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

Mathematics

Nickolay Korabel¹  Sergei Fedotov¹  Ilya Starodumov²  Dmitri Alexandrov² 

[1] Department of Mathematics, The University of Manchester, Manchester M13 9PL, UK;Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, 620000 Ekaterinburg, Russia;

关键词: stochastic ODE’s;    virus–endosome fusion;    endosomal escape;    viruses;    pH-responsive nanoparticles;   

DOI  :  10.3390/math10030375

来源: DOAJ

【 摘 要 】

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.

【 授权许可】

Unknown