Journal
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
Volume 493, Issue -, Pages 286-300Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.physa.2017.10.021
Keywords
Quantum mechanics; Schrodinger equation; Folding rates; Structure-based model
Categories
Funding
- FAPESP [2011/17658-3]
- FAPEMIG [APQ-00941-14]
- CAPES
- CNPq [441730/2014-0]
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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.
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