Estimation of reactive fluxes in gradient stochastic systems using an analogy with electric circuits

We propose an approach for finding dominant reactive channels and calculating percentages of reactive flux through each channel in chemical systems driven by a deterministic potential force and a small thermal noise. We assume that the temperature is low enough so that the reactive flux focuses around a finite number of paths connecting the reactant and the product states. These paths can be found in a systematic way by solving a Hamilton–Jacobi equation for the so called MaxFlux functional. We argue that the name “MaxFlux” is misleading: it should be called the resistivity functional instead. Once the network of transition paths is found, one can define an equivalent electric circuit and find the currents through each of its wires. These currents give estimates of the reactive flux along the corresponding transition paths. We test our approach on the problem of finding transition paths in the Alanine-Dipeptide with two dihedral angles where the reactive current can be computed exactly. The percentages of the reactive flux through each reactive channel given by our approach turn out to be in remarkable agreement with the exact ones. We apply this approach to the problem of finding escape paths of a CO molecule from a Myoglobin protein. We find a collection of exit locations and establish percentages of the reactive flux through each of them.