Non-homogeneous random walks, subdiffusive migration of cells and anomalous chemotaxis

TL;DR

This paper develops a non-homogeneous, non-local in time random walk model to describe subdiffusive cell migration and anomalous chemotaxis, deriving related fractional equations and analyzing conditions for cell aggregation.

Contribution

It introduces a structured probability density framework for non-homogeneous subdiffusive transport and examines the stability and aggregation criteria of the resulting fractional equations.

Findings

Derived non-local in time master and fractional equations for cell movement.

Identified structural instability of fractional subdiffusive equations under parameter variations.

Established criteria for anomalous cell aggregation in semi-infinite domains.

Abstract

This paper is concerned with a non-homogeneous in space and non-local in time random walk model for anomalous subdiffusive transport of cells. Starting with a Markov model involving a structured probability density function, we derive the non-local in time master equation and fractional equation for the probability of cell position. We show the structural instability of fractional subdiffusive equation with respect to the partial variations of anomalous exponent. We find the criteria under which the anomalous aggregation of cells takes place in the semi-infinite domain.