Lane formation and critical coarsening in a model of bacterial competition

TL;DR

This study models bacterial competition in a 3D channel, revealing lane formation, coarsening dynamics, and phase transitions influenced by mutation and killing, with implications for understanding spatial bacterial organization.

Contribution

The paper introduces a lattice model for bacterial competition that captures lane formation, coarsening, and phase transitions, linking biological phenomena to statistical physics concepts.

Findings

Logarithmic slow coarsening similar to the voter model.

Phase transition from monopolistic to mixed phase with mutation and killing.

Critical behavior aligns with generalized voter and Ising classes.

Abstract

We study competition of two non-motile bacterial strains in a three-dimensional channel numerically, and analyze how their configuration evolves in space and time. We construct a lattice model that takes into account self-replication, mutation, and killing of bacteria. When mutation is not significant, the two strains segregate and form stripe patterns along the channel. The formed lanes are gradually rearranged, with increasing length scales in the two-dimensional cross-sectional plane. We characterize it in terms of coarsening and phase ordering in statistical physics. In particular, for the simple model without mutation and killing, we find logarithmically slow coarsening, which is characteristic of the two-dimensional voter model. With mutation and killing, we find a phase transition from a monopolistic phase, in which lanes are formed and coarsened until the system is eventually dominated by one of the two strains, to an equally mixed and disordered phase without lane structure. Critical behavior at the transition point is also studied and compared with the generalized voter class and the Ising class. These results are accounted for by continuum equations, obtained by applying a mean field approximation along the channel axis. Our findings indicate relevance of critical coarsening of two-dimensional systems in the problem of bacterial competition within anisotropic three-dimensional geometry.