Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations

doi:10.1051/MMNP/20105107

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Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations

Journal Article•DOI•

Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations

Americo Marrocco¹, Hervé Henry², I. B. Holland³, Mathis Plapp², S. J. Seror³, Benoît Perthame³, Benoît Perthame¹ - Show less +3 more•Institutions (3)

French Institute for Research in Computer Science and Automation¹, École Polytechnique², Centre national de la recherche scientifique³

01 Jan 2010-Mathematical Modelling of Natural Phenomena (EDP Sciences)-Vol. 5, Iss: 1, pp 148-162

TL;DR: A critical anal ysis of the validity of the model based on recent observations of the swarming bacteria which show that nutrients are not limitating but distinct subpopulations growing at different rates are lik ely present is presented.

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Abstract: Bacillus subtilis swarms rapidly over the surface of a synthetic medium creating remarkable hyperbranched dendritic communities. Models to reproduce such effects have been proposed under the form of parabolic Partial Differential Equations representing the dynamics of the active cells (both motile and multiplying), the passive cells (non-motile and non-growing) and nutrient concentration. We test the numerical behavior of such models and compare them to relevant experimental data together with a critical analysis of the validity of the models based on recent observations of the swarming bacteria which show that nutrients are not limitating but distinct subpopulations growing at different rates are likely present.

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Journal Article•DOI•

A model for using self-organized agents to visually map environmental profiles

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John Oyekan¹, Dongbing Gu², Huosheng Hu²•Institutions (2)

Cranfield University¹, University of Essex²

01 Sep 2014-Ecological Complexity

TL;DR: This work presents a novel mathematical model of the bacterium that has the capability of exploring the environment to search for sparsely distributed pollutants or food sources and then subsequently exploiting them upon discovery.

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7 citations

Cites background from "Models of Self-Organizing Bacterial..."

...Collectively, bacteria too are known to exhibit self organization as is evident when they form rings or other various shapes around food sources in the environment depending on the type (Shapiro, 1998; Ben-Jacob, 2003; Marrocco et al., 2010)....
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Dissertation•

Ecological and evolutionary implications of shapes during population expansion

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Christopher Lee Coles

09 Jan 2015

TL;DR: This chapter measures the rate of radial spatial spread of biofilms consisting of the Pseudomonas fluorescens SBW25 WS and SM morphologies on different viscosity agars and classify the rates as either constant, accelerating or decelerating, highlighting the unreliability of the constant rate of spread prediction.

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Abstract: The spread of invasive species is one of the most important issues in conservation, requiring accurate predictive models to help inform us of the most effective control methods to combat their threat. Predictive models of invasive species have classically used reaction-diffusion equations to represent the spread of populations. A key prediction made by these classic equations is a linear relationship between the population radius and time i.e. that the rate of radial spread is constant. While this simple relationship initially proved to be a robust prediction, recent empirical studies exhibiting non-constant rates of radial spread have called into question the reliability of these predictions. Consequently, there is a demand for more empirical evidence to ascertain the reliability of the constant rate of spread prediction and the validity of the assumptions made during the formulation of these classical models. However, to date there have been difficulties collecting sufficiently high-resolution empirical data to test these predictions. Due to its success in evolutionary ecology, we believe the microbial model system is an ideal solution. In this chapter, we measure the rate of radial spatial spread of biofilms consisting of the Pseudomonas fluorescens SBW25 WS and SM morphologies on different viscosity agars and we classify the rates as either constant, accelerating or decelerating. While 59.6% of colonies exhibit a constant rate of spread, 40.4% of colonies do not, with 17.6% and 22.8% of biofilms exhibiting an accelerating and decelerating rate of spread respectively. These results first agree with much of the literature by highlighting the unreliability of the constant rate of spread prediction. Secondly, these results illustrate the important influence of intrinsic and extrinsic factors upon the rate of spread, with some combinations more likely to result in accelerating rates of spread than others. We also find a relationship between the shape of spread and the rate of spread, with irregular patterns of spread typically exhibiting an accelerating rate of spread, possibly revealing a factor behind accelerating rates of spread not previously reported in the literature. Finally, this experiment illustrates the usefulness of bacteria as a model system in spatial ecology.

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5 citations

Cites background from "Models of Self-Organizing Bacterial..."

...With reaction-diffusion equations largely focused upon how biophysical factors give rise to the shape of spread, researchers must be careful that a strong empirical foundation informs the basis of the incorporation of certain factors in their models (Golding et al., 1998, Marrocco et al., 2010)....
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...…swarming motility, it is thought that irregular tendril/fractal-like patterns of spread are formed due to the localised movement exceeding the rate of bacterial growth (Kearns, 2010, Marrocco et al., 2010, Kozlovsky et al., 1999, Tremblay et al., 2007, Dechesne and Smets, 2012, Be'er et al., 2009)....
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...A review by (Marrocco et al., 2010) states that instabilities have typically been incorporated into reactiondiffusion equations describing microbial populations via the explicit modelling of either auto-chemotaxis or the gradient of nutrients in the environment....
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...Whether the ~ 55 ~ assumptions made by these models generalise across species is not clear and requires further investigation in order to answer whether there exists a set of governing principals behind the spatial pattern of spread during microbial growth (Marrocco et al., 2010)....
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...However, models based on auto-chemotaxis of chemo-attractants and chemo-repellents alone have been unable to convincingly describe the fractal-like patterns exhibited by some microbial colonies, such as P. dendritiformis (figure 1.9) or B. subtilis (Marrocco et al., 2010)....
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Journal Article•DOI•

Free boundary morphogenesis in living matter.

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Pasquale Ciarletta¹•Institutions (1)

Centre national de la recherche scientifique¹

11 Jul 2012-European Biophysics Journal

TL;DR: A novel approach for studying free boundary problems during morphogenesis is proposed in this work, where the presence of mass fluxes inside a biological system is coupled with the local gradient of diffusing morphogens.

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Abstract: Morphogenetic theories investigate the creation and the emergence of form in living organisms. A novel approach for studying free boundary problems during morphogenesis is proposed in this work. The presence of mass fluxes inside a biological system is coupled with the local gradient of diffusing morphogens. The contour stability of a growing material is studied using a two-dimensional system model with a rectilinear free border inside a Hele-Shaw cell. Modeling mass transport during morphogenesis allows fixing the velocity at the traveling wave solution as a function of one-dimensionless parameter. Performing a perturbation of the free boundary, the dispersion relation is derived in an implicit form. Although both the velocity of the moving front and the surface tension act as stabilizing effects at small wavelengths, the dispersion diagrams show that the rectilinear border is always unstable at large wavelengths. Further applications of this model can help give insights into a number of free boundary problems in biological systems.

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4 citations

Cites background or methods from "Models of Self-Organizing Bacterial..."

...…the complex patterns in living systems by using phenomenological P. Ciarletta (&) CNRS and Institut Jean le Rond d’Alembert, UMR 7190, 4 place Jussieu, case 162, 75005 Paris, France e-mail: pasquale.ciarletta@upmc.fr models with parabolic partial differential equations (Marrocco et al. 2010)....
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...Further applications of this model can be envisaged for studying the morphology of self-organizing bacterial communities, whose swarming over a synthetic surface is found to create remarkable hyperbranched dendritic shapes (Marrocco et al. 2010)....
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...models with parabolic partial differential equations (Marrocco et al. 2010)....
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Posted Content•DOI•

Physical factors contributing to regulation of bacterial surface motility

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Ben D Rhodeland¹, Kentaro Hoeger¹, Tristan Ursell¹•Institutions (1)

University of Oregon¹

30 Jul 2019-bioRxiv

TL;DR: These findings illuminate the physical structure of surface-motile groups and demonstrate that physical properties, like cellular packing fraction and flow, regulate motion from the scale of individual cells up to length scales of centimeters.

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Abstract: Microbes routinely face the challenge of acquiring territory and resources on wet surfaces. Cells move in large groups inside thin, surface-bound water layers, often achieving speeds of 30 μm/s within this environment, where viscous forces dominate over inertial forces (low Reynolds number). The canonical Gram-positive bacterium Bacillus subtilis is a model organism for the study of collective migration over surfaces with groups exhibiting motility on length scales three orders of magnitude larger than themselves within a few doubling times. Genetic and chemical studies clearly show that the secretion of endogenous surfactants and availability of free surface water are required for this fast group motility. Here we show that: (i) water availability is a sensitive control parameter modulating an abiotic jamming-like transition that determines whether the group remains fluidized and therefore collectively motile, (ii) groups self-organize into discrete layers as they travel, (iii) group motility does not require proliferation, rather groups are pulled from the front, and (iv) flow within expanding groups is capable of moving material from the parent colony into the expanding tip of a cellular dendrite with implications for expansion into regions of varying nutrient content. Together, these findings illuminate the physical structure of surface-motile groups and demonstrate that physical properties, like cellular packing fraction and flow, regulate motion from the scale of individual cells up to length scales of centimeters.

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4 citations

Posted Content•DOI•

Rapid and directed group motility in B. subtilis does not rely on individual motility or chemotaxis

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Ben D Rhodeland¹, Tristan Ursell¹•Institutions (1)

University of Oregon¹

30 Jul 2019-bioRxiv

TL;DR: The data suggest that rapid surface motility does not result from individual motility and chemotaxis properties of the bacteria, but rather that a combination of biologically generated surface tension gradients and abiotic granular jamming regulate this ubiquitous ecological process.

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Abstract: Microbes routinely face the challenge of acquiring territory and resources on wet surfaces. Cells move in large groups inside thin, surface bound water layers, often achieving speeds of 30 μm/s within this environment, where viscous forces dominate over inertial forces (low Reynolds number). The canonical Gram-positive bacterium Bacillus subtilis is a model organism for the study of directed, collective migration over surfaces with groups exhibiting motility on length scales three orders of magnitude larger than themselves within a few doubling times. Genetic and chemical studies clearly show that the secretion of endogenous surfactants and availability of free surface water are required for this ultrafast group motility. However, the relative importance of individual motility, chemosensing, and the presence of exogenous nutrient gradients in precipitating group surface motility are largely unknown. Here we demonstrate that, contrary to models, simulations and observations of surface motility in other bacterial species, (i) B. subtilis does not rely on chemotaxis to determine group motility direction, that (ii) the rate of dendritic expansion has only a weak dependence on motility and that rapid dendritic group motility is possible even with non-motile cells, and that (iii) water availability is likely a sensitive control parameter modulating an abiotic jamming transition that determines whether the group remains fluidized and therefore collectively motile. These data suggest that rapid surface motility does not result from individual motility and chemotaxis properties of the bacteria, but rather that a combination of biologically generated surface tension gradients and abiotic granular jamming regulate this ubiquitous ecological process.

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4 citations

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Journal Article•DOI•

Model for Chemotaxis

[...]

Evelyn Fox Keller¹, Lee A. Segel²•Institutions (2)

Cornell University¹, Rensselaer Polytechnic Institute²

01 Feb 1971-Journal of Theoretical Biology

TL;DR: The chemotactic response of unicellular microscopic organisms is viewed as analogous to Brownian motion, and a macroscopic flux is derived which is proportional to the chemical gradient.

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1,660 citations

"Models of Self-Organizing Bacterial..." refers methods in this paper

...One class of model concerns auto-chemotaxis (attraction of cells by a chemical substance emitted by the cells themselves) and gives rise to a Fokker-Planck equation that is commonly called the Keller-Segel system after the seminal work [12]....
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Book•

Transport Equations in Biology

[...]

Benoît Perthame

05 Sep 2008

TL;DR: In this paper, the renewal equation is used to describe the structure of a population from a point of view of population balance equations, which is an asymptotic view of the population dynamics.

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Abstract: From differential equations to structured population dynamics.- Adaptive dynamics an asymptotic point of view.- Population balance equations: the renewal equation.- Population balance equations: size structure.- Cell motion and chemotaxis.- General mathematical tools.

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932 citations

"Models of Self-Organizing Bacterial..." refers background in this paper

...This model is mathematically very challenging and has motivated numerous studies (see [3, 23] and the references therein); in particular this class of model typically leads to cell aggregation in one or several discrete spots (blow-up of the system as a Dirac mass solution)....
[...]

Journal Article•DOI•

The branching programme of mouse lung development

[...]

Ross J. Metzger¹, Ophir D. Klein², Gail R. Martin², Mark A. Krasnow¹•Institutions (2)

Stanford University¹, University of California, San Francisco²

05 Jun 2008-Nature

TL;DR: This work presents the complete three-dimensional branching pattern and lineage of the mouse bronchial tree, reconstructed from an analysis of hundreds of developmental intermediates, and proposes that each mode of branching is controlled by a genetically encoded subroutine, a series of local patterning and morphogenesis operations, which are themselvescontrolled by a more global master routine.

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Abstract: Mammalian lungs are branched networks containing thousands to millions of airways arrayed in intricate patterns that are crucial for respiration. How such trees are generated during development, and how the developmental patterning information is encoded, have long fascinated biologists and mathematicians. However, models have been limited by a lack of information on the normal sequence and pattern of branching events. Here we present the complete three-dimensional branching pattern and lineage of the mouse bronchial tree, reconstructed from an analysis of hundreds of developmental intermediates. The branching process is remarkably stereotyped and elegant: the tree is generated by three geometrically simple local modes of branching used in three different orders throughout the lung. We propose that each mode of branching is controlled by a genetically encoded subroutine, a series of local patterning and morphogenesis operations, which are themselves controlled by a more global master routine. We show that this hierarchical and modular programme is genetically tractable, and it is ideally suited to encoding and evolving the complex networks of the lung and other branched organs.

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720 citations

"Models of Self-Organizing Bacterial..." refers background in this paper

...Interestingly, this motif, termed domain branching, is observed in mouse lung tissue [18]....
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Journal Article•

Two-dimensional Keller-Segel model: Optimal critical mass and qualitative properties of the solutions

[...]

Adrien Blanchet, Jean Dolbeault, Benoît Perthame¹•Institutions (1)

École Normale Supérieure¹

06 Apr 2006-Electronic Journal of Differential Equations

TL;DR: The Keller-Segel system describes the collective motion of cells which are attracted by a chemical substance and are able to emit it in its simplest form it is a conservative drift-diffusion equation coupled to an elliptic equation for the chemo-attractant concentration as mentioned in this paper.

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Abstract: The Keller-Segel system describes the collective motion of cells which are attracted by a chemical substance and are able to emit it In its simplest form it is a conservative drift-diffusion equation for the cell density coupled to an elliptic equation for the chemo-attractant concentration It is known that, in two space dimensions, for small initial mass, there is global existence of solutions and for large initial mass blow-up occurs In this paper we complete this picture and give a detailed proof of the existence of weak solutions below the critical mass, above which any solution blows-up in finite time in the whole euclidean space Using hypercontractivity methods, we establish regularity results which allow us to prove an inequality relating the free energy and its time derivative For a solution with sub-critical mass, this allows us to give for large times an ``intermediate asymptotics'' description of the vanishing In self-similar coordinates, we actually prove a convergence result to a limiting self-similar solution which is not a simple reflect of the diffusion

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560 citations

"Models of Self-Organizing Bacterial..." refers background in this paper

...This model is mathematically very challenging and has motivated numerous studies (see [3, 23] and the references therein); in particular this class of model typically leads to cell aggregation in one or several discrete spots (blow-up of the system as a Dirac mass solution)....
[...]

Journal Article•DOI•

Autocatalytic reactions in the isothermal, continuous stirred tank reactor: Isolas and other forms of multistability

[...]

P. Gray¹, Stephen K. Scott¹•Institutions (1)

University of Leeds¹

01 Jan 1983-Chemical Engineering Science

TL;DR: In this paper, the authors consider the simple case of uniform temperatures and concentrations in the isothermal CSTR and the simplest of reaction schemes: (i) quadratic autocatalysis (A + B →2 B ); and (ii) cubic autoccatalysis ( A + 2 B →3 B ).

...read moreread less

526 citations