# msmtools.flux.ReactiveFlux¶

class msmtools.flux.ReactiveFlux(A, B, flux, mu=None, qminus=None, qplus=None, gross_flux=None)

A->B reactive flux from transition path theory (TPT)

This object describes a reactive flux, i.e. a network of fluxes from a set of source states A, to a set of sink states B, via a set of intermediate nodes. Every node has three properties: the stationary probability mu, the forward committor qplus and the backward committor qminus. Every pair of edges has the following properties: a flux, generally a net flux that has no unnecessary back-fluxes, and optionally a gross flux.

Flux objects can be used to compute transition pathways (and their weights) from A to B, the total flux, the total transition rate or mean first passage time, and they can be coarse-grained onto a set discretization of the node set.

Fluxes can be computed in EMMA using transition path theory - see msmtools.tpt()

Parameters: A (array_like) – List of integer state labels for set A B (array_like) – List of integer state labels for set B flux ((n,n) ndarray or scipy sparse matrix) – effective or net flux of A->B pathways mu ((n,) ndarray (optional)) – Stationary vector qminus ((n,) ndarray (optional)) – Backward committor for A->B reaction qplus ((n,) ndarray (optional)) – Forward committor for A-> B reaction gross_flux ((n,n) ndarray or scipy sparse matrix) – gross flux of A->B pathways, if available

Notes

Reactive flux contains a flux network from educt states (A) to product states (B).

msmtools.tpt

__init__(A, B, flux, mu=None, qminus=None, qplus=None, gross_flux=None)

x.__init__(…) initializes x; see help(type(x)) for signature

Methods

 __init__(A, B, flux[, mu, qminus, qplus, …]) x.__init__(…) initializes x; see help(type(x)) for signature coarse_grain(user_sets) Coarse-grains the flux onto user-defined sets. major_flux([fraction]) Returns the main pathway part of the net flux comprising at most the requested fraction of the full flux. pathways([fraction, maxiter]) Decompose flux network into dominant reaction paths.

Attributes

 A Returns the set of reactant (source) states. B Returns the set of product (target) states I Returns the set of intermediate states backward_committor Returns the backward committor probability committor Returns the forward committor probability flux Returns the effective or net flux forward_committor Returns the forward committor probability gross_flux Returns the gross A–>B flux mfpt Returns the rate (inverse mfpt) of A–>B transitions net_flux Returns the effective or net flux nstates Returns the number of states. rate Returns the rate (inverse mfpt) of A–>B transitions stationary_distribution Returns the stationary distribution total_flux Returns the total flux
A

Returns the set of reactant (source) states.

B

Returns the set of product (target) states

I

Returns the set of intermediate states

backward_committor

Returns the backward committor probability

coarse_grain(user_sets)

Coarse-grains the flux onto user-defined sets.

Parameters: user_sets (list of int-iterables) – sets of states that shall be distinguished in the coarse-grained flux. (sets, tpt) – sets contains the sets tpt is computed on. The tpt states of the new tpt object correspond to these sets of states in this order. Sets might be identical, if the user has already provided a complete partition that respects the boundary between A, B and the intermediates. If not, Sets will have more members than provided by the user, containing the “remainder” states and reflecting the splitting at the A and B boundaries. tpt contains a new tpt object for the coarse-grained flux. All its quantities (gross_flux, net_flux, A, B, committor, backward_committor) are coarse-grained to sets. (list of int-iterables, tpt-object)

Notes

All user-specified sets will be split (if necessary) to preserve the boundary between A, B and the intermediate states.

committor

Returns the forward committor probability

flux

Returns the effective or net flux

forward_committor

Returns the forward committor probability

gross_flux

Returns the gross A–>B flux

major_flux(fraction=0.9)

Returns the main pathway part of the net flux comprising at most the requested fraction of the full flux.

mfpt

Returns the rate (inverse mfpt) of A–>B transitions

net_flux

Returns the effective or net flux

nstates

Returns the number of states.

pathways(fraction=1.0, maxiter=1000)

Decompose flux network into dominant reaction paths.

Parameters: fraction (float, optional) – Fraction of total flux to assemble in pathway decomposition maxiter (int, optional) – Maximum number of pathways for decomposition paths (list) – List of dominant reaction pathways capacities (list) – List of capacities corresponding to each reactions pathway in paths

References

 [1] P. Metzner, C. Schuette and E. Vanden-Eijnden. Transition Path Theory for Markov Jump Processes. Multiscale Model Simul 7: 1192-1219 (2009)
rate

Returns the rate (inverse mfpt) of A–>B transitions

stationary_distribution

Returns the stationary distribution

total_flux

Returns the total flux