Models of Self-Organizing Bacterial Communities and Comparisons with Experimental Observations
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.
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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TL;DR: In this paper, an off-lattice simulation of the growth of bacterial colonies is proposed, where bacteria are modelled as rigid circles and nutrients are point-like, Brownian particles.
Abstract: In the growth of bacterial colonies, a great variety of complex patterns are observed in experiments, depending on external conditions and the bacterial species. Typically, existing models employ systems of reaction-diffusion equations or consist of growth processes based on rules, and are limited to a discrete lattice. In contrast, the two-dimensional model proposed here is an off-lattice simulation, where bacteria are modelled as rigid circles and nutrients are point-like, Brownian particles. Varying the nutrient diffusion and concentration, we simulate a wide range of morphologies compatible with experimental observations, from round and compact to extremely branched patterns. A scaling relationship is found between the number of cells in the interface and the total number of cells, with two characteristic regimes. These regimes correspond to the compact and branched patterns, which are exhibited for sufficiently small and large colonies, respectively. In addition, we characterise the screening effect observed in the structures by analysing the multifractal properties of the growth probability.
Dissertation•
30 Nov 2017
TL;DR: In this paper, the authors describe the formation of a gradient de nutriment in a colonie of S. cerevisiae and quantifie les motifs d'expression of genes impliques dans different parties du metabolisme des glucides.
Abstract: L’environnement naturel des levures est constitue d’une communaute de cellules. Les chercheurs, cependant, preferent etudier les levures dans des environnements plus simples et homogenes, comme des cultures en cellule unique ou en population, s’affranchissant ainsi de la complexite de la croissance spatiotemporelle, la differentiation, l’auto-organisation, ainsi que la facon dont ces caracteristiques sont formees et s’entrelacent a travers l’evolution et l’ecologie. Nous avons mis en place un dispositif microfluidique multicouches permettant la croissance de colonie de levures dans des environnements dynamiques, spatialement structures, controles, partant d’une monocouche de levures a une colonie multicouches. La croissance des colonies, dans son ensemble comme a des positions specifiques, est le resultat de la formation d’un gradient de nutriment au sein de celles-ci - gradient qui trouve son origine dans le different taux de diffusion des nutriments, des taux d’absorption de ceux-ci par les cellules, ainsi que de leurs concentrations initiales. Lorsqu’un nutriment en quantite limitante (par exemple le glucose ou un acide amine) est epuise, a une distance specifique de la source de nutriments, les cellules au sein de la colonie cessent de croitre. Nous avons ete en mesure de moduler cette distance specifique en variant la concentration initiale de nutriments ainsi que le taux d’absorption des cellules. Les motifs d’expression de genes de la colonie nous ont donne des informations sur la formation de micro environnements specifiques ainsi que sur le developpement subsequent, la differentiation et l’auto-organisation. Nous avons quantifie les motifs d’expression de sept genes de transport du glucose (HXT1-7), chacun exprime specifiquement suivant la concentration de glucose, ce qui nous a permis de reconstituer la formation de gradients de glucose au sein d’une colonie. En etudiant des genes specifiques de la fermentation et de la respiration, nous avons pu observer la differentiation en deux sous-populations. Nous avons de plus cartographie l’expression de genes impliques dans differentes parties du metabolisme des glucides, suivi et quantifie la dynamique spatio-temporelle de croissance et d’expression genetique et finalement modelise la croissance de la colonie ainsi que la formation du gradient de nutriment. Pour la premiere fois, nous avons observe la croissance, la differentiation et l’auto-organisation des colonies de S. cerevisiae avec une resolution spatio-temporelle jusqu’a maintenant inegalee
TL;DR: X. Xue et al. as discussed by the authors investigated the linear stability analysis of a pathway-based diffusion model (PBDM), which characterizes the dynamics of the engineered Escherichia coli populations, and introduced an asymptotic preserving (AP) scheme for the PBDM that converges to a stable limit scheme consistent with the anisotropic diffusion model.
Abstract: We investigate the linear stability analysis of a pathway-based diffusion model (PBDM), which characterizes the dynamics of the engineered Escherichia coli populations [X. Xue and C. Xue and M. Tang, P LoS Computational Biology, 14 (2018), pp. e1006178]. This stability analysis considers small perturbations of the density and chemical concentration around two non-trivial steady states, and the linearized equations are transformed into a generalized eigenvalue problem. By formal analysis, when the internal variable responds to the outside signal fast enough, the PBDM converges to an anisotropic diffusion model, for which the probability density distribution in the internal variable becomes a delta function. We introduce an asymptotic preserving (AP) scheme for the PBDM that converges to a stable limit scheme consistent with the anisotropic diffusion model. Further numerical simulations demonstrate the theoretical results of linear stability analysis, i.e., the pattern formation, and the convergence of the AP scheme.
References
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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.
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•
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.
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.
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)....
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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.
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.
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•
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.
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
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)....
[...]
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 ).
526 citations
Additional excerpts
...Gray-Scott system [7] is a simple and classical example which writes as ∂...
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