An agent-based model of metabolic signaling oscillations in Bacillus subtilis biofilms
Obadiah J. Mulder, Maya Peters Kostman, Abdulrahmen Almodaimegh, Michael D. Edge, Joseph W. Larkin
Abstract
Microbes of nearly every species can form biofilms, communities of cells bound together by a self-produced matrix. It is not understood how variation at the cellular level impacts putatively beneficial, colony-level behaviors, such as cell-to-cell signaling. Here we investigate this problem with an agent-based computational model of metabolically driven electrochemical signaling in Bacillus subtilis biofilms. In this process, glutamate-starved interior cells release potassium, triggering a depolarizing wave that spreads to exterior cells and limits their glutamate uptake.
Introduction
Bacterial biofilms are large communities of cells that exist in nearly every environment [1]. They are bound together by an extracellular matrix that provides both stability and protection [2–4]. Biofilms exhibit a variety of emergent behaviors that give biofilm-dwelling microbes advantages unavailable to planktonic cells [5–7]. For example, cells within biofilms differentiate into heterogeneous phenotypes [8–11], divide labor [12,13], and coordinate behavior via chemical signals [14–17]. These group phenomena have led some researchers to assert that biofilms represent a transition between single-celled and multicellular life [18,19].
Materials and method
Model development
Our model is a network agent-based model, where cells are simulated as individual “agents,” each with their own set of rules for interacting with each other and their environment. Cells are placed on a network, where each cell is on a node and can interact with its neighbors. In the context of biofilms, neighbors are adjacent cells. During each unit of time (a “tick,” representing 1.2 minutes in this model) every cell performs actions according to their governing equations, and the environment is updated. We model the biofilm as hexagonal, matching observations by Larkin et al. [27] that cells in these biofilms have a modal value of 6 immediate neighbors.
Results
Model overview
Our model aims to describe an oscillating hyperpolarization-depolarization behavior observed in B. subtilis biofilms grown in flow cells [20,21]. In such scenarios, when a biofilm grows past a certain size, metabolically stressed interior cells release potassium ions. The primary source of nitrogen in flow-cell experiments is glutamate [20], and cells absorb glutamate via a transporter whose activity depends on membrane potential.
Discussion
We introduced a computational model of metabolic signaling in B. subtilis biofilms. Previous models of this behavior have either been limited in scope, focusing on local cellular behaviors and omitting nutrients, or broad in scope, but unable to capture heterogeneity in cell-level behavior. [25,28].
Acknowledgments
We thank C. Bergstrom, T. Kessinger, M. Lachmann, C.B. Ogbunu, J. Van Cleve, and members of the Edge, Mooney, Pennell, and Larkin labs for helpful comments on this study.
Citation: Mulder OJ, Peters Kostman M, Almodaimegh A, Edge MD, Larkin JW (2025) An agent-based model of metabolic signaling oscillations in Bacillus subtilis biofilms. PLoS Comput Biol 21(12): e1013746. https://doi.org/10.1371/journal.pcbi.1013746
Editor: Attila Csikász-Nagy, Pázmány Péter Catholic University: Pazmany Peter Katolikus Egyetem, HUNGARY
Received: December 20, 2024; Accepted: November 13, 2025; Published: December 4, 2025
Copyright: © 2025 Mulder et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
Data Availability: Code used to generate the simulations and figures that appear in this manuscript is available at https://github.com/Muldero/AgentBasedBsubtilis.
Funding: Funding was provided by NIH grant R35GM137758 to MDE and NIH grant R35GM142584, NSF grant 2027108, and a CASI award from the Burroughs Wellcome Fund to JWL. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
Competing interests: The authors have declared that no competing interests exist.
