Format

Send to

Choose Destination
Proc Natl Acad Sci U S A. 2018 Sep 4;115(36):E8333-E8340. doi: 10.1073/pnas.1805004115. Epub 2018 Aug 20.

Bistable emergence of oscillations in growing Bacillus subtilis biofilms.

Author information

1
Department of Experimental and Health Sciences, Universitat Pompeu Fabra, 08003 Barcelona, Spain.
2
Center for Infectious Diseases Research, School of Medicine, Tsinghua University, Beijing 100084, China.
3
Tsinghua-Peking Center for Life Sciences, Tsinghua University, Beijing 100084, China.
4
Division of Biological Sciences, University of California, San Diego, La Jolla, CA 92093.
5
San Diego Center for Systems Biology, University of California, San Diego, La Jolla, CA 92093.
6
Center for Microbiome Innovation, University of California, San Diego, La Jolla, CA 92093.
7
Department of Experimental and Health Sciences, Universitat Pompeu Fabra, 08003 Barcelona, Spain; jordi.g.ojalvo@upf.edu.

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 nonzero 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 nonoscillating 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 nonzero amplitude via a discontinuous transition.

KEYWORDS:

biofilm growth; biological oscillations; delay-induced oscillations; delayed negative feedback; subcritical Hopf bifurcation

PMID:
30127028
PMCID:
PMC6130386
DOI:
10.1073/pnas.1805004115
[Indexed for MEDLINE]
Free PMC Article

Supplemental Content

Full text links

Icon for HighWire Icon for PubMed Central
Loading ...
Support Center