Stochastic dynamics of chemotactic colonies with logistic growth

¹ Sorbonne Université & CNRS, Laboratoire de Physique Théorique de la Matière Condensée, LPTMC F-75005, Paris, France
² Max- Planck-Institut für Physik komplexer Systeme - D-01187 Dresden, Germany
³ Rudolf Peierls Centre for Theoretical Physics, University of Oxford - Oxford OX1 3PU, UK
⁴ Max Planck Institute for Dynamics and Self- Organization (MPIDS) - D-37077 Göttingen, Germany
⁵ SISSA –International School for Advanced Studies & INFN - via Bonomea 265, I-34136 Trieste, Italy

^(a) riccardo.baz@pm.me (corresponding author)

Received: 15 November 2021
Accepted: 6 January 2022

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.