Smoluchowski Equation in Cumulant Approximation

Abstract

Binding energies of many biological complexes are on the order of thermal energy and can become less than that, if a complex is subjected to a dissociative force. In such cases of extended spatial transition regions from one state to another the dynamics of complex decomposition cannot be described correctly by two-variable rate equations, and it is necessary to apply more rigorous approaches. In this work, we use the Smoluchowski equation for the distribution function to study the dynamics of the ligand moving in different profiles of the potential energy. We transform this equation into two different cumulant representations. In the first one the dynamics is represented by an infinite hierarchy of coupled equations for cumulants, while in the second one it is given as an exponential operator acting on cumulants at the initial moment of time. The method coupled equations for cumulants are applied to three different potentials: a fourth-degree polynomial, a Morse potential, and a step potential. Truncatio...