A one-dimensional three-state run-and-tumble model with a `cell cycle'

TL;DR

This paper introduces a one-dimensional three-state run-and-tumble model inspired by Caulobacter crescentus, analyzing stationary states, displacement behaviors, and structure formation including traveling bacterial waves.

Contribution

It presents a novel kinetic model incorporating cell cycle dynamics with mobile and sedentary states, analyzing stability and nonlinear structure formation.

Findings

Super-ballistic scaling of settled cell density ~t^3 at early times

Existence of traveling bacterial waves in the nonlinear regime

Stability analysis of mobile and sedentary state interactions

Abstract

We study a one-dimensional three-state run-and-tumble model motivated by the bacterium Caulobacter crescentus which displays a cell cycle between two non-proliferation mobile phase and a proliferating sedentary phase. Our model implements kinetic transitions between the two mobile and one sedentary states described in terms of their number densities, where mobility is allowed with different running speeds in forward and backward direction. We start by analyzing the stationary states of the system and compute the mean and squared-displacements for the distribution of all cells, as well as for the number density of settled cells. The latter displays a surprising super-ballistic scaling ~t^3 at early times. Including repulsive and attractive interactions between the mobile cell populations and the settled cells, we explore the stability of the system and then employ numerical methods to study structure formation in the fully nonlinear system. We find traveling waves of bacteria, whose occurrence is quantified in a nonequilibrium state diagram.