Density-Dependence Subdiffusion in Chemotaxis

TL;DR

This paper introduces a nonlinear, non-Markovian model of subdiffusive chemotactic transport where the chemotactic gradient influences cell movement and waiting times, leading to new insights into stationary density distributions.

Contribution

It develops a novel fractional master equation incorporating chemotactic effects at all times, extending previous models to include nonlinear density dependence and gradient influence.

Findings

Stationary solutions depend on the chemotactic gradient shape.

Gradient influences the subdiffusive transport behavior.

Model provides a framework for understanding chemotaxis with anomalous diffusion.

Abstract

The purpose of this work is to propose a nonlinear non-Markovian model of subdiffusive transport that involves chemotactic substance affecting the cells at all time, not only during the jump. This leads the random waiting time to be dependent on the chemotactic gradient, making the escape rates also dependent on the gradient as well as the nonlinear density dependence. We systematically derive subdiffusive fractional master equation, then we consider the diffusive limit of the fractional master equation. We finally solve the resulting fractional subdiffusive master equation stationery and analyse the role of the chemotactic gradient in the resulting stationary density with a constant and a quadratic chemotactic gradient.