msmbuilder.tpt.paths¶

msmbuilder.tpt.
paths
(sources, sinks, net_flux, remove_path='subtract', num_paths=inf, flux_cutoff=0.9999999999)¶ Get the top N paths by iteratively performing Dijkstra’s algorithm.
Parameters: sources : array_like, int
Onedimensional list of nodes to define the source states.
sinks : array_like, int
Onedimensional list of nodes to define the sink states.
net_flux : np.ndarray
Net flux of the MSM
remove_path : str or callable, optional
Function for removing a path from the net flux matrix. (if str, one of {‘subtract’, ‘bottleneck’}) See note below for more details.
num_paths : int, optional
Number of paths to find
flux_cutoff : float, optional
Quit looking for paths once the explained flux is greater than this cutoff (as a percentage of the total).
Returns: paths : list
List of paths. Each item is an array of nodes visited in the path.
fluxes : np.ndarray, shape = [n_paths,]
Flux of each path returned.
See also
msmbuilder.tpt.top_path
 function for computing the single highest flux pathway through a network.
Notes
The Dijkstra algorithm only allows for computing the single top flux pathway through the net flux matrix. If we want many paths, there are many ways of finding the second highest flux pathway.
The algorithm proceeds as follows:
 Using the Djikstra algorithm, find the highest flux pathway from the sources to the sink states
 Remove that pathway from the net flux matrix by some criterion
 Repeat (1) with the modified net flux matrix
Currently, there are two schemes for step (2):
 ‘subtract’ : Remove the path by subtracting the flux of the path from every edge in the path. This was suggested by Metzner, Schutte, and VandenEijnden. Transition Path Theory for Markov Jump Processes. Multiscale Model. Simul. 7, 11921219 (2009).
 ‘bottleneck’ : Remove the path by only removing the edge that corresponds to the bottleneck of the path.
If a new scheme is desired, the user may pass a function that takes the net_flux and the path to remove and returns the new net flux matrix.
References
[R68] Weinan, E. and VandenEijnden, E. Towards a theory of transition paths. J. Stat. Phys. 123, 503523 (2006). [R69] Metzner, P., Schutte, C. & VandenEijnden, E. Transition path theory for Markov jump processes. Multiscale Model. Simul. 7, 11921219 (2009). [R70] Berezhkovskii, A., Hummer, G. & Szabo, A. Reactive flux and folding pathways in network models of coarsegrained protein dynamics. J. Chem. Phys. 130, 205102 (2009). [R71] Dijkstra, E. W. A Note on Two Problems in Connexion with Graphs. Numeriche Mathematik 1, 269271 (1959). [R72] Noe, Frank, et al. “Constructing the equilibrium ensemble of folding pathways from short offequilibrium simulations.” PNAS 106.45 (2009): 1901119016.