metadynamics studies of crystal nucleation}},
  doi      = {10.1107/s2052252514027626},
  issn     = {2052-2525},
  number   = {2},
  pages    = {256--266},
  volume   = {2},
  abstract = {{Crystallization processes are characterized by activated events and long timescales. These characteristics prevent standard molecular dynamics techniques from being efficiently used for the direct investigation of processes such as nucleation. This short review provides an overview on the use of metadynamics, a state-of-the-art enhanced sampling technique, for the simulation of phase transitions involving the production of a crystalline solid. In particular the principles of metadynamics are outlined, several order parameters are described that have been or could be used in conjunction with metadynamics to sample nucleation events and then an overview is given of recent metadynamics results in the field of crystal nucleation.}},
  journal  = {IUCrJ},
  keywords = {Metadynamics Reviews},
  pmcid    = {PMC4392418},
  pmid     = {25866662},
  year     = {2015},
}

@Article{zuckerman-lyman:jctc:2006:replica-exchange-efficiency,
  author  = {Daniel M. Zuckerman and Edward Lyman},
  title   = {A second look at canonical sampling of biomolecules using replica exchange simulation},
  doi     = {10.1021/ct0600464},
  pages   = {1200--1202},
  volume  = {2},
  journal = {J. Chem. Theory Comput.},
  year    = {2006},
}

@Article{Celerse2021,
  author    = {Célerse, Fréderic and Jaffrelot-Inizan, Theo and Lagardère, Louis and Adjoua, Olivier and Monmarché, Pierre and Miao, Yinglong and Derat, Etienne and Piquemal, Jean-Philip},
  title     = {An Efficient GaMD Multi-Level Enhanced Sampling Strategy: Application to Polarizable Force Fields Simulations of Large Biological Systems},
  doi       = {10.33774/chemrxiv-2021-ggjfx-v2},
  journal   = {ChemRxiv},
  place     = {Cambridge},
  publisher = {Cambridge Open Engage},
  year      = {2021},
}

@Article{GilLey_TargetMetaD_2016,
  author   = {Gil-Ley, Alejandro and Bottaro, Sandro and Bussi, Giovanni},
  title    = {{Empirical Corrections to the Amber RNA Force Field with Target Metadynamics}},
  doi      = {10.1021/acs.jctc.6b00299},
  eprint   = {1605.00934},
  issn     = {1549-9618},
  number   = {6},
  pages    = {2790--2798},
  volume   = {12},
  abstract = {{The computational study of conformational transitions in nucleic acids still faces many challenges. For example, in the case of single stranded RNA tetranucleotides, agreement between simulations and experiments is not satisfactory due to inaccuracies in the force fields commonly used in molecular dynamics simulations. We here use experimental data collected from high-resolution X-ray structures to attempt an improvement of the latest version of the AMBER force field. A modified metadynamics algorithm is used to calculate correcting potentials designed to enforce experimental distributions of backbone torsion angles. Replica-exchange simulations of tetranucleotides including these correcting potentials show significantly better agreement with independent solution experiments for the oligonucleotides containing pyrimidine bases. Although the proposed corrections do not seem to be portable to generic RNA systems, the simulations revealed the importance of the α and ζ backbone angles for the modulation of the RNA conformational ensemble. The correction protocol presented here suggests a systematic procedure for force-field refinement.}},
  journal  = {J. Chem. Theory Comput.},
  pmcid    = {PMC4910146},
  pmid     = {27153317},
  year     = {2016},
}


% * G. Fort, B. Jourdain, E. Kuhn, TL and G. Stoltz, Convergence of the
% Wang-Landau algorithm, Mathematics of Computation, 84(295), 2297–2327,
% (2015).

@Article{fort-jourdain-kuhn-lelievre-stoltz-15,
  author  = {Fort, G. and Jourdain, B. and Kuhn, E. and Leli\`evre, T. and Stoltz, G.},
  title   = {Convergence of the {W}ang-{L}andau algorithm},
  doi     = {10.1090/s0025-5718-2015-02952-4},
  number  = {295},
  pages   = {2297-2327},
  volume  = {84},
  journal = {Math. Comput.},
  year    = {2015},
}

@Article{geyer-thompson:j-am-stat-assoc:1995:expanded-ensembles,
  author  = {Charles J. Geyer and Elizabeth A. Thompson},
  title   = {Annealing {Markov chain Monte Carlo} with applications to ancestral inference},
  pages   = {909--920},
  volume  = {90},
  journal = {J. Am. Stat. Assoc.},
  year    = {1995},
  doi = {10.2307/2291325}
}

@Article{bonomi_rewt,
  author        = {Bonomi, Massimiliano and Barducci, Alessandro and Parrinello, Michele},
  title         = {Reconstructing the equilibrium Boltzmann distribution from well-tempered metadynamics},
  doi           = {10.1002/jcc.21305},
  number        = {11},
  pages         = {1615--1621},
  volume        = {30},
  date-modified = {2015-07-17 14:03:26 +0000},
  journal       = {J. Comp. Chem.},
  publisher     = {Wiley Subscription Services, Inc., A Wiley Company},
  year          = {2009},
}

@Article{10.1063/1.5123498,
  author   = {Marinova, Veselina and Salvalaglio, Matteo},
  title    = {{Time-independent free energies from metadynamics via mean force integration}},
  doi      = {10.1063/1.5123498},
  eprint   = {1907.08472},
  issn     = {0021-9606},
  number   = {16},
  pages    = {164115},
  volume   = {151},
  abstract = {{Inspired by thermodynamic integration, we propose a method for the calculation of time-independent free energy profiles from history-dependent biased simulations via Mean Force Integration (MFI). MFI circumvents the need for computing the ensemble average of the bias acting on the system c(t) and can be applied to different variants of metadynamics. Moreover, MFI naturally extends to aggregate information obtained from independent metadynamics simulations, allowing to converge free energy surfaces without the need to sample recrossing events in a single continuous trajectory. We validate MFI against one- and two-dimensional analytical potentials and by computing the conformational free energy landscape of ibuprofen in the bulk of its most common crystal phase.}},
  journal  = {J. Chem. Phys.},
  pmid     = {31675889},
  year     = {2019},
}

@Article{Mones2016,
  author    = {Letif Mones and Noam Bernstein and G{\'{a}}bor Cs{\'{a}}nyi},
  title     = {Exploration, Sampling, And Reconstruction of Free Energy Surfaces with Gaussian Process Regression},
  doi       = {10.1021/acs.jctc.6b00553},
  number    = {10},
  pages     = {5100--5110},
  volume    = {12},
  journal   = {J. Chem. Theory Comput.},
  month     = {sep},
  publisher = {American Chemical Society ({ACS})},
  year      = {2016},
}

@Article{CP2K_2020,
  author   = {Kühne, Thomas D. and Iannuzzi, Marcella and Ben, Mauro Del and Rybkin, Vladimir V. and Seewald, Patrick and Stein, Frederick and Laino, Teodoro and Khaliullin, Rustam Z. and Schütt, Ole and Schiffmann, Florian and Golze, Dorothea and Wilhelm, Jan and Chulkov, Sergey and Bani-Hashemian, Mohammad Hossein and Weber, Valéry and Borštnik, Urban and Taillefumier, Mathieu and Jakobovits, Alice Shoshana and Lazzaro, Alfio and Pabst, Hans and Müller, Tiziano and Schade, Robert and Guidon, Manuel and Andermatt, Samuel and Holmberg, Nico and Schenter, Gregory K. and Hehn, Anna and Bussy, Augustin and Belleflamme, Fabian and Tabacchi, Gloria and Glöß, Andreas and Lass, Michael and Bethune, Iain and Mundy, Christopher J. and Plessl, Christian and Watkins, Matt and VandeVondele, Joost and Krack, Matthias and Hutter, Jürg},
  title    = {{CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations}},
  doi      = {10.1063/5.0007045},
  eprint   = {2003.03868},
  issn     = {0021-9606},
  number   = {19},
  pages    = {194103},
  volume   = {152},
  abstract = {{CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post–Hartree–Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.}},
  journal  = {J. Chem. Phys.},
  pmid     = {33687235},
  year     = {2020},
}

@Article{Micheletti_MetaE_Energy_2004,
  author   = {Micheletti, Cristian and Laio, Alessandro and Parrinello, Michele},
  title    = {{Reconstructing the Density of States by History-Dependent Metadynamics}},
  doi      = {10.1103/physrevlett.92.170601},
  eprint   = {cond-mat/0405296},
  issn     = {0031-9007},
  number   = {17},
  pages    = {170601},
  volume   = {92},
  abstract = {{We present a novel method for the calculation of the energy density of states D(E) for systems described by classical statistical mechanics. The method builds on an extension of a recently proposed strategy that allows the free-energy profile of a canonical system to be recovered within a preassigned accuracy [A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)PNASA60027-8424]. The method allows a good control over the error on the recovered system entropy. This fact is exploited to obtain D(E) more efficiently by combining measurements at different temperatures. The accuracy and efficiency of the method are tested for the two-dimensional Ising model (up to size 50×50) by comparison with both exact results and previous studies. This method is a general one and should be applicable to more realistic model systems.}},
  journal  = {Phys. Rev. Lett.},
  pmid     = {15169135},
  year     = {2003},
}

@Article{Henin2021integration,
  author    = {J{\'{e}}r{\^{o}}me H{\'{e}}nin},
  title     = {Fast and Accurate Multidimensional Free Energy Integration},
  doi       = {10.1021/acs.jctc.1c00593},
  number    = {11},
  pages     = {6789--6798},
  url       = {https://doi.org/10.1021/acs.jctc.1c00593},
  volume    = {17},
  journal   = {J. Chem. Theory Comput.},
  month     = oct,
  publisher = {American Chemical Society ({ACS})},
  year      = {2021},
}

@Article{Shell-JCP-2008,
  author        = {Shell, M. Scott},
  title         = {The relative entropy is fundamental to multiscale and inverse thermodynamic problems},
  doi           = {10.1063/1.2992060},
  issn          = {1089-7690},
  number        = {14},
  pages         = {144108},
  url           = {http://dx.doi.org/10.1063/1.2992060},
  volume        = {129},
  bdsk-url-1    = {http://dx.doi.org/10.1063/1.2992060},
  date-added    = {2018-04-23 00:14:02 +0000},
  date-modified = {2018-04-23 00:14:32 +0000},
  journal       = {J. Chem. Phys.},
  month         = {Oct},
  publisher     = {AIP Publishing},
  year          = {2008},
}

@Article{Grubmueller1996,
  author    = {H. Grubm\"uller and B. Heymann and P. Tavan},
  title     = {Ligand Binding: Molecular Mechanics Calculation of the Streptavidin-Biotin Rupture Force},
  doi       = {10.1126/science.271.5251.997},
  number    = {5251},
  pages     = {997--999},
  volume    = {271},
  journal   = {Science},
  month     = {feb},
  publisher = {American Association for the Advancement of Science ({AAAS})},
  year      = {1996},
}

@Article{Brooks2009,
  author   = {Brooks, B. R. and Brooks III, C. L. and Mackerell Jr., A. D. and Nilsson, L. and Petrella, R. J. and Roux, B. and Won, Y. and Archontis, G. and Bartels, C. and Boresch, S. and Caflisch, A. and Caves, L. and Cui, Q. and Dinner, A. R. and Feig, M. and Fischer, S. and Gao, J. and Hodoscek, M. and Im, W. and Kuczera, K. and Lazaridis, T. and Ma, J. and Ovchinnikov, V. and Paci, E. and Pastor, R. W. and Post, C. B. and Pu, J. Z. and Schaefer, M. and Tidor, B. and Venable, R. M. and Woodcock, H. L. and Wu, X. and Yang, W. and York, D. M. and Karplus, M.},
  title    = {CHARMM: The biomolecular simulation program},
  doi      = {10.1002/jcc.21287},
  eprint   = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/jcc.21287},
  number   = {10},
  pages    = {1545-1614},
  url      = {https://onlinelibrary.wiley.com/doi/abs/10.1002/jcc.21287},
  volume   = {30},
  journal  = {J. Comput. Chem.},
  keywords = {biomolecular simulation, CHARMM program, molecular mechanics, molecular dynamics, molecular modeling, biophysical computation, energy function},
  year     = {2009},
}

@Article{doi:10.1021/ct900620b,
  author  = {Bowman, Gregory R. and Ensign, Daniel L. and Pande, Vijay S.},
  title   = {Enhanced Modeling via Network Theory: Adaptive Sampling of Markov State Models},
  doi     = {10.1021/ct900620b},
  eprint  = {https://doi.org/10.1021/ct900620b},
  number  = {3},
  pages   = {787-794},
  url     = {https://doi.org/10.1021/ct900620b},
  volume  = {6},
  journal = {J. Chem. Theory Comput.},
  pmid    = {23626502},
  year    = {2010},
}

@Article{doi:10.1021/acs.jcim.5b00702,
  author  = {Cuzzolin, Alberto and Sturlese, Mattia and Deganutti, Giuseppe and Salmaso, Veronica and Sabbadin, Davide and Ciancetta, Antonella and Moro, Stefano},
  title   = {Deciphering the Complexity of Ligand–Protein Recognition Pathways Using Supervised Molecular Dynamics (SuMD) Simulations},
  doi     = {10.1021/acs.jcim.5b00702},
  eprint  = {https://doi.org/10.1021/acs.jcim.5b00702},
  number  = {4},
  pages   = {687-705},
  url     = {https://doi.org/10.1021/acs.jcim.5b00702},
  volume  = {56},
  journal = {J. Chem. Inf. Model.},
  pmid    = {27019343},
  year    = {2016},
}

@Article{Dama-JCTC-2014,
  author        = {Dama, James F. and Rotskoff, Grant and Parrinello, Michele and Voth, Gregory A.},
  title         = {Transition-Tempered Metadynamics: Robust, Convergent Metadynamics via On-the-Fly Transition Barrier Estimation},
  doi           = {10.1021/ct500441q},
  issn          = {1549-9626},
  number        = {9},
  pages         = {3626--3633},
  url           = {http://dx.doi.org/10.1021/ct500441q},
  volume        = {10},
  bdsk-url-1    = {http://dx.doi.org/10.1021/ct500441q},
  date-added    = {2015-07-17 09:35:47 +0000},
  date-modified = {2015-07-17 09:35:57 +0000},
  journal       = {J. Chem. Theory Comput.},
  month         = {Sep},
  publisher     = {American Chemical Society (ACS)},
  year          = {2014},
}

@Article{kumars:WHAM,
  author  = {S. Kumar and D. Bouzida and R. H. Swendsen and P. A. Kollman and J. M. Rosenberg},
  title   = {The weighted histogram analysis method for free-energy calculations on biomolecules .1. the method},
  number  = {8},
  pages   = {1011 -- 1021},
  volume  = {13},
  journal = {J. Comput. Chem.},
  year    = {1992},
  doi     = {10.1002/jcc.540130812,}
}

@Article{Barducci-WIREsCMS-2011,
  author        = {Barducci, Alessandro and Bonomi, Massimiliano and Parrinello, Michele},
  title         = {Metadynamics},
  doi           = {10.1002/wcms.31},
  issn          = {1759-0876},
  number        = {5},
  pages         = {826--843},
  url           = {http://dx.doi.org/10.1002/wcms.31},
  volume        = {1},
  bdsk-url-1    = {http://dx.doi.org/10.1002/wcms.31},
  date-added    = {2014-06-23 09:06:55 +0000},
  date-modified = {2015-03-25 10:47:47 +0000},
  journal       = {WIREs Comput. Mol. Sci.},
  month         = {Sep},
  publisher     = {Wiley-Blackwell},
  year          = {2011},
}

@Article{doi:10.1021/acs.jpcb.8b06521,
  author  = {Shamsi, Zahra and Cheng, Kevin J. and Shukla, Diwakar},
  title   = {Reinforcement Learning Based Adaptive Sampling: REAPing Rewards by Exploring Protein Conformational Landscapes},
  doi     = {10.1021/acs.jpcb.8b06521},
  eprint  = {https://doi.org/10.1021/acs.jpcb.8b06521},
  pmid = {30126271},
  number  = {35},
  pages   = {8386-8395},
  url     = {https://doi.org/10.1021/acs.jpcb.8b06521},
  volume  = {122},
  journal = {J. Phys. Chem. B},
  year    = {2018},
}

@Article{Shalini_Review_2019,
  author   = {Awasthi, Shalini and Nair, Nisanth N.},
  title    = {{Exploring high‐dimensional free energy landscapes of chemical reactions}},
  doi      = {10.1002/wcms.1398},
  issn     = {1759-0876},
  number   = {3},
  pages    = {e1398},
  volume   = {9},
  abstract = {{Molecular dynamics (MD) techniques are widely used in computing free energy changes for conformational transitions and chemical reactions, mainly in condensed matter systems. Most of the MD‐based approaches employ biased sampling of a priori selected coarse‐grained coordinates or collective variables (CVs) and thereby accelerate otherwise infrequent transitions from one free energy basin to the other. A quick convergence in free energy estimations can be achieved by enhanced sampling of large number of CVs. Conventional enhanced sampling approaches become exponentially slower with increasing dimensionality of the CV space, and thus they turn out to be highly inefficient in sampling high‐dimensional free energy landscapes. Here, we focus on some of the novel methods that are designed to overcome this limitation. In particular, we discuss four methods: bias‐exchange metadynamics, parallel‐bias metadynamics, adiabatic free energy dynamics/temperature‐accelerated MD, and temperature‐accelerated sliced sampling. The basic idea behind these techniques is presented and applications using these techniques are illustrated. Advantages and disadvantages of these techniques are also delineated. This article is categorized under: Structure and Mechanism > Reaction Mechanisms and Catalysis Molecular and Statistical Mechanics > Free Energy Methods Theoretical and Physical Chemistry > Statistical Mechanics Advanced methods to efficiently explore the free energy landscapes of chemical reactions are discussed in this review.}},
  journal  = {WIREs Comput. Mol. Sci.},
  year     = {2019},
}

@Article{Paliwal_comparison_2011,
  author  = {Himansu Paliwal and Michael R. Shirts},
  title   = {A benchmark test set for alchemical free energy transformations and its use to quantify error in common free energy methods},
  doi     = {10.1021/ct2003995},
  eprint  = {https://doi.org/10.1021/ct2003995},
  number  = {12},
  pages   = {4115--4134},
  url     = {https://doi.org/10.1021/ct2003995},
  volume  = {7},
  journal = {J. Chem. Theory Comput.},
  year    = {2011},
}

@Article{Wu_VES-RGMC_PRE2019,
  author   = {Wu, Yantao and Car, Roberto},
  title    = {{Determination of the critical manifold tangent space and curvature with Monte Carlo renormalization group}},
  doi      = {10.1103/physreve.100.022138},
  eprint   = {1903.08231},
  issn     = {2470-0045},
  number   = {2},
  pages    = {022138},
  volume   = {100},
  abstract = {{We show that the critical manifold of a statistical mechanical system in the vicinity of a critical point is locally accessible through correlation functions at that point. A practical numerical method is presented to determine the tangent space and the curvature to the critical manifold with variational Monte Carlo renormalization group. Because of the use of a variational bias potential of the coarse-grained variables, critical slowing down is greatly alleviated in the Monte Carlo simulation. In addition, this method is free of truncation error. We study the isotropic Ising model on square and cubic lattices, the anisotropic Ising model, and the tricritical Ising model on square lattices to illustrate the method.}},
  journal  = {Phys. Rev. E},
  pmid     = {31574704},
  year     = {2019},
}

@Article{doi:10.1021/jp805039u,
  author  = {Abrams, Jerry B. and Tuckerman, Mark E.},
  title   = {Efficient and Direct Generation of Multidimensional Free Energy Surfaces via Adiabatic Dynamics without Coordinate Transformations},
  doi     = {10.1021/jp805039u},
  eprint  = {https://doi.org/10.1021/jp805039u},
  number  = {49},
  pages   = {15742-15757},
  url     = {https://doi.org/10.1021/jp805039u},
  volume  = {112},
  journal = {J. Phys. Chem. B},
  year    = {2008},
}

@Article{Ciccotti2005,
  author    = {Giovanni Ciccotti and Raymond Kapral and Eric Vanden-Eijnden},
  title     = {Blue moon sampling, vectorial reaction coordinates, and unbiased constrained dynamics},
  doi       = {10.1002/cphc.200400669},
  number    = {9},
  pages     = {1809--1814},
  url       = {http://dx.doi.org/10.1002/cphc.200400669},
  volume    = {6},
  abstract  = {We give a new formula expressing the components of the mean force in terms of a conditional expectation which can be computed by Blue Moon sampling. This generalizes to the vectorial case a formula first derived by Ruiz-Montero et al. for a scalar reaction coordinate. We also discuss how to compute this conditional average by means of constrained stochastic dynamics which, unlike the usual constrained molecular dynamics, introduces no bias. Finally, we give a new perspective on bias removal by using constrained molecular dynamics.},
  file      = {Ciccotti Kapral vandenEijnden BLueMoon Vector RC unbiased constr dynamics CPC 2005.pdf:nergy_configurational/PMFs/Ciccotti Kapral vandenEijnden BLueMoon Vector RC unbiased constr dynamics CPC 2005.pdf:PDF},
  journal   = {ChemPhysChem},
  owner     = {jhenin},
  pmid      = {16144000},
  timestamp = {2007.11.20},
  year      = {2005},
}

@Article{doi:10.1063/1.3456985,
  author  = {Bhatt,Divesh and Zhang,Bin W. and Zuckerman,Daniel M.},
  title   = {Steady-state simulations using weighted ensemble path sampling},
  doi     = {10.1063/1.3456985},
  eprint  = {https://doi.org/10.1063/1.3456985},
  number  = {1},
  pages   = {014110},
  url     = {https://doi.org/10.1063/1.3456985},
  volume  = {133},
  journal = {J. Chem. Phys.},
  year    = {2010},
}

@Article{doi:10.1063/1.1562614,
  author  = {van Erp,Titus S. and Moroni,Daniele and Bolhuis,Peter G.},
  title   = {A novel path sampling method for the calculation of rate constants},
  doi     = {10.1063/1.1562614},
  eprint  = {https://doi.org/10.1063/1.1562614},
  number  = {17},
  pages   = {7762-7774},
  url     = {https://doi.org/10.1063/1.1562614},
  volume  = {118},
  journal = {J. Chem. Phys.},
  year    = {2003},
}

@Article{laio-gervasio-08,
  author  = {Laio, A. and Gervasio, F.L.},
  title   = {Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science},
  doi     = {10.1088/0034-4885/71/12/126601},
  number  = {12},
  pages   = {126601},
  volume  = {71},
  journal = {Rep. Prog. Phys.},
  year    = {2008},
}

@Book{Peters2017,
  author    = {Peters, Baron},
  title     = {{Reaction Rate Theory and Rare Events}},
  isbn      = {978-0-444-56349-1},
  publisher = {Elsevier},
  url       = {https://www.elsevier.com/books/reaction-rate-theory-and-rare-events/peters/978-0-444-56349-1},
  keywords  = {Books},
  year      = {2017},
}

@Article{Camilloni_RAM-2_JACS20214,
  author    = {Camilloni, Carlo and Vendruscolo, Michele},
  title     = {{Statistical Mechanics of the Denatured State of a Protein Using Replica-Averaged Metadynamics}},
  doi       = {10.1021/ja5027584},
  issn      = {0002-7863},
  number    = {25},
  pages     = {8982--8991},
  volume    = {136},
  abstract  = {{The characterization of denatured states of proteins is challenging because the lack of permanent structure in these states makes it difficult to apply to them standard methods of structural biology. In this work we use all-atom replica-averaged metadynamics (RAM) simulations with NMR chemical shift restraints to determine an ensemble of structures representing an acid-denatured state of the 86-residue protein ACBP. This approach has enabled us to reach convergence in the free energy landscape calculations, obtaining an ensemble of structures in relatively accurate agreement with independent experimental data used for validation. By observing at atomistic resolution the transient formation of native and non-native structures in this acid-denatured state of ACBP, we rationalize the effects of single-point mutations on the folding rate, stability, and transition-state structures of this protein, thus characterizing the role of the unfolded state in determining the folding process.}},
  journal   = {J. Am. Chem. Soc.},
  local-url = {file://localhost/Users/valsson/Documents/Papers%20Library/Journal%20of%20the%20American%20Chemical%20Society/2014/Camilloni-Vendruscolo-2014-Journal%20of%20the%20American%20Chemical%20Society.pdf},
  pmid      = {24884637},
  year      = {2014},
}

@Article{Lesage2017,
  author       = {Adrien Lesage and Tony Leli{\`{e}}vre and Gabriel Stoltz and J{\'{e}}r{\^{o}}me H{\'{e}}nin},
  date         = {2016-12},
  journaltitle = {J. Phys. Chem. B},
  title        = {Smoothed Biasing Forces Yield Unbiased Free Energies with the Extended-System Adaptive Biasing Force Method},
  doi          = {10.1021/acs.jpcb.6b10055},
  number       = {15},
  pages        = {3676--3685},
  volume       = {121},
  journal      = {J. Phys. Chem. B},
  publisher    = {American Chemical Society ({ACS})},
  year         = {2017},
}

@Article{chelli:jctc:2010:optimal-weights-expanded-ensembles,
  author  = {Riccardo Chelli},
  title   = {Optimal weights in serial generalized-ensemble simulations},
  doi     = {10.1021/ct100105z},
  pages   = {1935--1950},
  volume  = {6},
  journal = {J. Chem. Theory Comput.},
  year    = {2010},
}

@Article{Zhu2011,
  author    = {Fangqiang Zhu and Gerhard Hummer},
  title     = {Convergence and error estimation in free energy calculations using the weighted histogram analysis method},
  doi       = {10.1002/jcc.21989},
  number    = {4},
  pages     = {453--465},
  url       = {https://doi.org/10.1002/jcc.21989},
  volume    = {33},
  journal   = {J. Comput. Chem.},
  month     = nov,
  publisher = {Wiley},
  year      = {2011},
}

@Article{10.1063/1.4978939,
  author   = {Hošek, Petr and Kříž, Pavel and Toulcová, Daniela and Spiwok, Vojtěch},
  title    = {{Multisystem altruistic metadynamics—Well-tempered variant}},
  doi      = {10.1063/1.4978939},
  issn     = {0021-9606},
  number   = {12},
  pages    = {125103},
  volume   = {146},
  abstract = {{Metadynamics method has been widely used to enhance sampling in molecular simulations. Its original form suffers two major drawbacks, poor convergence in complex (especially biomolecular) systems and its serial nature. The first drawback has been addressed by introduction of a convergent variant known as well-tempered metadynamics. The second was addressed by introduction of a parallel multisystem metadynamics referred to as altruistic metadynamics. Here, we combine both approaches into well-tempered altruistic metadynamics. We provide mathematical arguments and trial simulations to show that it accurately predicts free energy surfaces.}},
  journal  = {J. Chem. Phys.},
  pmid     = {28388169},
  year     = {2017},
}

@Article{Allison_Review_2020,
  author   = {Allison, Jane R},
  title    = {{Computational methods for exploring protein conformations}},
  doi      = {10.1042/bst20200193},
  issn     = {0300-5127},
  number   = {4},
  pages    = {1707--1724},
  volume   = {48},
  abstract = {{Proteins are dynamic molecules that can transition between a potentially wide range of structures comprising their conformational ensemble. The nature of these conformations and their relative probabilities are described by a high-dimensional free energy landscape. While computer simulation techniques such as molecular dynamics simulations allow characterisation of the metastable conformational states and the transitions between them, and thus free energy landscapes, to be characterised, the barriers between states can be high, precluding efficient sampling without substantial computational resources. Over the past decades, a dizzying array of methods have emerged for enhancing conformational sampling, and for projecting the free energy landscape onto a reduced set of dimensions that allow conformational states to be distinguished, known as collective variables (CVs), along which sampling may be directed. Here, a brief description of what biomolecular simulation entails is followed by a more detailed exposition of the nature of CVs and methods for determining these, and, lastly, an overview of the myriad different approaches for enhancing conformational sampling, most of which rely upon CVs, including new advances in both CV determination and conformational sampling due to machine learning.}},
  journal  = {Biochem. Soc. Trans.},
  pmid     = {32756904},
  year     = {2020},
}

@Article{Celerse2019,
  author  = {Fr{\'{e}}d{\'{e}}ric C{\'{e}}lerse and Louis Lagard{\`{e}}re and Etienne Derat and Jean-Philip Piquemal},
  title   = {Massively Parallel Implementation of Steered Molecular Dynamics in Tinker-HP: Comparisons of Polarizable and Non-Polarizable Simulations of Realistic Systems},
  doi     = {10.1021/acs.jctc.9b00199},
  eprint  = {https://doi.org/10.1021/acs.jctc.9b00199},
  number  = {6},
  pages   = {3694-3709},
  url     = {https://doi.org/10.1021/acs.jctc.9b00199},
  volume  = {15},
  journal = {J. Chem. Theory Comput.},
  pmid    = {31059250},
  year    = {2019},
}

@Article{doi:10.1146/annurev.physchem.53.082301.113146,
  author   = {Bolhuis, Peter G. and Chandler, David and Dellago, Christoph and Geissler, Phillip L.},
  title    = {TRANSITION PATH SAMPLING: Throwing Ropes Over Rough Mountain Passes, in the Dark},
  doi      = {10.1146/annurev.physchem.53.082301.113146},
  eprint   = {https://doi.org/10.1146/annurev.physchem.53.082301.113146},
  number   = {1},
  pages    = {291-318},
  url      = {https://doi.org/10.1146/annurev.physchem.53.082301.113146},
  volume   = {53},
  abstract = {▪ Abstract This article reviews the concepts and methods of transition path sampling. These methods allow computational studies of rare events without requiring prior knowledge of mechanisms, reaction coordinates, and transition states. Based upon a statistical mechanics of trajectory space, they provide a perspective with which time dependent phenomena, even for systems driven far from equilibrium, can be examined with the same types of importance sampling tools that in the past have been applied so successfully to static equilibrium properties.},
  journal  = {Annu. Rev. Phys. Chem.},
  year     = {2002},
}

@Article{Chen_GAMD-MetaD-eABF_JCTC2021,
  author   = {Chen, Haochuan and Fu, Haohao and Chipot, Christophe and Shao, Xueguang and Cai, Wensheng},
  title    = {{Overcoming Free-Energy Barriers with a Seamless Combination of a Biasing Force and a Collective Variable-Independent Boost Potential}},
  doi      = {10.1021/acs.jctc.1c00103},
  issn     = {1549-9618},
  abstract = {{Amid collective-variable (CV)-based importance-sampling algorithms, a hybrid of the extended adaptive biasing force and the well-tempered metadynamics algorithms (WTM-eABF) has proven particularly cost-effective for exploring the rugged free-energy landscapes that underlie biological processes. However, as an inherently CV-based algorithm, this hybrid scheme does not explicitly accelerate sampling in the space orthogonal to the chosen CVs, thereby limiting its efficiency and accuracy, most notably in those cases where the slow degrees of freedom of the process at hand are not accounted for in the model transition coordinate. Here, inspired by Gaussian-accelerated molecular dynamics (GaMD), we introduce the same CV-independent harmonic boost potential into WTM-eABF, yielding a hybrid algorithm coined GaWTM-eABF. This algorithm leans on WTM-eABF to explore the transition coordinate with a GaMD-mollified potential and recovers the unbiased free-energy landscape through thermodynamic integration followed by proper reweighting. As illustrated in our numerical tests, GaWTM-eABF effectively overcomes the free-energy barriers in orthogonal space and correctly recovers the unbiased potential of mean force (PMF). Furthermore, applying both GaWTM-eABF and WTM-eABF to two biologically relevant processes, namely, the reversible folding of (i) deca-alanine and (ii) chignolin, our results indicate that GaWTM-eABF reduces the uncertainty in the PMF calculation and converges appreciably faster than WTM-eABF. Obviating the need of multiple-copy strategies, GaWTM-eABF is a robust, computationally efficient algorithm to surmount the free-energy barriers in orthogonal space and maps with utmost fidelity the free-energy landscape along selections of CVs. Moreover, our strategy that combines WTM-eABF with GaMD can be easily extended to other biasing-force algorithms.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {34106706},
  year     = {2021},
}

@Article{Klimovich_Shirts_Mobley_2015,
  author       = {Klimovich, Pavel V. and Shirts, Michael R. and Mobley, David L.},
  title        = {Guidelines for the analysis of free energy calculations},
  doi          = {10.1007/s10822-015-9840-9},
  issn         = {1573-4951},
  number       = {5},
  pages        = {397–411},
  volume       = {29},
  abstractnote = {Free energy calculations based on molecular dynamics simulations show considerable promise for applications ranging from drug discovery to prediction of physical properties and structure-function studies. But these calculations are still difficult and tedious to analyze, and best practices for analysis are not well defined or propagated. Essentially, each group analyzing these calculations needs to decide how to conduct the analysis and, usually, develop its own analysis tools. Here, we review and recommend best practices for analysis yielding reliable free energies from molecular simulations. Additionally, we provide a Python tool, alchemical-analysis.py, freely available on GitHub as part of the pymbar package (located at http://github.com/choderalab/pymbar), that implements the analysis practices reviewed here for several reference simulation packages, which can be adapted to handle data from other packages. Both this review and the tool covers analysis of alchemical calculations generally, including free energy estimates via both thermodynamic integration and free energy perturbation-based estimators. Our Python tool also handles output from multiple types of free energy calculations, including expanded ensemble and Hamiltonian replica exchange, as well as standard fixed ensemble calculations. We also survey a range of statistical and graphical ways of assessing the quality of the data and free energy estimates, and provide prototypes of these in our tool. We hope this tool  and discussion will serve as a foundation for more standardization of and agreement on best practices for analysis of free energy calculations.},
  journal      = {J. Comput. Aided Mol. Des.},
  month        = {5},
  year         = {2015},
}

@Article{10.1103/physrevlett.109.020601,
  author   = {Leines, Grisell Díaz and Ensing, Bernd},
  title    = {{Path Finding on High-Dimensional Free Energy Landscapes}},
  doi      = {10.1103/physrevlett.109.020601},
  issn     = {0031-9007},
  number   = {2},
  pages    = {020601},
  volume   = {109},
  abstract = {{We present a method for determining the average transition path and the free energy along this path in the space of selected collective variables. The formalism is based upon a history-dependent bias along a flexible path variable within the metadynamics framework but with a trivial scaling of the cost with the number of collective variables. Controlling the sampling of the orthogonal modes recovers the average path and the minimum free energy path as the limiting cases. The method is applied to resolve the path and the free energy of a conformational transition in alanine dipeptide.}},
  journal  = {Phys. Rev. Lett.},
  pmid     = {23030145},
  year     = {2012},
}

@Article{shirts_gibbssamp,
  author   = {Chodera, John D and Shirts, Michael R},
  title    = {{Replica exchange and expanded ensemble simulations as Gibbs sampling: simple improvements for enhanced mixing.}},
  doi      = {10.1063/1.3660669},
  issn     = {1089-7690},
  language = {en},
  number   = {19},
  pages    = {194110},
  volume   = {135},
  abstract = {The widespread popularity of replica exchange and expanded ensemble algorithms for simulating complex molecular systems in chemistry and biophysics has generated much interest in discovering new ways to enhance the phase space mixing of these protocols in order to improve sampling of uncorrelated configurations. Here, we demonstrate how both of these classes of algorithms can be considered as special cases of Gibbs sampling within a Markov chain Monte Carlo framework. Gibbs sampling is a well-studied scheme in the field of statistical inference in which different random variables are alternately updated from conditional distributions. While the update of the conformational degrees of freedom by Metropolis Monte Carlo or molecular dynamics unavoidably generates correlated samples, we show how judicious updating of the thermodynamic state indices--corresponding to thermodynamic parameters such as temperature or alchemical coupling variables--can substantially increase mixing while still sampling from the desired distributions. We show how state update methods in common use can lead to suboptimal mixing, and present some simple, inexpensive alternatives that can increase mixing of the overall Markov chain, reducing simulation times necessary to obtain estimates of the desired precision. These improved schemes are demonstrated for several common applications, including an alchemical expanded ensemble simulation, parallel tempering, and multidimensional replica exchange umbrella sampling.},
  journal  = {J. Chem. Phys.},
  keywords = {Algorithms, Molecular Dynamics Simulation, Monte Carlo Method, Thermodynamics},
  month    = nov,
  pmid     = {22112069},
  year     = {2011},
}

@Article{https://doi.org/10.1002/wcms.1455,
  author   = {Limongelli, Vittorio},
  title    = {Ligand binding free energy and kinetics calculation in 2020},
  doi      = {10.1002/wcms.1455},
  eprint   = {https://wires.onlinelibrary.wiley.com/doi/pdf/10.1002/wcms.1455},
  number   = {4},
  pages    = {e1455},
  url      = {https://wires.onlinelibrary.wiley.com/doi/abs/10.1002/wcms.1455},
  volume   = {10},
  abstract = {Abstract Ligand/protein binding (LPB) is a major topic in medicine, chemistry and biology. Since the advent of computers, many scientists have put efforts in developing theoretical models that could decode the alphabet of the LPB interaction. The success of this task passes by the resolution of the molecular mechanism of LPB. In the past century, major attention was dedicated to the thermodynamics of LPB, while more recent studies have revealed that ligand (un)binding kinetics is at least as important as ligand binding thermodynamics in determining the drug in vivo efficacy. In the present review, we introduce the most widely used computational methods to study LPB thermodynamics and kinetics. It is important to say that no method outperforms another, they all have pros and cons and the choice of the user should take carefully into account the system under investigation, the available structural and experimental data, and the goal of the research. A perspective on future directions of method development and research on LPB concludes the discussion. This article is categorized under: Molecular and Statistical Mechanics > Free Energy Methods Structure and Mechanism > Computational Biochemistry and Biophysics Molecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods},
  journal  = {WIREs Comput. Mol. Sci.},
  keywords = {free energy calculations, funnel-metadynamics, ligand binding free energy, ligand binding thermodynamics, ligand binding kinetics, molecular dynamics, molecular docking},
  year     = {2020},
}

@Article{Whitmer_BFS_2014,
  author   = {Whitmer, Jonathan K. and Chiu, Chi-cheng and Joshi, Abhijeet A. and Pablo, Juan J. de},
  title    = {{Basis Function Sampling: A New Paradigm for Material Property Computation}},
  doi      = {10.1103/physrevlett.113.190602},
  issn     = {0031-9007},
  number   = {19},
  pages    = {190602},
  volume   = {113},
  abstract = {{Wang–Landau sampling, and the associated class of flat histogram simulation methods have been remarkably helpful for calculations of the free energy in a wide variety of physical systems. Practically, convergence of these calculations to a target free energy surface is hampered by reliance on parameters which are unknown a priori. Here, we derive and implement a method built upon orthogonal functions which is fast, parameter-free, and (importantly) geometrically robust. The method is shown to be highly effective in achieving convergence. An important feature of this method is its ability to attain arbitrary levels of description for the free energy. It is thus ideally suited to in silico measurement of elastic moduli and other material properties related to free energy perturbations. We demonstrate the utility of such applications by applying our method to calculate the Frank elastic constants of the Lebwohl–Lasher model of liquid crystals.}},
  journal  = {Phys. Rev. Lett.},
  pmid     = {25415892},
  year     = {2014},
}

@Article{McCarty-PRL-2015,
  author   = {McCarty, James and Valsson, Omar and Tiwary, Pratyush and Parrinello, Michele},
  title    = {{Variationally Optimized Free-Energy Flooding for Rate Calculation}},
  doi      = {10.1103/physrevlett.115.070601},
  eprint   = {1506.02545},
  issn     = {0031-9007},
  number   = {7},
  pages    = {070601},
  volume   = {115},
  abstract = {{We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to construct a bias potential as a function of several collective variables that is designed to flood the associated free energy surface up to a predefined level. The resulting bias potential effectively accelerates transitions between metastable free energy minima while ensuring bias-free transition states, thus allowing accurate kinetic rates to be obtained. We test the method on a few illustrative systems for which we obtain an order of magnitude improvement in efficiency relative to previous approaches and several orders of magnitude relative to unbiased molecular dynamics. We expect an even larger improvement in more complex systems. This and the ability of the variational approach to deal efficiently with a large number of collective variables will greatly enhance the scope of these calculations. This work is a vindication of the potential that the variational principle has if applied in innovative ways.}},
  journal  = {Phys. Rev. Lett.},
  keywords = {My Papers},
  pmid     = {26317704},
  year     = {2015},
}

@Article{doi:10.1021/jacs.8b10735,
  author  = {Adhikari, Upendra and Mostofian, Barmak and Copperman, Jeremy and Subramanian, Sundar Raman and Petersen, Andrew A. and Zuckerman, Daniel M.},
  title   = {Computational Estimation of Microsecond to Second Atomistic Folding Times},
  doi     = {10.1021/jacs.8b10735},
  eprint  = {https://doi.org/10.1021/jacs.8b10735},
  number  = {16},
  pages   = {6519-6526},
  url     = {https://doi.org/10.1021/jacs.8b10735},
  volume  = {141},
  journal = {J. Am. Chem. Soc.},
  year    = {2019},
}

@Article{Piana2007_bemeta,
  author    = {Piana, Stefano and Laio, Alessandro},
  title     = {A Bias-Exchange Approach to Protein Folding},
  doi       = {10.1021/jp067873l},
  issn      = {1520-5207},
  number    = {17},
  pages     = {4553–4559},
  url       = {http://dx.doi.org/10.1021/jp067873l},
  volume    = {111},
  journal   = {J. Phys. Chem. B},
  month     = {May},
  publisher = {American Chemical Society (ACS)},
  year      = {2007},
}

@Article{Kapakayala_WS-MetaD+REST2_JCC2021,
  author   = {Kapakayala, Anji Babu and Nair, Nisanth N.},
  title    = {{Boosting the conformational sampling by combining replica exchange with solute tempering and well‐sliced metadynamics}},
  doi      = {10.1002/jcc.26752},
  issn     = {0192-8651},
  abstract = {{Methods that combine collective variable (CV) based enhanced sampling and global tempering approaches are used in speeding‐up the conformational sampling and free energy calculation of large and soft systems with a plethora of energy minima. In this paper, a new method of this kind is proposed in which the well‐sliced metadynamics approach (WSMTD) is united with replica exchange with solute tempering (REST2) method. WSMTD employs a divide‐and‐conquer strategy wherein high‐dimensional slices of a free energy surface are independently sampled and combined. The method enables one to accomplish a controlled exploration of the CV‐space with a restraining bias as in umbrella sampling, and enhance‐sampling of one or more orthogonal CVs using a metadynamics like bias. The new hybrid method proposed here enables boosting the sampling of more slow degrees of freedom in WSMTD simulations, without the need to specify associated CVs, through a replica exchange scheme within the framework of REST2. The high‐dimensional slices of the probability distributions of CVs computed from the united WSMTD and REST2 simulations are subsequently combined using the weighted histogram analysis method to obtain the free energy surface. We show that the new method proposed here is accurate, improves the conformational sampling, and achieves quick convergence in free energy estimates. We demonstrate this by computing the conformational free energy landscapes of solvated alanine tripeptide and Trp‐cage mini protein in explicit water. A new method is proposed for efficient sampling of conformational space of large soft matter systems. The method permits one to drive a conformational change along a collective variable (CV) in a controlled fashion and exhaustive sampling of orthogonal coordinates through accelerating global motions (without specifying any CVs) and biased sampling of a priori chosen CVs. The method is shown to be very accurate and quite efficient for problems such as protein folding.}},
  journal  = {J. Comput. Chem.},
  pmid     = {34585768},
  year     = {2021},
}

@Article{Henin2004,
  author  = {H\'enin, J. and Chipot, C.},
  title   = {Overcoming free energy barriers using unconstrained molecular dynamics simulations},
  pages   = {2904--2914},
  volume  = {121},
  file    = {2004_ABF_JCP.pdf:/home/jhenin/Documents/Publis/2004_ABF_JCP.pdf:PDF},
  journal = {J. Chem. Phys.},
  year    = {2004},
  doi     = {10.1063/1.1773132},
}

@Article{Whitmer_GFS_2015,
  author  = {Whitmer, Jonathan K and Fluitt, Aaron M and Antony, Lucas and Qin, Jian and McGovern, Michael and Pablo, Juan J de},
  title   = {{Sculpting bespoke mountains: Determining free energies with basis expansions}},
  doi     = {10.1063/1.4927147},
  issn    = {0021-9606},
  number  = {4},
  pages   = {044101},
  volume  = {143},
  journal = {J. Chem. Phys.},
  pmid    = {26233101},
  year    = {2015},
}

% * G. Fort, B. Jourdain, TL and G. Stoltz, Self-Healing Umbrella
% Sampling: Convergence and efficiency, Statistics and computing, 27(1),
% 147-168, (2017).

@Article{fort-jourdain-lelievre-stoltz-17,
  author  = {Fort, G. and Jourdain, B. and Leli\`evre, T. and Stoltz, G.},
  title   = {{S}elf-{H}ealing {U}mbrella {S}ampling: Convergence and efficiency},
  doi     = {10.1007/s11222-015-9613-2},
  number  = {1},
  pages   = {147-168},
  volume  = {27},
  journal = {Stat. Comput.},
  year    = {2017},
}

@Article{Yang_SITS_2009,
  author   = {Yang, Lijiang and Gao, Yi Qin},
  title    = {{A selective integrated tempering method}},
  doi      = {10.1063/1.3266563},
  issn     = {0021-9606},
  number   = {21},
  pages    = {214109},
  volume   = {131},
  abstract = {{In this paper, based on the integrated tempering sampling we introduce a selective integrated tempering sampling (SITS) method for the efficient conformation sampling and thermodynamics calculations for a subsystem in a large one, such as biomolecules solvated in aqueous solutions. By introducing a potential surface scaled with temperature, the sampling over the configuration space of interest (e.g., the solvated biomolecule) is selectively enhanced but the rest of the system (e.g., the solvent) stays largely unperturbed. The applications of this method to biomolecular systems allow highly efficient sampling over both energy and configuration spaces of interest. Comparing to the popular and powerful replica exchange molecular dynamics (REMD), the method presented in this paper is significantly more efficient in yielding relevant thermodynamics quantities (such as the potential of mean force for biomolecular conformational changes in aqueous solutions). It is more important that SITS but not REMD yielded results that are consistent with the traditional umbrella sampling free energy calculations when explicit solvent model is used since SITS avoids the sampling of the irrelevant phase space (such as the boiling water at high temperatures).}},
  journal  = {J. Chem. Phys.},
  pmid     = {19968339},
  year     = {2009},
}



% * G. Fort, B. Jourdain, TL and G. Stoltz, Convergence and efficiency of
% adaptive importance sampling techniques with partial biasing, Journal of
% Statistical Physics, 171(2), 220-268 (2018)

@Article{fort-jourdain-lelievre-stoltz-18,
  author  = {Fort, G. and Jourdain, B. and Kuhn, E. and Leli\`evre, T. and Stoltz, G.},
  title   = {Convergence and Efficiency of Adaptive Importance Sampling Techniques with Partial Biasing},
  doi     = {10.1007/s10955-018-1992-2},
  pages   = {220-268},
  volume  = {171},
  journal = {J. Stat. Phys},
  year    = {2018},
}

@Article{Bonati2019_NN-VES,
  author    = {Bonati, Luigi and Zhang, Yue-Yu and Parrinello, Michele},
  title     = {Neural networks-based variationally enhanced sampling},
  doi       = {10.1073/pnas.1907975116},
  issn      = {1091-6490},
  number    = {36},
  pages     = {17641–17647},
  url       = {http://dx.doi.org/10.1073/pnas.1907975116},
  volume    = {116},
  journal   = {Proc. Natl. Acad. Sci.},
  month     = {Aug},
  publisher = {Proc. Natl. Acad. Sci. U.S.A.},
  year      = {2019},
}

@Article{10.1021/acs.jpcb.6b00087,
  author   = {Hošek, Petr and Toulcová, Daniela and Bortolato, Andrea and Spiwok, Vojtěch},
  title    = {{Altruistic Metadynamics: Multisystem Biased Simulation}},
  doi      = {10.1021/acs.jpcb.6b00087},
  issn     = {1520-6106},
  number   = {9},
  pages    = {2209--2215},
  volume   = {120},
  abstract = {{We present a new simple extension of multiple walker metadynamics which makes it possible to simulate simultaneously multiple different molecular systems and to predict their free energy surfaces, named Altruistic metadynamics. Similarly to basic metadynamics, it uses a bias potential in the form of hills summed over the simulation. Each system adds a big hill to its "own" bias potential and smaller hills to bias potentials of other systems, hence, each system enhances sampling of other systems. This makes it possible to achieve either faster reaching of the stationary point or higher accuracy of the calculated free energy surfaces. This should be efficient in modeling of series of chemically similar systems, for example, in computational drug screening by metadynamics. The method was tested on model energy surfaces, alanine dipeptide modeled in different force fields and monosaccharides of D-hexopyranose series.}},
  journal  = {J. Phys. Chem. B},
  pmid     = {26852938},
  year     = {2016},
}

@Article{Hansmann-PRL-2002,
  author    = {Hansmann, Ulrich and Wille, Luc},
  title     = {Global optimization by energy landscape paving},
  doi       = {10.1103/physrevlett.88.068105},
  issn      = {1079-7114},
  number    = {6},
  pages     = {068105},
  url       = {http://dx.DOI.org/10.1103/PhysRevLett.88.068105},
  volume    = {88},
  journal   = {Phys. Rev. Lett.},
  month     = {Jan},
  publisher = {American Physical Society (APS)},
  year      = {2002},
}

@Article{doi:10.1021/ct401065r,
  author  = {Suárez, Ernesto and Lettieri, Steven and Zwier, Matthew C. and Stringer, Carsen A. and Subramanian, Sundar Raman and Chong, Lillian T. and Zuckerman, Daniel M.},
  title   = {Simultaneous Computation of Dynamical and Equilibrium Information Using a Weighted Ensemble of Trajectories},
  doi     = {10.1021/ct401065r},
  eprint  = {https://doi.org/10.1021/ct401065r},
  number  = {7},
  pages   = {2658-2667},
  url     = {https://doi.org/10.1021/ct401065r},
  volume  = {10},
  journal = {J. Chem. Theory Comput.},
  pmid    = {25246856},
  year    = {2014},
}

@Article{Johnston_MetaD-US-4_PLos2012,
  author   = {Johnston, Jennifer M. and Wang, Hao and Provasi, Davide and Filizola, Marta},
  title    = {{Assessing the Relative Stability of Dimer Interfaces in G Protein-Coupled Receptors}},
  doi      = {10.1371/journal.pcbi.1002649},
  issn     = {1553-734X},
  number   = {8},
  pages    = {e1002649},
  volume   = {8},
  abstract = {{Considerable evidence has accumulated in recent years suggesting that G protein-coupled receptors (GPCRs) associate in the plasma membrane to form homo- and/or heteromers. Nevertheless, the stoichiometry, fraction and lifetime of such receptor complexes in living cells remain topics of intense debate. Motivated by experimental data suggesting differing stabilities for homomers of the cognate human β1- and β2-adrenergic receptors, we have carried out approximately 160 microseconds of biased molecular dynamics simulations to calculate the dimerization free energy of crystal structure-based models of these receptors, interacting at two interfaces that have often been implicated in GPCR association under physiological conditions. Specifically, results are presented for simulations of coarse-grained (MARTINI-based) and atomistic representations of each receptor, in homodimeric configurations with either transmembrane helices TM1/H8 or TM4/3 at the interface, in an explicit lipid bilayer. Our results support a definite contribution to the relative stability of GPCR dimers from both interface sequence and configuration. We conclude that β1- and β2-adrenergic receptor homodimers with TM1/H8 at the interface are more stable than those involving TM4/3, and that this might be reconciled with experimental studies by considering a model of oligomerization in which more stable TM1 homodimers diffuse through the membrane, transiently interacting with other protomers at interfaces involving other TM helices.}},
  journal  = {PLoS Comput. Biol.},
  pmcid    = {PMC3420924},
  pmid     = {22916005},
  year     = {2012},
}

@Article{Carter1989,
  author    = {Carter, E, A. and Ciccotti, G. and Hynes, J. T. and Kapral, R.},
  title     = {Constrained reaction coordinate dynamics for the simulation of rare events},
  pages     = {472-477},
  volume    = {156},
  comment   = {Free energy},
  journal   = {Chem. Phys. Lett.},
  owner     = {jhenin},
  timestamp = {2007.11.20},
  year      = {1989},
  doi       = {10.1016/S0009-2614(89)87314-2},
}

@Article{Gao_ITS_Review_2015,
  author  = {Yang, Lijiang and Liu, Cheng-Wen and Shao, Qiang and Zhang, Jun and Gao, Yi Qin},
  title   = {{From Thermodynamics to Kinetics: Enhanced Sampling of Rare Events}},
  doi     = {10.1021/ar500267n},
  issn    = {0001-4842},
  number  = {4},
  pages   = {947--955},
  volume  = {48},
  journal = {Acc. Chem. Res.},
  pmid    = {25781363},
  year    = {2015},
}

@Article{Valsson2016_ARPC_MetaD,
  author    = {Valsson, Omar and Tiwary, Pratyush and Parrinello, Michele},
  title     = {Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint},
  doi       = {10.1146/annurev-physchem-040215-112229},
  issn      = {1545-1593},
  number    = {1},
  pages     = {159–184},
  url       = {http://dx.doi.org/10.1146/annurev-physchem-040215-112229},
  volume    = {67},
  journal   = {Annu. Rev. Phys. Chem.},
  month     = {May},
  publisher = {Annual Reviews},
  year      = {2016},
}

@Article{doi:10.1021/ct2004484,
  author  = {Weber, Jeffrey K. and Pande, Vijay S.},
  title   = {Characterization and Rapid Sampling of Protein Folding Markov State Model Topologies},
  doi     = {10.1021/ct2004484},
  eprint  = {https://doi.org/10.1021/ct2004484},
  number  = {10},
  pages   = {3405-3411},
  url     = {https://doi.org/10.1021/ct2004484},
  volume  = {7},
  journal = {J. Chem. Theory Comput.},
  pmid    = {22140370},
  year    = {2011},
}

@Article{Cesari_MaximumEntropyPrinciple_Review_Comp2018,
  author   = {Cesari, Andrea and Reißer, Sabine and Bussi, Giovanni},
  title    = {{Using the Maximum Entropy Principle to Combine Simulations and Solution Experiments}},
  doi      = {10.3390/computation6010015},
  eprint   = {1801.05247},
  number   = {1},
  pages    = {15},
  volume   = {6},
  abstract = {{Molecular dynamics (MD) simulations allow the investigation of the structural dynamics of biomolecular systems with unrivaled time and space resolution. However, in order to compensate for the inaccuracies of the utilized empirical force fields, it is becoming common to integrate MD simulations with experimental data obtained from ensemble measurements. We review here the approaches that can be used to combine MD and experiment under the guidance of the maximum entropy principle. We mostly focus on methods based on Lagrangian multipliers, either implemented as reweighting of existing simulations or through an on-the-fly optimization. We discuss how errors in the experimental data can be modeled and accounted for. Finally, we use simple model systems to illustrate the typical difficulties arising when applying these methods.}},
  journal  = {Computation},
  year     = {2018},
}

% Simulated scaling

@Article{li-fajer-yang:jcp:2007:simulated-scaling,
  author  = {Hongzhi Li and Mikolai Fajer and Wei Yang},
  title   = {Simulated scaling method for localized enhanced sampling and simultaneous ``alchemical'' free energy simulations: A general method for molecular mechanical, quantum mechanical, and quantum mechanical/molecular mechanical simulations},
  doi     = {10.1063/1.2424700},
  pages   = {024106},
  volume  = {126},
  journal = {J. Chem. Phys.},
  year    = {2007},
}

@Article{shenfeld-xu:pre:2009:thermodynamic-length,
  author  = {Daniel K. Shenfeld and Huafeng Xu and Michael P. Eastwood and Ron O. Dror and David E. Shaw},
  title   = {Minimizing thermodynamic length to select intermediate states for free energy calculations and replica-exchange simulations},
  doi     = {10.1103/physreve.80.046705},
  pages   = {To appear},
  journal = {Phys. Rev. E},
  year    = {2009},
}

@Article{Bogetti2019Suite,
  author    = {Bogetti, Anthony T. and Mostofian, Barmak and Dickson, Alex and Pratt, A. J. and Saglam, Ali S. and Harrison, Page O. and Adelman, Joshua L. and Dudek, Max and Torrillo, Paul A. and DeGrave, Alex J. and Adhikari, Upendra and Zwier, Matthew C. and Zuckerman, Daniel M. and Chong, Lillian T.},
  date      = {2019-10-04},
  title     = {A Suite of Tutorials for the WESTPA Rare-Events Sampling Software [Article v1.0]},
  doi       = {10.33011/livecoms.1.2.10607},
  number    = {2},
  pages     = {10607},
  volume    = {1},
  day       = {4},
  journal   = {LiveCoMS},
  month     = {10},
  publisher = {University of Colorado Boulder},
  year      = {2019},
}

@Article{HOOMD-blue_2020,
  author   = {Anderson, Joshua A. and Glaser, Jens and Glotzer, Sharon C.},
  title    = {{HOOMD-blue: A Python package for high-performance molecular dynamics and hard particle Monte Carlo simulations}},
  doi      = {10.1016/j.commatsci.2019.109363},
  issn     = {0927-0256},
  pages    = {109363},
  volume   = {173},
  abstract = {{HOOMD-blue is a particle simulation engine designed for nano- and colloidal-scale molecular dynamics and hard particle Monte Carlo simulations. It has been actively developed since March 2007 and available open source since August 2008. HOOMD-blue is a Python package with a high performance C++/CUDA backend that we built from the ground up for GPU acceleration. The Python interface allows users to combine HOOMD-blue with other packages in the Python ecosystem to create simulation and analysis workflows. We employ software engineering practices to develop, test, maintain, and expand the code.}},
  journal  = {Comput. Mater. Sci.},
  year     = {2020},
}

@Article{Valsson_VES_PRL_2014,
  author        = {Valsson, Omar and Parrinello, Michele},
  title         = {{Variational Approach to Enhanced Sampling and Free Energy Calculations}},
  doi           = {10.1103/physrevlett.113.090601},
  issn          = {0031-9007},
  number        = {9},
  pages         = {090601},
  url           = {http://dx.doi.org/10.1103/PhysRevLett.113.090601},
  volume        = {113},
  bdsk-url-1    = {http://dx.doi.org/10.1103/PhysRevLett.113.090601},
  bdsk-url-2    = {http://dx.doi.org/10.1103/physrevlett.113.090601},
  date-added    = {2014-09-10 14:54:16 +0000},
  date-modified = {2015-03-25 10:53:03 +0000},
  journal       = {Phys. Rev. Lett.},
  keywords      = {My Papers},
  month         = {Aug},
  pmid          = {25215968},
  publisher     = {American Physical Society (APS)},
  year          = {2014},
}

@InProceedings{bhatnagar-randall:acm:2004:torpid-mixing,
  author    = {Nayantara Bhatnagar and Dana Randall},
  booktitle = {{SODA} '04: Proceedings of the fifteenth annual {ACM-SIAM} symposium on Discrete algorithms},
  title     = {Torpid mixing of simulated tempering on the {Potts} model},
  isbn      = {0-89871-558-X},
  location  = {New Orleans, Louisiana},
  pages     = {478--487},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia, PA, USA},
  year      = {2004},
}

@Article{Singh-JStatPhys-2011,
  author        = {Singh, Sadanand and Chiu, Chi-cheng and de Pablo, Juan J.},
  title         = {Flux Tempered Metadynamics},
  doi           = {10.1007/s10955-011-0301-0},
  issn          = {1572-9613},
  number        = {4},
  pages         = {932--945},
  url           = {http://dx.doi.org/10.1007/s10955-011-0301-0},
  volume        = {145},
  bdsk-url-1    = {http://dx.doi.org/10.1007/s10955-011-0301-0},
  date-added    = {2015-01-28 10:14:59 +0000},
  date-modified = {2015-07-28 14:38:18 +0000},
  journal       = {J. Stat. Phys.},
  month         = {Sep},
  publisher     = {Springer Science + Business Media},
  year          = {2011},
}

@Article{Badin_MetaD-US-1_JCP2006,
  author  = {Babin, Volodymyr and Roland, Christopher and Darden, Thomas A and Sagui, Celeste},
  title   = {{The free energy landscape of small peptides as obtained from metadynamics with umbrella sampling corrections}},
  doi     = {10.1063/1.2393236},
  issn    = {0021-9606},
  number  = {20},
  pages   = {204909},
  volume  = {125},
  journal = {J. Chem. Phys.},
  pmid    = {17144742},
  year    = {2006},
}

@Article{Comer2015,
  author      = {Comer, Jeffrey and Gumbart, James C. and H{\'{e}}nin, J{\'{e}}r{\^{o}}me and Leli{\`{e}}vre, Tony and Pohorille, Andrew and Chipot, Christophe},
  title       = {The adaptive biasing force method: everything you always wanted to know but were afraid to ask.},
  doi         = {10.1021/jp506633n},
  number      = {3},
  pages       = {1129--1151},
  url         = {http://dx.doi.org/10.1021/jp506633n},
  volume      = {119},
  abstract    = {In the host of numerical schemes devised to calculate free energy differences by way of geometric transformations, the adaptive biasing force algorithm has emerged as a promising route to map complex free-energy landscapes. It relies upon the simple concept that as a simulation progresses, a continuously updated biasing force is added to the equations of motion, such that in the long-time limit it yields a Hamiltonian devoid of an average force acting along the transition coordinate of interest. This means that sampling proceeds uniformly on a flat free-energy surface, thus providing reliable free-energy estimates. Much of the appeal of the algorithm to the practitioner is in its physically intuitive underlying ideas and the absence of any requirements for prior knowledge about free-energy landscapes. Since its inception in 2001, the adaptive biasing force scheme has been the subject of considerable attention, from in-depth mathematical analysis of convergence properties to novel developments and extensions. The method has also been successfully applied to many challenging problems in chemistry and biology. In this contribution, the method is presented in a comprehensive, self-contained fashion, discussing with a critical eye its properties, applicability, and inherent limitations, as well as introducing novel extensions. Through free-energy calculations of prototypical molecular systems, many methodological aspects are examined, from stratification strategies to overcoming the so-called hidden barriers in orthogonal space, relevant not only to the adaptive biasing force algorithm but also to other importance-sampling schemes. On the basis of the discussions in this paper, a number of good practices for improving the efficiency and reliability of the computed free-energy differences are proposed.},
  institution = {Laboratoire International Associé Centre National de la Recherche Scientifique et University of Illinois at Urbana-Champaign, Unité Mixte de Recherche CNRS n°7565, Université de Lorraine , B.P. 70239, 54506 Vandoeuvre-lès-Nancy cedex, France.},
  journal     = {J. Phys. Chem. B},
  medline-pst = {ppublish},
  pmc         = {PMC4306294},
  pmid        = {25247823},
  year        = {2015},
}

@Article{Invernizzi2020opus,
  author    = {Invernizzi, Michele and Parrinello, Michele},
  title     = {{Rethinking metadynamics: From bias potentials to probability distributions}},
  doi       = {10.1021/acs.jpclett.0c00497},
  issn      = {1948-7185},
  number    = {7},
  pages     = {2731--2736},
  url       = {http://dx.DOI.org/10.1021/acs.jpclett.0c00497},
  volume    = {11},
  journal   = {J. Phys. Chem. Lett.},
  month     = {Mar},
  publisher = {American Chemical Society (ACS)},
  year      = {2020},
}

@Article{madras-randall:annals-appl-prob:2002:decomposition-theorem,
  author  = {Neal Madras and Dana Randall},
  title   = {{Markov Chain} decomposition for convergence rate analysis},
  doi     = {10.1214/aoap/1026915617},
  number  = {2},
  pages   = {581--606},
  volume  = {12},
  journal = {Annals Appl. Prob.},
  year    = {2002},
}

@Article{sugita-okamoto:chem-phys-lett:1999:parallel-tempering-md,
  author  = {Yugi Sugita and Yuko Okamoto},
  title   = {Replica-exchange molecular dynamics method for protein folding},
  doi     = {10.1016/s0009-2614(99)01123-9},
  pages   = {141--151},
  volume  = {314},
  journal = {Chem. Phys. Lett.},
  year    = {1999},
}

@Article{Palazzesi2017_JPCL,
  author    = {Palazzesi, Ferruccio and Valsson, Omar and Parrinello, Michele},
  title     = {Conformational Entropy as Collective Variable for Proteins},
  doi       = {10.1021/acs.jpclett.7b01770},
  issn      = {1948-7185},
  number    = {19},
  pages     = {4752–4756},
  url       = {http://dx.doi.org/10.1021/acs.jpclett.7b01770},
  volume    = {8},
  journal   = {J. Phys. Chem. Lett.},
  month     = {Sep},
  publisher = {American Chemical Society (ACS)},
  year      = {2017},
}
	
% replica-exchange and parallel tempering

@InProceedings{geyer:conference-proceedings:1991:replica-exchange,
  author    = {Charles J. Geyer},
  booktitle = {Computing Science and Statistics: The 23rd symposium on the interface},
  title     = {Markov chain {Monte Carlo} maximum likelihood},
  pages     = {156--163},
  publisher = {Interface Foundation},
  address   = {Fairfax},
  year      = {1991},
}

@Article{doi:10.1080/0892702042000270214,
  author    = {Giovanni Ciccotti and Mauro Ferrario},
  title     = {Blue Moon Approach to Rare Events},
  doi       = {10.1080/0892702042000270214},
  eprint    = {https://doi.org/10.1080/0892702042000270214},
  number    = {11-12},
  pages     = {787-793},
  url       = {https://doi.org/10.1080/0892702042000270214},
  volume    = {30},
  journal   = {Mol. Simul.},
  publisher = {Taylor & Francis},
  year      = {2004},
}

@Article{Marsili2006,
  author    = {Simone Marsili and Alessandro Barducci and Riccardo Chelli and Piero Procacci and Vincenzo Schettino},
  title     = {{S}elf-healing umbrella sampling: a non-equilibrium approach for quantitative free energy calculations.},
  doi       = {10.1021/jp062755j},
  number    = {29},
  pages     = {14011--14013},
  url       = {http://dx.doi.org/10.1021/jp062755j},
  volume    = {110},
  abstract  = {We propose a new approach for the umbrella sampling method in molecular dynamics simulations of complex systems. An accelerated sampling of the slow degrees of freedom is achieved by generating a single self-adaptive trajectory that tends to span uniformly the reaction coordinate using a time dependent bias potential derived from the preceding history of the system. To show the convergent behavior and the efficiency of the method, we present the free energy surface of alanine dipeptide in water as a function of the backbone dihedral angles.},
  journal   = {J. Phys. Chem. B},
  keywords  = {16854090},
  owner     = {jhenin},
  pmid      = {16854090},
  timestamp = {2006.08.15},
  year      = {2006},
}

@Article{Yang_MetaD-ITS_1_2016,
  author   = {Yang, Y. Isaac and Zhang, Jun and Che, Xing and Yang, Lijiang and Gao, Yi Qin},
  title    = {{Efficient sampling over rough energy landscapes with high barriers: A combination of metadynamics with integrated tempering sampling}},
  doi      = {10.1063/1.4943004},
  issn     = {0021-9606},
  number   = {9},
  pages    = {094105},
  volume   = {144},
  abstract = {{In order to efficiently overcome high free energy barriers embedded in a complex energy landscape and calculate overall thermodynamics properties using molecular dynamics simulations, we developed and implemented a sampling strategy by combining the metadynamics with (selective) integrated tempering sampling (ITS/SITS) method. The dominant local minima on the potential energy surface (PES) are partially exalted by accumulating history-dependent potentials as in metadynamics, and the sampling over the entire PES is further enhanced by ITS/SITS. With this hybrid method, the simulated system can be rapidly driven across the dominant barrier along selected collective coordinates. Then, ITS/SITS ensures a fast convergence of the sampling over the entire PES and an efficient calculation of the overall thermodynamic properties of the simulation system. To test the accuracy and efficiency of this method, we first benchmarked this method in the calculation of ϕ − ψ distribution of alanine dipeptide in explicit solvent. We further applied it to examine the design of template molecules for aromatic meta-C—H activation in solutions and investigate solution conformations of the nonapeptide Bradykinin involving slow cis-transisomerizations of three proline residues.}},
  journal  = {J. Chem. Phys.},
  pmid     = {26957155},
  year     = {2016},
}

@Article{Maragakis-JPCB-2009,
  author     = {Maragakis, Paul and van der Vaart, Arjan and Karplus, Martin},
  title      = {Gaussian-mixture umbrella sampling},
  doi        = {10.1021/jp808381s},
  issn       = {1520-5207},
  number     = {14},
  pages      = {4664--4673},
  url        = {http://dx.DOI.org/10.1021/jp808381s},
  volume     = {113},
  bdsk-url-1 = {http://dx.DOI.org/10.1021/jp808381s},
  journal    = {J. Phys. Chem. B},
  month      = {Apr},
  publisher  = {American Chemical Society (ACS)},
  year       = {2009},
}

@Article{Fu_MetaD-eABF_JCIM2020,
  author   = {Fu, Haohao and Chen, Haochuan and Wang, Xin’ao and Chai, Hao and Shao, Xueguang and Cai, Wensheng and Chipot, Christophe},
  title    = {{Finding an Optimal Pathway on a Multidimensional Free-Energy Landscape}},
  doi      = {10.1021/acs.jcim.0c00279},
  issn     = {1549-9596},
  abstract = {{An ad-hoc, yet widely adopted approach to investigate complex molecular objects in motion using importance-sampling schemes involves two steps, namely (i) mapping the multidimensional free-energy landscape that characterizes the movements in the molecular object at hand and (ii) finding the most probable transition path connecting basins of the free-energy hyperplane. To achieve this goal, we turn to an importance-sampling algorithm, coined well-tempered metadynamics-extended adaptive biasing force (WTM-eABF), aimed at mapping rugged free-energy landscapes, combined with a path-searching algorithm, which we call multidimensional lowest energy (MULE), to identify the underlying minimum free-energy pathway in the collective-variable space of interest. First, the well-tempered feature of the importance-sampling scheme confers to the latter an asymptotic convergence, while the overall algorithm inherits the advantage of high sampling efficiency of its predecessor, meta-eABF, making its performance less sensitive to user-defined parameters. Second, the Dijkstra algorithm implemented in MULE is able to identify with utmost efficiency a pathway that satisfies minimum free energy of activation among all the possible routes in the multidimensional free-energy landscape. Numerical simulations of three molecular assemblies indicate that association of WTM-eABF and MULE constitutes a reliable, efficient and robust approach for exploring coupled movements in complex molecular objects. On account of its ease of use and intrinsic performance, we expect WTM-eABF and MULE to become a tool of choice for both experts and nonexperts interested in the thermodynamics and the kinetics of processes relevant to chemistry and biology.}},
  journal  = {J. Chem. Inf. Model.},
  pmid     = {32402199},
  year     = {2020},
}

@Article{Fu2019,
  author    = {Haohao Fu and Xueguang Shao and Wensheng Cai and Christophe Chipot},
  title     = {Taming Rugged Free Energy Landscapes Using an Average Force},
  doi       = {10.1021/acs.accounts.9b00473},
  number    = {11},
  pages     = {3254--3264},
  url       = {https://doi.org/10.1021/acs.accounts.9b00473},
  volume    = {52},
  journal   = {Acc. Chem. Res.},
  month     = nov,
  publisher = {American Chemical Society ({ACS})},
  year      = {2019},
}

@Article{hartmann-schuette-zhang-19,
  author  = {C. Hartmann and C. Sch{\"u}tte and W. Zhang},
  title   = {Jarzynski equality, fluctuation theorems, and variance reduction: Mathematical analysis and numerical algorithms},
  doi     = {10.1007/s10955-019-02286-4},
  number  = {6},
  pages   = {1214-1261},
  volume  = {175},
  journal = {J. Stat. Phys.},
  year    = {2019},
}

@Article{straub:jcp:2010:generalized-replica-exchange,
  author  = {Jaegil Kim and Thomas Keyes and John E. Straub},
  title   = {Generalized replica exchange method},
  doi     = {10.1063/1.3432176},
  pages   = {224107},
  volume  = {132},
  journal = {J. Chem. Phys.},
  year    = {2010},
}

@Article{Voter-PRL-1997,
  author        = {Voter, Arthur F.},
  title         = {Hyperdynamics: Accelerated Molecular Dynamics of Infrequent Events},
  doi           = {10.1103/physrevlett.78.3908},
  issn          = {1079-7114},
  number        = {20},
  pages         = {3908--3911},
  url           = {http://dx.doi.org/10.1103/PhysRevLett.78.3908},
  volume        = {78},
  bdsk-url-1    = {http://dx.doi.org/10.1103/PhysRevLett.78.3908},
  bdsk-url-2    = {http://dx.doi.org/10.1103/physrevlett.78.3908},
  date-added    = {2015-04-14 10:09:46 +0000},
  date-modified = {2015-04-14 10:09:56 +0000},
  journal       = {Phys. Rev. Lett.},
  month         = {May},
  publisher     = {American Physical Society (APS)},
  year          = {1997},
}

@Article{10.1038/s41596-020-0342-4,
  author   = {Raniolo, Stefano and Limongelli, Vittorio},
  title    = {{Ligand binding free-energy calculations with funnel metadynamics}},
  doi      = {10.1038/s41596-020-0342-4},
  issn     = {1754-2189},
  number   = {9},
  pages    = {2837--2866},
  volume   = {15},
  abstract = {{The accurate resolution of the binding mechanism of a ligand to its molecular target is fundamental to develop a successful drug design campaign. Free-energy calculations, which provide the energy value of the ligand–protein binding complex, are essential for resolving the binding mode of the ligand. The accuracy of free-energy calculation methods is counteracted by their poor user-friendliness, which hampers their broad application. Here we present the Funnel-Metadynamics Advanced Protocol (FMAP), which is a flexible and user-friendly graphical user interface (GUI)-based protocol to perform funnel metadynamics, a binding free-energy method that employs a funnel-shape restraint potential to reveal the ligand binding mode and accurately calculate the absolute ligand–protein binding free energy. FMAP guides the user through all phases of the free-energy calculation process, from preparation of the input files, to production simulation, to analysis of the results. FMAP delivers the ligand binding mode and the absolute protein–ligand binding free energy as outputs. Alternative binding modes and the role of waters are also elucidated, providing a detailed description of the ligand binding mechanism. The entire protocol on the paradigmatic system benzamidine–trypsin, composed of \textbackslashtextasciitilde105 k atoms, took \textbackslashtextasciitilde2.8 d using the Cray XC50 piz Daint cluster at the Swiss National Supercomputing Centre. Here the authors describe a GUI-based protocol called FMAP for using funnel metadynamics to calculate the absolute binding free energy of a ligand to its molecular target and predict the ligand binding mode and mechanism.}},
  journal  = {Nat. Protoc.},
  pmid     = {32814837},
  year     = {2020},
}

@Article{Piaggi2016_Faraday,
  author    = {Piaggi, Pablo M. and Valsson, Omar and Parrinello, Michele},
  title     = {A variational approach to nucleation simulation},
  doi       = {10.1039/c6fd00127k},
  issn      = {1364-5498},
  pages     = {557–568},
  url       = {http://dx.doi.org/10.1039/c6fd00127k},
  volume    = {195},
  journal   = {Faraday Discuss.},
  publisher = {Royal Society of Chemistry (RSC)},
  year      = {2016},
}

@Article{Piaggi_MultiVES+CV_2019,
  author   = {Piaggi, Pablo M and Parrinello, Michele},
  title    = {{Calculation of phase diagrams in the multithermal-multibaric ensemble}},
  doi      = {10.1063/1.5102104},
  eprint   = {1904.05624},
  issn     = {0021-9606},
  number   = {24},
  pages    = {244119},
  volume   = {150},
  abstract = {{From the Ising model and the Lennard-Jones fluid to water and the iron-carbon system, phase diagrams are an indispensable tool to understand phase equilibria. Despite the effort of the simulation community, the calculation of a large portion of a phase diagram using computer simulation is still today a significant challenge. Here, we propose a method to calculate phase diagrams involving liquid and solid phases by the reversible transformation of the liquid and the solid. To this end, we introduce an order parameter that breaks the rotational symmetry and we leverage our recently introduced method to sample the multithermal-multibaric ensemble. In this way, in a single molecular dynamics simulation, we are able to compute the liquid-solid coexistence line for entire regions of the temperature and pressure phase diagram. We apply our approach to the bcc-liquid phase diagram of sodium and the fcc-bcc-liquid phase diagram of aluminum.}},
  journal  = {J. Chem. Phys.},
  pmid     = {31255056},
  year     = {2019},
}

@Article{shirts-chodera:jcp:2008:mbar,
  author   = {Shirts, Michael R and Chodera, John D},
  title    = {{Statistically optimal analysis of samples from multiple equilibrium states.}},
  doi      = {10.1063/1.2978177},
  issn     = {1089-7690},
  language = {en},
  number   = {12},
  pages    = {124105},
  volume   = {129},
  abstract = {We present a new estimator for computing free energy differences and thermodynamic expectations as well as their uncertainties from samples obtained from multiple equilibrium states via either simulation or experiment. The estimator, which we call the multistate Bennett acceptance ratio estimator (MBAR) because it reduces to the Bennett acceptance ratio estimator (BAR) when only two states are considered, has significant advantages over multiple histogram reweighting methods for combining data from multiple states. It does not require the sampled energy range to be discretized to produce histograms, eliminating bias due to energy binning and significantly reducing the time complexity of computing a solution to the estimating equations in many cases. Additionally, an estimate of the statistical uncertainty is provided for all estimated quantities. In the large sample limit, MBAR is unbiased and has the lowest variance of any known estimator for making use of equilibrium data collected from multiple states. We illustrate this method by producing a highly precise estimate of the potential of mean force for a DNA hairpin system, combining data from multiple optical tweezer measurements under constant force bias.},
  journal  = {J. Chem. Phys.},
  keywords = {DNA, DNA: chemistry, Data Interpretation, Laboratories, Statistical, Thermodynamics, Uncertainty},
  month    = sep,
  pmid     = {19045004},
  year     = {2008},
}

@Article{Phillips2020,
  author       = {James Phillips and David Hardy and Julio Maia and John Stone and Joao Ribeiro and Rafael Bernardi and Ronak Buch and Giacomo Fiorin and J\'er\^ome H\'enin and Wei Jiang and Ryan McGreevy and Melo, Marcelo Cardoso dos Reis and Brian Radak and Robert Skeel and Abhishek Singharoy and Yi Wang and Beno\^it Roux and Aleksei Aksimentiev and Zan Luthey-Schulten and Laxmikant Kale and Klaus Schulten and Christophe Chipot and Emad Tajkhorshid},
  date         = {2020-07},
  journaltitle = {J. Chem. Phys.},
  title        = {Scalable molecular dynamics on {CPU} and {GPU} architectures with {NAMD}},
  doi          = {10.1063/5.0014475},
  number       = {4},
  pages        = {044130},
  volume       = {153},
  journal      = {J. Chem. Phys.},
  publisher    = {{AIP} Publishing},
  year         = {2020},
}

@Article{Dickson_ABP-Review_2017,
  author    = {Dickson, Bradley M},
  title     = {{Survey of adaptive biasing potentials: comparisons and outlook}},
  doi       = {10.1016/j.sbi.2016.11.007},
  issn      = {0959-440X},
  pages     = {63--67},
  volume    = {43},
  abstract  = {{Adaptive biasing potentials are becoming a standard tool of the trade for problems in chemistry, material science, biology, and drug discovery. These methods are easy to use, easy to distribute, reliable, and make otherwise impossible simulations possible. In this review we survey a number of adaptive bias potentials, and take a critical look at how they work. The biases fall into two basic classes, each having distinct attributes and levels of complexity. The vantage point from which the biases are discussed has only emerged in the last couple of years, and allows for a unified treatment of all the biases. We conclude with remarks about computational efficiency of the biases, which is largely overlooked in the current literature.}},
  journal   = {Curr. Opin. Struct. Biol.},
  local-url = {file://localhost/Users/valsson/Documents/Papers%20Library/Current%20Opinion%20in%20Structural%20Biology/2017/Dickson-Dickson-2017-Current%20Opinion%20in%20Structural%20Biology.pdf},
  pmid      = {27883951},
  year      = {2017},
}

@Article{Dama-PRL-2014,
  author        = {Dama, James F. and Parrinello, Michele and Voth, Gregory A.},
  title         = {Well-Tempered Metadynamics Converges Asymptotically},
  doi           = {10.1103/physrevlett.112.240602},
  issn          = {1079-7114},
  number        = {24},
  pages         = {240602},
  volume        = {112},
  bdsk-url-1    = {http://dx.doi.org/10.1103/PhysRevLett.112.240602},
  bdsk-url-2    = {http://dx.doi.org/10.1103/physrevlett.112.240602},
  date-added    = {2014-06-23 11:00:04 +0000},
  date-modified = {2015-06-03 10:30:01 +0000},
  journal       = {Phys. Rev. Lett.},
  month         = {Jun},
  publisher     = {American Physical Society (APS)},
  year          = {2014},
}

@Article{Piaggi_MultiVES_2019,
  author   = {Piaggi, Pablo M. and Parrinello, Michele},
  title    = {{Multithermal-Multibaric Molecular Simulations from a Variational Principle}},
  doi      = {10.1103/physrevlett.122.050601},
  eprint   = {1811.08253},
  issn     = {0031-9007},
  number   = {5},
  pages    = {050601},
  volume   = {122},
  abstract = {{We present a method for performing multithermal-multibaric molecular dynamics simulations that sample entire regions of the temperature-pressure (TP) phase diagram. The method uses a variational principle [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)PRLTAO0031-900710.1103/PhysRevLett.113.090601] in order to construct a bias that leads to a uniform sampling in energy and volume. The intervals of temperature and pressure are taken as inputs and the relevant energy and volume regions are determined on the fly. In this way the method guarantees adequate statistics for the chosen TP region. We show that our multithermal-multibaric simulations can be used to calculate all static physical quantities for all temperatures and pressures in the targeted region of the TP plane. We illustrate our approach by studying the density anomaly of TIP4P/ice water.}},
  journal  = {Phys. Rev. Lett.},
  pmid     = {30822009},
  year     = {2019},
}

@Article{Kim2006_PRL_STMD,
  author    = {Kim, Jaegil and Straub, John E. and Keyes, Thomas},
  title     = {Statistical-Temperature Monte Carlo and Molecular Dynamics Algorithms},
  doi       = {10.1103/physrevlett.97.050601},
  issn      = {1079-7114},
  number    = {5},
  url       = {http://dx.doi.org/10.1103/PhysRevLett.97.050601},
  volume    = {97},
  journal   = {Phys. Rev. Lett.},
  month     = {Aug},
  publisher = {American Physical Society (APS)},
  year      = {2006},
}

@Article{10.1080/08927022.2014.923574,
  author   = {Zheng, Shaohui and Pfaendtner, Jim},
  title    = {{Enhanced sampling of chemical and biochemical reactions with metadynamics}},
  doi      = {10.1080/08927022.2014.923574},
  issn     = {0892-7022},
  number   = {1-3},
  pages    = {55--72},
  volume   = {41},
  abstract = {{Metadynamics (MetaD) is a method that augments molecular dynamics (MD) calculations of all types (classical and quantum) to help systems overcome energy barriers and explore regions of phase space that would otherwise not be seen during a simulation. The method has seen wide ranging uses, and it has proven especially useful for the study of reactions in which bonds break and form. In such cases, the timescale challenges of MD are profoundly limiting, and the advent of this new paradigm for biasing simulations has proven to be incredibly useful. In this review, we set out to summarise the large body of work that uses MetaD for studying reactions so that others can more easily implement this method in their own work. After a brief introduction of the method, we provide detailed summaries of the method applied in various contexts including condensed phase and biological reactions.}},
  journal  = {Mol. Simul.},
  keywords = {Metadynamics Reviews},
  year     = {2014},
}

@Article{Prakash2018_pbmetad-families,
  author   = {Prakash, Arushi and Fu, Christopher D and Bonomi, Massimiliano and Pfaendtner, Jim},
  title    = {{Biasing Smarter, Not Harder, by Partitioning Collective Variables into Families in Parallel Bias Metadynamics}},
  doi      = {10.1021/acs.jctc.8b00448},
  issn     = {1549-9618},
  number   = {10},
  pages    = {4985--4990},
  volume   = {14},
  abstract = {{Molecular simulations of systems with multiple copies of identical atoms or molecules may require the biasing of numerous, degenerate collective variables (CVs) to accelerate sampling. Recently, a variation of metadynamics (MetaD) named parallel bias metadynamics (PBMetaD) has been shown to make biasing of many CVs more tractable. We extended the PBMetaD scheme so that it partitions degenerate CVs into families that share the same bias potential, consequently expediting convergence of the free-energy landscape. We tested our method, named parallel bias metadynamics with partitioned families, on 3, 21, and 78 CV systems and obtained an approximately proportional increase in convergence speed compared to standard PBMetaD.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {30075630},
  year     = {2018},
}

@Article{Huang19765,
  author    = {Xuhui Huang and Gregory R. Bowman and Sergio Bacallado and Vijay S. Pande},
  title     = {Rapid equilibrium sampling initiated from nonequilibrium data},
  doi       = {10.1073/pnas.0909088106},
  eprint    = {https://www.pnas.org/content/106/47/19765.full.pdf},
  issn      = {0027-8424},
  number    = {47},
  pages     = {19765--19769},
  url       = {https://www.pnas.org/content/106/47/19765},
  volume    = {106},
  abstract  = {Simulating the conformational dynamics of biomolecules is extremely difficult due to the rugged nature of their free energy landscapes and multiple long-lived, or metastable, states. Generalized ensemble (GE) algorithms, which have become popular in recent years, attempt to facilitate crossing between states at low temperatures by inducing a random walk in temperature space. Enthalpic barriers may be crossed more easily at high temperatures; however, entropic barriers will become more significant. This poses a problem because the dominant barriers to conformational change are entropic for many biological systems, such as the short RNA hairpin studied here. We present a new efficient algorithm for conformational sampling, called the adaptive seeding method (ASM), which uses nonequilibrium GE simulations to identify the metastable states, and seeds short simulations at constant temperature from each of them to quantitatively determine their equilibrium populations. Thus, the ASM takes advantage of the broad sampling possible with GE algorithms but generally crosses entropic barriers more efficiently during the seeding simulations at low temperature. We show that only local equilibrium is necessary for ASM, so very short seeding simulations may be used. Moreover, the ASM may be used to recover equilibrium properties from existing datasets that failed to converge, and is well suited to running on modern computer clusters.},
  journal   = {Proc. Natl. Acad. Sci. USA},
  publisher = {National Academy of Sciences},
  year      = {2009},
}

@Article{Wu_VES-RGMC_PRL2020,
  author   = {Wu, Yantao and Car, Roberto},
  title    = {{Monte Carlo Renormalization Group for Classical Lattice Models with Quenched Disorder}},
  doi      = {10.1103/physrevlett.125.190601},
  eprint   = {1810.09579},
  issn     = {0031-9007},
  number   = {19},
  pages    = {190601},
  volume   = {125},
  abstract = {{We extend to quenched-disordered systems the variational scheme for real-space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow of the renormalized Hamiltonian distribution, from which one can compute the critical exponents if the correlations of the renormalized couplings retain finite range. Key to the variational approach is the bias potential found by minimizing a convex functional in statistical mechanics. This potential reduces dramatically the Monte Carlo relaxation time in large disordered systems. We demonstrate the method with applications to the two-dimensional dilute Ising model, the random transverse field quantum Ising chain, and the random field Ising in two- and three-dimensional lattices.}},
  journal  = {Phys. Rev. Lett.},
  pmid     = {33216587},
  year     = {2020},
}

@Article{Debnath_GAMBES_2020,
  author       = {Debnath, Jayashrita and Parrinello, Michele},
  date         = {2020-06},
  journaltitle = {J. Phys. Chem. Lett.},
  title        = {{Gaussian Mixture-Based Enhanced Sampling for Statics and Dynamics}},
  doi          = {10.1021/acs.jpclett.0c01125},
  eprint       = {1909.07773},
  issn         = {1948-7185},
  number       = {13},
  pages        = {5076--5080},
  volume       = {11},
  abstract     = {{We introduce an enhanced sampling method that is based on constructing a model probability density from which a bias potential is derived. The model relies on the fact that in a physical system most of the configurations visited can be grouped into isolated metastable islands. With each island we associate a distribution that is fitted to a Gaussian mixture. The different distributions are linearly combined together with coefficients that are computed self-consistently. This leads to an integrated procedure for discovering new metastable states, exploring reaction pathways, computing free energy differences, and estimating reaction rates.}},
  journal      = {J. Phys. Chem. Lett.},
  pmid         = {32510225},
  publisher    = {American Chemical Society ({ACS})},
  year         = {2020},
}

@Article{gallicchio-levy:pnas:2007:replica-exchange,
  author  = {Weihua Zheng and Michael Andrec and Emilio Gallicchio and Ronald M. Levy},
  title   = {Simulating replica exchange simulations of protein folding with a kinetic network model},
  doi     = {10.1073/pnas.0704418104},
  pages   = {15340--15345},
  volume  = {104},
  journal = {Proc. Natl. Acad. Sci. USA},
  year    = {2007},
}

@Article{Okumura_MultiTP_2004,
  author   = {Okumura, Hisashi and Okamoto, Yuko},
  title    = {{Monte Carlo simulations in multibaric–multithermal ensemble}},
  doi      = {10.1016/j.cplett.2003.10.152},
  eprint   = {cond-mat/0306144},
  issn     = {0009-2614},
  number   = {3-4},
  pages    = {391--396},
  volume   = {383},
  abstract = {{We propose a new generalized-ensemble algorithm, which we refer to as the multibaric–multithermal Monte Carlo method. The multibaric–multithermal Monte Carlo simulations perform random walks widely both in volume space and in potential energy space. From only one simulation run, one can calculate isobaric–isothermal–ensemble averages at any pressure and any temperature. We test the effectiveness of this algorithm by applying it to the Lennard–Jones 12–6 potential system with 500 particles. It is found that a single simulation of the new method indeed gives accurate average quantities in isobaric–isothermal ensemble for a wide range of pressure and temperature.}},
  journal  = {Chem. Phys. Lett.},
  year     = {2004},
}

@Article{Bussi-JACS-2006,
  author        = {Bussi, Giovanni and Gervasio, Francesco Luigi and Laio, Alessandro and Parrinello, Michele},
  title         = {{Free-Energy Landscape for $\beta$ Hairpin Folding from Combined Parallel Tempering and Metadynamics}},
  doi           = {10.1021/ja062463w},
  number        = {41},
  pages         = {13435-13441},
  volume        = {128},
  bdsk-url-1    = {http://dx.doi.org/10.1021/ja062463w},
  date-added    = {2014-10-10 10:10:47 +0000},
  date-modified = {2015-03-25 10:49:10 +0000},
  journal       = {J. Am. Chem. Soc.},
  month         = {Oct},
  publisher     = {American Chemical Society},
  year          = {2006},
}

@Article{doi:10.1021/acs.jcim.9b01094,
  author  = {Deganutti, Giuseppe and Moro, Stefano and Reynolds, Christopher A.},
  title   = {A Supervised Molecular Dynamics Approach to Unbiased Ligand–Protein Unbinding},
  doi     = {10.1021/acs.jcim.9b01094},
  eprint  = {https://doi.org/10.1021/acs.jcim.9b01094},
  number  = {3},
  pages   = {1804-1817},
  url     = {https://doi.org/10.1021/acs.jcim.9b01094},
  volume  = {60},
  journal = {J. Chem. Inf. Model.},
  pmid    = {32126172},
  year    = {2020},
}

@Article{Pal_TASS-2_JCC2021,
  author   = {Pal, Asit and Pal, Subhendu and Verma, Shivani and Shiga, Motoyuki and Nair, Nisanth N.},
  title    = {{Mean force based temperature accelerated sliced sampling: Efficient reconstruction of high dimensional free energy landscapes}},
  doi      = {10.1002/jcc.26727},
  issn     = {0192-8651},
  abstract = {{Temperature accelerated sliced sampling (TASS) is an efficient method to compute high dimensional free energy landscapes. The original TASS method employs the weighted histogram analysis method (WHAM) which is an iterative post‐processing to reweight and stitch high dimensional probability distributions in sliced windows that are obtained in the presence of restraining biases. The WHAM necessitates that TASS windows lie close to each other for proper overlap of distributions and span the collective variable space of interest. On the other hand, increase in number of TASS windows implies more number of simulations, and thus it affects the efficiency of the method. To overcome this problem, we propose herein a new mean‐force (MF) based reweighting scheme called TASS‐MF, which enables accurate computation with a fewer number of windows devoid of the WHAM post‐processing. Application of the technique is demonstrated for alanine di‐ and tripeptides in vacuo to compute their two‐ and four‐dimensional free energy landscapes, the latter of which is formidable in conventional umbrella sampling and metadynamics. The landscapes are computed within a kcal mol−1 accuracy, ensuring a safe usage for broad applications in computational chemistry. Temperature accelerated sliced sampling (TASS) is a powerful method for the exploration and computation of high‐dimensional free energy landscapes (HDFEL). Here we introduce a new method for the reconstruction of HDFEL for TASS. With this method, weighted histogram analysis method can be completely avoided and TASS can be performed with less number of windows without compromising on the accuracy. The proposed method significantly improves the efficiency of the TASS approach.}},
  journal  = {J. Comput. Chem.},
  pmid     = {34398461},
  year     = {2021},
}

@Book{Elber2020,
  author    = {Ron Elber and Dmitrii E. Makarov and Henri Orland},
  title     = {Molecular Kinetics in Condensed Phases},
  doi       = {10.1002/9781119176800},
  publisher = {Wiley},
  url       = {https://doi.org/10.1002/9781119176800},
  month     = jan,
  year      = {2020},
}

@Article{doi:10.1021/acs.jctc.0c00355,
  author  = {Gkeka, Paraskevi and Stoltz, Gabriel and Barati Farimani, Amir and Belkacemi, Zineb and Ceriotti, Michele and Chodera, John D. and Dinner, Aaron R. and Ferguson, Andrew L. and Maillet, Jean-Bernard and Minoux, Hervé and Peter, Christine and Pietrucci, Fabio and Silveira, Ana and Tkatchenko, Alexandre and Trstanova, Zofia and Wiewiora, Rafal and Lelièvre, Tony},
  title   = {Machine Learning Force Fields and Coarse-Grained Variables in Molecular Dynamics: Application to Materials and Biological Systems},
  doi     = {10.1021/acs.jctc.0c00355},
  eprint  = {https://doi.org/10.1021/acs.jctc.0c00355},
  number  = {8},
  pages   = {4757-4775},
  url     = {https://doi.org/10.1021/acs.jctc.0c00355},
  volume  = {16},
  journal = {J. Chem. Theory Comput.},
  pmid    = {32559068},
  year    = {2020},
}

@Article{Bonomi_MetadynamicMetainference_SciRep2016,
  author   = {Bonomi, Massimiliano and Camilloni, Carlo and Vendruscolo, Michele},
  title    = {{Metadynamic metainference: Enhanced sampling of the metainference ensemble using metadynamics}},
  doi      = {10.1038/srep31232},
  number   = {1},
  pages    = {31232},
  volume   = {6},
  abstract = {{Accurate and precise structural ensembles of proteins and macromolecular complexes can be obtained with metainference, a recently proposed Bayesian inference method that integrates experimental information with prior knowledge and deals with all sources of errors in the data as well as with sample heterogeneity. The study of complex macromolecular systems, however, requires an extensive conformational sampling, which represents a separate challenge. To address such challenge and to exhaustively and efficiently generate structural ensembles we combine metainference with metadynamics and illustrate its application to the calculation of the free energy landscape of the alanine dipeptide.}},
  journal  = {Sci. Rep.},
  pmcid    = {PMC4999896},
  pmid     = {27561930},
  year     = {2016},
}

@Article{fukunishi-watanabe-takada:jcp:2002:hamiltonian-exchange,
  author  = {Hiroaki Fukunishi and Osamu Watanabe and Shoji Takada},
  title   = {On the {Hamiltonian} replica exchange method for efficient sampling of biomolecular systems: Application to protein structure prediction},
  pages   = {9058},
  volume  = {116},
  journal = {J. Chem. Phys.},
  doi = {10.1063/1.1472510},
  year    = {2002},
}

@Article{Deighan2012_ptwte_efficient,
  author   = {Deighan, Michael and Bonomi, Massimiliano and Pfaendtner, Jim},
  title    = {{Efficient Simulation of Explicitly Solvated Proteins in the Well-Tempered Ensemble}},
  doi      = {10.1021/ct300297t},
  issn     = {1549-9618},
  number   = {7},
  pages    = {2189--2192},
  volume   = {8},
  abstract = {{Herein, we report significant reduction in the cost of combined parallel tempering and metadynamics simulations (PTMetaD). The efficiency boost is achieved using the recently proposed well-tempered ensemble (WTE) algorithm. We studied the convergence of PTMetaD-WTE conformational sampling and free energy reconstruction of an explicitly solvated 20-residue tryptophan-cage protein (trp-cage). A set of PTMetaD-WTE simulations was compared to a corresponding standard PTMetaD simulation. The properties of PTMetaD-WTE and the convergence of the calculations were compared. The roles of the number of replicas, total simulation time, and adjustable WTE parameter γ were studied.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {26588950},
  year     = {2012},
}

@Article{hansmann:chem-phys-lett:1997:parallel-tempering-monte-carlo,
  author  = {Ulrich H. E. Hansmann},
  title   = {Parallel tempering algorithm for conformational studies of biological molecules},
  pages   = {140--150},
  volume  = {281},
  journal = {Chem. Phys. Lett.},
  year    = {1997},
  doi = {10.1016/S0009-2614(97)01198-6}
}

@Article{park-ensign-pande:pre:2006:bayesian-weight-update,
  author  = {Sanghyun Park and Daniel L. Ensign and Vijay S. Pande},
  title   = {Bayesian update method for adaptive weighted sampling},
  doi     = {10.1103/physreve.74.066703},
  pages   = {066703},
  volume  = {74},
  journal = {Phys. Rev. E},
  year    = {2006},
}

@Article{Wu_VES-RGMC_PRL2017,
  author   = {Wu, Yantao and Car, Roberto},
  title    = {{Variational Approach to Monte Carlo Renormalization Group}},
  doi      = {10.1103/physrevlett.119.220602},
  eprint   = {1707.08683},
  issn     = {0031-9007},
  number   = {22},
  pages    = {220602},
  volume   = {119},
  abstract = {{We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The two-dimensional Ising model is used to illustrate the method.}},
  journal  = {Phys. Rev. Lett.},
  pmid     = {29286777},
  year     = {2017},
}

@Article{Zhang_TALOS_2019,
  author   = {Zhang, Jun and Yang, Yi Isaac and Noé, Frank},
  title    = {{Targeted Adversarial Learning Optimized Sampling}},
  doi      = {10.1021/acs.jpclett.9b02173},
  issn     = {1948-7185},
  number   = {19},
  pages    = {5791--5797},
  volume   = {10},
  abstract = {{Boosting transitions of rare events is critical to simulations of chemical and biophysical dynamic systems in order to close the time scale gaps between theoretical modeling and experiments. We present a novel approach, called targeted adversarial learning optimized sampling (TALOS), to modify the potential energy surface in order to drive the system to a user-defined target distribution where the free-energy barrier is lowered. Combining statistical mechanics and generative learning, TALOS formulates a competing game between a sampling engine and a virtual discriminator, enables unsupervised construction of bias potentials, and seeks for an optimal transport plan that transforms the system into a target. Through multiple experiments, we show that on-the-fly training of TALOS benefits from the state-of-art optimization techniques in deep learning and thus is efficient, robust, and interpretable. TALOS is also closely connected to the actor-critic reinforcement learning and hence leads to a new way of flexibly manipulating the many-body Hamiltonian systems.}},
  journal  = {J. Phys. Chem. Lett.},
  pmid     = {31522495},
  year     = {2019},
}

@Article{10.1002/jcc.25066,
  author   = {Khanjari, Neda and Eslami, Hossein and Müller‐Plathe, Florian},
  title    = {{Adaptive‐numerical‐bias metadynamics}},
  doi      = {10.1002/jcc.25066},
  issn     = {1096-987X},
  number   = {31},
  pages    = {2721--2729},
  volume   = {38},
  abstract = {{A metadynamics scheme is presented in which the free energy surface is filled with progressively adding adaptive biasing potentials, obtained from the accumulated probability distribution of the collective variables. Instead of adding Gaussians with assigned height and width in conventional metadynamics method, here we add a more realistic adaptive biasing potential to the Hamiltonian of the system. The shape of the adaptive biasing potential is adjusted on the fly by sampling over the visited states. As the top of the barrier is approached, the biasing potentials become wider. This decreases the problem of trapping the system in the niches, introduced by the addition of Gaussians of fixed height in metadynamics. Our results for the free energy profiles of three test systems show that this method is more accurate and converges more quickly than the conventional metadynamics, and is quite comparable (in accuracy and convergence rate) with the well-tempered metadynamics method. © 2017 Wiley Periodicals, Inc.}},
  journal  = {J. Comput. Chem.},
  pmid     = {28948616},
  year     = {2017},
}

@Article{nymeyer:jctc:2008:replica-exchange-efficiency,
  author  = {Hugh Nymeyer},
  title   = {How efficient is replica exchange molecular dynamics? An analytic approach},
  doi     = {10.1021/ct7003337},
  pages   = {626},
  volume  = {4},
  journal = {J. Chem. Theory Comput.},
  year    = {2008},
}

@incollection{Valsson2020Handbook_VES,
  author    = {Valsson, Omar and Parrinello, Michele},
  editor    = {Andreoni, W. and Yip, S.},
  title     = {Variationally Enhanced Sampling},
  doi       = {10.1007/978-3-319-44677-6_50},
  pages     = {621-634},
  url       = {http://dx.doi.org/10.1007/978-3-319-44677-6_50},
  isbn      = {9783319446776},
  booktitle = {Handbook of Materials Modeling},
  publisher = {Springer International Publishing},
  year      = {2020}
}

@Article{Invernizzi_VES_DelteF_2019,
  author    = {Invernizzi, Michele and Parrinello, Michele},
  title     = {{Making the Best of a Bad Situation: A Multiscale Approach to Free Energy Calculation}},
  doi       = {10.1021/acs.jctc.9b00032},
  eprint    = {1901.04455},
  issn      = {1549-9618},
  number    = {4},
  pages     = {2187--2194},
  volume    = {15},
  abstract  = {{Many enhanced sampling techniques rely on the identification of a number of collective variables that describe all the slow modes of the system. By constructing a bias potential in this reduced space, one is then able to sample efficiently and reconstruct the free energy landscape. In methods such as metadynamics, the quality of these collective variables plays a key role in convergence efficiency. Unfortunately in many systems of interest it is not possible to identify an optimal collective variable, and one must deal with the nonideal situation of a system in which some slow modes are not accelerated. We propose a two-step approach in which, by taking into account the residual multiscale nature of the problem, one is able to significantly speed up convergence. To do so, we combine an exploratory metadynamics run with an optimization of the free energy difference between metastable states, based on the recently proposed variationally enhanced sampling method. This new method is well parallelizable and is especially suited for complex systems, because of its simplicity and clear underlying physical picture.}},
  journal   = {J. Chem. Theory Comput.},
  local-url = {file://localhost/Users/valsson/Documents/Papers%20Library/Journal%20of%20Chemical%20Theory%20and%20Computation/2019/Invernizzi-Parrinello-2019-Journal%20of%20Chemical%20Theory%20and%20Computation.pdf},
  pmid      = {30822383},
  year      = {2019},
}

@Article{Minoukadeh2010,
  author  = {Minoukadeh, K. and Chipot, C. and Leli\`evre, T.},
  title   = {Potential of Mean Force Calculations: A Multiple-Walker Adaptive Biasing Force Approach},
  doi     = {10.1021/ct900524t},
  eprint  = {http://pubs.acs.org/doi/pdf/10.1021/ct900524t},
  number  = {4},
  pages   = {1008-1017},
  url     = {http://pubs.acs.org/doi/abs/10.1021/ct900524t},
  volume  = {6},
  journal = {J. Chem. Theory Comput.},
  year    = {2010},
}

@Article{Dickson:2017:1568-0266:2626,
  author        = {Dickson, Alex and Tiwary, Pratyush and Vashisth, Harish},
  title         = {Kinetics of Ligand Binding Through Advanced Computational Approaches: A Review},
  doi           = {10.2174/1568026617666170414142908},
  issn          = {1568-0266},
  number        = {23},
  pages         = {2626-2641},
  url           = {https://www.ingentaconnect.com/content/ben/ctmc/2017/00000017/00000023/art00007},
  volume        = {17},
  abstract      = {Ligand residence times and binding rates have been found to be useful quantities to consider during drug design. The underlying structural and dynamic determinants of these kinetic quantities are difficult to discern. Driven by developments in computational hardware and simulation methodologies,
molecular dynamics (MD) studies on full binding and unbinding pathways have emerged recently, showing these structural and dynamic determinants in atomic detail. However, the long timescales related to drug binding and release are still prohibitive to conventional MD simulation. Here we discuss
a suite of enhanced sampling methods that have been applied to the study of full ligand binding or unbinding pathways, and reveal the kinetics of drug binding and/or release. We divide these sampling methods into three families (trajectory parallelization, metadynamics, and temperature- based
methods), and discuss recent applications of each, as well as their basic theoretical underpinnings including how kinetic information is extracted. We then present an outlook for how the field could evolve, and how the rich variety of sampling methods discussed here can be leveraged in the
future for computationally driven drug design.},
  itemtype      = {ARTICLE},
  journal       = {Curr. Top. Med. Chem.},
  keyword       = {Simulation methodologies, Metadynamics, Molecular dynamics, Drug design, NMR, Kinetics},
  parent_itemid = {infobike://ben/ctmc},
  publishercode = {ben},
  year          = {2017},
}

@Article{Branduardi-JCTC-2012,
  author        = {Branduardi, Davide and Bussi, Giovanni and Parrinello, Michele},
  title         = {Metadynamics with Adaptive Gaussians},
  doi           = {10.1021/ct3002464},
  eprint        = {1205.4300},
  issn          = {1549-9626},
  number        = {7},
  pages         = {2247--2254},
  volume        = {8},
  abstract      = {{Metadynamics is an established sampling method aimed at reconstructing the free-energy surface relative to a set of appropriately chosen collective variables. In standard metadynamics, the free-energy surface is filled by the addition of Gaussian potentials of preassigned and typically diagonal covariance. Asymptotically the free-energy surface is proportional to the bias deposited. Here, we consider the possibility of using Gaussians whose variance is adjusted on the fly to the local properties of the free-energy surface. We suggest two different prescriptions: one is based on the local diffusivity and the other on the local geometrical properties. We further examine the problem of extracting the free-energy surface when using adaptive Gaussians. We show that the standard relation between the bias and the free energy does not hold. In the limit of narrow Gaussians an explicit correction can be evaluated. In the general case, we propose to use instead a relation between bias and free energy borrowed from umbrella sampling. This relation holds for all kinds of incrementally deposited bias. We illustrate on the case of alanine dipeptide the advantage of using adaptive Gaussians in conjunction with the new free-energy estimator both in terms of accuracy and speed of convergence.}},
  bdsk-url-1    = {http://dx.doi.org/10.1021/ct3002464},
  date-added    = {2014-10-10 10:10:47 +0000},
  date-modified = {2015-03-25 10:47:30 +0000},
  journal       = {J. Chem. Theory Comput.},
  month         = {Jul},
  pmid          = {26588957},
  publisher     = {American Chemical Society (ACS)},
  year          = {2012},
}

@Article{Plimpton1995,
  author  = {Plimpton, S.},
  title   = {Fast parallel algorithms for short-range molecular-dynamics},
  doi     = {10.1006/jcph.1995.1039},
  number  = {1},
  pages   = {1-19},
  volume  = {117},
  journal = {J. Comput. Phys.},
  year    = {1995},
}

@Article{HUBER199697,
  author   = {G.A. Huber and S. Kim},
  title    = {Weighted-ensemble Brownian dynamics simulations for protein association reactions},
  doi      = {10.1016/S0006-3495(96)79552-8},
  issn     = {0006-3495},
  number   = {1},
  pages    = {97-110},
  url      = {https://www.sciencedirect.com/science/article/pii/S0006349596795528},
  volume   = {70},
  abstract = {A new method, weighted-ensemble Brownian dynamics, is proposed for the simulation of protein-association reactions and other events whose frequencies of outcomes are constricted by free energy barriers. The method features a weighted ensemble of trajectories in configuration space with energy levels dictating the proper correspondence between "particles" and probability. Instead of waiting a very long time for an unlikely event to occur, the probability packets are split, and small packets of probability are allowed to diffuse almost immediately into regions of configuration space that are less likely to be sampled. The method has been applied to the Northrup and Erickson (1992) model of docking-type diffusion-limited reactions and yields reaction rate constants in agreement with those obtained by direct Brownian simulation, but at a fraction of the CPU time (10(-4) to 10(-3), depending on the model). Because the method is essentially a variant of standard Brownian dynamics algorithms, it is anticipated that weighted-ensemble Brownian dynamics, in conjunction with biophysical force models, can be applied to a large class of association reactions of interest to the biophysics community.},
  journal  = {Biophys. J.},
  year     = {1996},
}

@Article{10.1007/978-1-4939-9608-7_8,
  author   = {Pfaendtner, Jim},
  title    = {{Biomolecular Simulations, Methods and Protocols}},
  doi      = {10.1007/978-1-4939-9608-7_8},
  issn     = {1064-3745},
  pages    = {179--200},
  volume   = {2022},
  abstract = {{Molecular dynamics is a powerful simulation method to provide detailed atomic-scale insight into a range of biological processes including protein folding, biochemical reactions, ligand binding, and many others. Over the last several decades, enhanced sampling methods have been developed to address the large separation in time scales between a molecular dynamics simulation (usually microseconds or shorter) and the time scales of biological processes (often orders of magnitude longer). This chapter specifically focuses on the metadynamics family of methods, which achieves enhanced sampling through the introduction of a history-dependent bias potential that is based on one or more slow degrees of freedom, called collective variables. We introduce the method and its recent variants related to biomolecular studies and then discuss frontier areas of the method. A large part of this chapter is devoted to helping new users of the method understand how to choose metadynamics parameters properly and apply the method to their system of interest.}},
  journal  = {Methods Mol Biol},
  keywords = {Metadynamics Reviews},
  pmid     = {31396904},
  year     = {2019},
}

@Article{HREX_Bussi_2013,
  author   = {Bussi, Giovanni},
  title    = {{Hamiltonian replica exchange in GROMACS: a flexible implementation}},
  doi      = {10.1080/00268976.2013.824126},
  eprint   = {1307.5144},
  issn     = {0026-8976},
  number   = {3-4},
  pages    = {379--384},
  volume   = {112},
  abstract = {{A simple and general implementation of Hamiltonian replica exchange for the popular molecular dynamics software GROMACS is presented. In this implementation, arbitrarily different Hamiltonians can be used for the different replicas without incurring in any significant performance penalty. The implementation was validated on a simple toy model – alanine dipeptide in water – and applied to study the rearrangement of an RNA tetraloop, where it was used to compare recently proposed force-field corrections.}},
  journal  = {Mol. Phys.},
  year     = {2013},
}

@Article{neuhaus-magiera-hansmann:pre:2007:parallel-tempering-first-order,
  author  = {T. Neuhaus and M. P. Magiera and U. H. E. Hansmann},
  title   = {Efficient parallel tempering for first-order phase transitions},
  doi     = {10.1103/physreve.76.045701},
  pages   = {045701},
  volume  = {76},
  journal = {Phys. Rev. E},
  year    = {2007},
}

@Article{doi:10.1021/acs.jctc.0c00205,
  author  = {Pérez, Adrià and Herrera-Nieto, Pablo and Doerr, Stefan and De Fabritiis, Gianni},
  title   = {AdaptiveBandit: A Multi-armed Bandit Framework for Adaptive Sampling in Molecular Simulations},
  doi     = {10.1021/acs.jctc.0c00205},
  eprint  = {https://doi.org/10.1021/acs.jctc.0c00205},
  number  = {7},
  pages   = {4685-4693},
  url     = {https://doi.org/10.1021/acs.jctc.0c00205},
  volume  = {16},
  journal = {J. Chem. Theory Comput.},
  pmid    = {32539384},
  year    = {2020},
}

@Article{kwak-hansmann:prl:2005:hamiltonian-exchange,
  author  = {Wooseop Kwak and Ulrich H. E. Hansmann},
  title   = {Efficient sampling of protein structures by model hopping},
  pages   = {138102},
  volume  = {95},
  journal = {Phys. Rev. Lett.},
  year    = {2005},
  doi = {10.1103/PhysRevLett.95.138102}
}

@Article{Sucur2016,
  author    = {Zoran {\v{S}}u{\'{c}}ur and Vojt{\v{e}}ch Spiwok},
  title     = {Sampling Enhancement and Free Energy Prediction by the Flying Gaussian Method},
  doi       = {10.1021/acs.jctc.6b00551},
  number    = {9},
  pages     = {4644--4650},
  volume    = {12},
  journal   = {J. Chem. Theory Comput.},
  month     = {aug},
  publisher = {American Chemical Society ({ACS})},
  year      = {2016},
}

@Article{Alrachid2015,
  author         = {Houssam Alrachid and Tony Leli{\`e}vre},
  title          = {Long-time convergence of an adaptive biasing force method: Variance reduction by Helmholtz projection},
  doi            = {10.5802/smai-jcm.4},
  eprint         = {1501.07094},
  pages          = {55-82},
  volume         = {1},
  abstract       = {In this paper, we propose an improvement of the adaptive biasing force (ABF) method, by projecting the estimated mean force onto a gradient. The associated stochastic process satisfies a non linear stochastic differential equation. Using entropy techniques, we prove exponential convergence to the stationary state of this stochastic process. We finally show on some numerical examples that the variance of the approximated mean force is reduced using this technique, which makes the algorithm more efficient than the standard ABF method.},
  comments       = {33 pages, 20 figures},
  journal        = {SMAI-Journal of Computational Mathematics},
  oai2identifier = {1501.07094},
  year           = {2015},
}

@Article{shamsi_enhanced_2017,
  author    = {Shamsi, Zahra and Moffett, Alexander S. and Shukla, Diwakar},
  title     = {Enhanced unbiased sampling of protein dynamics using evolutionary coupling information},
  doi       = {10.1038/s41598-017-12874-7},
  issn      = {2045-2322},
  language  = {en},
  note      = {Number: 1 Publisher: Nature Publishing Group},
  number    = {1},
  pages     = {12700},
  url       = {https://www.nature.com/articles/s41598-017-12874-7},
  urldate   = {2021-06-08},
  volume    = {7},
  abstract  = {One of the major challenges in atomistic simulations of proteins is efficient sampling of pathways associated with rare conformational transitions. Recent developments in statistical methods for computation of direct evolutionary couplings between amino acids within and across polypeptide chains have allowed for inference of native residue contacts, informing accurate prediction of protein folds and multimeric structures. In this study, we assess the use of distances between evolutionarily coupled residues as natural choices for reaction coordinates which can be incorporated into Markov state model-based adaptive sampling schemes and potentially used to predict not only functional conformations but also pathways of conformational change, protein folding, and protein-protein association. We demonstrate the utility of evolutionary couplings in sampling and predicting activation pathways of the β2-adrenergic receptor (β2-AR), folding of the FiP35 WW domain, and dimerization of the E. coli molybdopterin synthase subunits. We find that the time required for β2-AR activation and folding of the WW domain are greatly diminished using evolutionary couplings-guided adaptive sampling. Additionally, we were able to identify putative molybdopterin synthase association pathways and near-crystal structure complexes from protein-protein association simulations.},
  copyright = {2017 The Author(s)},
  file      = {Full Text PDF:/Users/lucie/Zotero/storage/XPWCFH92/Shamsi et al. - 2017 - Enhanced unbiased sampling of protein dynamics usi.pdf:application/pdf;Snapshot:/Users/lucie/Zotero/storage/LI4TNIUD/s41598-017-12874-7.html:text/html},
  journal   = {Sci. Rep.},
  month     = oct,
  year      = {2017},
}

@Article{Kirkwood1935,
  author    = {Kirkwood, J. G.},
  title     = {Statistical mechanics of fluid mixtures},
  pages     = {300-313},
  volume    = {3},
  journal   = {J. Chem. Phys.},
  owner     = {jhenin},
  timestamp = {2007.04.01},
  year      = {1935},
  doi       = {10.1063/1.1749657},
}

@Article{Lidmar2012,
  author    = {Lidmar, Jack},
  title     = {{Improving the efficiency of extended ensemble simulations: The accelerated weight histogram method}},
  doi       = {10.1103/PhysRevE.85.056708},
  number    = {5},
  pages     = {56708},
  volume    = {85},
  journal   = {Phys. Rev. E},
  month     = may,
  publisher = {American Physical Society},
  year      = {2012},
}

@Article{Amirkulova_PTWTE-EDS_JPCB2020,
  author   = {Amirkulova, Dilnoza B and Chakraborty, Maghesree and White, Andrew D},
  title    = {{Experimentally Consistent Simulation of A$\beta_{21-30}$ Peptides with a Minimal NMR Bias}},
  doi      = {10.1021/acs.jpcb.0c07129},
  issn     = {1520-6106},
  number   = {38},
  pages    = {8266--8277},
  volume   = {124},
  abstract = {{Misfolded amyloid peptides are neurotoxic molecules associated with Alzheimer's disease. The Aβ21-30 peptide fragment is a decapeptide fragment of the complete Aβ42 peptide which is a hypothesized cause of Alzheimer's disease via amyloid fibrillogenesis. Aβ21-30 is investigated here with a combination of NMR (nuclear magnetic resonance) spectroscopy experiments and molecular dynamics simulations with experiment directed simulation (EDS). EDS is a maximum entropy biasing method that augments a molecular dynamics simulation with experimental data (NMR chemical shifts) to improve agreement with experiments and thus accuracy. EDS molecular dynamics shows that the Aβ21-30 monomer has a β turn stabilized by the following interactions: S26-K28, D23-S26, and D23-K28. NMR, total correlation spectroscopy, and rotating frame Overhauser effect spectroscopy experiments provide independent agreement. Subsequent two- and four-monomer EDS simulations show aggregation. Diffusion coefficients calculated from molecular simulation also agreed with experimentally measured values only after using EDS, providing independent assessment of accuracy. This work demonstrates how accuracy can be improved by directly using experimental data in molecular dynamics of complex processes like self-assembly.}},
  journal  = {J. Phys. Chem. B},
  pmid     = {32845146},
  year     = {2020},
}

@Article{doi:10.1021/acs.jctc.6b00503,
  author  = {Kukharenko, Oleksandra and Sawade, Kevin and Steuer, Jakob and Peter, Christine},
  title   = {Using Dimensionality Reduction to Systematically Expand Conformational Sampling of Intrinsically Disordered Peptides},
  doi     = {10.1021/acs.jctc.6b00503},
  eprint  = {https://doi.org/10.1021/acs.jctc.6b00503},
  number  = {10},
  pages   = {4726-4734},
  url     = {https://doi.org/10.1021/acs.jctc.6b00503},
  volume  = {12},
  journal = {J. Chem. Theory Comput.},
  pmid    = {27588692},
  year    = {2016},
}

@Article{MV06,
  author  = {L. Maragliano and E. Vanden-Eijnden},
  title   = {A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations},
  doi     = {10.1016/j.cplett.2006.05.062},
  number  = {1-3},
  pages   = {168 - 175},
  volume  = {426},
  journal = {Chem. Phys. Lett.},
  year    = {2006},
}

@Article{Maragliano2008,
  author    = {Luca Maragliano and Eric Vanden-Eijnden},
  title     = {Single-sweep methods for free energy calculations},
  doi       = {10.1063/1.2907241},
  number    = {18},
  pages     = {184110},
  url       = {https://doi.org/10.1063/1.2907241},
  volume    = {128},
  journal   = {J. Chem. Phys.},
  month     = may,
  publisher = {{AIP} Publishing},
  year      = {2008},
}

@Article{Chipot2011,
  author    = {Christophe Chipot and Tony Leli{\`{e}}vre},
  title     = {Enhanced Sampling of Multidimensional Free-Energy Landscapes Using Adaptive Biasing Forces},
  doi       = {10.1137/10080600x},
  number    = {5},
  pages     = {1673--1695},
  volume    = {71},
  journal   = {{SIAM} Journal on Applied Mathematics},
  month     = {jan},
  publisher = {Society for Industrial {\&} Applied Mathematics ({SIAM})},
  year      = {2011},
}

@Article{Sidky2018,
  author    = {Hythem Sidky and Yamil J. Col{\'{o}}n and Julian Helfferich and Benjamin J. Sikora and Cody Bezik and Weiwei Chu and Federico Giberti and Ashley Z. Guo and Xikai Jiang and Joshua Lequieu and Jiyuan Li and Joshua Moller and Michael J. Quevillon and Mohammad Rahimi and Hadi Ramezani-Dakhel and Vikramjit S. Rathee and Daniel R. Reid and Emre Sevgen and Vikram Thapar and Michael A. Webb and Jonathan K. Whitmer and Juan J. de Pablo},
  title     = {{SSAGES}: Software Suite for Advanced General Ensemble Simulations},
  doi       = {10.1063/1.5008853},
  eprint    = {https://doi.org/10.1063/1.5008853},
  number    = {4},
  pages     = {044104},
  url       = {https://doi.org/10.1063/1.5008853},
  volume    = {148},
  journal   = {J. Chem. Phys.},
  month     = {jan},
  publisher = {{AIP} Publishing},
  year      = {2018},
}

@Article{ChiavazzoE5494,
  author    = {Chiavazzo, Eliodoro and Covino, Roberto and Coifman, Ronald R. and Gear, C. William and Georgiou, Anastasia S. and Hummer, Gerhard and Kevrekidis, Ioannis G.},
  title     = {Intrinsic map dynamics exploration for uncharted effective free-energy landscapes},
  doi       = {10.1073/pnas.1621481114},
  eprint    = {https://www.pnas.org/content/114/28/E5494.full.pdf},
  issn      = {0027-8424},
  number    = {28},
  pages     = {E5494--E5503},
  url       = {https://www.pnas.org/content/114/28/E5494},
  volume    = {114},
  abstract  = {Direct simulations explore the dynamics of physical systems at their natural pace. Molecular dynamics (MD) simulations (e.g., of macromolecular folding) extensively revisit typical configurations until rare and interesting transition events occur. Biasing the simulator away from regions already explored can, therefore, drastically accelerate the discovery of features. We propose an enhanced sampling simulation framework, where MD and machine learning adaptively bootstrap each other. Machine learning guides the search for important configurations by processing information from previous explorations. This search proceeds iteratively in an algorithmically orchestrated fashion without advance knowledge of suitable collective variables. Applied to a molecular sensor of lipid saturation in membranes, a helix dissociation pathway not seen in millisecond simulations is discovered at the second iteration.We describe and implement a computer-assisted approach for accelerating the exploration of uncharted effective free-energy surfaces (FESs). More generally, the aim is the extraction of coarse-grained, macroscopic information from stochastic or atomistic simulations, such as molecular dynamics (MD). The approach functionally links the MD simulator with nonlinear manifold learning techniques. The added value comes from biasing the simulator toward unexplored phase-space regions by exploiting the smoothness of the gradually revealed intrinsic low-dimensional geometry of the FES.},
  journal   = {Proc. Natl. Acad. Sci.},
  publisher = {National Academy of Sciences},
  year      = {2017},
}

@Article{Schlitter1994,
  author      = {Schlitter, J. and Engels, M. and Kr\"uger, P.},
  title       = {Targeted molecular dynamics: a new approach for searching pathways of conformational transitions},
  language    = {eng},
  number      = {2},
  pages       = {84--89},
  volume      = {12},
  abstract    = {Molecular dynamics simulations have proven to be a valuable tool to investigate the dynamic behavior of stable macromolecules at finite temperatures. However, considerable conformational transitions take place during a simulation only accidentally or at exceptionally high temperatures far from the range of experimental conditions. Targeted molecular dynamics (TMD) is a method to induce a conformational change to a known target structure at ordinary temperature by applying a time-dependent, purely geometrical constraint. The transition is enforced independently of the height of energy barriers, while the dynamics of the molecule is only minimally influenced by the constraint. Simulations of decaalanine and insulin show the ability of the method to explore the configurational space for pathways accessible at a given temperature. The transitions studied at insulin comprise unfolding of an alpha-helical portion and, in the reverse direction, refolding from an extended conformation. A possible application of TMD is the search for energy barriers and stable intermediates from rather local changes up to protein denaturation.},
  institution = {Institut für Biophysik, Ruhr-Universität Bochum, Germany.},
  journal     = {J. Mol. Graph.},
  keywords    = {Computer Graphics; Computer Simulation; Insulin, chemistry; Models, Chemical; Models, Molecular; Oligopeptides, chemistry; Peptides, chemistry; Protein Conformation; Thermodynamics},
  medline-pst = {ppublish},
  owner       = {jhenin},
  pmid        = {7918256},
  timestamp   = {2011.09.06},
  year        = {1994},
  doi         = {10.1016/0263-7855(94)80072-3},
}

@Article{Mitsuta_SHS-MetaD_JCTC2020,
  author   = {Mitsuta, Yuki and Shigeta, Yasuteru},
  title    = {{Analytical Method Using a Scaled Hypersphere Search for High-Dimensional Metadynamics Simulations}},
  doi      = {10.1021/acs.jctc.0c00010},
  issn     = {1549-9618},
  number   = {6},
  pages    = {3869--3878},
  volume   = {16},
  abstract = {{Metadynamics (MTD) is one of the most effective methods for calculating the free energy surface and finding rare events. Nevertheless, numerous studies using MTD have been carried out using 3D or lower dimensional collective variables (CVs), as higher dimensional CVs require costly computational resources and the obtained results are too complex to understand the important events. The latter issue can be conveniently solved by utilizing the free energy reaction network (FERN), which is a graph structure consisting of edges of minimum free energy paths (MFEPs), nodes of equation (EQ) points, and transition state (TS) points. In the present article, a new method for exploring FERNs on high-dimensional CVs using MTD and the scaled hypersphere search (SHS) method is described. A test calculation based on the MTD-SHS simulation of met-enkephalin in explicit water with 7 CVs was conducted. As a result, 889 EQ points and 1805 TS points were found. The MTD-SHS approach can find MFEPs exhaustively; therefore, the FERNs can be estimated without any a priori knowledge of the EQ and TS points.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {32384233},
  year     = {2020},
}

@Article{Debnath_VES-TS_2019,
  author   = {Debnath, Jayashrita and Invernizzi, Michele and Parrinello, Michele},
  title    = {{Enhanced Sampling of Transition States}},
  doi      = {10.1021/acs.jctc.8b01283},
  eprint   = {1812.09032},
  issn     = {1549-9618},
  number   = {4},
  pages    = {2454--2459},
  volume   = {15},
  abstract = {{The free energy landscapes of several fundamental processes are characterized by high barriers separating long-lived metastable states. In order to explore these type of landscapes, enhanced sampling methods are used. While many such methods are able to obtain sufficient sampling in order to draw the free energy, the transition states are often sparsely sampled. We propose an approach based on the Variationally Enhanced Sampling Method to enhance sampling in the transition region. To this effect, we introduce a dynamic target distribution which uses the derivative of the instantaneous free energy surface to locate the transition regions on the fly and modulate the probability of sampling different regions. Finally, we exemplify the effectiveness of this approach in enriching the number of configurations in the transition state region in the cases of a chemical reaction and of a nucleation process.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {30779567},
  year     = {2019},
}

@Article{Sugita2000_REUS,
  author    = {Sugita, Yuji and Kitao, Akio and Okamoto, Yuko},
  title     = {Multidimensional replica-exchange method for free-energy calculations},
  doi       = {10.1063/1.1308516},
  issn      = {1089-7690},
  number    = {15},
  pages     = {6042–6051},
  url       = {http://dx.doi.org/10.1063/1.1308516},
  volume    = {113},
  journal   = {J. Chem. Phys.},
  month     = {Oct},
  publisher = {AIP Publishing},
  year      = {2000},
}

@Article{Ryckaert1977,
  author    = {J. Ryckaert and G. Ciccotti and H. J. C. Berendsen},
  title     = {Numerical integration of the cartesian equations of motion of a system with constraints: {M}olecular dynamics of $n$-alkanes},
  doi       = {10.1016/0021-9991(77)90098-5},
  number    = {3},
  pages     = {327--341},
  volume    = {23},
  journal   = {J. Comput. Phys.},
  month     = {mar},
  publisher = {Elsevier {BV}},
  year      = {1977},
}

@Article{Abraham2015,
  author    = {Abraham, Mark James and Murtola, Teemu and Schulz, Roland and P{\'a}ll, Szil{\'a}rd and Smith, Jeremy C and Hess, Berk and Lindahl, Erik},
  title     = {{GROMACS}: High performance molecular simulations through multi-level parallelism from laptops to supercomputers},
  doi       = {10.1016/j.softx.2015.06.001},
  pages     = {19--25},
  volume    = {1-2},
  journal   = {{SoftwareX}},
  month     = {sep},
  publisher = {Elsevier {BV}},
  year      = {2015},
}

@Article{lelievre-rousset-stoltz-07-a,
  author  = {Leli\`evre, T. and Rousset, M. and Stoltz, G.},
  title   = {Computation of free energy differences through nonequilibrium stochastic dynamics: {T}he reaction coordinate case},
  number  = {2},
  pages   = {624-643},
  volume  = {222},
  journal = {J. Comput. Phys.},
  year    = {2007},
  doi     = {10.1016/j.jcp.2006.08.003},
}

@Article{jarzynski-97,
  author  = {Jarzynski, C.},
  title   = {Equilibrium free energy differences from nonequilibrium measurements: {A} master equation approach},
  number  = {5},
  pages   = {5018-5035},
  volume  = {56},
  journal = {Phys. Rev. E},
  year    = {1997},
  doi     = {10.1103/PhysRevE.56.5018},
}

@Article{simmerling:jctc:2007:reservoir-replica-exchange,
  author  = {Asim Okur and Daniel R. Roe and Guanglei Cui and Viktor Hornak and Carlos Simmerling},
  title   = {Improving convergence of replica-exchange simulations through coupling to a high-temperature structure reservoir},
  doi     = {10.1021/ct600263e},
  pages   = {557},
  volume  = {3},
  journal = {J. Chem. Theory Comput.},
  year    = {2007},
}

@Article{Rosta2014,
  author    = {Edina Rosta and Gerhard Hummer},
  title     = {Free Energies from Dynamic Weighted Histogram Analysis Using Unbiased Markov State Model},
  doi       = {10.1021/ct500719p},
  number    = {1},
  pages     = {276--285},
  url       = {https://doi.org/10.1021/ct500719p},
  volume    = {11},
  journal   = {J. Chem. Theory Comput.},
  month     = dec,
  publisher = {American Chemical Society ({ACS})},
  year      = {2014},
}

@Article{Marinelli_EnsembleBiased_2015,
  author   = {Marinelli, Fabrizio and Faraldo-Gómez, José D.},
  title    = {{Ensemble-Biased Metadynamics: A Molecular Simulation Method to Sample Experimental Distributions}},
  doi      = {10.1016/j.bpj.2015.05.024},
  issn     = {0006-3495},
  number   = {12},
  pages    = {2779--2782},
  volume   = {108},
  abstract = {{ We introduce an enhanced-sampling method for molecular dynamics (MD) simulations referred to as ensemble-biased metadynamics (EBMetaD). The method biases a conventional MD simulation to sample a molecular ensemble that is consistent with one or more probability distributions known a priori, e.g., experimental intramolecular distance distributions obtained by double electron-electron resonance or other spectroscopic techniques. To this end, EBMetaD adds an adaptive biasing potential throughout the simulation that discourages sampling of configurations inconsistent with the target probability distributions. The bias introduced is the minimum necessary to fulfill the target distributions, i.e., EBMetaD satisfies the maximum-entropy principle. Unlike other methods, EBMetaD does not require multiple simulation replicas or the introduction of Lagrange multipliers, and is therefore computationally efficient and straightforward in practice. We demonstrate the performance and accuracy of the method for a model system as well as for spin-labeled T4 lysozyme in explicit water, and show how EBMetaD reproduces three double electron-electron resonance distance distributions concurrently within a few tens of nanoseconds of simulation time. EBMetaD is integrated in the open-source PLUMED plug-in (www.plumed-code.org), and can be therefore readily used with multiple MD engines.}},
  journal  = {Biophys. J.},
  pmcid    = {PMC4472218},
  pmid     = {26083917},
  year     = {2015},
}

@Article{Belardinelli2008,
  author  = {Belardinelli, R. and Manzi, S. and Pereyra, V.},
  title   = {{Analysis of the convergence of the {1/t} and Wang-Landau algorithms in the calculation of multidimensional integrals}},
  doi     = {10.1103/PhysRevE.78.067701},
  issn    = {1539-3755},
  number  = {6},
  volume  = {78},
  journal = {Phys. Rev. E},
  month   = dec,
  year    = {2008},
}

@Article{No2009,
  author    = {Frank No{\'{e}} and Christof Sch\"{u}tte and Eric Vanden-Eijnden and Lothar Reich and Thomas R. Weikl},
  title     = {Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations},
  doi       = {10.1073/pnas.0905466106},
  number    = {45},
  pages     = {19011--19016},
  url       = {https://doi.org/10.1073/pnas.0905466106},
  volume    = {106},
  journal   = {Proc. Natl. Acad. Sci.},
  month     = nov,
  publisher = {Proc. Natl. Acad. Sci. U.S.A.},
  year      = {2009},
}

@Article{Belardinelli2007,
  author   = {Belardinelli, R E and Pereyra, V D},
  title    = {{Wang-Landau algorithm: a theoretical analysis of the saturation of the error.}},
  doi      = {10.1063/1.2803061},
  issn     = {0021-9606},
  language = {en},
  number   = {18},
  pages    = {184105},
  volume   = {127},
  abstract = {In this work we present a theoretical analysis of the convergence of the Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] which was introduced years ago to calculate the density of states in statistical models. We study the dynamical behavior of the error in the calculation of the density of states. We conclude that the source of the saturation of the error is due to the decreasing variations of the refinement parameter. To overcome this limitation, we present an analytical treatment in which the refinement parameter is scaled down as a power law instead of exponentially. An extension of the analysis to the N-fold way variation of the method is also discussed.},
  journal  = {J. Chem. Phys.},
  keywords = {Ising model, convergence, error analysis, random processes, statistical analysis},
  month    = nov,
  pmid     = {18020628},
  year     = {2007},
}

@Article{teo-mayne-schulten-lelievre-16,
  author  = {Teo, I. and Mayne, C.G. and Schulten, K. and Leli{\`e}vre, T.},
  title   = {Adaptive multilevel splitting method for molecular dynamics calculation of benzamidine-trypsin dissociation time},
  doi     = {10.1021/acs.jctc.6b00277},
  number  = {6},
  pages   = {2983-2989},
  volume  = {12},
  journal = {J. Chem. Theory Comput.},
  year    = {2016},
}

@Article{ABRAMS2012114,
  author   = {Cameron F. Abrams and Eric Vanden-Eijnden},
  title    = {On-the-fly free energy parameterization via temperature accelerated molecular dynamics},
  doi      = {10.1016/j.cplett.2012.07.064},
  issn     = {0009-2614},
  pages    = {114-119},
  url      = {https://www.sciencedirect.com/science/article/pii/S0009261412008846},
  volume   = {547},
  abstract = {We discuss a method for parametric calculation of free energy functions in arbitrary collective variables using molecular simulations. The method uses a variant of temperature accelerated molecular dynamics to evolve on-the-fly the parameters of the free energy function to their optimum values by minimization of a cumulative gradient error. We illustrate how the method performs using simple examples and discuss its application in the derivation of effective pairwise potentials for multiscale molecular simulations.},
  journal  = {Chem. Phys. Lett.},
  year     = {2012},
}

@Article{sindhikara-emerson-roitberg:jctc:2010:exchange-often-and-properly,
  author  = {Daniel Sindhikara and Daniel J. Emerson and Adrian E. Roitberg},
  title   = {Exchange often and properly in replica exchange molecular dynamics},
  pages   = {2804--2808},
  volume  = {6},
  journal = {J. Chem. Theory Comput.},
  year    = {2010},
  doi = {10.1021/ct100281c}
}

@Article{McCarty2016_JCTC,
  author    = {McCarty, James and Valsson, Omar and Parrinello, Michele},
  title     = {Bespoke Bias for Obtaining Free Energy Differences within Variationally Enhanced Sampling},
  doi       = {10.1021/acs.jctc.6b00125},
  issn      = {1549-9626},
  number    = {5},
  pages     = {2162–2169},
  url       = {http://dx.doi.org/10.1021/acs.jctc.6b00125},
  volume    = {12},
  journal   = {J. Chem. Theory Comput.},
  month     = {Apr},
  publisher = {American Chemical Society (ACS)},
  year      = {2016},
}

@Article{iba:intl-j-mod-phys-c:2001:extended-ensemble,
  author  = {Yukito Iba},
  title   = {Extended ensemble {Monte Carlo}},
  pages   = {623},
  volume  = {12},
  journal = {Intl. J. Mod. Phys. C},
  year    = {2001},
  doi = {10.1142/S0129183101001912}
}

@Article{No2007,
  author    = {Frank No{\'{e}} and Illia Horenko and Christof Sch\"{u}tte and Jeremy C. Smith},
  title     = {Hierarchical analysis of conformational dynamics in biomolecules: Transition networks of metastable states},
  doi       = {10.1063/1.2714539},
  number    = {15},
  pages     = {155102},
  url       = {https://doi.org/10.1063/1.2714539},
  volume    = {126},
  journal   = {J. Chem. Phys.},
  month     = apr,
  publisher = {{AIP} Publishing},
  year      = {2007},
}

@Article{BACCI2015889,
  author   = {Marco Bacci and Andreas Vitalis and Amedeo Caflisch},
  title    = {A molecular simulation protocol to avoid sampling redundancy and discover new states},
  doi      = {10.1016/j.bbagen.2014.08.013},
  issn     = {0304-4165},
  note     = {Recent developments of molecular dynamics},
  number   = {5},
  pages    = {889-902},
  url      = {https://www.sciencedirect.com/science/article/pii/S030441651400289X},
  volume   = {1850},
  abstract = {Background
For biomacromolecules or their assemblies, experimental knowledge is often restricted to specific states. Ambiguity pervades simulations of these complex systems because there is no prior knowledge of relevant phase space domains, and sampling recurrence is difficult to achieve. In molecular dynamics methods, ruggedness of the free energy surface exacerbates this problem by slowing down the unbiased exploration of phase space. Sampling is inefficient if dwell times in metastable states are large.
Methods
We suggest a heuristic algorithm to terminate and reseed trajectories run in multiple copies in parallel. It uses a recent method to order snapshots, which provides notions of “interesting” and “unique” for individual simulations. We define criteria to guide the reseeding of runs from more “interesting” points if they sample overlapping regions of phase space.
Results
Using a pedagogical example and an α-helical peptide, the approach is demonstrated to amplify the rate of exploration of phase space and to discover metastable states not found by conventional sampling schemes. Evidence is provided that accurate kinetics and pathways can be extracted from the simulations.
Conclusions
The method, termed PIGS for Progress Index Guided Sampling, proceeds in unsupervised fashion, is scalable, and benefits synergistically from larger numbers of replicas. Results confirm that the underlying ideas are appropriate and sufficient to enhance sampling.
General Significance
In molecular simulations, errors caused by not exploring relevant domains in phase space are always unquantifiable and can be arbitrarily large. Our protocol adds to the toolkit available to researchers in reducing these types of errors. This article is part of a Special Issue entitled “Recent Developments of Molecular Dynamics.”},
  journal  = {Biochimica et Biophysica Acta (BBA) - General Subjects},
  keywords = {Enhanced sampling, Molecular dynamics, Biomolecules, Simulation convergence, Transition path, Scalable algorithm},
  year     = {2015},
}

@Article{White_EDM_2015,
  author   = {White, Andrew D. and Dama, James F. and Voth, Gregory A.},
  title    = {{Designing Free Energy Surfaces That Match Experimental Data with Metadynamics}},
  doi      = {10.1021/acs.jctc.5b00178},
  issn     = {1549-9618},
  number   = {6},
  pages    = {2451--2460},
  volume   = {11},
  abstract = {{  Creating models that are consistent with experimental data is essential in molecular modeling. This is often done by iteratively tuning the molecular force field of a simulation to match experimental data. An alternative method is to bias a simulation, leading to a hybrid model composed of the original force field and biasing terms. We previously introduced such a method called experiment directed simulation (EDS). EDS minimally biases simulations to match average values. In this work, we introduce a new method called experiment directed metadynamics (EDM) that creates minimal biases for matching entire free energy surfaces such as radial distribution functions and phi/psi angle free energies. It is also possible with EDM to create a tunable mixture of the experimental data and free energy of the unbiased ensemble with explicit ratios. EDM can be proven to be convergent, and we also present proof, via a maximum entropy argument, that the final bias is minimal and unique. Examples of its use are given in the construction of ensembles that follow a desired free energy. The example systems studied include a Lennard-Jones fluid made to match a radial distribution function, an atomistic model augmented with bioinformatics data, and a three-component electrolyte solution where ab initio simulation data is used to improve a classical empirical model.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {26575545},
  year     = {2015},
}

@Article{nadler-hansmann:pre:2007:generalized-ensemble,
  author  = {Walter Nadler and Ulrich H. E. Hansmann},
  title   = {Generalized ensemble and tempering simulations: A unified view},
  doi     = {10.1103/physreve.75.026109},
  pages   = {026109},
  volume  = {75},
  journal = {Phys. Rev. E},
  year    = {2007},
}

@Article{Zhang_MetaD-US-3_JCTC2013,
  author  = {Zhang, Yong and Voth, Gregory A},
  title   = {{Combined Metadynamics and Umbrella Sampling Method for the Calculation of Ion Permeation Free Energy Profiles}},
  doi     = {10.1021/ct200100e},
  issn    = {1549-9618},
  number  = {7},
  pages   = {2277--2283},
  volume  = {7},
  journal = {J. Chem. Theory Comput.},
  pmid    = {25100923},
  year    = {2011},
}

@Article{doi:10.1146/annurev.physchem.040808.090412,
  author   = {E, Weinan and Vanden-Eijnden, Eric},
  title    = {Transition-Path Theory and Path-Finding Algorithms for the Study of Rare Events},
  doi      = {10.1146/annurev.physchem.040808.090412},
  eprint   = {https://doi.org/10.1146/annurev.physchem.040808.090412},
  number   = {1},
  pages    = {391-420},
  url      = {https://doi.org/10.1146/annurev.physchem.040808.090412},
  volume   = {61},
  abstract = {Transition-path theory is a theoretical framework for describing rare events in complex systems. It can also be used as a starting point for developing efficient numerical algorithms for analyzing such rare events. Here we review the basic components of transition-path theory and path-finding algorithms. We also discuss connections with the classical transition-state theory.},
  journal  = {Annu. Rev. Phys. Chem.},
  pmid     = {18999998},
  year     = {2010},
}

@Article{BussiLaio_ReviewMetaD_2020,
  author   = {Bussi, Giovanni and Laio, Alessandro},
  title    = {{Using metadynamics to explore complex free-energy landscapes}},
  doi      = {10.1038/s42254-020-0153-0},
  number   = {4},
  pages    = {200--212},
  volume   = {2},
  journal  = {Nat. Rev. Phys.},
  keywords = {Metadynamics Reviews},
  year     = {2020},
}

@Article{doi:10.1021/acs.jctc.6b00762,
  author  = {Noé, Frank and Banisch, Ralf and Clementi, Cecilia},
  title   = {Commute Maps: Separating Slowly Mixing Molecular Configurations for Kinetic Modeling},
  doi     = {10.1021/acs.jctc.6b00762},
  eprint  = {https://doi.org/10.1021/acs.jctc.6b00762},
  number  = {11},
  pages   = {5620-5630},
  url     = {https://doi.org/10.1021/acs.jctc.6b00762},
  volume  = {12},
  journal = {J. Chem. Theory Comput.},
  pmid    = {27696838},
  year    = {2016},
}

@Article{benaim-brehier-monmarche-20,
  author    = {Bena{\"\i}m, Michel and Br{\'e}hier, Charles-Edouard and Monmarch{\'e}, Pierre},
  title     = {Analysis of an Adaptive Biasing Force method based on self-interacting dynamics},
  doi       = {10.1214/20-ejp490},
  pages     = {1--28},
  volume    = {25},
  journal   = {Electron J Probab},
  publisher = {Institute of Mathematical Statistics and Bernoulli Society},
  year      = {2020},
}

@Article{rousset2006equilibrium,
  author    = {Rousset, Mathias and Stoltz, Gabriel},
  title     = {Equilibrium sampling from nonequilibrium dynamics},
  doi       = {10.1007/s10955-006-9090-2},
  number    = {6},
  pages     = {1251--1272},
  volume    = {123},
  journal   = {J. Stat. Phys.},
  publisher = {Springer},
  year      = {2006},
}

@Article{gallicchio-levy-parashar:j-comput-chem:2008:asynchronous-replica-exchange,
  author  = {Emilio Gallicchio and Ronald M. Levy and Manish Parashar},
  title   = {Asynchronous replica exchange for molecular simulations},
  doi     = {10.1002/jcc.20839},
  pages   = {288--794},
  volume  = {29},
  journal = {J. Comput. Chem.},
  year    = {2008},
}

@Article{Bonomi_Metainference_SciAdv2016,
  author   = {Bonomi, Massimiliano and Camilloni, Carlo and Cavalli, Andrea and Vendruscolo, Michele},
  title    = {{Metainference: A Bayesian inference method for heterogeneous systems}},
  doi      = {10.1126/sciadv.1501177},
  issn     = {2375-2548},
  number   = {1},
  pages    = {e1501177},
  volume   = {2},
  abstract = {{Modeling a complex system is almost invariably a challenging task. The incorporation of experimental observations can be used to improve the quality of a model and thus to obtain better predictions about the behavior of the corresponding system. This approach, however, is affected by a variety of different errors, especially when a system simultaneously populates an ensemble of different states and experimental data are measured as averages over such states. To address this problem, we present a Bayesian inference method, called “metainference,” that is able to deal with errors in experimental measurements and with experimental measurements averaged over multiple states. To achieve this goal, metainference models a finite sample of the distribution of models using a replica approach, in the spirit of the replica-averaging modeling based on the maximum entropy principle. To illustrate the method, we present its application to a heterogeneous model system and to the determination of an ensemble of structures corresponding to the thermal fluctuations of a protein molecule. Metainference thus provides an approach to modeling complex systems with heterogeneous components and interconverting between different states by taking into account all possible sources of errors.}},
  journal  = {Sci. Adv.},
  pmcid    = {PMC4737209},
  pmid     = {26844300},
  year     = {2016},
}

@Article{minh-adlib-08,
  author  = {D. D. L. Minh and A. B. Adib},
  title   = {Optimized Free Energies from Bidirectional Single-Molecule Force Spectroscopy},
  doi     = {10.1103/physrevlett.100.180602},
  pages   = {180602},
  volume  = {100},
  journal = {Phys. Rev. Lett.},
  year    = {2008},
}

@Article{Rubinstein-MetCompAppProb-1999,
  author        = {Rubinstein, Reuven},
  title         = {The Cross-Entropy Method for Combinatorial and Continuous Optimization},
  doi           = {10.1023/a:1010091220143},
  issn          = {1387-5841},
  number        = {2},
  pages         = {127--190},
  url           = {http://dx.doi.org/10.1023/A:1010091220143},
  volume        = {1},
  bdsk-url-1    = {http://dx.doi.org/10.1023/A:1010091220143},
  bdsk-url-2    = {http://dx.doi.org/10.1023/a:1010091220143},
  date-added    = {2018-04-23 00:17:16 +0000},
  date-modified = {2018-04-23 00:17:34 +0000},
  journal       = {Methodol. Comput. Appl. Probab.},
  publisher     = {Springer Nature},
  year          = {1999},
}

% expanded ensembles and simulated tempering

@Article{lyubartsev:jcp:1992:expanded-ensembles,
  author  = {A. P. Lyubartsev and A. A. Martsinovski and S. V. Shevkunov and P. N. Vorontsov-Velyaminov},
  title   = {New approach to {Monte Carlo} calculation of the free energy: Method of expanded ensembles},
  doi     = {10.1063/1.462133},
  pages   = {1776--1783},
  volume  = {96},
  journal = {J. Chem. Phys.},
  year    = {1992},
}

@Article{marinari-parisi:europhys-lett:1992:simulated-tempering,
  author  = {E. Marinari and G. Parisi},
  title   = {Simulated tempering: a new {Monte Carlo} scheme},
  doi     = {10.1209/0295-5075/19/6/002},
  number  = {6},
  pages   = {451--458},
  volume  = {19},
  journal = {Europhys. Lett.},
  year    = {1992},
}

@Article{10.1063/1.4937939,
  author   = {Dickson, Bradley M.},
  title    = {{$\mu$-tempered metadynamics: Artifact independent convergence times for wide hills}},
  doi      = {10.1063/1.4937939},
  issn     = {0021-9606},
  number   = {23},
  pages    = {234109},
  volume   = {143},
  abstract = {{Recent analysis of well-tempered metadynamics (WTmetaD) showed that it converges without mollification artifacts in the bias potential. Here, we explore how metadynamics heals mollification artifacts, how healing impacts convergence time, and whether alternative temperings may be used to improve efficiency. We introduce “μ-tempered” metadynamics as a simple tempering scheme, inspired by a related mollified adaptive biasing potential, that results in artifact independent convergence of the free energy estimate. We use a toy model to examine the role of artifacts in WTmetaD and solvated alanine dipeptide to compare the well-tempered and μ-tempered frameworks demonstrating fast convergence for hill widths as large as 60∘ for μTmetaD.}},
  journal  = {J. Chem. Phys.},
  pmid     = {26696048},
  year     = {2015},
}

@Article{Raiteri-JPCB-2006,
  author        = {Raiteri, Paolo and Laio, Alessandro and Gervasio, Francesco Luigi and Micheletti, Cristian and Parrinello, Michele},
  title         = {Efficient Reconstruction of Complex Free Energy Landscapes by Multiple Walkers Metadynamics †},
  doi           = {10.1021/jp054359r},
  issn          = {1520-5207},
  number        = {8},
  pages         = {3533--3539},
  url           = {http://dx.doi.org/10.1021/jp054359r},
  volume        = {110},
  bdsk-url-1    = {http://dx.doi.org/10.1021/jp054359r},
  date-added    = {2014-06-17 15:31:24 +0000},
  date-modified = {2015-03-25 10:49:51 +0000},
  journal       = {J. Phys. Chem. B},
  month         = {Mar},
  publisher     = {American Chemical Society (ACS)},
  year          = {2006},
}

@Article{Giberti_IterRew_JCTC2019,
  author   = {Giberti, F and Cheng, B and Tribello, G A and Ceriotti, M},
  title    = {{Iterative Unbiasing of Quasi-Equilibrium Sampling}},
  doi      = {10.1021/acs.jctc.9b00907},
  issn     = {1549-9618},
  number   = {1},
  pages    = {100--107},
  volume   = {16},
  abstract = {{Atomistic modeling of phase transitions, chemical reactions, or other rare events that involve overcoming high free energy barriers usually entails prohibitively long simulation times. Introducing a bias potential as a function of an appropriately chosen set of collective variables can significantly accelerate the exploration of phase space, albeit at the price of distorting the distribution of microstates. Efficient reweighting to recover the unbiased distribution can be nontrivial when employing adaptive sampling techniques such as metadynamics, variationally enhanced sampling, or parallel bias metadynamics, in which the system evolves in a quasi-equilibrium manner under a time-dependent bias. We introduce an iterative unbiasing scheme that makes efficient use of all the trajectory data and that does not require the distribution to be evaluated on a grid. The method can thus be used even when the bias has a high dimensionality. We benchmark this approach against some of the existing schemes on model systems with different complexity and dimensionality.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {31743021},
  year     = {2019},
}

@Article{kofke:2002:jcp:acceptance-probability,
  author  = {David A. Kofke},
  title   = {On the acceptance probability of replica-exchange {Monte Carlo} trials},
  doi     = {10.1063/1.1507776},
  pages   = {6911},
  volume  = {117},
  journal = {J. Chem. Phys.},
  year    = {2002},
}

@Article{doi:10.1063/1.5053582,
  author  = {Hruska,Eugen and Abella,Jayvee R. and Nüske,Feliks and Kavraki,Lydia E. and Clementi,Cecilia},
  title   = {Quantitative comparison of adaptive sampling methods for protein dynamics},
  doi     = {10.1063/1.5053582},
  eprint  = {https://doi.org/10.1063/1.5053582},
  number  = {24},
  pages   = {244119},
  url     = {https://doi.org/10.1063/1.5053582},
  volume  = {149},
  journal = {J. Chem. Phys.},
  year    = {2018},
}

@Article{doi:10.1063/1.1448491,
  author  = {Rosso,Lula and Mináry,Peter and Zhu,Zhongwei and Tuckerman,Mark E.},
  title   = {On the use of the adiabatic molecular dynamics technique in the calculation of free energy profiles},
  doi     = {10.1063/1.1448491},
  eprint  = {https://doi.org/10.1063/1.1448491},
  number  = {11},
  pages   = {4389-4402},
  url     = {https://doi.org/10.1063/1.1448491},
  volume  = {116},
  journal = {J. Chem. Phys.},
  year    = {2002},
}

% Weight update for expanded ensembles and simulated tempering

@Article{wang-landau:prl:2001:wang-landau,
  author  = {Fugao Wang and D. P. Landau},
  title   = {Efficient, multiple-range random walk algorithm to calculate density of states},
  doi     = {10.1103/physrevlett.86.2050},
  pages   = {2050--2053},
  volume  = {86},
  journal = {Phys. Rev. Lett.},
  year    = {2001},
}

% combinations of expanded ensembles and replica exchange

@Article{fenwick-escobedo:jcp:2003:replica-exchange-expanded-ensembles,
  author  = {Michael K. Fenwick and Fernando A. Escobedo},
  title   = {Expanded ensemble and replica exchange methods for simulation of protein-like systems},
  pages   = {11998},
  volume  = {119},
  journal = {J. Chem. Phys.},
  year    = {2003},
  doi = {10.1063/1.1624822},
}

@Article{lecina_adaptive_2017,
  author    = {Lecina, Daniel and Gilabert, Joan F. and Guallar, Victor},
  title     = {Adaptive simulations, towards interactive protein-ligand modeling},
  doi       = {10.1038/s41598-017-08445-5},
  issn      = {2045-2322},
  language  = {en},
  note      = {Number: 1 Publisher: Nature Publishing Group},
  number    = {1},
  pages     = {8466},
  url       = {https://www.nature.com/articles/s41598-017-08445-5},
  urldate   = {2021-06-08},
  volume    = {7},
  abstract  = {Modeling the dynamic nature of protein-ligand binding with atomistic simulations is one of the main challenges in computational biophysics, with important implications in the drug design process. Although in the past few years hardware and software advances have significantly revamped the use of molecular simulations, we still lack a fast and accurate ab initio description of the binding mechanism in complex systems, available only for up-to-date techniques and requiring several hours or days of heavy computation. Such delay is one of the main limiting factors for a larger penetration of protein dynamics modeling in the pharmaceutical industry. Here we present a game-changing technology, opening up the way for fast reliable simulations of protein dynamics by combining an adaptive reinforcement learning procedure with Monte Carlo sampling in the frame of modern multi-core computational resources. We show remarkable performance in mapping the protein-ligand energy landscape, being able to reproduce the full binding mechanism in less than half an hour, or the active site induced fit in less than 5 minutes. We exemplify our method by studying diverse complex targets, including nuclear hormone receptors and GPCRs, demonstrating the potential of using the new adaptive technique in screening and lead optimization studies.},
  copyright = {2017 The Author(s)},
  file      = {Full Text PDF:/Users/lucie/Zotero/storage/7KE35RA2/Lecina et al. - 2017 - Adaptive simulations, towards interactive protein-.pdf:application/pdf},
  journal   = {Sci. Rep.},
  month     = aug,
  year      = {2017},
}

@Article{giberti2021atlas,
  author  = {Giberti, F and Tribello, G A and Ceriotti, M},
  title   = {{Global Free-Energy Landscapes as a Smoothly Joined Collection of Local Maps}},
  doi     = {10.1021/acs.jctc.0c01177},
  issn    = {1549-9618},
  journal = {J. Chem. Theory Comput.},
  pmid    = {34003008},
  year    = {2021},
}

@Article{VJ08,
  author  = {S. Vaikuntanathan and C. Jarzynski},
  title   = {Escorted Free Energy Simulations: {I}mproving Convergence by Reducing Dissipation},
  doi     = {10.1103/physrevlett.100.190601},
  pages   = {190601},
  volume  = {100},
  journal = {Phys. Rev. Lett.},
  year    = {2008},
}

@Article{10.1073/pnas.1011511107,
  author   = {Tribello, Gareth A. and Ceriotti, Michele and Parrinello, Michele},
  title    = {{A self-learning algorithm for biased molecular dynamics}},
  doi      = {10.1073/pnas.1011511107},
  eprint   = {1009.1236},
  issn     = {0027-8424},
  number   = {41},
  pages    = {17509--17514},
  volume   = {107},
  abstract = {{A new self-learning algorithm for accelerated dynamics, reconnaissance metadynamics, is proposed that is able to work with a very large number of collective coordinates. Acceleration of the dynamics is achieved by constructing a bias potential in terms of a patchwork of one-dimensional, locally valid collective coordinates. These collective coordinates are obtained from trajectory analyses so that they adapt to any new features encountered during the simulation. We show how this methodology can be used to enhance sampling in real chemical systems citing examples both from the physics of clusters and from the biological sciences.}},
  journal  = {Proc. Natl. Acad. Sci.},
  pmcid    = {PMC2955137},
  pmid     = {20876135},
  year     = {2010},
}

@Article{Zheng_OSRW-2_JCP2009,
  author   = {Zheng, Lianqing and Chen, Mengen and Yang, Wei},
  title    = {{Simultaneous escaping of explicit and hidden free energy barriers: Application of the orthogonal space random walk strategy in generalized ensemble based conformational sampling}},
  doi      = {10.1063/1.3153841},
  issn     = {0021-9606},
  number   = {23},
  pages    = {234105},
  volume   = {130},
  abstract = {{To overcome the pseudoergodicity problem, conformational sampling can be accelerated via generalized ensemble methods, e.g., through the realization of random walks along prechosen collective variables, such as spatial order parameters, energy scaling parameters, or even system temperatures or pressures, etc. As usually observed, in generalized ensemble simulations, hidden barriers are likely to exist in the space perpendicular to the collective variable direction and these residual free energy barriers could greatly abolish the sampling efficiency. This sampling issue is particularly severe when the collective variable is defined in a low-dimension subset of the target system; then the "Hamiltonian lagging" problem, which reveals the fact that necessary structural relaxation falls behind the move of the collective variable, may be likely to occur. To overcome this problem in equilibrium conformational sampling, we adopted the orthogonal space random walk (OSRW) strategy, which was originally developed in the context of free energy simulation [L. Zheng, M. Chen, and W. Yang, Proc. Natl. Acad. Sci. U.S.A. 105, 20227 (2008)]. Thereby, generalized ensemble simulations can simultaneously escape both the explicit barriers along the collective variable direction and the hidden barriers that are strongly coupled with the collective variable move. As demonstrated in our model studies, the present OSRW based generalized ensemble treatments show improved sampling capability over the corresponding classical generalized ensemble treatments.}},
  journal  = {J. Chem. Phys.},
  pmid     = {19548709},
  year     = {2009},
}

@Article{doi:10.1021/jp0777059,
  author  = {Pan, Albert C. and Sezer, Deniz and Roux, Benoît},
  title   = {Finding Transition Pathways Using the String Method with Swarms of Trajectories},
  doi     = {10.1021/jp0777059},
  eprint  = {https://doi.org/10.1021/jp0777059},
  pmid = {18290641},
  number  = {11},
  pages   = {3432-3440},
  url     = {https://doi.org/10.1021/jp0777059},
  volume  = {112},
  journal = {J. Phys. Chem. B},
  year    = {2008},
}

@Article{Valsson-JCTC-2013,
  author        = {Valsson, Omar and Parrinello, Michele},
  title         = {{Thermodynamical Description of a Quasi-First-Order Phase Transition from the Well-Tempered Ensemble}},
  doi           = {10.1021/ct400859f},
  number        = {12},
  pages         = {5267--5276},
  volume        = {9},
  date-added    = {2015-06-03 10:20:51 +0000},
  date-modified = {2015-06-03 10:21:05 +0000},
  journal       = {J. Chem. Theory Comput.},
  year          = {2013},
}

@Article{Kastner2005,
  author    = {Kastner, J. and Thiel, W.},
  title     = {Bridging the gap between thermodynamic integration and umbrella sampling provides a novel analysis method: ``Umbrella integration''},
  doi       = {10.1063/1.2052648},
  number    = {14},
  pages     = {144104},
  url       = {http://link.aip.org/link/?JCP/123/144104/1},
  volume    = {123},
  journal   = {J. Chem. Phys.},
  keywords  = {integration, error analysis, molecular dynamics method, Monte Carlo methods, free energy},
  owner     = {henin},
  publisher = {AIP},
  timestamp = {2006.01.25},
  year      = {2005},
}

@Article{Crooks99,
  author   = {G. E. Crooks},
  title    = {Entropy production fluctuation theorem and the nonequilibrium work relation for free-energy differences},
  doi      = {10.1103/physreve.60.2721},
  number   = {3},
  pages    = {2721--2726},
  volume   = {60},
  journal  = {Phys. Rev. E},
  numpages = {5},
  year     = {1999},
}

@Article{Wang2021,
  author    = {Jinan Wang and Pablo R. Arantes and Apurba Bhattarai and Rohaine V. Hsu and Shristi Pawnikar and Yu-ming M. Huang and Giulia Palermo and Yinglong Miao},
  title     = {Gaussian accelerated molecular dynamics: Principles and applications},
  doi       = {10.1002/wcms.1521},
  journal   = {WIREs Comput. Mol. Sci.},
  month     = {mar},
  publisher = {Wiley},
  year      = {2021},
}

@Article{Valsson-JCTC-2015,
  author        = {Valsson, Omar and Parrinello, Michele},
  title         = {{Well-Tempered Variational Approach to Enhanced Sampling}},
  doi           = {10.1021/acs.jctc.5b00076},
  number        = {5},
  pages         = {1996--2002},
  volume        = {11},
  date-added    = {2015-06-03 10:19:59 +0000},
  date-modified = {2015-06-03 10:20:29 +0000},
  journal       = {J. Chem. Theory Comput.},
  year          = {2015},
}

@Article{doi:10.1021/jp9074898,
  author  = {Glowacki, David R. and Paci, Emanuele and Shalashilin, Dmitrii V.},
  title   = {Boxed Molecular Dynamics: A Simple and General Technique for Accelerating Rare Event Kinetics and Mapping Free Energy in Large Molecular Systems},
  doi     = {10.1021/jp9074898},
  eprint  = {https://doi.org/10.1021/jp9074898},
  pmid =  {19961166},
  number  = {52},
  pages   = {16603-16611},
  url     = {https://doi.org/10.1021/jp9074898},
  volume  = {113},
  journal = {J. Phys. Chem. B},
  year    = {2009},
}

@Article{trebst-troyer-hansmann:jcp:2006:optimized-replica-selection,
  author  = {Simon Trebst and Matthias Troyer and Ulrich H. E. Hansmann},
  title   = {Optimized parallel tempering simulations of proteins},
  doi     = {10.1063/1.2186639},
  pages   = {174903},
  volume  = {124},
  journal = {J. Chem. Phys.},
  year    = {2006},
}

@Article{10.1021/jz200808x,
  author  = {Wu, Pan and Hu, Xiangqian and Yang, Weitao},
  title   = {{$\lambda$-Metadynamics Approach To Compute Absolute Solvation Free Energy}},
  doi     = {10.1021/jz200808x},
  issn    = {1948-7185},
  number  = {17},
  pages   = {2099--2103},
  volume  = {2},
  journal = {J. Phys. Chem. Lett.},
  pmid    = {23678385},
  year    = {2011},
}

@Article{Bottaro_Science2018,
  author   = {Bottaro, Sandro and Lindorff-Larsen, Kresten},
  title    = {{Biophysical experiments and biomolecular simulations: A perfect match?}},
  doi      = {10.1126/science.aat4010},
  issn     = {0036-8075},
  number   = {6400},
  pages    = {355--360},
  volume   = {361},
  abstract = {{A fundamental challenge in biological research is achieving an atomic-level description and mechanistic understanding of the function of biomolecules. Techniques for biomolecular simulations have undergone substantial developments, and their accuracy and scope have expanded considerably. Progress has been made through an increasingly tight integration of experiments and simulations, with experiments being used to refine simulations and simulations used to interpret experiments. Here we review the underpinnings of this progress, including methods for more efficient conformational sampling, accuracy of the physical models used, and theoretical approaches to integrate experiments and simulations. These developments are enabling detailed studies of complex biomolecular assemblies.}},
  journal  = {Science},
  pmid     = {30049874},
  year     = {2018},
}

@Article{Darve2008,
  author      = {Eric Darve and David Rodr{\'i}guez-G{\'o}mez and Andrew Pohorille},
  title       = {Adaptive biasing force method for scalar and vector free energy calculations},
  doi         = {10.1063/1.2829861},
  number      = {14},
  pages       = {144120},
  url         = {http://dx.doi.org/10.1063/1.2829861},
  volume      = {128},
  abstract    = {In free energy calculations based on thermodynamic integration, it is necessary to compute the derivatives of the free energy as a function of one (scalar case) or several (vector case) order parameters. We derive in a compact way a general formulation for evaluating these derivatives as the average of a mean force acting on the order parameters, which involves first derivatives with respect to both Cartesian coordinates and time. This is in contrast with the previously derived formulas, which require first and second derivatives of the order parameter with respect to Cartesian coordinates. As illustrated in a concrete example, the main advantage of this new formulation is the simplicity of its use, especially for complicated order parameters. It is also straightforward to implement in a molecular dynamics code, as can be seen from the pseudocode given at the end. We further discuss how the approach based on time derivatives can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calculations. Using the backbone dihedral angles Phi and Psi in N-acetylalanyl-N(')-methylamide as a numerical example, we present a technique to reconstruct the free energy from its derivatives, a calculation that presents some difficulties in the vector case because of the statistical errors affecting the derivatives.},
  file        = {Darve RG Pohorille vector ABF JCP 2008.pdf:nergy_configurational/ABF/Darve RG Pohorille vector ABF JCP 2008.pdf:PDF},
  institution = {Mechanical Engineering Department, Stanford University, Stanford, California 94305-4040, USAExobiology Branch, MS 239-4, NASA Ames Research Center, Moffett Field, California 94035, USADepartment of Pharmaceutical Chemistry, University of California San Francisco, 600 16th Street, San Francisco, California 94143-2280, USA.},
  journal     = {J. Chem. Phys.},
  owner       = {jhenin},
  pmid        = {18412436},
  timestamp   = {2008.05.19},
  year        = {2008},
}

@Article{mitsutake-okamoto:jcp:2004:rest,
  author  = {Ayori Mitsutake and Yuko Okamoto},
  title   = {Replica-exchange extensions of simulated tempering method},
  doi     = {10.1063/1.1766015},
  pages   = {2491},
  volume  = {121},
  journal = {J. Chem. Phys.},
  year    = {2004},
}

@Article{Moradi_DrivenMetaD_JPCL2013,
  author   = {Moradi, Mahmoud and Tajkhorshid, Emad},
  title    = {{Driven Metadynamics: Reconstructing Equilibrium Free Energies from Driven Adaptive-Bias Simulations}},
  doi      = {10.1021/jz400816x},
  issn     = {1948-7185},
  number   = {11},
  pages    = {1882--1887},
  volume   = {4},
  abstract = {{We present a novel free-energy calculation method that constructively integrates two distinct classes of nonequilibrium sampling techniques, namely, driven (e.g., steered molecular dynamics) and adaptive-bias (e.g., metadynamics) methods. By employing nonequilibrium work relations, we design a biasing protocol with an explicitly time- and history-dependent bias that uses on-the-fly work measurements to gradually flatten the free-energy surface. The asymptotic convergence of the method is discussed, and several relations are derived for free-energy reconstruction and error estimation. Isomerization reaction of an atomistic polyproline peptide model is used to numerically illustrate the superior efficiency and faster convergence of the method compared with its adaptive-bias and driven components in isolation.}},
  journal  = {J. Phys. Chem. Lett.},
  pmcid    = {PMC3688312},
  pmid     = {23795244},
  year     = {2013},
}

@Article{woodard_conditions_2009,
  author   = {Dawn B. Woodard},
  title    = {Conditions for rapid mixing of parallel and simulated tempering on multimodal distributions},
  doi      = {10.1214/08-aap555},
  number   = {2},
  pages    = {617--640},
  volume   = {19},
  abstract = {We give conditions under which a Markov chain constructed via parallel or simulated tempering is guaranteed to be rapidly mixing, which are applicable to a wide range of multimodal distributions arising in Bayesian statistical inference and statistical mechanics. We provide lower bounds on the spectral gaps of parallel and simulated tempering. These bounds imply a single set of sufficient conditions for rapid mixing of both techniques. A direct consequence of our results is rapid mixing of parallel and simulated tempering for several normal mixture models, and for the mean-field Ising model.},
  journal  = {Ann. Appl. Prob.},
  month    = apr,
  year     = {2009},
}

@Article{doi:10.1146/annurev-physchem-042018-052340,
  author   = {Bernetti, Mattia and Masetti, Matteo and Rocchia, Walter and Cavalli, Andrea},
  title    = {Kinetics of Drug Binding and Residence Time},
  doi      = {10.1146/annurev-physchem-042018-052340},
  eprint   = {https://doi.org/10.1146/annurev-physchem-042018-052340},
  number   = {1},
  pages    = {143-171},
  url      = {https://doi.org/10.1146/annurev-physchem-042018-052340},
  volume   = {70},
  abstract = {The kinetics of drug binding and unbinding is assuming an increasingly crucial role in the long, costly process of bringing a new medicine to patients. For example, the time a drug spends in contact with its biological target is known as residence time (the inverse of the kinetic constant of the drug-target unbinding, 1/koff). Recent reports suggest that residence time could predict drug efficacy in vivo, perhaps even more effectively than conventional thermodynamic parameters (free energy, enthalpy, entropy). There are many experimental and computational methods for predicting drug-target residence time at an early stage of drug discovery programs. Here, we review and discuss the methodological approaches to estimating drug binding kinetics and residence time. We first introduce the theoretical background of drug binding kinetics from a physicochemical standpoint. We then analyze the recent literature in the field, starting from the experimental methodologies and applications thereof and moving to theoretical and computational approaches to the kinetics of drug binding and unbinding. We acknowledge the central role of molecular dynamics and related methods, which comprise a great number of the computational methods and applications reviewed here. However, we also consider kinetic Monte Carlo. We conclude with the outlook that drug (un)binding kinetics may soon become a go/no go step in the discovery and development of new medicines.},
  journal  = {Annu. Rev. Phys. Chem.},
  pmid     = {30786217},
  year     = {2019},
}

@InCollection{Bussi2020,
  author    = {Giovanni Bussi and Alessandro Laio and Pratyush Tiwary},
  booktitle = {Handbook of Materials Modeling},
  title     = {Metadynamics: A Unified Framework for Accelerating Rare Events and Sampling Thermodynamics and Kinetics},
  doi       = {10.1007/978-3-319-44677-6_49},
  pages     = {565--595},
  publisher = {Springer International Publishing},
  url       = {https://doi.org/10.1007/978-3-319-44677-6_49},
  year      = {2020},
}

@Article{Berg1992_Multicanonical,
  author    = {Berg, Bernd A. and Neuhaus, Thomas},
  title     = {Multicanonical ensemble: A new approach to simulate first-order phase transitions},
  doi       = {10.1103/physrevlett.68.9},
  issn      = {0031-9007},
  number    = {1},
  pages     = {9–12},
  url       = {http://dx.doi.org/10.1103/PhysRevLett.68.9},
  volume    = {68},
  journal   = {Phys. Rev. Lett.},
  month     = {Jan},
  publisher = {American Physical Society (APS)},
  year      = {1992},
}

@Article{Tiwary-PRL-2013,
  author        = {Tiwary, Pratyush and Parrinello, Michele},
  title         = {From Metadynamics to Dynamics},
  doi           = {10.1103/physrevlett.111.230602},
  issn          = {1079-7114},
  number        = {23},
  pages         = {230602},
  url           = {http://dx.doi.org/10.1103/PhysRevLett.111.230602},
  volume        = {111},
  bdsk-url-1    = {http://dx.doi.org/10.1103/PhysRevLett.111.230602},
  bdsk-url-2    = {http://dx.doi.org/10.1103/physrevlett.111.230602},
  date-added    = {2014-06-17 15:38:41 +0000},
  date-modified = {2015-07-26 12:14:50 +0000},
  journal       = {Phys. Rev. Lett.},
  month         = {Dec},
  publisher     = {American Physical Society (APS)},
  year          = {2013},
}

@Article{Fu2016,
  author               = {Fu, Haohao and Shao, Xueguang and Chipot, Christophe and Cai, Wensheng},
  title                = {Extended Adaptive Biasing Force algorithm. An on-the-fly implementation for accurate free-energy calculations.},
  doi                  = {10.1021/acs.jctc.6b00447},
  issn                 = {1549-9626},
  issue                = {8},
  pages                = {3506--3513},
  volume               = {12},
  abstract             = {Proper use of the adaptive biasing force (ABF) algorithm in free-energy calculations needs certain prerequisites to be met, namely, that the Jacobian for the metric transformation and its first derivative be available and the coarse variables be independent and fully decoupled from any holonomic constraint or geometric restraint, thereby limiting singularly the field of application of the approach. The extended ABF (eABF) algorithm circumvents these intrinsic limitations by applying the time-dependent bias onto a fictitious particle coupled to the coarse variable of interest by means of a stiff spring. However, with the current implementation of eABF in the popular molecular dynamics engine NAMD, a trajectory-based post-treatment is necessary to derive the underlying free-energy change. Usually, such a posthoc analysis leads to a decrease in the reliability of the free-energy estimates due to the inevitable loss of information, as well as to a drop in efficiency, which stems from substantial read-write accesses to file systems. We have developed a user-friendly, on-the-fly code for performing eABF simulations within NAMD. In the present contribution, this code is probed in eight illustrative examples. The performance of the algorithm is compared with traditional ABF, on the one hand, and the original eABF implementation combined with a posthoc analysis, on the other hand. Our results indicate that the on-the-fly eABF algorithm (i) supplies the correct free-energy landscape in those critical cases where the coarse variables at play are coupled to either each other or to geometric restraints or holonomic constraints, (ii) greatly improves the reliability of the free-energy change, compared to the outcome of a posthoc analysis, and (iii) represents a negligible additional computational effort compared to regular ABF. Moreover, in the proposed implementation, guidelines for choosing two parameters of the eABF algorithm, namely the stiffness of the spring and the mass of the fictitious particles, are proposed. The present on-the-fly eABF implementation can be viewed as the second generation of the ABF algorithm, expected to be widely utilized in the theoretical investigation of recognition and association phenomena relevant to physics, chemistry, and biology.},
  citation-subset      = {IM},
  country              = {United States},
  created              = {2016-08-09},
  issn-linking         = {1549-9618},
  journal              = {J. Chem. Theory Comput.},
  journal-abbreviation = {J Chem Theory Comput},
  month                = {Aug},
  nlm-id               = {101232704},
  owner                = {NLM},
  pmid                 = {27398726},
  pubmodel             = {Print-Electronic},
  status               = {In-Data-Review},
  year                 = {2016},
}

@Article{Fiorin2013,
  author  = {Fiorin, Giacomo and Klein, Michael L. and H\'enin, J\'er\^ome},
  title   = {Using collective variables to drive molecular dynamics simulations},
  doi     = {10.1080/00268976.2013.813594},
  eprint  = {http://www.tandfonline.com/doi/pdf/10.1080/00268976.2013.813594},
  number  = {22-23},
  pages   = {3345-3362},
  url     = {http://www.tandfonline.com/doi/abs/10.1080/00268976.2013.813594},
  volume  = {111},
  journal = {Mol. Phys.},
  year    = {2013},
}

@TechReport{Darve2000,
  author      = {Darve, Eric and Pohorille, Andrew},
  institution = {Center for Turbulence Research Annual Research Briefs},
  title       = {Calculating free energies using scaled-force molecular dynamics algorithm},
  doi         = {10.1080/08927020211975},
  owner       = {jhenin},
  timestamp   = {2014.03.13},
  year        = {2000},
}

@Article{Darve2001,
  author  = {Darve, E. and Pohorille, A.},
  title   = {Calculating free energies using average force},
  doi     = {10.1063/1.1410978},
  pages   = {9169--9183},
  volume  = {115},
  file    = {Darve Pohorille-JCP 2001.pdf:nergy_configurational/ABF/Darve Pohorille-JCP 2001.pdf:PDF},
  journal = {J. Chem. Phys.},
  year    = {2001},
}

@Article{Darve2002,
  author    = {Darve, E. and Wilson, M. and Pohorille, A.},
  title     = {Calculating Free Energies Using a Scaled-Force Molecular Dynamics Algorithm},
  doi       = {10.1080/08927020211975},
  pages     = {113-144},
  volume    = {28},
  comment   = {Free energy},
  journal   = {Mol. Sim.},
  owner     = {jhenin},
  timestamp = {2007.03.10},
  year      = {2002},
}
% Hamiltonian exchange

@Article{sugita-kitao-okamoto:jcp:2000:hamiltonian-exchange,
  author  = {Yugi Sugita and Akio Kitao and Yuko Okamoto},
  title   = {Multidimensional replica-exchange method for free-energy calculations},
  doi     = {10.1063/1.1308516},
  pages   = {6042},
  volume  = {113},
  journal = {J. Chem. Phys.},
  year    = {2000},
}

@Article{Awasthi_MetaD-US-5_JCC2016,
  author   = {Awasthi, Shalini and Kapil, Venkat and Nair, Nisanth N.},
  title    = {{Sampling free energy surfaces as slices by combining umbrella sampling and metadynamics}},
  doi      = {10.1002/jcc.24349},
  issn     = {1096-987X},
  number   = {16},
  pages    = {1413--1424},
  volume   = {37},
  abstract = {{Metadynamics (MTD) is a very powerful technique to sample high-dimensional free energy landscapes, and due to its self-guiding property, the method has been successful in studying complex reactions and conformational changes. MTD sampling is based on filling the free energy basins by biasing potentials and thus for cases with flat, broad, and unbound free energy wells, the computational time to sample them becomes very large. To alleviate this problem, we combine the standard Umbrella Sampling (US) technique with MTD to sample orthogonal collective variables (CVs) in a simultaneous way. Within this scheme, we construct the equilibrium distribution of CVs from biased distributions obtained from independent MTD simulations with umbrella potentials. Reweighting is carried out by a procedure that combines US reweighting and Tiwary–Parrinello MTD reweighting within the Weighted Histogram Analysis Method (WHAM). The approach is ideal for a controlled sampling of a CV in a MTD simulation, making it computationally efficient in sampling flat, broad, and unbound free energy surfaces. This technique also allows for a distributed sampling of a high-dimensional free energy surface, further increasing the computational efficiency in sampling. We demonstrate the application of this technique in sampling high-dimensional surface for various chemical reactions using ab initio and QM/MM hybrid molecular dynamics simulations. Further, to carry out MTD bias reweighting for computing forward reaction barriers in ab initio or QM/MM simulations, we propose a computationally affordable approach that does not require recrossing trajectories. © 2016 Wiley Periodicals, Inc.}},
  journal  = {J. Comput. Chem.},
  pmid     = {27059305},
  year     = {2016},
}

@Software{samuel_d_lotz_2020_4270219,
  author    = {Samuel D. Lotz and Nazanin Donyapour and Alex Dickson and Tom Dixon and Nicole Roussey and Rob Hall},
  title     = {ADicksonLab/wepy: 1.0.0 Major version release},
  doi       = {10.5281/zenodo.4270219},
  url       = {https://doi.org/10.5281/zenodo.4270219},
  version   = {v1.0.0},
  month     = aug,
  publisher = {Zenodo},
  year      = {2020},
}

@Article{reweighting_mixture_distribution,
  author        = {Shirts, Michael R.},
  title         = {Reweighting from the Mixture Distribution as a Better Way to Describe the {{Multistate Bennett Acceptance Ratio}}},
  eprint        = {1704.00891},
  eprinttype    = {arxiv},
  abstract      = {The multistate Bennett Acceptance Ratio is provably the lowest variance unbiased estimator of both free energies and ensemble averages, and has a number of important advantages over previous methods, such as WHAM. Despite its advantages, the original MBAR paper was rather dense and mathematically complicated, limiting the extent to which people could expand and apply it. We present here a different way to think about MBAR that is much more intuitive and makes it clearer why the method works so well.},
  archiveprefix = {arXiv},
  journal       = {ArXiv170400891 Cond-Mat},
  keywords      = {Condensed Matter - Statistical Mechanics},
  month         = dec,
  primaryclass  = {cond-mat},
  year          = {2017},
}

@Article{Bonomi_StructEnsembleDeterm_Review_COSB2017,
  author   = {Bonomi, Massimiliano and Heller, Gabriella T. and Camilloni, Carlo and Vendruscolo, Michele},
  title    = {{Principles of protein structural ensemble determination}},
  doi      = {10.1016/j.sbi.2016.12.004},
  issn     = {0959-440X},
  pages    = {106--116},
  volume   = {42},
  abstract = {{The biological functions of protein molecules are intimately dependent on their conformational dynamics. This aspect is particularly evident for disordered proteins, which constitute perhaps one-third of the human proteome. Therefore, structural ensembles often offer more useful representations of proteins than individual conformations. Here, we describe how the well-established principles of protein structure determination should be extended to the case of protein structural ensembles determination. These principles concern primarily how to deal with conformationally heterogeneous states, and with experimental measurements that are averaged over such states and affected by a variety of errors. We first review the growing literature of recent methods that combine experimental and computational information to model structural ensembles, highlighting their similarities and differences. We then address some conceptual problems in the determination of structural ensembles and define future goals towards the establishment of objective criteria for the comparison, validation, visualization and dissemination of such ensembles.}},
  journal  = {Curr. Opin. Struct. Biol.},
  pmid     = {28063280},
  year     = {2017},
}

@Article{Zwanzig1954,
  author    = {Zwanzig, R. W.},
  title     = {High-temperature equation of state by a perturbation method. I. Nonpolar gases},
  pages     = {1420-1426},
  volume    = {22},
  file      = {Zwanzig JCP 1954.pdf:nergy_alchemical/Zwanzig JCP 1954.pdf:PDF},
  journal   = {J. Chem. Phys.},
  owner     = {jhenin},
  timestamp = {2007.04.01},
  year      = {1954},
  doi       = {10.1063/1.1740409},
}

@Article{Roux_MaxEnt_JCP2013,
  author   = {Roux, Benoît and Weare, Jonathan},
  title    = {{On the statistical equivalence of restrained-ensemble simulations with the maximum entropy method}},
  doi      = {10.1063/1.4792208},
  issn     = {0021-9606},
  number   = {8},
  pages    = {084107},
  volume   = {138},
  abstract = {{An issue of general interest in computer simulations is to incorporate information from experiments into a structural model. An important caveat in pursuing this goal is to avoid corrupting the resulting model with spurious and arbitrary biases. While the problem of biasing thermodynamic ensembles can be formulated rigorously using the maximum entropy method introduced by Jaynes, the approach can be cumbersome in practical applications with the need to determine multiple unknown coefficients iteratively. A popular alternative strategy to incorporate the information from experiments is to rely on restrained-ensemble molecular dynamics simulations. However, the fundamental validity of this computational strategy remains in question. Here, it is demonstrated that the statistical distribution produced by restrained-ensemble simulations is formally consistent with the maximum entropy method of Jaynes. This clarifies the underlying conditions under which restrained-ensemble simulations will yield results that are consistent with the maximum entropy method.}},
  journal  = {J. Chem. Phys.},
  pmcid    = {PMC3598863},
  pmid     = {23464140},
  year     = {2013},
}

@Article{Gao_ITS_2008,
  author    = {Gao, Yi Qin},
  title     = {{An integrate-over-temperature approach for enhanced sampling}},
  doi       = {10.1063/1.2825614},
  issn      = {0021-9606},
  number    = {6},
  pages     = {064105},
  volume    = {128},
  abstract  = {{A simple method is introduced to achieve efficient random walking in the energy space in molecular dynamics simulations which thus enhances the sampling over a large energy range. The approach is closely related to multicanonical and replica exchange simulation methods in that it allows configurations of the system to be sampled in a wide energy range by making use of Boltzmann distribution functions at multiple temperatures. A biased potential is quickly generated using this method and is then used in accelerated molecular dynamics simulations.}},
  journal   = {J. Chem. Phys.},
  local-url = {file://localhost/Users/valsson/Documents/Papers%20Library/The%20Journal%20of%20Chemical%20Physics/2008/Gao-Gao-2008-The%20Journal%20of%20Chemical%20Physics.pdf},
  pmid      = {18282026},
  year      = {2008},
}

@Article{Sidky_ANNSampling_2018,
  author   = {Sidky, Hythem and Whitmer, Jonathan K},
  title    = {{Learning free energy landscapes using artificial neural networks}},
  doi      = {10.1063/1.5018708},
  eprint   = {1712.02840},
  issn     = {0021-9606},
  number   = {10},
  pages    = {104111},
  volume   = {148},
  abstract = {{Existing adaptive bias techniques, which seek to estimate free energies and physical properties from molecular simulations, are limited by their reliance on fixed kernels or basis sets which hinder their ability to efficiently conform to varied free energy landscapes. Further, user-specified parameters are in general non-intuitive yet significantly affect the convergence rate and accuracy of the free energy estimate. Here we propose a novel method, wherein artificial neural networks (ANNs) are used to develop an adaptive biasing potential which learns free energy landscapes. We demonstrate that this method is capable of rapidly adapting to complex free energy landscapes and is not prone to boundary or oscillation problems. The method is made robust to hyperparameters and overfitting through Bayesian regularization which penalizes network weights and auto-regulates the number of effective parameters in the network. ANN sampling represents a promising innovative approach which can resolve complex free energy landscapes in less time than conventional approaches while requiring minimal user input.}},
  journal  = {J. Chem. Phys.},
  pmid     = {29544298},
  year     = {2018},
}

@Article{rosta-hummer:jcp:2009:replica-exchange-efficiency,
  author  = {Edina Rosta and Gerhard Hummer},
  title   = {Error and efficiency of replica exchange molecular dynamics simulations},
  doi     = {10.1063/1.3249608},
  pages   = {165102},
  volume  = {131},
  journal = {J. Chem. Phys.},
  year    = {2009},
}

@Article{invernizzi2020unified,
  author  = {Invernizzi, Michele and Piaggi, Pablo Miguel and Parrinello, Michele},
  title   = {Unified approach to enhanced sampling},
  doi     = {10.1103/PhysRevX.10.041034},
  pages   = {041034},
  volume  = {10},
  journal = {Phys. Rev. X},
  year    = {2020},
}

@Article{shirts_comparison_2005,
  author  = {Michael R. Shirts and Vijay S. Pande},
  title   = {Comparison of efficiency and bias of free energies computed by exponential averaging, the Bennett acceptance ratio, and thermodynamic integration},
  doi     = {10.1063/1.1873592},
  eprint  = {https://doi.org/10.1063/1.1873592},
  number  = {14},
  pages   = {144107},
  url     = {https://doi.org/10.1063/1.1873592},
  volume  = {122},
  journal = {J. Chem. Phys.},
  year    = {2005},
}

@Article{park-khalili-araghi-tajkhorshid-schulten-03,
  author  = {Park, S. and Khalili-Araghi, F. and Tajkhorshid, E. and Schulten, K.},
  title   = {Free energy calculation from steered molecular dynamics simulations using Jarzynski's equality},
  doi     = {10.1063/1.1590311},
  number  = {6},
  pages   = {3559-3566},
  volume  = {119},
  journal = {J. Chem. Phys.},
  year    = {2003},
}

@Article{reinhardt:cpl:2000:step-size-adjustment,
  author  = {Mark A. Miller and Lynn M. Amon and William P. Reinhardt},
  title   = {Should one adjust the maximum step size in a {Metropolis Monte Carlo} simulation?},
  doi     = {10.1016/s0009-2614(00)01217-3},
  pages   = {278},
  volume  = {331},
  journal = {Chem. Phys. Lett.},
  year    = {2000},
}

@Article{bussi.equilibriummetadynamics,
  author    = {Bussi, Giovanni and Laio, Alessandro and Parrinello, Michele},
  title     = {Equilibrium Free Energies from Nonequilibrium Metadynamics},
  doi       = {10.1103/physrevlett.96.090601},
  issue     = {9},
  pages     = {090601},
  volume    = {96},
  journal   = {Phys. Rev. Lett.},
  month     = {Mar},
  numpages  = {4},
  publisher = {American Physical Society},
  year      = {2006},
}

@Article{rosta-hummer:jcp:2010:simulated-tempering-efficiency,
  author  = {Rosta, Edina and Hummer, Gerhard},
  title   = {{Error and efficiency of simulated tempering simulations}},
  doi     = {10.1063/1.3290767},
  pages   = {34102},
  volume  = {132},
  journal = {J. Chem. Phys.},
  year    = {2010},
}

@Article{Yonezawa_MulticanonicalMetaD_2011,
  author   = {Yonezawa, Yasushige and Shimoyama, Hiromitsu and Nakamura, Haruki},
  title    = {{Multicanonical molecular dynamics simulations combined with Metadynamics for the free energy landscape of a biomolecular system with high energy barriers}},
  doi      = {10.1016/j.cplett.2010.11.061},
  issn     = {0009-2614},
  number   = {4-6},
  pages    = {598--602},
  volume   = {501},
  abstract = {{Multicanonical molecular-dynamics (McMD) simulation and Metadynamics (MetaD) are useful for obtaining the free-energies, and can be mutually complementary. We combined McMD with MetaD, and applied it to the conformational free energy calculations of a proline dipeptide. First, MetaD was performed along the dihedral angle at the prolyl bond and we obtained a coarse biasing potential. After adding the biasing potential to the dihedral angle potential energy, we conducted McMD with the modified potential energy. Enhanced sampling was achieved for all degrees-of-freedom, and the sampling of the dihedral angle space was facilitated. After reweighting, we obtained an accurate free energy landscape.}},
  journal  = {Chem. Phys. Lett.},
  year     = {2011},
}

@Article{Barducci-PRL-2008,
  author        = {Barducci, Alessandro and Bussi, Giovanni and Parrinello, Michele},
  title         = {Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method},
  doi           = {10.1103/physrevlett.100.020603},
  number        = {2},
  pages         = {020603},
  volume        = {100},
  bdsk-url-1    = {http://dx.doi.org/10.1103/PhysRevLett.100.020603},
  date-added    = {2014-10-10 10:10:47 +0000},
  date-modified = {2015-03-25 10:53:11 +0000},
  journal       = {Phys. Rev. Lett.},
  month         = {Jan},
  publisher     = {American Physical Society},
  year          = {2008},
}

@Article{doi:10.1021/acs.jctc.5b00737,
  author  = {Zimmerman, Maxwell I. and Bowman, Gregory R.},
  title   = {FAST Conformational Searches by Balancing Exploration/Exploitation Trade-Offs},
  doi     = {10.1021/acs.jctc.5b00737},
  eprint  = {https://doi.org/10.1021/acs.jctc.5b00737},
  number  = {12},
  pages   = {5747-5757},
  url     = {https://doi.org/10.1021/acs.jctc.5b00737},
  volume  = {11},
  journal = {J. Chem. Theory Comput.},
  pmid    = {26588361},
  year    = {2015},
}

@Article{lelievre-rousset-stoltz-12,
  author  = {Leli\`evre, T. and Rousset, M. and Stoltz, G.},
  title   = {Langevin dynamics with constraints and computation of free energy differences},
  doi     = {10.1090/s0025-5718-2012-02594-4},
  number  = {280},
  pages   = {2071-2125},
  volume  = {81},
  journal = {Math. Comput.},
  year    = {2012},
}

@Article{doi:10.1146/annurev-biophys-070816-033834,
  author   = {Zuckerman, Daniel M. and Chong, Lillian T.},
  title    = {Weighted Ensemble Simulation: Review of Methodology, Applications, and Software},
  doi      = {10.1146/annurev-biophys-070816-033834},
  eprint   = {https://doi.org/10.1146/annurev-biophys-070816-033834},
  number   = {1},
  pages    = {43-57},
  url      = {https://doi.org/10.1146/annurev-biophys-070816-033834},
  volume   = {46},
  abstract = {The weighted ensemble (WE) methodology orchestrates quasi-independent parallel simulations run with intermittent communication that can enhance sampling of rare events such as protein conformational changes, folding, and binding. The WE strategy can achieve superlinear scaling—the unbiased estimation of key observables such as rate constants and equilibrium state populations to greater precision than would be possible with ordinary parallel simulation. WE software can be used to control any dynamics engine, such as standard molecular dynamics and cell-modeling packages. This article reviews the theoretical basis of WE and goes on to describe successful applications to a number of complex biological processes—protein conformational transitions, (un)binding, and assembly processes, as well as cell-scale processes in systems biology. We furthermore discuss the challenges that need to be overcome in the next phase of WE methodological development. Overall, the combined advances in WE methodology and software have enabled the simulation of long-timescale processes that would otherwise not be practical on typical computing resources using standard simulation.},
  journal  = {Annu Rev Bioph Biom},
  pmid     = {28301772},
  year     = {2017},
}

@Article{Camilloni_RAM_2013,
  author   = {Camilloni, Carlo and Cavalli, Andrea and Vendruscolo, Michele},
  title    = {{Replica-Averaged Metadynamics}},
  doi      = {10.1021/ct4006272},
  issn     = {1549-9618},
  number   = {12},
  pages    = {5610--5617},
  volume   = {9},
  abstract = {{A statistical mechanics description of complex molecular systems involves the determination of ensembles of conformations that represent their Boltzmann distributions. The observable properties of these systems can be then predicted by calculating averages over such ensembles. In principle, given accurate energy functions and efficient sampling methods, these ensembles can be generated by molecular dynamics simulations. In practice, however, often the energy functions are known only approximately and the sampling can be carried out only in a limited manner. We describe here a method that enables to increase simultaneously both the quality of the energy functions and of the extent of the sampling in a system-dependent manner. The method is based on the incorporation of experimental data as replica-averaged structural restraints in molecular dynamics simulations and exploits the metadynamics framework to enhance the sampling. The application to the case of α-conotoxin SI, a 13-residue peptide that has been characterized extensively by experimental measurements, shows that the approach that we describe enables accurate free energy landscapes to be generated. The analysis of these landscapes indicates the presence of a low population state in equilibrium with the native state in which the only aromatic residue of α-conotoxin SI is exposed to the solvent, which is a feature that may predispose the peptide to interact with its partners.}},
  journal  = {J. Chem. Theory Comput.},
  pmid     = {26592295},
  year     = {2013},
}

@Article{doi:10.1063/1.2740261,
  author  = {Hinrichs,Nina Singhal and Pande,Vijay S.},
  title   = {Calculation of the distribution of eigenvalues and eigenvectors in Markovian state models for molecular dynamics},
  doi     = {10.1063/1.2740261},
  eprint  = {https://doi.org/10.1063/1.2740261},
  number  = {24},
  pages   = {244101},
  url     = {https://doi.org/10.1063/1.2740261},
  volume  = {126},
  journal = {J. Chem. Phys.},
  year    = {2007},
}

@Article{Bal_ReweightedJarzynski_2021,
  author  = {Bal, Kristof M.},
  title   = {{Reweighted Jarzynski Sampling: Acceleration of Rare Events and Free Energy Calculation with a Bias Potential Learned from Nonequilibrium Work}},
  doi     = {10.1021/acs.jctc.1c00574},
  issn    = {1549-9618},
  journal = {J. Chem. Theory Comput.},
  pmid    = {34714088},
  year    = {2021},
}

@Article{okamoto:biopolymers:2001:generalized-ensemble,
  author  = {Ayori Mitsutake and Yuji Sugita and Yuko Okamoto},
  title   = {Generalized-ensemble algorithms for molecular simulations of biopolymers},
  pages   = {96--123},
  volume  = {60},
  journal = {Biopolymers},
  year    = {2001},
  doi = {10.1002/1097-0282(2001)60:2<96::AID-BIP1007>3.0.CO;2-F}
}

@Article{Lu2003,
  author    = {Nandou Lu and David A. Kofke and Thomas B. Woolf},
  title     = {Improving the efficiency and reliability of free energy perturbation calculations using overlap sampling methods},
  doi       = {10.1002/jcc.10369},
  number    = {1},
  pages     = {28--40},
  volume    = {25},
  journal   = {J. Comput. Chem.},
  publisher = {Wiley},
  year      = {2003},
}
		
% Efficiency studies

@Article{park-pande:pre:2007:choosing-weights-simulated-tempering,
  author  = {Sanghyun Park and Vijay S. Pande},
  title   = {Choosing weights for simulated tempering},
  doi     = {10.1103/physreve.76.016703},
  pages   = {016703},
  volume  = {76},
  journal = {Phys. Rev. E},
  year    = {2007},
}

@Article{park:pre:2008:simulated-tempering,
  author  = {Park, Sanghyun},
  title   = {{Comparison of the serial and parallel algorithms of generalized ensemble simulations: An analytical approach}},
  doi     = {10.1103/physreve.77.016709},
  pages   = {16709},
  volume  = {77},
  journal = {Phys. Rev. E},
  year    = {2008},
}

@Article{doi:10.1063/1.1738640,
  author  = {Faradjian,Anton K. and Elber,Ron},
  title   = {Computing time scales from reaction coordinates by milestoning},
  doi     = {10.1063/1.1738640},
  eprint  = {https://doi.org/10.1063/1.1738640},
  number  = {23},
  pages   = {10880-10889},
  url     = {https://doi.org/10.1063/1.1738640},
  volume  = {120},
  journal = {J. Chem. Phys.},
  year    = {2004},
}

@Article{rhee-pande:biophys-j:2003:multiplexed-replica-exchange,
  author  = {Young Min Rhee and Vijay S. Pande},
  title   = {Multiplexed-replica exchange molecular dynamics method for protein folding simulation},
  doi     = {10.1016/s0006-3495(03)74897-8},
  pages   = {775--786},
  volume  = {84},
  journal = {Biophys. J.},
  year    = {2003},
}

@Article{nadler-hansmann:pre:2007:optimized-replica-exchange-moves,
  author  = {Walter Nadler and Ulrich H. E. Hansmann},
  title   = {Optimized replica exchange moves for molecular dynamics},
  doi     = {10.1103/physreve.76.057102},
  pages   = {057102},
  volume  = {76},
  journal = {Phys. Rev. E},
  year    = {2007},
}
	
% elaborations on expanded ensembles and replica exchange

@Article{mitsutake-sugita-okamoto:2003:remuca,
  author  = {Ayori Mitsutake and Yuji Sugita and Yuko Okamoto},
  title   = {Replica-exchange multicanonical and multicanonical replica-exchange {Monte Carlo} simulations of peptides. {I.} {Formulation} and benchmark test},
  doi     = {10.1063/1.1555847},
  pages   = {6664},
  volume  = {118},
  journal = {J. Chem. Phys.},
  year    = {2003},
}

@Article{Humphrey1996,
  author      = {W. Humphrey and A. Dalke and K. Schulten},
  title       = {VMD: visual molecular dynamics},
  doi         = {10.1016/0263-7855(96)00018-5},
  number      = {1},
  pages       = {33--8, 27-8},
  volume      = {14},
  abstract    = {VMD is a molecular graphics program designed for the display and analysis of molecular assemblies, in particular biopolymers such as proteins and nucleic acids. VMD can simultaneously display any number of structures using a wide variety of rendering styles and coloring methods. Molecules are displayed as one or more "representations," in which each representation embodies a particular rendering method and coloring scheme for a selected subset of atoms. The atoms displayed in each representation are chosen using an extensive atom selection syntax, which includes Boolean operators and regular expressions. VMD provides a complete graphical user interface for program control, as well as a text interface using the Tcl embeddable parser to allow for complex scripts with variable substitution, control loops, and function calls. Full session logging is supported, which produces a VMD command script for later playback. High-resolution raster images of displayed molecules may be produced by generating input scripts for use by a number of photorealistic image-rendering applications. VMD has also been expressly designed with the ability to animate molecular dynamics (MD) simulation trajectories, imported either from files or from a direct connection to a running MD simulation. VMD is the visualization component of MDScope, a set of tools for interactive problem solving in structural biology, which also includes the parallel MD program NAMD, and the MDCOMM software used to connect the visualization and simulation programs. VMD is written in C++, using an object-oriented design; the program, including source code and extensive documentation, is freely available via anonymous ftp and through the World Wide Web.},
  institution = {Theoretical Biophysics Group, University of Illinois, Urbana 61801, USA.},
  journal     = {J. Mol. Graph.},
  keywords    = {Computer Graphics; Computer Simulation; Computers; Models, Molecular; Nucleic Acids; Proteins; User-Computer Interface},
  owner       = {grace},
  pii         = {0263785596000185},
  pmid        = {8744570},
  timestamp   = {2008.02.27},
  year        = {1996},
}

@Software{Case_2021,
  author = {D.A. Case and H.M. Aktulga and K. Belfon and I.Y. Ben-Shalom and S.R. Brozell and D.S. Cerutti and T.E. Cheatham and III and V.W.D. Cruzeiro and T.A. Darden and R.E. Duke and G. Giambasu and M.K. Gilson and H. Gohlke and A.W. Goetz and R. Harris and S. Izadi and S.A. Izmailov and C. Jin and K. Kasavajhala and M.C. Kaymak and E. King and A. Kovalenko and T. Kurtzman and T.S. Lee and S. LeGrand and P. Li and C. Lin and J. Liu and T. Luchko and R. Luo and M. Machado and V. Man and M. Manathunga and K.M. Merz and Y. Miao and O. Mikhailovskii and G. Monard and H. Nguyen and K.A. O’Hearn and A. Onufriev and F. Pan and S. Pantano and R. Qi and A. Rahnamoun and D.R. Roe and A. Roitberg and C. Sagui and S. Schott-Verdugo and J. Shen and C.L. Simmerling and N.R. Skrynnikov and J. Smith and J. Swails and R.C. Walker and J. Wang and H. Wei and R.M. Wolf and X. Wu and Y. Xue and D.M. York and S. Zhao and and P.A. Kollman},
  title  = {Amber 2021},
  year   = {2021},
}

@Article{lelievre-rousset-stoltz-08,
  author  = {Leli\`evre, T. and Rousset, M. and Stoltz, G.},
  title   = {Long-time convergence of an Adaptive Biasing Force method},
  doi     = {10.1088/0951-7715/21/6/001},
  pages   = {1155-1181},
  volume  = {21},
  journal = {Nonlinearity},
  year    = {2008},
}

@Article{Zheng_OSRW-1_PNAS2008,
  author   = {Zheng, Lianqing and Chen, Mengen and Yang, Wei},
  title    = {{Random walk in orthogonal space to achieve efficient free-energy simulation of complex systems}},
  doi      = {10.1073/pnas.0810631106},
  issn     = {0027-8424},
  number   = {51},
  pages    = {20227--20232},
  volume   = {105},
  abstract = {{In the past few decades, many ingenious efforts have been made in the development of free-energy simulation methods. Because complex systems often undergo nontrivial structural transition during state switching, achieving efficient free-energy calculation can be challenging. As identified earlier, the “Hamiltonian” lagging, which reveals the fact that necessary structural relaxation falls behind the order parameter move, has been a primary problem for generally low free-energy simulation efficiency. Here, we propose an algorithm by achieving a random walk in both the order parameter space and its generalized force space; thereby, the order parameter move and the required conformational relaxation can be efficiently synchronized. As demonstrated in both the alchemical transition and the conformational transition, a leapfrog improvement in free-energy simulation efficiency can be obtained; for instance, (i) it allows us to solve a notoriously challenging problem: accurately predicting the pKa value of a buried titratable residue, Asp-66, in the interior of the V66E staphylococcal nuclease mutant, and (ii) it allows us to gain superior efficiency over the metadynamics algorithm.}},
  journal  = {Proc. Natl. Acad. Sci.},
  pmcid    = {PMC2629259},
  pmid     = {19075242},
  year     = {2008},
}

@Article{10.1063/1.5027392,
  author   = {Ortíz, A Pérez de Alba and Tiwari, A and Puthenkalathil, R C and Ensing, Bernd},
  title    = {{Advances in enhanced sampling along adaptive paths of collective variables}},
  doi      = {10.1063/1.5027392},
  issn     = {0021-9606},
  number   = {7},
  pages    = {072320},
  volume   = {149},
  abstract = {{Study of complex activated molecular transitions by molecular dynamics (MD) simulation can be a daunting task, especially when little knowledge is available on the reaction coordinate describing the mechanism of the process. Here, we assess the path-metadynamics enhanced sampling approach in combination with force field and ab initio [density functional theory (DFT)] MD simulations of conformational and chemical transitions that require three or more collective variables (CVs) to describe the processes. We show that the method efficiently localizes the average transition path of each process and simultaneously obtains the free energy profile along the path. The new multiple-walker implementation greatly speeds-up the calculation, with an almost trivial scaling of the number of parallel replicas. Increasing the dimensionality by expanding the set of CVs leads to a less than linear increase in the computational cost, as shown by applying the method to a conformational change in increasingly longer polyproline peptides. Combined with DFT-MD to model acid (de-)protonation in explicit water solvent, the transition path and associated free energy profile were obtained in less than 100 ps of simulation. A final application to hydrogen fuel production catalyzed by a hydrogenase enzyme showcases the unique mechanistic insight and chemical understanding that can be obtained from the average transition path.}},
  journal  = {J. Chem. Phys.},
  pmid     = {30134692},
  year     = {2018},
}

@Article{katzberger-trebst-huse-troyer:j-stat-mech:2006:feedback-optimized-parallel-tempering,
  author  = {Helmut G. Katzgraber and Simon Trebst and David A. Huse and Matthias Troyer},
  title   = {Feedback-optimized parallel tempering {Monte Carlo}},
  doi     = {10.1088/1742-5468/2006/03/p03018},
  pages   = {03018},
  volume  = {2006},
  journal = {J. Stat. Mech.},
  year    = {2006},
}

@Article{Wang2018_FA-MetaD,
  author    = {Wang, Yong and Valsson, Omar and Tiwary, Pratyush and Parrinello, Michele and Lindorff-Larsen, Kresten},
  title     = {Frequency adaptive metadynamics for the calculation of rare-event kinetics},
  doi       = {10.1063/1.5024679},
  issn      = {1089-7690},
  number    = {7},
  pages     = {072309},
  url       = {http://dx.doi.org/10.1063/1.5024679},
  volume    = {149},
  journal   = {J. Chem. Phys.},
  month     = {Aug},
  publisher = {AIP Publishing},
  year      = {2018},
}

@Article{Cao2014,
  author  = {Cao, Lingling and Stoltz, Gabriel and Lelièvre, Tony and Marinica, Mihai-Cosmin and Athènes, Manuel},
  title   = {Free energy calculations from adaptive molecular dynamics simulations with adiabatic reweighting},
  doi     = {10.1063/1.4866811},
  eid     = {104108},
  number  = {10},
  url     = {http://scitation.aip.org/content/aip/journal/jcp/140/10/10.1063/1.4866811},
  volume  = {140},
  journal = {J. Chem. Phys.},
  year    = {2014},
}

@Article{plumed-nest,
  author  = {{The PLUMED Consortium}},
  title   = {{Promoting transparency and reproducibility in enhanced molecular simulations}},
  doi     = {10.1038/s41592-019-0506-8},
  note    = {{For the full list of researches from the PLUMED Consortium, see \url{https://www.plumed-nest.org/consortium.html}.}},
  pages   = {670--673},
  volume  = {16},
  journal = {Nat. Methods},
  year    = {2019},
}

@Article{Fu_MetaD-eABF_JPCL2018,
  author   = {Fu, Haohao and Zhang, Hong and Chen, Haochuan and Shao, Xueguang and Chipot, Christophe and Cai, Wensheng},
  title    = {{Zooming across the Free-Energy Landscape: Shaving Barriers, and Flooding Valleys}},
  doi      = {10.1021/acs.jpclett.8b01994},
  issn     = {1948-7185},
  number   = {16},
  pages    = {4738--4745},
  volume   = {9},
  abstract = {{A robust importance-sampling algorithm for mapping free-energy surfaces over geometrical variables, coined meta-eABF, is introduced. This algorithm shaves the free-energy barriers and floods valleys by incorporating a history-dependent potential term in the extended adaptive biasing force (eABF) framework. Numerical applications on both toy models and nontrivial examples indicate that meta-eABF explores the free-energy surface significantly faster than either eABF or metadynamics (MtD) alone, without the need to stratify the reaction pathway. In some favorable cases, meta-eABF can be as much as five times faster than other importance-sampling algorithms. Many of the shortcomings inherent to eABF and MtD, like kinetic trapping in regions of configurational space already adequately sampled, the requirement of prior knowledge of the free-energy landscape to set up the simulation, are readily eliminated in meta-eABF. Meta-eABF, therefore, represents an appealing solution for a broad range of applications, especially when both eABF and MtD fail to achieve the desired result.}},
  journal  = {J. Phys. Chem. Lett.},
  pmid     = {30074802},
  year     = {2018},
}

@Article{deem:jcp:1999:balance,
  author  = {Vasilios I. Manousiouthakis and Michael W. Deem},
  title   = {Strict detailed balance is unnecessary in {Monte Carlo} simulation},
  pages   = {2753},
  volume  = {110},
  journal = {J. Chem. Phys.},
  year    = {1999},
  doi = {10.1063/1.477973},
}

@Article{Bilionis-JCompPhys-2012,
  author        = {Bilionis, I. and Koutsourelakis, P.S.},
  title         = {Free energy computations by minimization of Kullback--Leibler divergence: An efficient adaptive biasing potential method for sparse representations},
  doi           = {10.1016/j.jcp.2012.01.033},
  issn          = {0021-9991},
  number        = {9},
  pages         = {3849--3870},
  url           = {http://dx.doi.org/10.1016/j.jcp.2012.01.033},
  volume        = {231},
  bdsk-url-1    = {http://dx.doi.org/10.1016/j.jcp.2012.01.033},
  date-added    = {2014-12-22 09:56:35 +0000},
  date-modified = {2015-03-25 10:53:37 +0000},
  journal       = {J. Comput. Phys.},
  month         = {May},
  publisher     = {Elsevier BV},
  year          = {2012},
}

@Article{Postma1982,
  author    = {Johan P. M. Postma and Herman J. C. Berendsen and Jan R. Haak},
  title     = {Thermodynamics of cavity formation in water. A molecular dynamics study},
  doi       = {10.1039/fs9821700055},
  pages     = {55},
  url       = {https://doi.org/10.1039/fs9821700055},
  volume    = {17},
  journal   = {Faraday Symposia of the Chemical Society},
  publisher = {Royal Society of Chemistry ({RSC})},
  year      = {1982},
}

@Article{TORRIE1977187,
  author   = {G.M. Torrie and J.P. Valleau},
  title    = {Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling},
  doi      = {10.1016/0021-9991(77)90121-8},
  issn     = {0021-9991},
  number   = {2},
  pages    = {187-199},
  url      = {https://www.sciencedirect.com/science/article/pii/0021999177901218},
  volume   = {23},
  abstract = {The free energy difference between a model system and some reference system can easily be written as an ensemble average, but the conventional Monte Carlo methods of obtaining such averages are inadequate for the free-energy case. That is because the Boltzmann-weighted sampling distribution ordinarily used is extremely inefficient for the purpose. This paper describes the use of arbitrary sampling distributions chosen to facilitate such estimates. The methods have been tested successfully on the Lennard-Jones system over a wide range of temperature and density, including the gas-liquid coexistence region, and are found to be extremely powerful and economical.},
  journal  = {J. Comput. Phys.},
  year     = {1977},
}

@Article{Schafer_RewMetaD_2020,
  author    = {Schäfer, Timo M and Settanni, Giovanni},
  title     = {{Data Reweighting in Metadynamics Simulations}},
  doi       = {10.1021/acs.jctc.9b00867},
  issn      = {1549-9618},
  number    = {4},
  pages     = {2042--2052},
  volume    = {16},
  abstract  = {{The data collected along a metadynamics simulation can be used to recover information about the underlying unbiased system by means of a reweighting procedure. Here, we analyze the behavior of several reweighting techniques in terms of the quality of the reconstruction of the underlying unbiased free energy landscape in the early stages of the simulation and propose a simple reweighting scheme that we relate to the other techniques. We then show that the free energy landscape reconstructed from reweighted data can be more accurate than the negative bias potential depending on the reweighting technique, the stage of the simulation, and the adoption of well-tempered or standard metadynamics. While none of the tested reweighting techniques from the literature provides the most accurate results in all the analyzed situations, the one proposed here, in addition to helping simplifying the reweighting procedure, converges quickly and precisely to the underlying free energy surface in all the considered cases, thus allowing for an efficient use of limited simulation data.}},
  journal   = {J. Chem. Theory Comput.},
  local-url = {file://localhost/Users/valsson/Documents/Papers%20Library/Journal%20of%20Chemical%20Theory%20and%20Computation/2020/Schäfer-Settanni-2020-Journal%20of%20Chemical%20Theory%20and%20Computation.pdf},
  pmid      = {32192340},
  year      = {2020},
}

@Article{siderius_2013,
  author  = {Daniel W. Siderius and Vincent K. Shen},
  title   = {Use of the Grand Canonical Transition-Matrix Monte Carlo Method to Model Gas Adsorption in Porous Materials},
  doi     = {10.1021/jp400480q},
  number  = {11},
  pages   = {5861-5872},
  volume  = {117},
  journal = {J. Phys. Chem. C},
  year    = {2013},
}

@Article{Desmond2006,
  author   = {Bowers, K.J. and Chow, E. and Xu, Huageng and Dror, R.O. and Eastwood, M.P. and Gregersen, B.A. and Klepeis, J.L. and Kolossvary, I. and Moraes, M.A. and Sacerdoti, F.D. and Salmon, J.K. and Shan, Y. and Shaw, D.E.},
  title    = {{Scalable Algorithms for Molecular Dynamics Simulations on Commodity Clusters}},
  doi      = {10.1109/sc.2006.54},
  pages    = {43--43},
  abstract = {{Although molecular dynamics (MD) simulations of biomolecular systems often run for days to months, many events of great scientific interest and pharmaceutical relevance occur on long time scales that remain beyond reach. We present several new algorithms and implementation techniques that significantly accelerate parallel MD simulations compared with current state-of-the-art codes. These include a novel parallel decomposition method and message-passing techniques that reduce communication requirements, as well as novel communication primitives that further reduce communication time. We have also developed numerical techniques that maintain high accuracy while using single precision computation in order to exploit processor-level vector instructions. These methods are embodied in a newly developed MD code called Desmond that achieves unprecedented simulation throughput and parallel scalability on commodity clusters. Our results suggest that Desmond's parallel performance substantially surpasses that of any previously described code. For example, on a standard benchmark, Desmond's performance on a conventional Opteron cluster with 2K processors slightly exceeded the reported performance of IBM's Blue Gene/L machine with 32K processors running its Blue Matter MD code}},
  journal  = {ACM/IEEE SC 2006 Conference (SC'06)},
  year     = {2006},
}

@Article{PhysRevLett.86.4983,
  author    = {Shirts, Michael R. and Pande, Vijay S.},
  title     = {Mathematical Analysis of Coupled Parallel Simulations},
  doi       = {10.1103/PhysRevLett.86.4983},
  issue     = {22},
  pages     = {4983--4987},
  url       = {https://link.aps.org/doi/10.1103/PhysRevLett.86.4983},
  volume    = {86},
  journal   = {Phys. Rev. Lett.},
  month     = {May},
  numpages  = {0},
  publisher = {American Physical Society},
  year      = {2001},
}

@Article{Laio-PNAS-2002,
  author        = {Laio, Alessandro and Parrinello, Michele},
  title         = {Escaping free-energy minima},
  doi           = {10.1073/pnas.202427399},
  number        = {20},
  pages         = {12562-12566},
  volume        = {99},
  bdsk-url-1    = {http://dx.doi.org/10.1073/pnas.202427399},
  date-added    = {2014-05-22 06:54:15 +0000},
  date-modified = {2015-03-25 10:49:37 +0000},
  journal       = {Proc. Natl. Acad. Sci. U.S.A.},
  month         = {Sep},
  publisher     = {Proc. Natl. Acad. Sci. U.S.A.},
  year          = {2002},
}

@Article{Gersende_SelfHealing_2017,
  author   = {Fort, Gersende and Jourdain, Benjamin and Lelièvre, Tony and Stoltz, Gabriel},
  title    = {{Self-healing umbrella sampling: convergence and efficiency}},
  doi      = {10.1007/s11222-015-9613-2},
  issn     = {0960-3174},
  number   = {1},
  pages    = {147--168},
  volume   = {27},
  abstract = {{The Self-Healing Umbrella Sampling (SHUS) algorithm is an adaptive biasing algorithm which has been proposed in Marsili et al. (J Phys Chem B 110(29):14011–14013, 2006) in order to efficiently sample a multimodal probability measure. We show that this method can be seen as a variant of the well-known Wang–Landau algorithm Wang and Landau (Phys Rev E 64:056101, 2001a; Phys Rev Lett 86(10):2050–2053, 2001b). Adapting results on the convergence of the Wang-Landau algorithm obtained in Fort et al. (Math Comput 84(295):2297–2327, 2014a), we prove the convergence of the SHUS algorithm. We also compare the two methods in terms of efficiency. We finally propose a modification of the SHUS algorithm in order to increase its efficiency, and exhibit some similarities of SHUS with the well-tempered metadynamics method Barducci et al. (Phys Rev Lett 100:020,603, 2008).}},
  journal  = {Stat Comput},
  year     = {2017},
}

@Article{Lagardere2018,
  author    = {Louis Lagard{\`{e}}re and Luc-Henri Jolly and Filippo Lipparini and F{\'{e}}lix Aviat and Benjamin Stamm and Zhifeng F. Jing and Matthew Harger and Hedieh Torabifard and G. Andr{\'{e}}s Cisneros and Michael J. Schnieders and Nohad Gresh and Yvon Maday and Pengyu Y. Ren and Jay W. Ponder and Jean-Philip Piquemal},
  title     = {Tinker-{HP}: a massively parallel molecular dynamics package for multiscale simulations of large complex systems with advanced point dipole polarizable force fields},
  doi       = {10.1039/c7sc04531j},
  number    = {4},
  pages     = {956--972},
  volume    = {9},
  journal   = {Chem Sci},
  publisher = {Royal Society of Chemistry ({RSC})},
  year      = {2018},
}

@Article{gront-kolinski:j-phys-condens-matter:2007:optimized-replica-selection,
  author  = {Gront, Dominik and Kolinski, Andrzej},
  title   = {{Efficient scheme for optimization of parallel tempering \{Monte Carlo\} method}},
  doi     = {10.1088/0953-8984/19/3/036225},
  pages   = {36225},
  volume  = {19},
  journal = {J. Phys.: Condens. Matter},
  year    = {2007},
}

@Article{Chipot2005,
  author  = {Christophe Chipot and J\'er\^ome H\'enin},
  title   = {Exploring the free energy landscape of a short peptide using an average force},
  doi     = {10.1063/1.2138694},
  pages   = {244906},
  volume  = {123},
  journal = {J. Chem. Phys.},
  year    = {2005},
}

@Article{Escobedo_unified_2005,
  author  = {Escobedo,Fernando A.},
  title   = {A unified methodological framework for the simulation of nonisothermal ensembles},
  doi     = {10.1063/1.1938190},
  eprint  = {https://doi.org/10.1063/1.1938190},
  number  = {4},
  pages   = {044110},
  url     = {https://doi.org/10.1063/1.1938190},
  volume  = {123},
  journal = {J. Chem. Phys.},
  year    = {2005},
}

@Article{escobedo_transition_2006,
  author  = {Escobedo,Fernando A. and Abreu,Charlles R. A.},
  title   = {On the use of transition matrix methods with extended ensembles},
  doi     = {10.1063/1.2174010},
  eprint  = {https://doi.org/10.1063/1.2174010},
  number  = {10},
  pages   = {104110},
  url     = {https://doi.org/10.1063/1.2174010},
  volume  = {124},
  journal = {J. Chem. Phys.},
  year    = {2006},
}

@Article{tan_binless_2012,
  author  = {Tan,Zhiqiang and Gallicchio,Emilio and Lapelosa,Mauro and Levy,Ronald M.},
  title   = {Theory of binless multi-state free energy estimation with applications to protein-ligand binding},
  doi     = {10.1063/1.3701175},
  eprint  = {https://doi.org/10.1063/1.3701175},
  number  = {14},
  pages   = {144102},
  url     = {https://doi.org/10.1063/1.3701175},
  volume  = {136},
  journal = {J. Chem. Phys.},
  year    = {2012},
}

@article{tan_optimally_2017,
  title = {Optimally {{Adjusted Mixture Sampling}} and {{Locally Weighted Histogram Analysis}}},
  author = {Tan, Zhiqiang},
  year = {2017},
  month = jan,
  journal = {J. Comput. Graph. Stat.},
  volume = {26},
  number = {1},
  pages = {54--65},
  doi = {10.1080/10618600.2015.1113975},
  abstract = {Consider the two problems of simulating observations and estimating expectations and normalizing constants for multiple distributions. First, we present a self-adjusted mixture sampling method, which accommodates both adaptive serial tempering and a generalized Wang–Landau algorithm. The set of distributions are combined into a labeled mixture, with the mixture weights depending on the initial estimates of log normalizing constants (or free energies). Then, observations are generated by Markov transitions, and free energy estimates are adjusted online by stochastic approximation. We propose two stochastic approximation schemes by Rao–Blackwellization of the scheme commonly used, and derive the optimal choice of a gain matrix, resulting in the minimum asymptotic variance for free energy estimation, in a simple and feasible form. Second, we develop an offline method, locally weighted histogram analysis, for estimating free energies and expectations, using all the simulated data from multiple distributions by either self-adjusted mixture sampling or other sampling algorithms. This method can be computationally much faster, with little sacrifice of statistical efficiency, than a global method currently used, especially when a large number of distributions are involved. We provide both theoretical results and numerical studies to demonstrate the advantages of the proposed methods.},
}

@Article{abreu_framework_2006,
  author  = {Abreu,Charlles R. A. and Escobedo,Fernando A.},
  title   = {A general framework for non-Boltzmann Monte Carlo sampling},
  doi     = {10.1063/1.2165188},
  eprint  = {https://doi.org/10.1063/1.2165188},
  number  = {5},
  pages   = {054116},
  url     = {https://doi.org/10.1063/1.2165188},
  volume  = {124},
  journal = {J. Chem. Phys.},
  year    = {2006},
}

@article{Zhang:JPCL:2015,
  title = {A {{Stochastic Solution}} to the {{Unbinned WHAM Equations}}},
  author = {Zhang, Bin W. and Xia, Junchao and Tan, Zhiqiang and Levy, Ronald M.},
  year = {2015},
  month = oct,
  journal = {J. Phys. Chem. Lett.},
  volume = {6},
  number = {19},
  pages = {3834--3840},
  publisher = {{American Chemical Society}},
  doi = {10.1021/acs.jpclett.5b01771},
  abstract = {The weighted histogram analysis method (WHAM) and unbinned versions such as the multistate Bennett acceptance ratio (MBAR) and unbinned WHAM (UWHAM) are widely used to compute free energies and expectations from data generated by independent or coupled parallel simulations. Here we introduce a replica exchange-like algorithm (RE-SWHAM) that can be used to solve the UWHAM equations stochastically. This method is capable of analyzing large data sets generated by hundreds or even thousands of parallel simulations that are too large to be “WHAMMED” using standard methods. We illustrate the method by applying it to obtain free energy weights for each of the 240 states in a simulation of host–guest ligand binding containing ∼3.5 × 10^7 data elements collected from 16 parallel Hamiltonian replica exchange simulations, performed at 15 temperatures. In addition to using much less memory, RE-SWHAM showed a nearly 80-fold improvement in computational time compared with UWHAM.},
}

@article{Liu:Biometrika:1996,
  title = {Peskun's Theorem and a Modified Discrete-State {{Gibbs}} Sampler},
  author = {Liu, Jun S.},
  year = {1996},
  month = sep,
  journal = {Biometrika},
  volume = {83},
  number = {3},
  pages = {681--682},
  doi = {10.1093/biomet/83.3.681},
  abstract = {Attention is drawn to the use of Peskun's theorem in improving statistical efficiency of discrete-state Gibbs sampling.},
}

@article{Wang:JCTC:2013,
  title = {Modeling {{Local Structural Rearrangements Using FEP}}/{{REST}}: Application to {{Relative Binding Affinity Predictions}} of {{CDK2 Inhibitors}}},
  shorttitle = {Modeling {{Local Structural Rearrangements Using FEP}}/{{REST}}},
  author = {Wang, Lingle and Deng, Yuqing and Knight, Jennifer L. and Wu, Yujie and Kim, Byungchan and Sherman, Woody and Shelley, John C. and Lin, Teng and Abel, Robert},
  year = {2013},
  month = feb,
  journal = {J. Chem. Theory Comput.},
  volume = {9},
  number = {2},
  pages = {1282--1293},
  publisher = {{American Chemical Society}},
  doi = {10.1021/ct300911a},
  abstract = {Accurate and reliable calculation of protein–ligand binding affinities remains a hotbed of computer-aided drug design research. Despite the potentially large impact FEP (free energy perturbation) may have in drug design projects, practical applications of FEP in industrial contexts have been limited. In this work, we use a recently developed method, FEP/REST (free energy perturbation/replica exchange with solute tempering), to calculate the relative binding affinities for a set of congeneric ligands binding to the CDK2 receptor. We compare the FEP/REST results with traditional FEP/MD (molecular dynamics)results and MM/GBSA (molecular mechanics/Generalized Born Surface Area model) results and examine why FEP/REST performed notably better than these other methods, as well as why certain ligand mutations lead to large increases of the binding affinity while others do not. We also introduce a mathematical framework for assessing the consistency and reliability of the calculations using cycle closures in FEP mutation paths.}
}

@article{Faizi:JCTC:2020,
  title = {Efficient {{Irreversible Monte Carlo Samplers}}},
  author = {Faizi, Fahim and Deligiannidis, George and Rosta, Edina},
  year = {2020},
  month = apr,
  journal = {J. Chem. Theory Comput.},
  volume = {16},
  number = {4},
  pages = {2124--2138},
  publisher = {{American Chemical Society}},
  doi = {10.1021/acs.jctc.9b01135},
  abstract = {We present here two irreversible Markov chain Monte Carlo algorithms for general discrete state systems. One of the algorithms is based on the random-scan Gibbs sampler for discrete states and the other on its improved version, the Metr opolized-Gibbs sampler. The algorithms we present incorporate the lifting framework with skewed detailed balance condition and construct irreversible Markov chains that satisfy the balance condition. We have applied our algorithms to 1D 4-state Potts model. The integrated autocorrelation times for magnetization and energy density indicate a reduction of the dynamical scaling exponent from z ≈ 1 to z ≈ 1/2. In addition, we have generalized an irreversible Metropolis–Hastings algorithm with skewed detailed balance, initially introduced by Turitsyn et al. [ Physica D 2011, 240, 410] for the mean field Ising model, to be now readily applicable to classical spin systems in general; application to 1D 4-state Potts model indicate a square root reduction of the mixing time at high temperatures.},
  file = {/Users/mrshirts/zoterodata/storage/7EUFDEWD/Faizi et al. - 2020 - Efficient Irreversible Monte Carlo Samplers.pdf}
}

@Article{DePablo_DOS_2012,
  author   = {Singh, Sadanand and Chopra, Manan and Pablo, Juan J. de},
  title    = {{Density of States–Based Molecular Simulations}},
  doi      = {10.1146/annurev-chembioeng-062011-081032},
  issn     = {1947-5438},
  number   = {1},
  pages    = {369--394},
  volume   = {3},
  abstract = {{One of the central problems in statistical mechanics is that of finding the density of states of a system. Knowledge of the density of states of a system is equivalent to knowledge of its fundamental equation, from which all thermodynamic quantities can be obtained. Over the past several years molecular simulations have made considerable strides in their ability to determine the density of states of complex fluids and materials. In this review we discuss some of the more promising approaches proposed in the recent literature along with their advantages and limitations.}},
  journal  = {Annu Rev Chem Biomol},
  pmid     = {22483263},
  year     = {2012},
}

@Article{Abrams:E:2014,
  author    = {Abrams, Cameron and Bussi, Giovanni},
  title     = {Enhanced {{Sampling}} in {{Molecular Dynamics Using Metadynamics}}, {{Replica}}-{{Exchange}}, and {{Temperature}}-{{Acceleration}}},
  doi       = {10.3390/e16010163},
  number    = {1},
  pages     = {163--199},
  volume    = {16},
  abstract  = {We review a selection of methods for performing enhanced sampling in molecular dynamics simulations. We consider methods based on collective variable biasing and on tempering, and offer both historical and contemporary perspectives. In collective-variable biasing, we first discuss methods stemming from thermodynamic integration that use mean force biasing, including the adaptive biasing force algorithm and temperature acceleration. We then turn to methods that use bias potentials, including umbrella sampling and metadynamics. We next consider parallel tempering and replica-exchange methods. We conclude with a brief presentation of some combination methods.},
  copyright = {http://creativecommons.org/licenses/by/3.0/},
  journal   = {Entropy},
  keywords  = {adaptive-biasing force algorithm, blue-moon sampling, collective variables, free energy, metadynamics, temperature-acceleration, umbrella sampling},
  langid    = {english},
  month     = jan,
  publisher = {{Multidisciplinary Digital Publishing Institute}},
  year      = {2014},
}

@Article{Gallicchio:CPC:2015,
  author   = {Gallicchio, Emilio and Xia, Junchao and Flynn, William F. and Zhang, Baofeng and Samlalsingh, Sade and Mentes, Ahmet and Levy, Ronald M.},
  title    = {Asynchronous Replica Exchange Software for Grid and Heterogeneous Computing},
  doi      = {10.1016/j.cpc.2015.06.010},
  pages    = {236--246},
  volume   = {196},
  abstract = {Parallel replica exchange sampling is an extended ensemble technique often used to accelerate the exploration of the conformational ensemble of atomistic molecular simulations of chemical systems. Inter-process communication and coordination requirements have historically discouraged the deployment of replica exchange on distributed and heterogeneous resources. Here we describe the architecture of a software (named ASyncRE) for performing asynchronous replica exchange molecular simulations on volunteered computing grids and heterogeneous high performance clusters. The asynchronous replica exchange algorithm on which the software is based avoids centralized synchronization steps and the need for direct communication between remote processes. It allows molecular dynamics threads to progress at different rates and enables parameter exchanges among arbitrary sets of replicas independently from other replicas. ASyncRE is written in Python following a modular design conducive to extensions to various replica exchange schemes and molecular dynamics engines. Applications of the software for the modeling of association equilibria of supramolecular and macromolecular complexes on BOINC campus computational grids and on the CPU/MIC heterogeneous hardware of the XSEDE Stampede supercomputer are illustrated. They show the ability of ASyncRE to utilize large grids of desktop computers running the Windows, MacOS, and/or Linux operating systems as well as collections of high performance heterogeneous hardware devices.},
  journal  = {Comput. Phys. Commun.},
  keywords = {BOINC, Distributed computing, Grid computing, Peptide dimerization, Protein–ligand binding, Replica exchange molecular dynamics},
  langid   = {english},
  month    = nov,
  year     = {2015},
}

@article{Hayashi:PRE:2019,
  title = {Efficient Simulation Protocol for Determining the Density of States: Combination of Replica-Exchange {{Wang}}-{{Landau}} Method and Multicanonical Replica-Exchange Method},
  shorttitle = {Efficient Simulation Protocol for Determining the Density of States},
  author = {Hayashi, Takuya and Okamoto, Yuko},
  year = {2019},
  month = oct,
  journal = {Phys. Rev. E},
  volume = {100},
  number = {4},
  pages = {043304},
  publisher = {{American Physical Society}},
  doi = {10.1103/PhysRevE.100.043304},
  abstract = {By combining two generalized-ensemble algorithms, the replica-exchange Wang-Landau (REWL) method and the multicanonical replica-exchange method (MUCAREM), we propose an effective simulation protocol to determine the density of states with high accuracy. The new protocol is referred to as REWL-MUCAREM, and REWL is first performed and then MUCAREM is performed. In order to verify the effectiveness of our protocol, we performed simulations of a square-lattice Ising model using the three methods, namely REWL, MUCAREM, and REWL-MUCAREM. The results showed that the density of states obtained by REWL-MUCAREM is more accurate than that is estimated by the two methods separately.},
}
{Kofke:JCP:2002,
%  title = {On the Acceptance Probability of Replica-Exchange {{Monte Carlo}} Trials},
%  author = {Kofke, David A.},
%  year = {2002},
%  month = oct,
%  journal = {J. Chem. Phys.},
% volume = {117},
% number = {15},
% pages = {6911--6914},
% publisher = {{American Institute of Physics}},
% doi = {10.1063/1.1507776},
%
%}

@Article{Liu:CPL:2018,
  author   = {Liu, Yang and Li, Weifeng and Mu, Yuguang},
  title    = {Optimization of Replica Exchange Temperature Ladder under the Well-Tempered Ensemble},
  doi      = {10.1016/j.cplett.2018.09.036},
  pages    = {66--72},
  volume   = {711},
  abstract = {Selection of temperature sequence and bias factor is a critical step for the preparation of Parallel Tempering simulations in a Well-Tempered Ensemble (PT-WTE). We provide a scheme in this study to generate the temperature sequence and the corresponding bias factor optimally. The number of replicas for a complete coverage of a specific temperature range is adjustable in this scheme, while keeping the average acceptance probability (AAP) between neighboring replica-pairs unchanged. Two series of PT-WTE simulations were tested with the number of replicas as 16 and 8 respectively. This work leads to a better understanding and application of PT-WTE simulations.},
  journal  = {Chem. Phys. Lett.},
  keywords = {PT-WTE, Temperature sequence optimization},
  langid   = {english},
  month    = nov,
  year     = {2018},
}


@article{Oshima:JCTC:2019,
  title = {Replica-{{Exchange Umbrella Sampling Combined}} with {{Gaussian Accelerated Molecular Dynamics}} for {{Free}}-{{Energy Calculation}} of {{Biomolecules}}},
  author = {Oshima, Hiraku and Re, Suyong and Sugita, Yuji},
  year = {2019},
  month = oct,
  journal = {J. Chem. Theory Comput.},
  volume = {15},
  number = {10},
  pages = {5199--5208},
  publisher = {{American Chemical Society}},
  doi = {10.1021/acs.jctc.9b00761},
  abstract = {We have developed an enhanced conformational sampling method combining replica-exchange umbrella sampling (REUS) with Gaussian accelerated molecular dynamics (GaMD). REUS enhances the sampling along predefined reaction coordinates, while GaMD accelerates the conformational dynamics by adding a boost potential to the system energy. The method, which we call GaREUS (Gaussian accelerated replica-exchange umbrella sampling), enhances the sampling more efficiently than REUS or GaMD, while the computational resource for GaREUS is the same as that required for REUS. The two-step reweighting procedure using the multistate Bennett acceptance ratio method and the cumulant expansion for the exponential average is applied to the simulation trajectories for obtaining the unbiased free-energy landscapes. We apply GaREUS to the calculations of free-energy landscapes for three different cases: conformational equilibria of N-glycan, folding of chignolin, and conformational change of adenyl kinase. We show that GaREUS speeds up the convergences of free-energy calculations using the same amount of computational resources as REUS. The free-energy landscapes reweighted from the trajectories of GaREUS agree with previously reported ones. GaREUS is applicable to free-energy calculations of various biomolecular dynamics and functions with reasonable computational costs.},
}

@InCollection{Qi:PSMaP:2018,
  author     = {Qi, Ruxi and Wei, Guanghong and Ma, Buyong and Nussinov, Ruth},
  booktitle  = {Peptide {{Self}}-{{Assembly}}: Methods and {{Protocols}}},
  title      = {Replica {{Exchange Molecular Dynamics}}: A {{Practical Application Protocol}} with {{Solutions}} to {{Common Problems}} and a {{Peptide Aggregation}} and {{Self}}-{{Assembly Example}}},
  doi        = {10.1007/978-1-4939-7811-3_5},
  editor     = {Nilsson, Bradley L. and Doran, Todd M.},
  isbn       = {978-1-4939-7811-3},
  pages      = {101--119},
  publisher  = {{Springer}},
  series     = {Methods in {{Molecular Biology}}},
  abstract   = {Protein aggregation is associated with many human diseases such as Alzheimer’s disease (AD), Parkinson’s disease (PD), and type II diabetes (T2D). Understanding the molecular mechanism of protein aggregation is essential for therapy development. Molecular dynamics (MD) simulations have been shown as powerful tools to study protein aggregation. However, conventional MD simulations can hardly sample the whole conformational space of complex protein systems within acceptable simulation time as it can be easily trapped in local minimum-energy states. Many enhanced sampling methods have been developed. Among these, the replica exchange molecular dynamics (REMD) method has gained great popularity. By combining MD simulation with the Monte Carlo algorithm, the REMD method is capable of overcoming high energy-barriers easily and of sampling sufficiently the conformational space of proteins. In this chapter, we present a brief introduction to REMD method and a practical application protocol with a case study of the dimerization of the 11–25 fragment of human islet amyloid polypeptide (hIAPP(11–25)), using the GROMACS software. We also provide solutions to problems that are often encountered in practical use, and provide some useful scripts/commands from our research that can be easily adapted to other systems.},
  address    = {{New York, NY}},
  keywords   = {Free energy landscape, GROMACS, Human islet amyloid polypeptide, Molecular dynamics simulations, Protein aggregation, REMD, Replica exchange method},
  langid     = {english},
  shorttitle = {Replica {{Exchange Molecular Dynamics}}},
  year       = {2018},
}
{Sindhikara:JCTC:2010,
%  ids = {Sindhikara:JCTC:2010a},
%  title = {Exchange {{Often}} and {{Properly}} in {{Replica Exchange Molecular Dynamics}}},
%  author = {Sindhikara, Daniel J. and Emerson, Daniel J. and Roitberg, Adrian E.},
%  year = {2010},
%  month = sep,
%  journal = {J. Chem. Theory Comput.},
%  volume = {6},
%  number = {9},
%  pages = {2804--2808},
%  publisher = {{American Chemical Society}},
%  doi = {10.1021/ct100281c},
%  abstract = {Previous work by us showed that in replica exchange molecular dynamics, exchanges should be attempted extremely often, providing gains in efficiency and no undesired effects. Since that time some questions have been raised about the extendability of these claims to the general case. In this work, we answer this question in two ways. First, we perform a study measuring the effect of exchange attempt frequency in explicit solvent simulations including thousands of atoms. This shows, consistent with the previous assertion, that high exchange attempt frequency allows an optimal rate of exploration of configurational space. Second, we present an explanation of many theoretical and technical pitfalls when implementing replica exchange that cause “improper” exchanges resulting in erroneous data, exacerbated by high exchange attempt frequency.},
%}

@InCollection{Sugita:BSMaP:2019,
  author    = {Sugita, Yuji and Kamiya, Motoshi and Oshima, Hiraku and Re, Suyong},
  booktitle = {Biomolecular {{Simulations}}: Methods and {{Protocols}}},
  title     = {Replica-{{Exchange Methods}} for {{Biomolecular Simulations}}},
  doi       = {10.1007/978-1-4939-9608-7_7},
  editor    = {Bonomi, Massimiliano and Camilloni, Carlo},
  isbn      = {978-1-4939-9608-7},
  pages     = {155--177},
  publisher = {{Springer}},
  series    = {Methods in {{Molecular Biology}}},
  abstract  = {In this study, a replica-exchange method was developed to overcome conformational sampling difficulties in computer simulations of spin glass or other systems with rugged free-energy landscapes. This method was then applied to the protein-folding problem in combination with molecular dynamics (MD) simulation. Owing to its simplicity and sampling efficiency, the replica-exchange method has been applied to many other biological problems and has been continuously improved. The method has often been combined with other sampling techniques, such as umbrella sampling, free-energy perturbation, metadynamics, and Gaussian accelerated MD (GaMD). In this chapter, we first summarize the original replica-exchange molecular dynamics (REMD) method and discuss how new algorithms related to the original method are implemented to add new features. Heterogeneous and flexible structures of an N-glycan in a solution are simulated as an example of applications by REMD, replica exchange with solute tempering, and GaMD. The sampling efficiency of these methods on the N-glycan system and the convergence of the free-energy changes are compared. REMD simulation protocols and trajectory analysis using the GENESIS software are provided to facilitate the practical use of advanced simulation methods.},
  address   = {{New York, NY}},
  keywords  = {Detailed balance and global balance, Free-energy landscape, N-Glycans, Replica exchange with solute tempering, Replica-exchange molecular dynamics method, Replica-exchange umbrella sampling, Reweighting approaches},
  langid    = {english},
  year      = {2019},
}

@Article{Yu:P:2016,
  author    = {Yu, Tang-Qing and Lu, Jianfeng and Abrams, Cameron F. and {Vanden-Eijnden}, Eric},
  title     = {Multiscale Implementation of Infinite-Swap Replica Exchange Molecular Dynamics},
  doi       = {10.1073/pnas.1605089113},
  number    = {42},
  pages     = {11744--11749},
  volume    = {113},
  abstract  = {Replica exchange molecular dynamics (REMD) is a popular method to accelerate conformational sampling of complex molecular systems. The idea is to run several replicas of the system in parallel at different temperatures that are swapped periodically. These swaps are typically attempted every few MD steps and accepted or rejected according to a Metropolis–Hastings criterion. This guarantees that the joint distribution of the composite system of replicas is the normalized sum of the symmetrized product of the canonical distributions of these replicas at the different temperatures. Here we propose a different implementation of REMD in which (i) the swaps obey a continuous-time Markov jump process implemented via Gillespie’s stochastic simulation algorithm (SSA), which also samples exactly the aforementioned joint distribution and has the advantage of being rejection free, and (ii) this REMD-SSA is combined with the heterogeneous multiscale method to accelerate the rate of the swaps and reach the so-called infinite-swap limit that is known to optimize sampling efficiency. The method is easy to implement and can be trivially parallelized. Here we illustrate its accuracy and efficiency on the examples of alanine dipeptide in vacuum and C-terminal β-hairpin of protein G in explicit solvent. In this latter example, our results indicate that the landscape of the protein is a triple funnel with two folded structures and one misfolded structure that are stabilized by H-bonds.},
  chapter   = {Physical Sciences},
  journal   = {PNAS},
  keywords  = {HMM, importance sampling, protein-folding, REMD, SSA},
  langid    = {english},
  month     = oct,
  pmid      = {27698148},
  publisher = {{National Academy of Sciences}},
  year      = {2016},
}

@article{Zhang:JPCB:2016,
  title = {Simulating {{Replica Exchange}}: Markov {{State Models}}, {{Proposal Schemes}}, and the {{Infinite Swapping Limit}}},
  shorttitle = {Simulating {{Replica Exchange}}},
  author = {Zhang, Bin W. and Dai, Wei and Gallicchio, Emilio and He, Peng and Xia, Junchao and Tan, Zhiqiang and Levy, Ronald M.},
  year = {2016},
  month = aug,
  journal = {J. Phys. Chem. B},
  volume = {120},
  number = {33},
  pages = {8289--8301},
  publisher = {{American Chemical Society}},
  doi = {10.1021/acs.jpcb.6b02015},
  abstract = {Replica exchange molecular dynamics is a multicanonical simulation technique commonly used to enhance the sampling of solvated biomolecules on rugged free energy landscapes. While replica exchange is relatively easy to implement, there are many unanswered questions about how to use this technique most efficiently, especially because it is frequently the case in practice that replica exchange simulations are not fully converged. A replica exchange cycle consists of a series of molecular dynamics steps of a set of replicas moving under different Hamiltonians or at different thermodynamic states followed by one or more replica exchange attempts to swap replicas among the different states. How the replica exchange cycle is constructed affects how rapidly the system equilibrates. We have constructed a Markov state model of replica exchange (MSMRE) using long molecular dynamics simulations of a host–guest binding system as an example, in order to study how different implementations of the replica exchange cycle can affect the sampling efficiency. We analyze how the number of replica exchange attempts per cycle, the number of MD steps per cycle, and the interaction between the two parameters affects the largest implied time scale of the MSMRE simulation. The infinite swapping limit is an important concept in replica exchange. We show how to estimate the infinite swapping limit from the diagonal elements of the exchange transition matrix constructed from MSMRE “simulations of simulations” as well as from relatively short runs of the actual replica exchange simulations.},
  }

@article{deOliveira:EPJB:1998,
  title = {Broad Histogram {{Monte Carlo}}},
  author = {{de Oliveira}, P.M.C. and Penna, T.J.P. and Herrmann, H.J.},
  year = {1998},
  month = jan,
  journal = {Eur. Phys. J. B},
  volume = {1},
  number = {2},
  pages = {205--208},
  doi = {10.1007/s100510050172},
  abstract = {We propose a new Monte Carlo technique in which the degeneracy of energy states is obtained with a Markovian process analogous to that of Metropolis used currently in canonical simulations. The obtained histograms are much broader than those of the canonical histogram technique studied by Ferrenberg and Swendsen. Thus we can reliably reconstruct thermodynamic functions over a much larger temperature scale also away from the critical point. We show for the two-dimensional Ising model how our new method reproduces exact results more accurately and using less computer time than the conventional histogram method. We also show data in three dimensions for the Ising ferromagnet and the Edwards Anderson spin glass.},
  langid = {english},
  file = {/Users/mrshirts/zoterodata/storage/UJ8RIXBA/de Oliveira et al. - 1998 - Broad histogram Monte Carlo.pdf}
}

@Article{Wang:JoSP:2002,
  author   = {Wang, Jian-Sheng and Swendsen, Robert H.},
  title    = {Transition {{Matrix Monte Carlo Method}}},
  doi      = {10.1023/A:1013180330892},
  number   = {1},
  pages    = {245--285},
  volume   = {106},
  abstract = {We present a formalism of the transition matrix Monte Carlo method. A stochastic matrix in the space of energy can be estimated from Monte Carlo simulation. This matrix is used to compute the density of states, as well as to construct multi-canonical and equal-hit algorithms. We discuss the performance of the methods. The results are compared with single histogram method, multi-canonical method, and other methods. In many aspects, the present method is an improvement over the previous methods.},
  file     = {/Users/mrshirts/zoterodata/storage/6UF2VNLP/Wang and Swendsen - 2002 - Transition Matrix Monte Carlo Method.pdf},
  journal  = {J. Stat. Phys.},
  langid   = {english},
  month    = jan,
  year     = {2002},
}

@article{Hastings_biometrika_1970,
    author = {Hastings, W. K.},
    title = "{Monte Carlo sampling methods using Markov chains and their applications}",
    journal = {Biometrika},
    volume = {57},
    number = {1},
    pages = {97-109},
    year = {1970},
    month = {04},
    abstract = "{A generalization of the sampling method introduced by Metropolis et al. (1953) is presented along with an exposition of the relevant theory, techniques of application and methods and difficulties of assessing the error in Monte Carlo estimates. Examples of the methods, including the generation of random orthogonal matrices and potential applications of the methods to numerical problems arising in statistics, are discussed.}",
    issn = {0006-3444},
    doi = {10.1093/biomet/57.1.97},
    url = {https://doi.org/10.1093/biomet/57.1.97},
    eprint = {https://academic.oup.com/biomet/article-pdf/57/1/97/23940249/57-1-97.pdf},
}

@Article{Siepmann_mp_1992,
  author    = {J. Ilja Siepmann and Daan Frenkel},
  title     = {Configurational bias Monte Carlo: a new sampling scheme for flexible chains},
  doi       = {10.1080/00268979200100061},
  eprint    = {https://doi.org/10.1080/00268979200100061},
  number    = {1},
  pages     = {59-70},
  url       = {https://doi.org/10.1080/00268979200100061},
  volume    = {75},
  journal   = {Mol. Physics},
  publisher = {Taylor & Francis},
  year      = {1992},
}

@Article{Kieninger2020,
  author    = {Stefanie Kieninger and Luca Donati and Bettina G Keller},
  title     = {Dynamical reweighting methods for Markov models},
  doi       = {10.1016/j.sbi.2019.12.018},
  pages     = {124--131},
  url       = {https://doi.org/10.1016/j.sbi.2019.12.018},
  volume    = {61},
  journal   = {Curr. Opin. Struct. Biol.},
  month     = apr,
  publisher = {Elsevier {BV}},
  year      = {2020},
}

@Article{Westerlund2017,
  author    = {Annie M. Westerlund and Tyler J. Harpole and Christian Blau and Lucie Delemotte},
  title     = {Inference of Calmodulin's Ca2+-Dependent Free Energy Landscapes via Gaussian Mixture Model Validation},
  doi       = {10.1021/acs.jctc.7b00346},
  number    = {1},
  pages     = {63--71},
  url       = {https://doi.org/10.1021/acs.jctc.7b00346},
  volume    = {14},
  journal   = {J. Chem. Theory Comput.},
  month     = dec,
  publisher = {American Chemical Society ({ACS})},
  year      = {2017},
}

@article{Itoh:JCTC:2013,
  title = {Replica-{{Permutation Method}} with the {{Suwa}}–{{Todo Algorithm}} beyond the {{Replica}}-{{Exchange Method}}},
  author = {Itoh, Satoru G. and Okumura, Hisashi},
  year = {2013},
  month = jan,
  journal = {J. Chem. Theory Comput.},
  volume = {9},
  number = {1},
  pages = {570--581},
  publisher = {{American Chemical Society}},
  doi = {10.1021/ct3007919}
}

@article{ValssonPampel_Wavelets_2022,
year = {2022}, 
title = {{Improving the Efficiency of Variationally Enhanced Sampling with Wavelet-Based Bias Potentials}}, 
author = {Pampel, Benjamin and Valsson, Omar}, 
journal = {J. Chem. Theory Comput.},
issn = {1549-9618}, 
doi = {10.1021/acs.jctc.2c00197}, 
pmid = {35762642},
pages = {4127--4141}, 
number = {7}, 
volume = {18}
}




@article{Leimkuhler2012,
  doi = {10.1093/amrx/abs010},
  url = {https://doi.org/10.1093/amrx/abs010},
  year = {2012},
  month = jun,
  publisher = {Oxford University Press ({OUP})},
  author = {B. Leimkuhler and C. Matthews},
  title = {Rational Construction of Stochastic Numerical Methods for Molecular Sampling},
  journal = {Appl. Math. Res. Express}
}

@Article{Skeel2002,
  author    = {Robert D. Skeel and Jes\'{u}s A. Izaguirre},
  title     = {An impulse integrator for Langevin dynamics},
  doi       = {10.1080/0026897021000018321},
  number    = {24},
  pages     = {3885--3891},
  url       = {https://doi.org/10.1080/0026897021000018321},
  volume    = {100},
  journal   = {Mol. Phys.},
  month     = dec,
  publisher = {Informa {UK} Limited},
  year      = {2002},
}

@article{alchemy_Gapsys_2020,
  ids = {Gapsys:CS:2020},
  title = {Large Scale Relative Protein Ligand Binding Affinities Using Non-Equilibrium Alchemy},
  author = {Gapsys, Vytautas and {P\'{e}rez-Benito}, Laura and Aldeghi, Matteo and Seeliger, Daniel and {van Vlijmen}, Herman and Tresadern, Gary and {de Groot}, Bert L.},
  year = {2020},
  journal = {Chem. Sci.},
  volume = {11},
  number = {4},
  pages = {1140--1152},
  publisher = {{The Royal Society of Chemistry}},
  doi = {10.1039/C9SC03754C},
}

@Book{Zuckerman2010,
  author    = {Daniel M. Zuckerman},
  publisher = {CRC Press},
  title     = {Statistical Physics of Biomolecules: An Introduction},
  year      = {2010},
  doi       = {10.1201/b18849},
}


@Book{Tuckerman2010,
  author    = {Mark E. Tuckerman},
  publisher = {Oxford University Press},
  title     = {Statistical mechanics: theory and molecular simulation},
  year      = {2010},
  isbn      = {9780198525264},
}

@Article{Russo_2022,
  author       = {John D. Russo and She Zhang and Jeremy M. G. Leung and Anthony T. Bogetti and Jeff P. Thompson and Alex J. DeGrave and Paul A. Torrillo and A. J. Pratt and Kim F. Wong and Junchao Xia and Jeremy Copperman and Joshua L. Adelman and Matthew C. Zwier and David N. LeBard and Daniel M. Zuckerman and Lillian T. Chong},
  date         = {2022-01},
  journaltitle = {Journal of Chemical Theory and Computation},
  title        = {{WESTPA} 2.0: High-Performance Upgrades for Weighted Ensemble Simulations and Analysis of Longer-Timescale Applications},
  doi          = {10.1021/acs.jctc.1c01154},
  number       = {2},
  pages        = {638--649},
  volume       = {18},
  year         = {2022},
  journal      = {J. Chem. Theory Comput.},
  publisher    = {American Chemical Society ({ACS})},
}

@article{KS_Test_JCTC_2014,
year = {2014},
title = {{Assessing the Reliability of the Dynamics Reconstructed from Metadynamics}},
author = {Salvalaglio, Matteo and Tiwary, Pratyush and Parrinello, Michele},
journal = {J. Chem. Theory Comput.},
issn = {1549-9618},
doi = {10.1021/ct500040r},
pmid = {26580360},
pages = {1420--1425},
number = {4},
volume = {10},
keywords = {}
}

                                                  

@article{Rizzi:JCAMD:2020a,
  title = {The {{SAMPL6 SAMPLing}} Challenge: Assessing the Reliability and Efficiency of Binding Free Energy Calculations},
  shorttitle = {The {{SAMPL6 SAMPLing}} Challenge},
  author = {Rizzi, Andrea and Jensen, Travis and Slochower, David R. and Aldeghi, Matteo and Gapsys, Vytautas and Ntekoumes, Dimitris and Bosisio, Stefano and Papadourakis, Michail and Henriksen, Niel M. and {de Groot}, Bert L. and Cournia, Zoe and Dickson, Alex and Michel, Julien and Gilson, Michael K. and Shirts, Michael R. and Mobley, David L. and Chodera, John D.},
  year = {2020},
  month = may,
  journal = {J. Comput. Aided Mol. Des.},
  volume = {34},
  number = {5},
  pages = {601--633},
  doi = {10.1007/s10822-020-00290-5},
}



@article{SPONGE_MD_Code_2022, 
year = {2022}, 
title = {{SPONGE: A GPU‐Accelerated Molecular Dynamics Package with Enhanced Sampling and AI‐Driven Algorithms}}, 
author = {Huang, Yu‐Peng and Xia, Yijie and Yang, Lijiang and Wei, Jiachen and Yang, Yi Isaac and Gao, Yi Qin}, 
journal = {Chin. J. Chem}, 
issn = {1001-604X}, 
doi = {10.1002/cjoc.202100456}, 
abstract = {{SPONGE (Simulation Package tOward Next GEneration molecular modeling) is a software package for molecular dynamics (MD) simulation of solution and surface molecular systems. In this version of SPONGE, the all‐ atom potential energy functions used in AMBER MD packages are used by default and other all‐atom/coarse‐ grained potential energy functions are also supported. SPONGE is designed to extend the timescale being approached in MD simulations by utilizing the latest CUDA‐ enabled graphical processing units (GPU) and adopting highly efficient enhanced sampling algorithms, such as integrated tempering, selective integrated tempering and enhanced sampling of reactive trajectories. It is highly modular and new algorithms and functions can be incorporated con veniently. Particularly, a specialized Python plugin can be easily used to perform the machine learning MD simulation with MindSpore, TensorFlow, PyTorch or other popular machine learning frameworks. Furthermore, a plugin of Finite‐Element Method (FEM) is also available to handle metallic surface systems. All these advanced features increase the power of SPONGE for modeling and simulation of complex chemical and biological systems. What is the most favorite and original chemistry developed in your research group? Our research centers at developing methods and theories to unravel molecular mechanisms of chemical and biological systems. By establishing theoretical models, developing enhanced sampling methods combined with machine learning techniques, we are able to conduct comprehensive thermodynamic and dynamic analyses for these complex systems. How do you get into this specific field? Could you please share some experiences with our readers? I got into theoretical chemistry as a PhD student. My PhD adviser Prof. Rudolph A. Marcus led me into this field and inspired me by his love of science. Enjoy life, always learn new things and be independent in thinking are something I learnt from my advisers (Professors Dalin Yang, Qihe Zhu, Rudy Marcus, and Martin Karplus) and would love to pass to my students. How do you supervise your students? We learn from each other. What is the most important personality for scientific research? Curiosity, passion, and persistence have been of great value to my career. What are your hobbies? What's your favorite book(s)? Reading, Ping‐Pong, and jogging. I always enjoy reading history. Who influences you mostly in your life? Too many, family, academic advisors, friends, students, and colleagues. This account describes the functions and features of the molecular dynamics simulation package: SPONGE developed by Prof. Yi Qin Gao's group.}}, 
pages = {160--168}, 
number = {1}, 
volume = {40}, 
keywords = {}
}


@article{GENESIS_MD_Code_2017,
year = {2017}, 
title = {{GENESIS 1.1: A hybrid‐parallel molecular dynamics simulator with enhanced sampling algorithms on multiple computational platforms}}, 
author = {Kobayashi, Chigusa and Jung, Jaewoon and Matsunaga, Yasuhiro and Mori, Takaharu and Ando, Tadashi and Tamura, Koichi and Kamiya, Motoshi and Sugita, Yuji}, 
journal = {J. Comp. Chem.}, 
issn = {0192-8651}, 
doi = {10.1002/jcc.24874}, 
pmid = {28718930}, 
abstract = {{GENeralized‐Ensemble SImulation System (GENESIS) is a software package for molecular dynamics (MD) simulation of biological systems. It is designed to extend limitations in system size and accessible time scale by adopting highly parallelized schemes and enhanced conformational sampling algorithms. In this new version, GENESIS 1.1, new functions and advanced algorithms have been added. The all‐atom and coarse‐grained potential energy functions used in AMBER and GROMACS packages now become available in addition to CHARMM energy functions. The performance of MD simulations has been greatly improved by further optimization, multiple time‐step integration, and hybrid (CPU + GPU) computing. The string method and replica‐exchange umbrella sampling with flexible collective variable choice are used for finding the minimum free‐energy pathway and obtaining free‐energy profiles for conformational changes of a macromolecule. These new features increase the usefulness and power of GENESIS for modeling and simulation in biological research. © 2017 Wiley Periodicals, Inc. We updated GENESIS software for molecular dynamics simulations of biological systems. In the update, AMBER force fields and several coarse‐grained models become available. The performance has been greatly improved by the use of multiple time‐step integration and hybrid (CPU + GPU) computing. The string method and replica‐exchange umbrella sampling with flexible collective variable choice are also implemented for free‐energy analysis on large conformational changes of proteins and nucleic acids.}}, 
pages = {2193--2206}, 
number = {25}, 
volume = {38}, 
keywords = {}, 
local-url = {file://localhost/Users/valsson/Documents/Papers%20Library/Journal%20of%20Computational%20Chemistry/2017/Kobayashi-Sugita-2017-Journal%20of%20Computational%20Chemistry.pdf}
}


@article{BaronPeters_RC_ARPC_2015, 
year = {2015}, 
keywords = {Reaction Coordinates}, 
title = {{Reaction Coordinates and Mechanistic Hypothesis Tests}}, 
author = {Peters, Baron}, 
journal = {Annu. Rev. Phys. Chem.}, 
issn = {0066-426X}, 
doi = {10.1146/annurev-physchem-040215-112215}, 
pmid = {27090846}, 
number = {1}, 
volume = {67}
}

@article{10.1039/d1cp04809k, 
year = {2021}, 
keywords = {Enhanced Sampling Reviews,Metadynamics Reviews}, 
title = {{Enhanced sampling without borders: on global biasing functions and how to reweight them}}, 
author = {Kamenik, Anna S. and Linker, Stephanie M. and Riniker, Sereina}, 
journal = {Phys. Chem. Chem. Phys.}, 
issn = {1463-9076}, 
doi = {10.1039/d1cp04809k}, 
pmid = {34935813}, 
abstract = {{Global enhanced sampling techniques bias the potential energy surface of biomolecules to overcome high energy barriers. Thereby, they aim to capture extensive conformational ensembles at comparably low computational cost.}}
}

@article{10.1016/j.bbagen.2014.10.019, 
year = {2015}, 
keywords = {Enhanced Sampling Reviews}, 
title = {{Enhanced sampling techniques in molecular dynamics simulations of biological systems}}, 
author = {Bernardi, Rafael C. and Melo, Marcelo C.R. and Schulten, Klaus}, 
journal = {Biochim. Biophys. Acta}, 
issn = {0304-4165}, 
doi = {10.1016/j.bbagen.2014.10.019}, 
pmid = {25450171}, 
pmcid = {PMC4339458}, 
abstract = {{BackgroundMolecular dynamics has emerged as an important research methodology covering systems to the level of millions of atoms. However, insufficient sampling often limits its application. The limitation is due to rough energy landscapes, with many local minima separated by high-energy barriers, which govern the biomolecular motion.Scope of reviewIn the past few decades methods have been developed that address the sampling problem, such as replica-exchange molecular dynamics, metadynamics and simulated annealing. Here we present an overview over theses sampling methods in an attempt to shed light on which should be selected depending on the type of system property studied.Major conclusionsEnhanced sampling methods have been employed for a broad range of biological systems and the choice of a suitable method is connected to biological and physical characteristics of the system, in particular system size. While metadynamics and replica-exchange molecular dynamics are the most adopted sampling methods to study biomolecular dynamics, simulated annealing is well suited to characterize very flexible systems. The use of annealing methods for a long time was restricted to simulation of small proteins; however, a variant of the method, generalized simulated annealing, can be employed at a relatively low computational cost to large macromolecular complexes.General significanceMolecular dynamics trajectories frequently do not reach all relevant conformational substates, for example those connected with biological function, a problem that can be addressed by employing enhanced sampling algorithms. This article is part of a Special Issue entitled Recent developments of molecular dynamics.}}, 
pages = {872--877}, 
number = {5}, 
volume = {1850}
}

@article{10.1063/1.5109531, 
year = {2019}, 
keywords = {Enhanced Sampling Reviews}, 
title = {{Enhanced sampling in molecular dynamics}}, 
author = {Yang, Yi Isaac and Shao, Qiang and Zhang, Jun and Yang, Lijiang and Gao, Yi Qin}, 
journal = {J. Chem. Phys.}, 
issn = {0021-9606}, 
doi = {10.1063/1.5109531}, 
pmid = {31438687}, 
abstract = {{Although molecular dynamics simulations have become a useful tool in essentially all fields of chemistry, condensed matter physics, materials science, and biology, there is still a large gap between the time scale which can be reached in molecular dynamics simulations and that observed in experiments. To address the problem, many enhanced sampling methods were introduced, which effectively extend the time scale being approached in simulations. In this perspective, we review a variety of enhanced sampling methods. We first discuss collective-variables-based methods including metadynamics and variationally enhanced sampling. Then, collective variable free methods such as parallel tempering and integrated tempering methods are presented. At last, we conclude with a brief introduction of some newly developed combinatory methods. We summarize in this perspective not only the theoretical background and numerical implementation of these methods but also the new challenges and prospects in the field of the enhanced sampling.}}, 
pages = {070902}, 
number = {7}, 
volume = {151}
}

@article{Wu1999SGMD,
  doi = {10.1063/1.478948},
  url = {https://doi.org/10.1063/1.478948},
  year = {1999},
  month = may,
  publisher = {{AIP} Publishing},
  volume = {110},
  number = {19},
  pages = {9401--9410},
  author = {Xiongwu Wu and Shaomeng Wang},
  title = {Enhancing systematic motion in molecular dynamics simulation},
  journal = {J. Chem. Phys.}
}

@article{Wu2003_SGLD,
title = {Self-guided Langevin dynamics simulation method},
journal = {Chem. Phys. Lett.},
volume = {381},
number = {3},
pages = {512-518},
year = {2003},
issn = {0009-2614},
doi = {https://doi.org/10.1016/j.cplett.2003.10.013},
url = {https://www.sciencedirect.com/science/article/pii/S0009261403017585},
author = {Xiongwu Wu and Bernard R. Brooks},
abstract = {This work presents a self-guided Langevin dynamics simulation method. The guiding force is calculated as a local average of the friction forces during a self-guided Langevin dynamics simulation. Three parameters, the local average time, tL, the guiding factor, λ, and the collision frequency, γ, control a self-guided Langevin dynamics simulation. It is demonstrated through three model systems that this simulation method has an enhanced conformational search ability while has little alteration in conformational distribution when the guiding factor is chosen within the limit of λγ<1 ps−1. This method is well suited for simulation studies where extensive conformational searching is required.}
}

@article{Wu2015_SGLD-GLE,
  doi = {10.1002/jcc.24015},
  url = {https://doi.org/10.1002/jcc.24015},
  year = {2015},
  month = jul,
  publisher = {Wiley},
  volume = {37},
  number = {6},
  pages = {595--601},
  author = {Xiongwu Wu and Bernard R. Brooks and Eric Vanden-Eijnden},
  title = {Self-guided Langevin dynamics via generalized Langevin equation},
  journal = {J. Comp. Chem.}
}

@article{Wu2020_SGLDg,
  doi = {10.1063/5.0019086},
  url = {https://doi.org/10.1063/5.0019086},
  year = {2020},
  month = sep,
  publisher = {{AIP} Publishing},
  volume = {153},
  number = {9},
  pages = {094112},
  author = {Xiongwu Wu and Bernard R. Brooks},
  title = {Reformulation of the self-guided molecular simulation method},
  journal = {J. Chem. Phys.}
}

@article{Invernizzi2022,
  doi = {10.1021/acs.jctc.2c00152},
  url = {https://doi.org/10.1021/acs.jctc.2c00152},
  year = {2022},
  month = may,
  publisher = {American Chemical Society ({ACS})},
  volume = {18},
  number = {6},
  pages = {3988--3996},
  author = {Michele Invernizzi and Michele Parrinello},
  title = {Exploration vs Convergence Speed in Adaptive-Bias Enhanced Sampling},
  journal = {J. Chem. Theory Comput.}
}

@article{PalacioRodriguez_Pietrucci_2022,
year = {2022}, 
keywords = {Langevin Dynamics,Transition Paths,Transition State Theory}, 
title = {{Free Energy Landscapes, Diffusion Coefficients, and Kinetic Rates from Transition Paths}}, 
author = {Palacio-Rodriguez, Karen and Pietrucci, Fabio}, 
journal = {J. Chem. Theory Comput.}, 
issn = {1549-9618}, 
doi = {10.1021/acs.jctc.2c00324}, 
pmid = {35899416}, 
abstract = {{We address the problem of constructing accurate mathematical models of the dynamics of complex systems projected on a collective variable. To this aim we introduce a conceptually simple yet effective algorithm for estimating the parameters of Langevin and Fokker–Planck equations from a set of short, possibly out-of-equilibrium molecular dynamics trajectories, obtained for instance from transition path sampling or as relaxation from high free-energy configurations. The approach maximizes the model likelihood based on any explicit expression of the short-time propagator, hence it can be applied to different evolution equations. We demonstrate the numerical efficiency and robustness of the algorithm on model systems, and we apply it to reconstruct the projected dynamics of pairs of C60 and C240 fullerene molecules in explicit water. Our methodology allows reconstructing the accurate thermodynamics and kinetics of activated processes, namely free energy landscapes, diffusion coefficients, and kinetic rates. Compared to existing enhanced sampling methods, we directly exploit short unbiased trajectories at a competitive computational cost.}}
}




@article{JungHummer_2021, 
year = {2021}, 
title = {{Autonomous artificial intelligence discovers mechanisms of molecular self-organization in virtual experiments}}, 
author = {Jung, Hendrik and Covino, Roberto and Arjun, A and Bolhuis, Peter G and Hummer, Gerhard}, 
journal = {arXiv}, 
eprint = {2105.06673}, 
abstract = {{Molecular self-organization driven by concerted many-body interactions produces the ordered structures that define both inanimate and living matter. Understanding the physical mechanisms that govern the formation of molecular complexes and crystals is key to controlling the assembly of nanomachines and new materials. We present an artificial intelligence (AI) agent that uses deep reinforcement learning and transition path theory to discover the mechanism of molecular self-organization phenomena from computer simulations. The agent adaptively learns how to sample complex molecular events and, on the fly, constructs quantitative mechanistic models. By using the mechanistic understanding for AI-driven sampling, the agent closes the learning cycle and overcomes time-scale gaps of many orders of magnitude. Symbolic regression condenses the mechanism into a human-interpretable form. Applied to ion association in solution, gas-hydrate crystal formation, and membrane-protein assembly, the AI agent identifies the many-body solvent motions governing the assembly process, discovers the variables of classical nucleation theory, and reveals competing assembly pathways. The mechanistic descriptions produced by the agent are predictive and transferable to close thermodynamic states and similar systems. Autonomous AI sampling has the power to discover assembly and reaction mechanisms from materials science to biology.}}, 
keywords = {}
}


@article{MaDinner_2005, 
year = {2005}, 
title = {{Automatic Method for Identifying Reaction Coordinates in Complex Systems †}}, 
author = {Ma, Ao and Dinner, Aaron R}, 
journal = {J.Phys. Chem. B}, 
issn = {1520-6106}, 
doi = {10.1021/jp045546c}, 
pmid = {16851762}, 
pages = {6769--6779}, 
number = {14}, 
volume = {109}, 
keywords = {}
}


@article{WuMa_2022, 
year = {2022}, 
keywords = {Dimensionality Reduction,Reaction Coordinates}, 
title = {{A Rigorous Method for Identifying a One-Dimensional Reaction Coordinate in Complex Molecules}}, 
author = {Wu, Shanshan and Li, Huiyu and Ma, Ao}, 
journal = {J. Chem. Theory Comp.}, 
issn = {1549-9618}, 
doi = {10.1021/acs.jctc.2c00132}, 
pmid = {35427129}, 
abstract = {{Understanding the mechanism of functional protein dynamics is critical to understanding protein functions. Reaction coordinate (RC) is a central topic in protein dynamics, and the grail is to find the one-dimensional RC (1D-RC) that can fully determine the value of a committor (i.e., the reaction probability in configuration space) for any protein configuration. We present a new method that, for the first time, uses a fundamental mechanical operator, the generalized work functional, to identify the rigorous 1D-RC in complex molecules. For a prototypical biomolecular isomerization reaction, the 1D-RC identified by the current method can determine the committor with an accuracy far exceeding what was achieved by previous methods. This method only requires modest computational cost and can be readily applied to large molecules. Most importantly, the generalized work functional is the physical determinant of the collectivity in functional protein dynamics and provides a tentative roadmap that connects the structure of a protein to its function.}}, 
pages = {2836--2844}, 
number = {5}, 
volume = {18}, 
}


@article{LiMa_2014, 
year = {2014}, 
title = {{Recent developments in methods for identifying reaction coordinates}}, 
author = {Li, Wenjin and Ma, Ao}, 
journal = {Mol. Sim.}, 
issn = {0892-7022}, 
doi = {10.1080/08927022.2014.907898}, 
pmid = {25197161}, 
eprint = {1510.07198}, 
abstract = {{In the study of rare events in complex systems with many degrees of freedom, a key element is to identify the reaction coordinates of a given process. Over recent years, a number of methods and protocols have been developed to extract the reaction coordinates based on limited information from molecular dynamics simulations. In this review, we provide a brief survey over a number of major methods developed in the past decade, some of which are discussed in greater detail, to provide an overview of the problems that are partially solved and challenges that still remain. A particular emphasis has been placed on methods for identifying reaction coordinates that are related to the committor.}}, 
pages = {784--793}, 
number = {10-11}, 
volume = {40}, 
keywords = {}
}


@article{BanushkinaKrivov_2016, 
year = {2016}, 
keywords = {Reaction Coordinates}, 
title = {{Optimal reaction coordinates}}, 
author = {Banushkina, Polina V. and Krivov, Sergei V.}, 
journal = {	Wiley Interdiscip. Rev. Comput. Mol. Sci.}, 
issn = {1759-0884}, 
doi = {10.1002/wcms.1276}, 
abstract = {{The dynamic behavior of complex systems with many degrees of freedom is often analyzed by projection onto one or a few reaction coordinates. The dynamics is then described in a simple and intuitive way as diffusion on the associated free-energy profile. In order to use such a picture for a quantitative description of the dynamics one needs to select the coordinate in an optimal way so as to minimize non-Markovian effects due to the projection. For equilibrium dynamics between two boundary states (e.g., a reaction), the optimal coordinate is known as the committor or the pfold coordinate in protein folding studies. While the dynamics projected on the committor is not Markovian, many important quantities of the original multidimensional dynamics on an arbitrarily complex landscape can be computed exactly. In this study, we summarize the derivation of this result, discuss different approaches to determine and validate the committor coordinate, and present three illustrative applications: protein folding, the game of chess, and patient recovery dynamics after kidney transplant. WIREs Comput Mol Sci 2016, 6:748–763. doi: 10.1002/wcms.1276 This article is categorized under:}}, 
pages = {748--763}, 
number = {6}, 
volume = {6}
}


@article{FrassekBolhuis_2021, 
year = {2021}, 
keywords = {ML Features,Reaction Coordinates}, 
title = {{An extended autoencoder model for reaction coordinate discovery in rare event molecular dynamics datasets}}, 
author = {Frassek, M. and Arjun, A. and Bolhuis, P. G.}, 
journal = {J. Chem. Phys.}, 
issn = {0021-9606}, 
doi = {10.1063/5.0058639}, 
abstract = {{The reaction coordinate (RC) is the principal collective variable or feature that determines the progress along an activated or reactive process. In a molecular simulation using enhanced sampling, a good description of the RC is crucial for generating sufficient statistics. Moreover, the RC provides invaluable atomistic insight into the process under study. The optimal RC is the committor, which represents the likelihood of a system to evolve toward a given state based on the coordinates of all its particles. As the interpretability of such a high dimensional function is low, a more practical approach is to describe the RC by some low-dimensional molecular collective variables or order parameters. While several methods can perform this dimensionality reduction, they usually require a preselection of these low-dimension collective variables (CVs). Here, we propose to automate this dimensionality reduction using an extended autoencoder, which maps the input (many CVs) onto a lower-dimensional latent space, which is subsequently used for the reconstruction of the input as well as the prediction of the committor function. As a consequence, the latent space is optimized for both reconstruction and committor prediction and is likely to yield the best non-linear low-dimensional representation of the committor. We test our extended autoencoder model on simple but nontrivial toy systems, as well as extensive molecular simulation data of methane hydrate nucleation. The extended autoencoder model can effectively extract the underlying mechanism of a reaction, make reliable predictions about the committor of a given configuration, and potentially even generate new paths representative for a reaction.}}, 
pages = {064103}, 
number = {6}, 
volume = {155}
}


@article{LiLinRen_2019, 
year = {2019}, 
title = {{Computing committor functions for the study of rare events using deep learning}}, 
author = {Li, Qianxiao and Lin, Bo and Ren, Weiqing}, 
journal = {J. Chem. Phys.}, 
issn = {0021-9606}, 
doi = {10.1063/1.5110439}, 
eprint = {1906.06285}, 
abstract = {{The committor function is a central object of study in understanding transitions between metastable states in complex systems. However, computing the committor function for realistic systems at low temperatures is a challenging task, due to the curse of dimensionality and the scarcity of transition data. In this paper, we introduce a computational approach that overcomes these issues and achieves good performance on complex benchmark problems with rough energy landscapes. The new approach combines deep learning, data sampling and feature engineering techniques. This establishes an alternative practical method for studying rare transition events between metastable states in complex, high dimensional systems.}}, 
pages = {054112}, 
number = {5}, 
volume = {151}, 
keywords = {}
}


@article{MoriMatubayasi_2020, 
year = {2020}, 
title = {{Learning reaction coordinates via cross-entropy minimization: Application to alanine dipeptide}}, 
author = {Mori, Yusuke and Okazaki, Kei-ichi and Mori, Toshifumi and Kim, Kang and Matubayasi, Nobuyuki}, 
journal = {J. Chem. Phys.}, 
issn = {0021-9606}, 
doi = {10.1063/5.0009066}, 
pmid = {32770909}, 
eprint = {2003.13186}, 
abstract = {{We propose a cross-entropy minimization method for finding the reaction coordinate from a large number of collective variables in complex molecular systems. This method is an extension of the likelihood maximization approach describing the committor function with a sigmoid. By design, the reaction coordinate as a function of various collective variables is optimized such that the distribution of the committor pB * values generated from molecular dynamics simulations can be described in a sigmoidal manner. We also introduce the L2-norm regularization used in the machine learning field to prevent overfitting when the number of considered collective variables is large. The current method is applied to study the isomerization of alanine dipeptide in vacuum, where 45 dihedral angles are used as candidate variables. The regularization parameter is determined by cross-validation using training and test datasets. It is demonstrated that the optimal reaction coordinate involves important dihedral angles, which are consistent with the previously reported results. Furthermore, the points with pB *∼0.5 clearly indicate a separatrix distinguishing reactant and product states on the potential of mean force using the extracted dihedral angles.}}, 
pages = {054115}, 
number = {5}, 
volume = {153}, 
keywords = {}, 
local-url = {file://localhost/Users/valsson/Documents/Papers%20Library/The%20Journal%20of%20Chemical%20Physics/2020/Mori-Matubayasi-2020-The%20Journal%20of%20Chemical%20Physics.pdf}
}

@article{Hrustak:JCP:2018,
author = {Hruska,Eugen  and Abella,Jayvee R.  and N\"{u}ske,Feliks  and Kavraki,Lydia E.  and Clementi,Cecilia },
title = {Quantitative comparison of adaptive sampling methods for protein dynamics},
journal = {J. Chem. Phys.},
volume = {149},
number = {24},
pages = {244119},
year = {2018},
doi = {10.1063/1.5053582},
}


@article{Wu:PNAS:2016a,
        title = {Multiensemble {Markov} models of molecular thermodynamics and kinetics},
        volume = {113},
        doi = {10.1073/pnas.1525092113},
        number = {23},
        urldate = {2022-08-06},
        journal = {Proc. Natl. Acad. Sci. U.S.A.},
        author = {Wu, Hao and Paul, Fabian and Wehmeyer, Christoph and No\'e, Frank},
        month = jun,
        year = {2016},
        pages = {E3221--E3230},
}


@article{Wu:JCP:2014,
        title = {Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states},
        volume = {141},
        doi = {10.1063/1.4902240},
        number = {21},
        journal = {J. Chem. Phys.},
        author = {Wu, Hao and Mey, Antonia S. J. S. and Rosta, Edina and No\'{e}, Frank},
        month = dec,
        year = {2014},
	pages = {214106},
}

@article{Wu:MMS:2014,
        title = {Optimal {Estimation} of {Free} {Energies} and {Stationary} {Densities} from {Multiple} {Biased} {Simulations}},
        volume = {12},
        doi = {10.1137/120895883},
        number = {1},
        journal = {Multiscale. Model. Simul.},
        author = {Wu, Hao and No\'{e}, Frank},
        month = jan,
        year = {2014},
        pages = {25--54},
}

@article{Hsu_alchemical_metadynamics,
  doi = {10.48550/arXiv.2206.01329},
  author = {Hsu, Wei-Tse and Merz, Pascal T. and Bussi, Giovanni and Shirts, Michael R.},
  title = {Adding alchemical variables to metadynamics to enhance sampling in free energy calculations},
  journal = {arXiv},
  pages = {2206.01329},
  year = {2022}
}


@article{10.1021/acs.jpclett.2c01807, 
year = {2022}, 
keywords = {Transition State Theory}, 
title = {{Transition Rates and Efficiency of Collective Variables from Time-Dependent Biased Simulations}}, 
author = {Palacio-Rodriguez, Karen and Vroylandt, Hadrien and Stelzl, Lukas S and Pietrucci, Fabio and Hummer, Gerhard and Cossio, Pilar}, 
journal = {J. Phys. Chem. Lett.}, 
issn = {1948-7185}, 
doi = {10.1021/acs.jpclett.2c01807}, 
pages = {7490--7496}
}



@article{10.1021/jacs.7b12191, 
year = {2018}, 
keywords = {Markov State Modeling}, 
title = {{Markov State Models: From an Art to a Science}}, 
author = {Husic, Brooke E and Pande, Vijay S}, 
journal = {J. Am. Chem. Soc.}, 
issn = {0002-7863}, 
doi = {10.1021/jacs.7b12191}, 
pmid = {29323881}, 
abstract = {{Markov state models (MSMs) are a powerful framework for analyzing dynamical systems, such as molecular dynamics (MD) simulations, that have gained widespread use over the past several decades. This perspective offers an overview of the MSM field to date, presented for a general audience as a timeline of key developments in the field. We sequentially address early studies that motivated the method, canonical papers that established the use of MSMs for MD analysis, and subsequent advances in software and analysis protocols. The derivation of a variational principle for MSMs in 2013 signified a turning point from expertise-driving MSM building to a systematic, objective protocol. The variational approach, combined with best practices for model selection and open-source software, enabled a wide range of MSM analysis for applications such as protein folding and allostery, ligand binding, and protein-protein association. To conclude, the current frontiers of methods development are highlighted, as well as exciting applications in experimental design and drug discovery.}}, 
pages = {2386--2396}, 
number = {7}, 
volume = {140}
}


@book{10.1007/978-94-007-7606-7, 
year = {2014}, 
keywords = {Markov State Modeling},
editors = {Gregory R. Bowman, Vijay S. Pande, Frank No\'{e}},
title = {{An Introduction to Markov State Models and Their Application to Long Timescale Molecular Simulation}}, 
series = {Advances in Experimental Medicine and Biology},
publisher = {Springer},
issn = {0065-2598}, 
doi = {10.1007/978-94-007-7606-7}
}


@article{Dietschreit2022,
author = {Dietschreit,Johannes C. B.  and Diestler,Dennis J.  and Ochsenfeld,Christian },
title = {How to obtain reaction free energies from free-energy profiles},
journal = {J. Chem. Phys.},
volume = {156},
number = {11},
pages = {114105},
year = {2022},
doi = {10.1063/5.0083423},
URL = { 
        https://doi.org/10.1063/5.0083423
},
eprint = { 
        https://doi.org/10.1063/5.0083423
}
}


@article{10.1073/pnas.1320077110, 
year = {2013}, 
title = {{Free-energy landscape of protein oligomerization from atomistic simulations}}, 
author = {Barducci, Alessandro and Bonomi, Massimiliano and Prakash, Meher K. and Parrinello, Michele}, 
journal = {Proc. Natl. Acad. Sci. U.S.A.}, 
issn = {0027-8424}, 
doi = {10.1073/pnas.1320077110}, 
pmid = {24248370}, 
pmcid = {PMC3856838}, 
abstract = {{In the realm of protein–protein interactions, the assembly process of homooligomers plays a fundamental role because the majority of proteins fall into this category. A comprehensive understanding of this multistep process requires the characterization of the driving molecular interactions and the transient intermediate species. The latter are often short-lived and thus remain elusive to most experimental investigations. Molecular simulations provide a unique tool to shed light onto these complex processes complementing experimental data. Here we combine advanced sampling techniques, such as metadynamics and parallel tempering, to characterize the oligomerization landscape of fibritin foldon domain. This system is an evolutionarily optimized trimerization motif that represents an ideal model for experimental and computational mechanistic studies. Our results are fully consistent with previous experimental nuclear magnetic resonance and kinetic data, but they provide a unique insight into fibritin foldon assembly. In particular, our simulations unveil the role of nonspecific interactions and suggest that an interplay between thermodynamic bias toward native structure and residual conformational disorder may provide a kinetic advantage.}}, 
pages = {E4708--E4713}, 
number = {49}, 
volume = {110}, 
keywords = {}
}


@article{10.1063/5.0020240, 
year = {2020}, 
title = {{Free energy barriers from biased molecular dynamics simulations}}, 
author = {Bal, Kristof M and Fukuhara, Satoru and Shibuta, Yasushi and Neyts, Erik C}, 
journal = {J. Chem. Phys.}, 
issn = {0021-9606}, 
doi = {10.1063/5.0020240}, 
pages = {114118}, 
number = {11}, 
volume = {153}
}


@article{10.1063/1.5027728, 
year = {2018}, 
title = {{Girsanov reweighting for metadynamics simulations}}, 
author = {Donati, Luca and Keller, Bettina G}, 
journal = {J. Chem. Phys.}, 
issn = {0021-9606}, 
doi = {10.1063/1.5027728}, 
pmid = {30134671}, 
abstract = {{Metadynamics is a computational method to explore the phase space of a molecular system. Gaussian functions are added along relevant coordinates on the fly during a molecular-dynamics simulation to force the system to escape from minima in the potential energy function. The dynamics in the resulting trajectory are however unphysical and cannot be used directly to estimate dynamical properties of the system. Girsanov reweighting is a recent method used to construct the Markov State Model (MSM) of a system subjected to an external perturbation. With the combination of these two techniques-metadynamics/Girsanov-reweighting-the unphysical dynamics in a metadynamics simulation can be reweighted to obtain the MSM of the unbiased system. We demonstrate the method on a one-dimensional diffusion process, alanine dipeptide, and the hexapeptide Val-Gly-Val-Ala-Pro-Gly (VGVAPG). The results are in excellent agreement with the MSMs obtained from direct unbiased simulations of these systems. We also apply metadynamics/Girsanov-reweighting to a β-hairpin peptide, whose dynamics is too slow to efficiently explore its phase space by direct simulation.}}, 
pages = {072335}, 
number = {7}, 
volume = {149}, 
keywords = {}
}


@article{10.1021/ar500356n, 
year = {2015}, 
title = {{Investigating Drug–Target Association and Dissociation Mechanisms Using Metadynamics-Based Algorithms}}, 
author = {Cavalli, Andrea and Spitaleri, Andrea and Saladino, Giorgio and Gervasio, Francesco L.}, 
journal = {Acc. Chem. Res.}, 
issn = {0001-4842}, 
doi = {10.1021/ar500356n}, 
pmid = {25496113}, 
abstract = {{  This Account highlights recent advances and discusses major challenges in the field of drug-target recognition, binding, and unbinding studied using metadynamics-based approaches, with particular emphasis on their role in structure-based design. Computational chemistry has significantly contributed to drug design and optimization in an extremely broad range of areas, including prediction of target druggability and drug likeness, de novo design, fragment screening, ligand docking, estimation of binding affinity, and modulation of ADMET (absorption, distribution, metabolism, excretion, toxicity) properties. Computationally driven drug discovery must continuously adapt to keep pace with the evolving knowledge of the factors that modulate the pharmacological action of drugs. There is thus an urgent need for novel computational approaches that integrate the vast amount of complex information currently available for small (bio)­organic compounds, biologically relevant targets and their complexes, while also accounting accurately for the thermodynamics and kinetics of drug-target association, the intrinsic dynamical behavior of biomolecular systems, and the complexity of protein–protein networks. Understanding the mechanism of drug binding to and unbinding from biological targets is fundamental for optimizing lead compounds and designing novel biologically active ones. One major challenge is the accurate description of the conformational complexity prior to and upon formation of drug–target complexes. Recently, enhanced sampling methods, including metadynamics and related approaches, have been successfully applied to investigate complex mechanisms of drugs binding to flexible targets. Metadynamics is a family of enhanced sampling techniques aimed at enhancing the rare events and reconstructing the underlying free energy landscape as a function of a set of order parameters, usually referred to as collective variables. Studies of drug binding mechanisms have predicted the most probable association and dissociation pathways and the related binding free energy profile. In addition, the availability of an efficient open-source implementation, running on cost-effective GPU (i.e., graphical processor unit) architectures, has considerably decreased the learning curve and the computational costs of the methods, and increased their adoption by the community. Here, we review the recent contributions of metadynamics and other enhanced sampling methods to the field of drug–target recognition and binding. We discuss how metadynamics has been used to search for transition states, to predict binding and unbinding paths, to treat conformational flexibility, and to compute free energy profiles. We highlight the importance of such predictions in drug discovery. Major challenges in the field and possible solutions will finally be discussed.}}, 
pages = {277--285}, 
number = {2}, 
volume = {48}, 
keywords = {}
}


@article{10.1103/physrevlett.110.108106, 
year = {2013}, 
title = {{Efficient Numerical Reconstruction of Protein Folding Kinetics with Partial Path Sampling and Pathlike Variables}}, 
author = {Juraszek, J. and Saladino, G. and Erp, T. S. van and Gervasio, F. L.}, 
journal = {Phys. Rev. Lett.}, 
issn = {0031-9007}, 
doi = {10.1103/physrevlett.110.108106}, 
pmid = {23521305}, 
abstract = {{Numerically predicting rate constants of protein folding and other relevant biological events is still a significant challenge. We show that the combination of partial path transition interface sampling with the optimal interfaces and free-energy profiles provided by path collective variables makes the rate calculation for practical biological applications feasible and efficient. This methodology can reproduce the experimental rate constant of Trp-cage miniprotein folding with the same level of accuracy as transition path sampling at a fraction of the cost.}}, 
pages = {108106}, 
number = {10}, 
volume = {110}, 
keywords = {}
}


@article{10.1371/journal.pcbi.1000452, 
year = {2009}, 
title = {{A Kinetic Model of Trp-Cage Folding from Multiple Biased Molecular Dynamics Simulations}}, 
author = {Marinelli, Fabrizio and Pietrucci, Fabio and Laio, Alessandro and Piana, Stefano}, 
journal = {	PLoS Comput. Biol.}, 
issn = {1553-734X}, 
doi = {10.1371/journal.pcbi.1000452}, 
pmid = {19662155}, 
pmcid = {PMC2711228}, 
abstract = {{Trp-cage is a designed 20-residue polypeptide that, in spite of its size, shares several features with larger globular proteins. Although the system has been intensively investigated experimentally and theoretically, its folding mechanism is not yet fully understood. Indeed, some experiments suggest a two-state behavior, while others point to the presence of intermediates. In this work we show that the results of a bias-exchange metadynamics simulation can be used for constructing a detailed thermodynamic and kinetic model of the system. The model, although constructed from a biased simulation, has a quality similar to those extracted from the analysis of long unbiased molecular dynamics trajectories. This is demonstrated by a careful benchmark of the approach on a smaller system, the solvated Ace-Ala3-Nme peptide. For the Trp-cage folding, the model predicts that the relaxation time of 3100 ns observed experimentally is due to the presence of a compact molten globule-like conformation. This state has an occupancy of only 3\% at 300 K, but acts as a kinetic trap. Instead, non-compact structures relax to the folded state on the sub-microsecond timescale. The model also predicts the presence of a state at of 4.4 Å from the NMR structure in which the Trp strongly interacts with Pro12. This state can explain the abnormal temperature dependence of the and chemical shifts. The structures of the two most stable misfolded intermediates are in agreement with NMR experiments on the unfolded protein. Our work shows that, using biased molecular dynamics trajectories, it is possible to construct a model describing in detail the Trp-cage folding kinetics and thermodynamics in agreement with experimental data.}}, 
pages = {e1000452}, 
number = {8}, 
volume = {5}, 
keywords = {}
}


@article{10.1021/ja903045y, 
year = {2009}, 
title = {{Substrate Binding Mechanism of HIV-1 Protease from Explicit-Solvent Atomistic Simulations}}, 
author = {Pietrucci, Fabio and Marinelli, Fabrizio and Carloni, Paolo and Laio, Alessandro}, 
journal = {J. Am. Chem. Soc.}, 
issn = {0002-7863}, 
doi = {10.1021/ja903045y}, 
pmid = {19645490}, 
abstract = {{The binding mechanism of a peptide substrate (Thr-Ile-Met-Met-Gln-Arg, cleavage site p2-NC of the viral polyprotein) to wild-type HIV-1 protease has been investigated by 1.6 μs biased all-atom molecular dynamics simulations in explicit water. The configuration space has been explored biasing seven reaction coordinates by the bias-exchange metadynamics technique. The structure of the Michaelis complex is obtained starting from the substrate outside the enzyme within a backbone rmsd of 0.9 Å. The calculated free energy of binding is −6 kcal/mol, and the kinetic constants for association and dissociation are 1.3 × 106 M−1 s−1 and 57 s−1, respectively, consistent with experiments. In the main binding pathway, the flaps of the protease do not open sizably. The substrate slides inside the enzyme cavity from the tight lateral channel. This may contrast with the natural polyprotein substrate which is expected to bind by opening the flaps. Thus, mutations might influence differently the binding kinetics of peptidomimetic ligands and of the natural substrate.}}, 
pages = {11811--11818}, 
number = {33}, 
volume = {131}, 
keywords = {}
}


@article{10.1103/physreve.98.052408, 
year = {2018}, 
title = {{Computing transition rates for rare events: When Kramers theory meets the free-energy landscape}}, 
author = {Sicard, François}, 
journal = {Phys. Rev. E}, 
issn = {2470-0045}, 
doi = {10.1103/physreve.98.052408}, 
eprint = {1803.03490}, 
abstract = {{Computing reactive trajectories and free-energy landscapes associated with rare-event kinetics is key to understanding the dynamics of complex systems. The analysis of the free-energy landscape on which the underlying dynamics takes place has become central to compute transition rates. In the overdamped limit, most often encountered in biophysics and soft condensed matter, the Kramers theory and its multidimensional extension derived by Langer have proved to be quite successful in recovering correct kinetics. However, the additional calculation to obtain rate constants in complex systems where configurational entropy is competing with energy is still challenging conceptually and computationally. Building on the Kramers theory and the metadynamics framework, we propose an expression for the rate in terms of the height of the free-energy barrier measured along the minimum free-energy path and an auxiliary measure of the configurational entropy in terms of the joint probability distribution of the reactive and nonreactive coordinates representing the slow modes of the system. We apply the formalism to three different problems where our approach shows good agreement with simulations and experiments and can present significant improvement over the Kramers-Langer's framework when slow entropic contribution, such as configurational entropy, predominates over enthalpic contribution.}}, 
pages = {052408}, 
number = {5}, 
volume = {98}, 
keywords = {}
}


@article{10.1063/5.0019100, 
year = {2020}, 
title = {{A combination of machine learning and infrequent metadynamics to efficiently predict kinetic rates, transition states, and molecular determinants of drug dissociation from G protein-coupled receptors}}, 
author = {Ribeiro, João Marcelo Lamim and Provasi, Davide and Filizola, Marta}, 
journal = {J. Chem. Phys.}, 
issn = {0021-9606}, 
doi = {10.1063/5.0019100}, 
pages = {124105}, 
number = {12}, 
volume = {153}, 
keywords = {}
}