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Garde2020-Minimal model describing metabolic oscillations in Bacillus subtilis biofilms

ABSTRACT: 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.

SUBMITTER: Ahmad Zyoud

PROVIDER: BIOMD0000000932 | BioModels | 2020-04-14

REPOSITORIES: BioModels

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Differential equation-based minimal model describing metabolic oscillations in <i>Bacillus subtilis</i> biofilms.

Garde Ravindra R Ibrahim Bashar B Kovács Ákos T ÁT Schuster Stefan S

Royal Society open science 20200205 2

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 <i>Bacillus subtilis</i> 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 ...[more]

PMID: 32257302

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Project description:During commitment of a multipotent stem or progenitor cell to a particular lineage, a large number of genes alter their expression in a coordinated manner orchestrated by the gene regulatory network (GRN). The constraints imposed by the GRN govern how cells move in the high-dimensional gene expression state space and can be understood as a dynamical system in which phenotypic cell states (cell types) are attractors that stabilize the cell-type characteristic gene expression pattern against molecular noise. Despite insights from various theoretical models, it remains elusive how multipotent cells, when committing to a specific lineage, exit their attractor and enter a new distinct attractor. Here we show, using single-cell resolution monitoring of transcript patterns by qPCR that commitment of multipotent blood progenitor cells to either the erythroid or the myeloid lineage is preceded by a destabilization of the progenitorsâ?? attractor state and a slowing-down of relaxation of cells from outlier states, indicating a critical state transition (â??tipping pointâ??). The high-dimensionality of the system (many genes) and availability of individual trajectories of a large ensemble of systems (many cells) affords a novel signature for critical transition which can be predicted from theory: Decrease of correlation between cells and concomitant increase of correlation between genes as the cell population approaches the tipping point. Consistent with a destabilizing bifurcation that simultaneously opens access to the erythroid and myeloid attractors, differentiation signal for either lineage caused some cells to commit to the â??wrongâ?? fate; moreover providing conflicting signals resulted in a delayed decision at the bifurcation point that however was ultimately resolved by commitment to one fate. These results suggest that the theoretical framework of â??early-warning signsâ?? and critical transitions can be applied to ensembles of high-dimensional systems, offering a formal tool for analyzing single-cell omics data beyond current descriptive computational pattern recognition. Mouse blood progenitor cells (EML cell line) was exposed to EPO, IL-3/GM-CSF or a mixture of both cytokines and gene expression change was measured in sorted subpopulations wrt Sca1 progenitor surface marker expression. In total, there was 4 conditions (including control), three time points (including d0) and 20 samples (10 samples in duplicates) were analyzed. Two independent experiments were performed for each condition. The untreated progenitor cell population was used as control.

Project description:During commitment of a multipotent stem or progenitor cell to a particular lineage, a large number of genes alter their expression in a coordinated manner orchestrated by the gene regulatory network (GRN). The constraints imposed by the GRN govern how cells move in the high-dimensional gene expression state space and can be understood as a dynamical system in which phenotypic cell states (cell types) are attractors that stabilize the cell-type characteristic gene expression pattern against molecular noise. Despite insights from various theoretical models, it remains elusive how multipotent cells, when committing to a specific lineage, exit their attractor and enter a new distinct attractor. Here we show, using single-cell resolution monitoring of transcript patterns by qPCR that commitment of multipotent blood progenitor cells to either the erythroid or the myeloid lineage is preceded by a destabilization of the progenitors’ attractor state and a slowing-down of relaxation of cells from outlier states, indicating a critical state transition (“tipping point”). The high-dimensionality of the system (many genes) and availability of individual trajectories of a large ensemble of systems (many cells) affords a novel signature for critical transition which can be predicted from theory: Decrease of correlation between cells and concomitant increase of correlation between genes as the cell population approaches the tipping point. Consistent with a destabilizing bifurcation that simultaneously opens access to the erythroid and myeloid attractors, differentiation signal for either lineage caused some cells to commit to the “wrong” fate; moreover providing conflicting signals resulted in a delayed decision at the bifurcation point that however was ultimately resolved by commitment to one fate. These results suggest that the theoretical framework of “early-warning signs” and critical transitions can be applied to ensembles of high-dimensional systems, offering a formal tool for analyzing single-cell omics data beyond current descriptive computational pattern recognition.

Project description:Wolf2000 - Cellular interaction on glycolytic oscillations in yeast A two-cell model of glycolysis. This model is described in the article: Effect of cellular interaction on glycolytic oscillations in yeast: a theoretical investigation. Wolf J, Heinrich R. Biochem. J. 2000 Jan; 345 Pt 2: 321-334 Abstract: On the basis of a detailed model of yeast glycolysis, the effect of intercellular dynamics is analysed theoretically. The model includes the main steps of anaerobic glycolysis, and the production of ethanol and glycerol. Transmembrane diffusion of acetaldehyde is included, since it has been hypothesized that this substance mediates the interaction. Depending on the kinetic parameter, the single-cell model shows both stationary and oscillatory behaviour. This agrees with experimental data with respect to metabolite concentrations and phase shifts. The inclusion of intercellular coupling leads to a variety of dynamical modes, such as synchronous oscillations, and different kinds of asynchronous behavior. These oscillations can co-exist, leading to bi- and tri-rhythmicity. The corresponding parameter regions have been identified by a bifurcation analysis. The oscillatory dynamics of synchronized cell populations are investigated by calculating the phase responses to acetaldehyde pulses. Simulations are performed with respect to the synchronization of two subpopulations that are oscillating out of phase before mixing. The effect of the various process on synchronization is characterized quantitatively. While continuous exchange of acetaldehyde might synchronize the oscillations for appropriate sets of parameter values, the calculated synchronization time is longer than that observed experimentally. It is concluded either that addition to the transmembrane exchange of acetaldehyde, other processes may contribute to intercellular coupling, or that intracellular regulator feedback plays a role in the acceleration of the synchronization. for appropriate sets of parameter values, the calculated synchronization time is longer than that observed experimentally. It is concluded either that addition to the transmembrane exchange of acetaldehyde, other processes may contribute to intercellular coupling, or that intracellular regulator feedback plays a role in the acceleration of the synchronization. This model is hosted on BioModels Database and identified by: BIOMD0000000691. To cite BioModels Database, please use: Chelliah V et al. BioModels: ten-year anniversary. Nucl. Acids Res. 2015, 43(Database issue):D542-8. To the extent possible under law, all copyright and related or neighbouring rights to this encoded model have been dedicated to the public domain worldwide. Please refer to CC0 Public Domain Dedication for more information.

Dataset Information

Garde2020-Minimal model describing metabolic oscillations in Bacillus subtilis biofilms

Publications

Differential equation-based minimal model describing metabolic oscillations in <i>Bacillus subtilis</i> biofilms.

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