Modeling Spatio-Temporal Patterns Generated byBacillus subtilis

Kawasaki, Kohkichi; Mochizuki, Atsushi; Matsushita, Mitsugu; Umeda, Tomoko; Shigesada, Nanako

doi:10.1006/jtbi.1997.0462

Cited by 238 publications

(269 citation statements)

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“…Similar morphological patterns have also been observed in growing yeast colonies [21]. Several studies [22][23][24][25][26][27][28], since then, have proposed mathematical models to investigate the phase-diagram of Ref. [23].…”

Section: Introductionsupporting

confidence: 64%

“…Several studies [22][23][24][25][26][27][28], since then, have proposed mathematical models to investigate the phase-diagram of Ref. [23]. These models can be broadly classified into two categories: (i) Agent based models -In these models each bacteria is treated as an entity and the collective spatiotemporal behavior largely depends upon the local interactions among them.…”

Section: Introductionmentioning

confidence: 99%

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Spreading of nonmotile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

2017

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We study spreading of a non-motile bacteria colony on a hard agar plate by using agent-based and continuum models. We show that the spreading dynamics depends on the initial nutrient concentration, the motility and the inherent demographic noise. Population fluctuations are inherent in an agent based model whereas, for the continuum model we model them by using a stochastic Langevin equation. We show that the intrinsic population fluctuations coupled with non-linear diffusivity lead to a transition from Diffusion Limited Aggregation (DLA) type morphology to an Eden-like morphology on decreasing the initial nutrient concentration.

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Section: Introductionsupporting

confidence: 64%

Section: Introductionmentioning

confidence: 99%

Spreading of nonmotile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

2017

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“…The main branching mechanism seems to be stable and is kept with B f ̸ = 0. This mechanism, since it does not use local nutrient depletion, is very different from that observed for reaction-diffusion systems (see 19,23,17,8 and the references therein). The system (2.1) can generate several types of instabilities and we study some of them below for simplified equations.…”

Section: Resultsmentioning

confidence: 78%

“…As observed in 21 , all past attempts to model branching patterns for B. subtilis are based on the assumption of a nutrition limited process (see 19,23,17,8 and the survey in 24 ). Most of them are related to dynamical pattern formations à la Gray-Scott 9 .…”

Section: Introductionmentioning

confidence: 99%

Waves for a Hyperbolic Keller–segel Model and Branching Instabilities

Cerreti

Perthame

Schmeiser

et al. 2011

Math. Models Methods Appl. Sci.

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Recent experiments for swarming of the bacteria Bacillus subtilis on nutrient-rich media show that these cells are able to proliferate and spread out in colonies exhibiting complex patterns as dendritic ramifications. Is it possible to explain this process with a model that does not use local nutrient depletion? We present a new class of models which is compatible with the experimental observations and which predict branching instabilities and does not use nutrient limitation. These conclusions are based on numerical simulations. The most complex of these models is also the biologically most accurate but the essential effects can also be obtained in simplified versions which are amenable to analysis. An example of instability mechanism is the transition from a shock wave to a rarefaction wave in a reduced two by two hyperbolic system.

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“…The reaction-diffusion model has successfully described the dynamics of pattern formation in bacterial colonies at continuum level [1,2,4,5]. Recently, a nonlinear reaction-diffusion with chemotaxis model has been proposed for studying the pattern formation in bacterial colonies exemplified by Paenibacillus dendritiformis grown on Petri dish [1,5,12,13].…”

mentioning

confidence: 99%

Self-similar dynamics of bacterial chemotaxis

Ngamsaad

Khompurngson

2012

Phys. Rev. E

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Colonies of bacteria grown on thin agar plate exhibit fractal patterns as a result of adaptation to their environments. The bacterial colony pattern formation is regulated crucially by chemotaxis, the movement of cells along a chemical concentration gradient. Here, the dynamics of pattern formation in bacterial colony is investigated theoretically through a continuum model that considers chemotaxis. In the case of the gradient sensed by the bacterium is nearly uniform, the bacterial colony patterns are self-similar, which they look the same at every scale. The scaling law of the bacterial colony growth has been revealed explicitly. Chemotaxis biases the movement of bacterial population in colony trend toward the chemical attractant. Moreover, the bacterial colonies evolve long time as the traveling wave with sharp front.

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Modeling Spatio-Temporal Patterns Generated byBacillus subtilis

Cited by 238 publications

References 0 publications

Spreading of nonmotile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

Spreading of nonmotile bacteria on a hard agar plate: Comparison between agent-based and stochastic simulations

Waves for a Hyperbolic Keller–segel Model and Branching Instabilities

Self-similar dynamics of bacterial chemotaxis

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