Stochastic dynamics of chemotactic colonies with logistic growth

TL;DR

This paper investigates the large-scale dynamics of dividing chemotactic bacterial colonies using a renormalization group approach, revealing emergent interactions and connections to the KPZ equation, indicating complex non-equilibrium behavior.

Contribution

It introduces a renormalization group analysis of chemotactic colonies with growth, uncovering fluctuation-induced interactions and linking colony dynamics to the KPZ universality class.

Findings

Fluctuations generate an unconventional chemotactic interaction.

No stable fixed point found at one-loop order, indicating complex dynamics.

Connection established between colony dynamics and the KPZ equation with long-range noise.

Abstract

The interplay between cellular growth and cell-cell signaling is essential for the aggregation and proliferation of bacterial colonies, as well as for the self-organization of cell tissues. To investigate this interplay, we focus here on the collective properties of dividing chemotactic cell colonies by studying their long-time and large-scale dynamics through a renormalization group (RG) approach. The RG analysis reveals that a relevant but unconventional chemotactic interaction -- corresponding to a polarity-induced mechanism -- is generated by fluctuations at macroscopic scales, even when an underlying mechanism is absent at the microscopic level. This emerges from the interplay of the well-known Keller--Segel (KS) chemotactic nonlinearity and cell birth and death processes. At one-loop order, we find no stable fixed point of the RG flow equations. We discuss a connection between the dynamics investigated here and the celebrated Kardar--Parisi--Zhang (KPZ) equation with long-range correlated noise, which points at the existence of a strong-coupling, nonperturbative fixed point.