Interplay of chemotaxis and chemokinesis mechanisms in bacterial dynamics

TL;DR

This paper models bacterial movement by integrating chemotaxis and chemokinesis mechanisms, analyzing how chemical signaling influences bacterial trajectories and diffusion behaviors through simulations and mathematical equations.

Contribution

It introduces a self-interacting random walk model capturing the interplay of chemotaxis and chemokinesis in bacteria, including derivation of Fokker-Planck equations and numerical solutions.

Findings

Identification of crossover behaviors among diffusion regimes

Derivation of cell positional distributions and moments

Analysis of average drift and mean squared displacement

Abstract

Motivated by observations of the dynamics of {\it Myxococcus xanthus}, we present a self-interacting random walk model that describes the competition between chemokinesis and chemotaxis. Cells are constrained to move in one dimension, but release a chemical chemoattractant at a steady state. The bacteria senses the chemical that it produces. The probability of direction reversals is modeled as a function of both the absolute level of chemoattractant sensed directly under each cell as well as the gradient sensed across the length of the cell. If the chemical does not degrade or diffuse rapidly, the one dimensional trajectory depends on the entire past history of the trajectory. We derive the corresponding Fokker-Planck equations, use an iterative mean field approach that we solve numerically for short times, and perform extensive Monte-Carlo simulations of the model. Cell positional distributions and the associated moments are computed in this feedback system. Average drift and mean squared displacements are found. Crossover behavior among different diffusion regimes are found.