Bistable emergence of oscillations in structured cell populations

TL;DR

This study combines experiments and modeling to show that biofilm oscillations can suddenly emerge with high amplitude through a bistable, discontinuous transition, influenced by colony size and stress.

Contribution

It demonstrates that oscillations in bacterial biofilms can arise via a subcritical Hopf bifurcation, enabling instant high amplitude oscillations and bistability, which was previously unclear.

Findings

Oscillations emerge through a subcritical Hopf bifurcation.

A bistable regime exists with coexisting oscillating and non-oscillating states.

Oscillation onset size decreases with increased stress.

Abstract

Biofilm communities of Bacillus subtilis bacteria have recently been shown to exhibit collective growth-rate oscillations mediated by electrochemical signaling to cope with nutrient starvation. These oscillations emerge once the colony reaches a large enough number of cells. However, it remains unclear whether the amplitude of the oscillations, and thus their effectiveness, builds up over time gradually, or if they can emerge instantly with a non-zero amplitude. Here we address this question by combining microfluidics-based time-lapse microscopy experiments with a minimal theoretical description of the system in the form of a delay-differential equation model. Analytical and numerical methods reveal that oscillations arise through a subcritical Hopf bifurcation, which enables instant high amplitude oscillations. Consequently, the model predicts a bistable regime where an oscillating and a non-oscillating attractor coexist in phase space. We experimentally validate this prediction by showing that oscillations can be triggered by perturbing the media conditions, provided the biofilm size lies within an appropriate range. The model also predicts that the minimum size at which oscillations start decreases with stress, a fact that we also verify experimentally. Taken together, our results show that collective oscillations in cell populations can emerge suddenly with non-zero amplitude via a discontinuous transition.