https://doi.org/10.1140/epje/s10189-022-00238-7
Regular Article - Living Systems
A one-dimensional three-state run-and-tumble model with a ‘cell cycle’
1 Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany
2 Unité de Glycobiologie Structurale et Fonctionnelle (UGSF), CNRS UMR8576, University of Lille, 59000, Lille, France
Received: 13 June 2022
Accepted: 10 October 2022
Published online: 19 October 2022
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-proliferating mobile phases 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 
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 employ numerical methods to study structure formation in the fully nonlinear system. We find traveling waves of bacteria, whose occurrence is quantified in a non-equilibrium state diagram.
© The Author(s) 2022
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