Transition Path Theory¶

Transition path theory (TPT) is a way to extract the highest-flux pathways of your system from an estimated MSM.

References¶

These are some 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.

[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).

[4]	Noé, Frank, et al. “Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations.” PNAS 106.45 (2009): 19011-19016.

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, errors, n_samples])	Gets the Mean First Passage Time (MFPT) for all states to a set of sinks.