IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v493y2018icp286-300.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437117310312
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2017.10.021?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. 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.
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    2. 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.
    3. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    4. Antoine Jacquier & Patrick Roome, 2015. "Black-Scholes in a CEV random environment," Papers 1503.08082, arXiv.org, revised Nov 2017.
    5. Damiano Brigo, 2008. "The general mixture-diffusion SDE and its relationship with an uncertain-volatility option model with volatility-asset decorrelation," Papers 0812.4052, arXiv.org.
    6. Hentati-Kaffel, R. & Prigent, J.-L., 2016. "Optimal positioning in financial derivatives under mixture distributions," Economic Modelling, Elsevier, vol. 52(PA), pages 115-124.
    7. Christa Cuchiero & Irene Klein & Josef Teichmann, 2017. "A fundamental theorem of asset pricing for continuous time large financial markets in a two filtration setting," Papers 1705.02087, arXiv.org.
    8. Gianluca Vagnani, 2009. "The Black-Scholes model as a determinant of the implied volatility smile: A simulation study," Post-Print hal-00736952, HAL.
    9. Detering, Nils & Packham, Natalie, 2018. "Model risk of contingent claims," IRTG 1792 Discussion Papers 2018-036, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    10. Rui, Weiguo & Yang, Xinsong & Chen, Fen, 2022. "Method of variable separation for investigating exact solutions and dynamical properties of the time-fractional Fokker–Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 595(C).
    11. Ramírez-Piscina, L. & Sancho, J.M., 2018. "Periodic spiking by a pair of ionic channels," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 345-354.
    12. Alessandro Ramponi, 2011. "Mixture Dynamics and Regime Switching Diffusions with Application to Option Pricing," Methodology and Computing in Applied Probability, Springer, vol. 13(2), pages 349-368, June.
    13. Xin Liu, 2016. "Asset Pricing with Random Volatility," Papers 1610.01450, arXiv.org, revised Sep 2018.
    14. Iain J. Clark & Saeed Amen, 2017. "Implied Distributions from GBPUSD Risk-Reversals and Implication for Brexit Scenarios," Risks, MDPI, vol. 5(3), pages 1-17, July.
    15. Murphy, David & Vasios, Michalis & Vause, Nick, 2014. "Financial Stability Paper No 29: An investigation into the procyclicality of risk-based initial margin models," Bank of England Financial Stability Papers 29, Bank of England.
    16. Donald Aingworth & Sanjiv Das & Rajeev Motwani, 2006. "A simple approach for pricing equity options with Markov switching state variables," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 95-105.
    17. Giorno, Virginia & Nobile, Amelia G., 2023. "On a time-inhomogeneous diffusion process with discontinuous drift," Applied Mathematics and Computation, Elsevier, vol. 451(C).
    18. Tao L. Wu & Shengqiang Xu, 2014. "A Random Field LIBOR Market Model," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(6), pages 580-606, June.
    19. Bhat, Harish S. & Kumar, Nitesh, 2012. "Option pricing under a normal mixture distribution derived from the Markov tree model," European Journal of Operational Research, Elsevier, vol. 223(3), pages 762-774.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:493:y:2018:i:c:p:286-300. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.