deeptime.markov.tools.flux.rate

deeptime.markov.tools.flux.rate(totflux, pi, qminus)

Transition rate for reaction A to B.

Parameters:

• totflux (float) – The total flux between reactant and product

• pi ((M,) ndarray) – Stationary distribution

• qminus ((M,) ndarray) – Backward comittor

Returns:

kAB – The reaction rate (per time step of the Markov chain)

Return type:

float

See also

committor, total_flux, flux_matrix

Notes

Computation of the rate relies on discrete transition path theory (TPT). The transition rate, i.e. the total number of reaction events per time step, is given in [1] as:

$$k_{AB}=\frac{1}{F} \sum_i \pi_i q_i^{(-)}$$

$F$ is the total flux for the transition from $A$ to $B$.

References

[1]

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)