Supersymmetric quantum mechanics method for the Fokker-Planck equation with applications to protein folding dynamics

Polotto, Franciele [UNESP]; Drigo Filho, Elso [UNESP]; Chahine, Jorge [UNESP]; Oliveira, Ronaldo Junio de

Supersymmetric quantum mechanics method for the Fokker-Planck equation with applications to protein folding dynamics

Arquivos

WOS000423892800025.pdf (1.78 MB)

Data

2018-03-01

Autores

Polotto, Franciele

Drigo Filho, Elso

Chahine, Jorge

Oliveira, Ronaldo Junio de

Editor

Elsevier B.V.

Tipo

Artigo

Direito de acesso

Acesso aberto

Resumo

This work developed analytical methods to explore the kinetics of the time-dependent probability distributions over thermodynamic free energy profiles of protein folding and compared the results with simulation. The Fokker-Planck equation is mapped onto a Schrodinger-type equation due to the well-known solutions of the latter. Through a semi analytical description, the supersymmetric quantum mechanics formalism is invoked and the time-dependent probability distributions are obtained with numerical calculations by using the variational method. A coarse-grained structure-based model of the two-state protein TmCSP was simulated at a C-alpha level of resolution and the thermodynamics and kinetics were fully characterized. Analytical solutions from non-equilibrium conditions were obtained with the simulated double-well free energy potential and kinetic folding times were calculated. It was found that analytical folding time as a function of temperature agrees, quantitatively, with simulations and experiments from the literature of TmCSP having the well-known 'U' shape of the Chevron Plots. The simple analytical model developed in this study has a potential to be used by theoreticians and experimentalists willing to explore, quantitatively, rates and the kinetic behavior of their system by informing the thermally activated barrier. The theory developed describes a stochastic process and, therefore, can be applied to a variety of biological as well as condensed-phase two-state systems. (C) 2017 Elsevier B.V. All rights reserved.