A Pseudospectral solution of a bistable Fokker–Planck equation that models protein folding

Abstract We consider the one-dimensional bistable Fokker–Planck equation proposed by Polotto et al. (2018), with specific drift and diffusion coefficients so as to model protein folding. In this paper, a pseudospectral method is used to solve the Fokker–Planck equation in terms of the eigenvalues ( λ n ) and eigenfunctions ( ψ n ) of the Fokker–Planck operator. Nonclassical polynomials, constructed orthogonal with respect to the equilibrium distribution of the Fokker–Planck equation, are used as basis functions. The eigenvalues determined with the pseudospectral method are compared with the Wentzel–Kramers–Brillouin (WKB) and the SUperSYmmetric (SUSY) Wentzel–Kramers–Brillouin (SWKB) approximations. The eigenvalues calculated differ significantly from those reported by Polotto et al. A detailed study of the role of the lowest non-zero eigenvalue, λ 1 , to model the rate coefficient for the transition between the bistable states is provided.