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Stochastic Model of Virus–Endosome Fusion and Endosomal Escape of pH-Responsive Nanoparticles

Author

Listed:
  • Sergei Fedotov

    (Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK)

  • Dmitri Alexandrov

    (Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia)

  • Ilya Starodumov

    (Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia)

  • Nickolay Korabel

    (Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK)

Abstract

In this paper, we set up a stochastic model for the dynamics of active Rab5 and Rab7 proteins on the surface of endosomes and the acidification process that govern the virus–endosome fusion and endosomal escape of pH-responsive nanoparticles. We employ a well-known cut-off switch model for Rab5 to Rab7 conversion dynamics and consider two random terms: white Gaussian and Poisson noises with zero mean. We derive the governing equations for the joint probability density function for the endosomal pH, Rab5 and Rab7 proteins. We obtain numerically the marginal density describing random fluctuations of endosomal pH. We calculate the probability of having a pH level inside the endosome below a critical threshold and therefore the percentage of viruses and pH-responsive nanoparticles escaping endosomes. Our results are in good qualitative agreement with experimental data on viral escape.

Suggested Citation

  • Sergei Fedotov & Dmitri Alexandrov & Ilya Starodumov & Nickolay Korabel, 2022. "Stochastic Model of Virus–Endosome Fusion and Endosomal Escape of pH-Responsive Nanoparticles," Mathematics, MDPI, vol. 10(3), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:375-:d:734167
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    References listed on IDEAS

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    1. Anja Zeigerer & Jerome Gilleron & Roman L. Bogorad & Giovanni Marsico & Hidenori Nonaka & Sarah Seifert & Hila Epstein-Barash & Satya Kuchimanchi & Chang Geng Peng & Vera M. Ruda & Perla Del Conte-Zer, 2012. "Rab5 is necessary for the biogenesis of the endolysosomal system in vivo," Nature, Nature, vol. 485(7399), pages 465-470, May.
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