English

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

Subcellular Processes 2021-07-22 v1 Statistical Mechanics Biological Physics

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.

Keywords

Cite

@article{arxiv.2101.02698,
  title  = {Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution},
  author = {Sergei Fedotov and Daniel Han and Andrey Yu. Zubarev and Mark Johnston and Victoria J Allan},
  journal= {arXiv preprint arXiv:2101.02698},
  year   = {2021}
}

Comments

arXiv admin note: text overlap with arXiv:1902.03087