pyemma.msm.tpt¶

pyemma.msm.tpt(msmobj, A, B)¶

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

The returned ReactiveFlux object can be used to extract various quantities of the flux, as well as to compute A -> B transition pathways, their weights, and to coarse-grain the flux onto sets of states.

Parameters:	msmobj (`MSM` object) – Markov state model (MSM) object A (array_like) – List of integer state labels for set A B (array_like) – List of integer state labels for set B
Returns:	tptobj – An object containing the reactive A->B flux network and several additional quantities, such as the stationary probability, committors and set definitions.
Return type:	`ReactiveFlux` object

See also

msmtools.tpt

Methods

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

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.
Returns:	(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.
Return type:	(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

get_model_params(deep=True)¶

Get parameters for this model.

Parameters:	deep (boolean, optional) – If True, will return the parameters for this estimator and contained subobjects that are estimators.
Returns:	params – Parameter names mapped to their values.
Return type:	mapping of string to any

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

Returns:

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

update_model_params(**params)¶: Update given model parameter if they are set to specific values

References

Transition path theory was introduced for space-continuous dynamical processes, such as Langevin dynamics, in [1]_, [2]_ introduces discrete transition path theory for Markov jump processes (Master equation models, rate matrices) and pathway decomposition algorithms. [3]_ introduces transition path theory for Markov state models (MSMs) and some analysis algorithms. In this function, the equations described in [3]_ are applied.

[1]	W. E and E. Vanden-Eijnden. Towards a theory of transition paths. J. Stat. Phys. 123: 503-523 (2006)

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

[3]	F. Noe, Ch. Schuette, E. Vanden-Eijnden, L. Reich and T. Weikl: Constructing the Full Ensemble of Folding Pathways from Short Off-Equilibrium Simulations. Proc. Natl. Acad. Sci. USA, 106, 19011-19016 (2009)

Computes the A->B reactive flux using transition path theory (TPT)

Parameters:

T ((M, M) ndarray or scipy.sparse matrix) – Transition matrix (default) or Rate matrix (if rate_matrix=True)
A (array_like) – List of integer state labels for set A
B (array_like) – List of integer state labels for set B
mu ((M,) ndarray (optional)) – Stationary vector
qminus ((M,) ndarray (optional)) – Backward committor for A->B reaction
qplus ((M,) ndarray (optional)) – Forward committor for A-> B reaction
= False (rate_matrix) – By default (False), T is a transition matrix. If set to True, T is a rate matrix.

Notes

The central object used in transition path theory is the forward and backward comittor function.

TPT (originally introduced in [1]) for continous systems has a discrete version outlined in [2]. Here, we use the transition matrix formulation described in [3].