Stochastic nonlinear model for nanoparticles and viruses escape from endosomes

A stochastic nonlinear model for Rab5 and Rab7 proteins describing the transformation of early endosomes into late endosomes was formulated. This model consists of two stochastic nonlinear differential equations for Rab5 and Rab7 protein levels on the endosome surface. The primary goal of this paper is to understand the impact of multiplicative noise on the nonlinear dynamics of Rab5 and Rab7. The main idea is to introduce the stochastic variable T, which defines the random time when the conversion from Rab5 to Rab7 occurs. It follows from the dynamics of pH level that T can also be considered as the escape time of pH-sensitive nanoparticles and viruses from endosomes. The probability density function for T was obtained numerically. It was shown that the average conversion time T is shifted to the right when compared to the deterministic one, potentially influencing the pH distribution function and, consequently, the average escape time of viruses and nanoparticles.