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

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

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.

Suggested Citation

  • Polotto, Franciele & Drigo Filho, Elso & Chahine, Jorge & Oliveira, Ronaldo Junio de, 2018. "Supersymmetric quantum mechanics method for the Fokker–Planck equation with applications to protein folding dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 286-300.
    • Handle: RePEc:eee:phsmap:v:493:y:2018:i:c:p:286-300
    DOI: 10.1016/j.physa.2017.10.021
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    References listed on IDEAS

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    1. Damiano Brigo & Fabio Mercurio, 2002. "Lognormal-Mixture Dynamics And Calibration To Market Volatility Smiles," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 5(04), pages 427-446.
    2. Lee, Kwonmoo & Sung, Wokyung, 2002. "Ion transport and channel transition in biomembranes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 315(1), pages 79-97.
    3. Borges, G.R.P. & Filho, Elso Drigo & Ricotta, R.M., 2010. "Variational supersymmetric approach to evaluate Fokker–Planck probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3892-3899.
    4. Caldas, Denise & Chahine, Jorge & Filho, Elso Drigo, 2014. "The Fokker–Planck equation for a bistable potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 92-100.
    5. Montagnon, Chris, 2015. "A closed solution to the Fokker–Planck equation applied to forecasting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 420(C), pages 14-22.
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    Cited by:

    1. Philipp, Lucas & Shizgal, Bernie D., 2019. "A Pseudospectral solution of a bistable Fokker–Planck equation that models protein folding," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 522(C), pages 158-166.
    2. Drigo Filho, Elso & Chahine, Jorge & Araujo, Marcelo Tozo & Ricotta, Regina Maria, 2022. "Probability distribution to obtain the characteristic passage time for different tri-stable potentials," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).

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