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arXiv · 2101.02698

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

Sergei Fedotov·Daniel Han·Andrey Yu. Zubarev·Mark Johnston·Victoria J Allan
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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.

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Sergei Fedotov, Daniel Han, Andrey Yu. Zubarev, Mark Johnston, Victoria J Allan. 2021-01-07. Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution. https://doi.org/10.1098/rsta.2020.0317

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