Transition Path Theory¶

Background¶

This module contains functions for analyzing Markov state models, with an emphasis on Transition Path Theory (TPT)

These are the canonical references for TPT. Note that TPT is really a specialization of ideas very familiar to the mathematical study of Markov chains, and there are many books, manuscripts in the mathematical literature that cover the same concepts.

References¶

[1]	E, Weinan and Vanden-Eijnden, Eric Towards a Theory of Transition Paths J. Stat. Phys. 123 503-523 (2006)

[2]	Metzner, P., Schutte, C. & Vanden-Eijnden, E. Transition path theory for Markov jump processes. Multiscale Model. Simul. 7, 1192-1219 (2009).

[3]	Berezhkovskii, A., Hummer, G. & Szabo, A. Reactive flux and folding pathways in network models of coarse-grained protein dynamics. J. Chem. Phys. 130, 205102 (2009).

Functions¶

`fluxes`(sources, sinks, msm[, for_committors])	Compute the transition path theory flux matrix.
`net_fluxes`(sources, sinks, msm[, for_committors])	Computes the transition path theory net flux matrix.
`fraction_visited`(source, sink, waypoint, msm)	Calculate the fraction of times a walker on tprob going from sources to sinks will travel through the set of states waypoints en route.
`hub_scores`(msm[, waypoints])	Calculate the hub score for one or more waypoints
`paths`(sources, sinks, net_flux[, ...])	Get the top N paths by iteratively performing Dijkstra’s algorithm.
`top_path`(sources, sinks, net_flux)	Use the Dijkstra algorithm for finding the shortest path connecting a set of source states from a set of sink states.
`committors`(sources, sinks, msm)	Get the forward committors of the reaction sources -> sinks.
`conditional_committors`(source, sink, ...)	Computes the conditional committors \(q^{ABC^+}\) which are is the probability of starting in one state and visiting state B before A while also visiting state C at some point.
`mfpts`(msm[, sinks, lag_time])	Gets the Mean First Passage Time (MFPT) for all states to a set of sinks.