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

Franciele Polotto, Elso Drigo Filho, Jorge Chahine and Ronaldo Junio de Oliveira

Physica A: Statistical Mechanics and its Applications, 2018, vol. 493, issue C, 286-300

Abstract: 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 Schrödinger-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 Tm CSP was simulated at a Cα 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 Tm CSP 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.

Keywords: Quantum mechanics; Schrödinger equation; Folding rates; Structure-based model (search for similar items in EconPapers)
Date: 2018
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