more notebook progress

gromacs-free-energy-tutorial.ipynb

@@ -395,6 +395,26 @@
        "\n",
        "**Question**: Look at the error bars for the individual $\\lambda$ points: they vary a lot between individual point pairs. What does this mean for the efficiency for the overall calculation? How could it be improved?\n"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+       " ## Where to go from here\n",
+       "After calculating the free energy of solvation, we’ve solved the first part of the free energy of binding of the earlier equations. The second part involves coupling a molecule into (or out of) a situation where it is bound to a protein. This introduces one additional complexity: we end up with a situation where a weakly coupled ligand wanders through our system:\n",
+       "![weak-couple.png](./images/weak-couple.png)\n",
+       "which is bad because this is a poorly reversible situation: there are suddenly very few states that map from a weakly coupled to a more strongly coupled molecule, which will drastically reduce the accuracy of the free energy calculation.\n",
+       "\n",
+       "This situation can be remedied by forcing the ligand to stay at a specific position relative to the protein. This can be done with the Gromacs ‘pull code’, which allows the specification of arbitrary forces or constraints onto with respect to centers of mass of any chosen set of atoms onto any other group of atoms. With a pull type of ‘umbrella’, we can specify that we want a quadratic potential to this specified location, forcing the ligand to stay at its native position even when it has been fully de-coupled.\n",
+       "\n",
+       "One way find out where to put the center of the force is by choosing a group of atoms in the protein close to the ligand, and doing a simulation with full ligand coupling, where the pull code is enabled, but with zero force. The pull code will then frequently output the coordinates of the ligand, from which an average position and an expected deviation can be calculated. This can then serve as a reference point for the location of the center of force for the pull code during the production runs, and the force constant of the pull code.\n",
+       "\n",
+       "Once the free energy has been calculated, care must be taken to correct for the fact that we have trapped our molecule. This can easily be done analytically.\n",
+       "\n",
+       "**Optional Question**: Given a measured standard deviation in the location of the center of mass of our ligand, how do we choose the force constant for the pull code?\n",
+       "\n",
+       "**Optional Question**: How do we correct for using the pull code: what is the contribution to the free energy of applying a quadratic potential to a molecule?\n"
+   ]
   }
  ],
  "metadata": {