Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution

TL;DR

This paper develops a space-dependent variable-order fractional master equation to model and analyze the non-uniform clustering of lysosomes within living cells, providing exact solutions and validating them through simulations.

Contribution

It introduces a novel space-dependent variable-order fractional master equation for modeling particle clustering in cells, linking it to fractional diffusion and validating with simulations.

Findings

Exact solutions for lysosome distribution in cells.

Clustering behavior explained by space-dependent fractional exponents.

Monte Carlo simulations confirm analytical results.

Abstract

In this paper, we formulate the space-dependent variable-order fractional master equation to model clustering of particles, organelles, inside living cells. We find its solution in the long time limit describing non-uniform distribution due to a space dependent fractional exponent. In the continuous space limit, the solution of this fractional master equation is found to be exactly the same as the space-dependent variable-order fractional diffusion equation. In addition, we show that the clustering of lysosomes, an essential organelle for healthy functioning of mammalian cells, exhibit space-dependent fractional exponents. Furthermore, we demonstrate that the non-uniform distribution of lysosomes in living cells is accurately described by the asymptotic solution of the space-dependent variable-order fractional master equation. Finally, Monte Carlo simulations of the fractional master equation validate our analytical solution.