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.
Highlights
Escape of Viruses use diverse processes to enter the host cell: some undergo membrane fusion and deliver genetic material directly into the cytoplasm; others use an endocytic pathway by hijacking endosomes and exploit the intracellular transport along microtubules to deliver a viral genome to sites of replication [1,2]
We introduce the noise terms ξ 5 (t) and ξ 7 (t) because experimental knowledge is yet to decipher the multitude of mechanisms that are responsible for random endosome evolution and dynamics of Rab5, Rab7 and pH value within the cell
We have presented the stochastic model for the random dynamics of active Rab5 and
Summary
Introduction and Endosomal Escape ofViruses use diverse processes to enter the host cell: some undergo membrane fusion and deliver genetic material directly into the cytoplasm; others use an endocytic pathway by hijacking endosomes and exploit the intracellular transport along microtubules to deliver a viral genome to sites of replication [1,2]. Viruses must escape from endosomes into the cytoplasm. This escape is mediated by the fusion of the endosomal and virus membrane that depends on conformational change of the viral glycoprotein hemagglutinin triggered by lowered pH [3,4,5]. The low internal pH of these membrane-bound vesicles is sustained by the active ATP-dependent proton pumps on their membranes. These key proteins on the surface of endosomes are the main factors in the identification of early and late endosomes, their biogenesis and fusion/fission processes [8]. Rab proteins mark early endosomes, whereas Rab proteins are localized to late endosomes and lysosomes
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