Internal stress drives ferromagnetic-like ordering in networks of proliferating bacteria

TL;DR

This study demonstrates that internal stress in proliferating bacteria within microchannel networks induces ferromagnetic-like ordering, revealing a surprising link between active growth dynamics and equilibrium statistical mechanics.

Contribution

It introduces a minimal model showing how internal stress drives collective ordering in proliferating bacteria, bridging active matter physics with equilibrium concepts.

Findings

Coherent growth patterns emerge in bacteria networks due to internal stress.

An effective equilibrium model captures the out-of-equilibrium dynamics.

Internal stress causes ferromagnetic-like interactions among growth nodes.

Abstract

Proliferation is a defining feature of life. Through growth, division, and death, living systems consume energy and inject mass, breaking conservation laws and driving collective phenomena from biofilm formation to embryonic development. Yet, while active matter physics has advanced our understanding of self-propelled agents, quantitative frameworks for proliferating systems are still emerging, and most work focuses on simplified settings. Here, we study \textit{E.coli} bacteria growing inside a network of single-file microchannels as a minimal model of structured environments. Competition for free volume drives the spontaneous emergence of coherent growth patterns that persist across generations but vanish when the channel links exceed the typical cell size at birth. Despite the strongly out-of-equilibrium character of the dynamics, the observed phenomenology can be quantitatively captured by an effective equilibrium description in which the flow state at each node is represented by a spin variable with ferromagnetic interactions. Simulations of growing elastic cells show that this coupling arises from internal stress accumulated at network nodes due to dynamical constraints. Our results reveal a surprising correspondence between proliferating active matter and equilibrium statistical mechanics, highlighting open fundamental questions and offering a first step toward describing growth phenomena in real-world complex environments.