IdentiFlow

Interaction strengths between nodes in directed networks can be quantified from observations of the network's response to perturbations. This package reveals the identifiability of the inferred network parameters and optimizes experimental design for network perturbation studies. See our publication for details.

You can install the IdentiFlow package with pip:

pip install git+https://github.com/GrossTor/IdentiFlow#egg=identiflow

The package is easy to use and we demonstrate its most relevant features in the example below. You find the example script in identiflow/examples. This folder also contains the scripts that were used to analyse the KEGG pathways, as described in our paper.

After successful installation of the package you are able to import it in your Python session.

import identiflow

Input

First we define the network topology as a networkx Digraph and specify perturbations and their targets in a dictionary.

import networkx as nx

edges = [('node 0', 'node 1'),
         ('node 0', 'node 2'),
         ('node 0', 'node 3'),
         ('node 1', 'node 3'),
         ('node 2', 'node 3'),
         ('node 3', 'node 0'),
         ('node 4', 'node 3'),
         ('node 4', 'node 5'),
         ('node 5', 'node 4')]

perturbations = {'P0': {'node 0', 'node 3'},
                 'P1': {'node 2'},
                 'P2': {'node 3', 'node 4'}}


net = nx.DiGraph(edges)

#There must be no self_loops. The next line ensures it.
net.remove_edges_from(nx.classes.selfloop_edges(net))

Identifiability

Next, we investigate which of the interaction and perturbation strengths are identifiable in this perturbation experiment. This can be done with the function infer_identifiability (or infer_identifiability_by_simulation, see function documentation for details). It returns dictionaries that specify the dimensionality of the associated solution spaces and the identifiability status. The latter can be depicted by the plotting function draw_identifiability_graph.

sol_space_dims, identifiability = \
    identiflow.infer_identifiability(net,perturbations)
sol_space_dims_simu, identifiability_simu = \
    identiflow.infer_identifiability_by_simulation(net,perturbations)

identiflow.draw_identifiability_graph(identifiability)

To elucidate the identifiability relationships between groups of network parameters we can can determine the cyclic flats using the function infer_identifiability_relationships and plot them with draw_lattice.

cyclic_flats_dict = \
    identiflow.infer_identifiability_relationships(net, perturbations)
for node in cyclic_flats_dict:
    if sol_space_dims[node]>0:
        fig,ax=identiflow.draw_lattice(cyclic_flats_dict[node])

Experimental design

IdentiFlow also allows to identify perturbation sequences that maximize the number of identifiable parameters with a minimal number of perturbations. The function optimize_experimental_design has different options to do so, that are described in detail in its documentation. Here we try a few and compare their performances.

nodes = list(net.nodes)

#we allow all single target perturbations

perturbations = {'P{0}'.format(i):{nodes[i]} for i in range(len(nodes))}
exhaustive = identiflow.optimize_experimental_design(net, perturbations,
                                strategy='exhaustive',sampling=False)

greedy = identiflow.optimize_experimental_design(net, perturbations,
                                strategy='greedy',sampling=False)

multi_target = identiflow.optimize_experimental_design(net, perturbations,
                                strategy='multi_target',sampling=False)

naive = identiflow.optimize_experimental_design(net, perturbations,
                                strategy='naive',sampling=False)

random = identiflow.optimize_experimental_design(net, perturbations,
                                strategy='random',sampling=True, n_samples=1)


import pprint
print('\nPerformance:\n\n   exhaustive: {0}\n   greedy: {1}\n   multi_target: {2}\n   naive: {3}\n   random: {4}'.format(
        exhaustive['ident_AUC'],greedy['ident_AUC'],multi_target['ident_AUC'],naive['ident_AUC'], random['ident_AUC']))

print('\nBest perturbation sequences:\n\n   greedy:\n')
pprint.pprint(greedy['best_pert_seqs'])
print('\n   multi-target:\n')
pprint.pprint([tuple(set(combi) for combi in seq) for seq in multi_target['best_pert_seqs']])

Performance:

   exhaustive: 0.7592592592592593
   greedy: 0.7592592592592593
   multi_target: 0.8148148148148148
   naive: 0.7407407407407407
   random: 0.48148148148148145

Best perturbation sequences:

   greedy:

[('P5', 'P0', 'P1', 'P2', 'P4'),
 ('P5', 'P0', 'P2', 'P1', 'P4'),
 ('P4', 'P0', 'P1', 'P2', 'P5'),
 ('P4', 'P0', 'P2', 'P1', 'P5')]

   multi-target:

[({'P5'}, {'P0', 'P4'}, {'P2'}, {'P1'}),
 ({'P5'}, {'P0', 'P4'}, {'P1'}, {'P2'}),
 ({'P4'}, {'P0', 'P5'}, {'P2'}, {'P1'}),
 ({'P4'}, {'P0', 'P5'}, {'P1'}, {'P2'})]