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