Open AccessDifferential equation-based minimal model describing metabolic oscillations in Bacillus subtilis biofilms
Author(s) -
Ravindra Garde,
Bashar Ibrahim,
Ákos T. Kovács,
Stefan Schuster
Publication year - 2020
Publication title -
royal society open science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.84
H-Index - 51
ISSN - 2054-5703
DOI - 10.1098/rsos.190810
Subject(s) - biofilm , bacillus subtilis , hopf bifurcation , biological system , bilinear interpolation , bifurcation , work (physics) , differential equation , mathematics , control theory (sociology) , computer science , statistical physics , physics , biology , nonlinear system , mathematical analysis , control (management) , bacteria , thermodynamics , artificial intelligence , statistics , genetics , quantum mechanics
Biofilms offer an excellent example of ecological interaction among bacteria. Temporal and spatial oscillations in biofilms are an emerging topic. In this paper, we describe the metabolic oscillations in Bacillus subtilis biofilms by applying the smallest theoretical chemical reaction system showing Hopf bifurcation proposed by Wilhelm and Heinrich in 1995. The system involves three differential equations and a single bilinear term. We specifically select parameters that are suitable for the biological scenario of biofilm oscillations. We perform computer simulations and a detailed analysis of the system including bifurcation analysis and quasi-steady-state approximation. We also discuss the feedback structure of the system and the correspondence of the simulations to biological observations. Our theoretical work suggests potential scenarios about the oscillatory behaviour of biofilms and also serves as an application of a previously described chemical oscillator to a biological system.