msmbuilder.tpt.top_path

msmbuilder.tpt.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.

Parameters:

sources : array_like, int

One-dimensional list of nodes to define the source states.

sinks : array_like, int

One-dimensional list of nodes to define the sink states.

net_flux : np.ndarray, shape = [n_states, n_states]

Net flux of the MSM

Returns:

top_path : np.ndarray

Array corresponding to the top path between sources and sinks. It is an array of states visited along the path.

flux : float

Flux traveling through this path – this is equal to the minimum flux over edges in the path.

See also

msmbuilder.tpt.paths

function for calculating many high flux paths through a network.

References

[1]	Weinan, E. and Vanden-Eijnden, E. 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]	Dijkstra, E. W. A Note on Two Problems in Connexion with Graphs. Numeriche Mathematik 1, 269-271 (1959).

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