Mathematical Aspects of Bacterial Chemotaxis

Keller, Evelyn Fox

doi:10.1159/000395425

Cited by 15 publications

(5 citation statements)

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“…21 is perhaps the predicted dependence of the expansion speed c on the attractant diffusion coefficient D a ( Fig. 2 D ), which was not considered in most previous models ( 33 , 34 , 70 , 71 ). Although this dependence itself is not so strong, it significantly affects the dependence of c on the cellular motility characteristics as we discuss next.…”

Section: Chemotaxis Regimementioning

confidence: 92%

“…2D) and its relation to Dρ (Fig. 3) reveals a crucial role of the molecular diffusion of the attractant, which has historically been assumed to be of a much smaller scale than the motilityinduced bacterial diffusion and chemotaxis (33,34,36,44,70,71,75). Large D a can be understood to result in a smoothening of the attractant gradient, thereby slowing down chemotaxis.…”

Section: Parameter Dependences Of the Expansion Speedmentioning

confidence: 92%

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A traveling-wave solution for bacterial chemotaxis with growth

Narla

Cremer

Hwa

2021

Proc. Natl. Acad. Sci. U.S.A.

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Bacterial cells navigate their environment by directing their movement along chemical gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial populations into previously unoccupied territories. However, despite numerous experimental and theoretical studies on this classical topic, chemotaxis-driven population expansion is not understood in quantitative terms. Building on recent experimental progress, we here present a detailed analytical study that provides a quantitative understanding of how chemotaxis and cell growth lead to rapid and stable expansion of bacterial populations. We provide analytical relations that accurately describe the dependence of the expansion speed and density profile of the expanding population on important molecular, cellular, and environmental parameters. In particular, expansion speeds can be boosted by orders of magnitude when the environmental availability of chemicals relative to the cellular limits of chemical sensing is high. Analytical understanding of such complex spatiotemporal dynamic processes is rare. Our analytical results and the methods employed to attain them provide a mathematical framework for investigations of the roles of taxis in diverse ecological contexts across broad parameter regimes.

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Section: Chemotaxis Regimementioning

confidence: 92%

Section: Parameter Dependences Of the Expansion Speedmentioning

confidence: 92%

A traveling-wave solution for bacterial chemotaxis with growth

Narla

Cremer

Hwa

2021

Proc. Natl. Acad. Sci. U.S.A.

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“…Here we think of a mechanism whereby the ratio 2~c/c would have a threshold value, where ~ cis the drop in concentration along the cell length and c the local concentration. (Bonner, 1947;Keller, 1974).…”

Section: Discussionmentioning

confidence: 99%

A diffusion model for mesoderm induction in amphibian embryos

1977

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In this paper we try to answer the question whether diffusion is a possible mechanism to explain mesoderm induction in Amphibians. First the embryological data are discussed and a hypothesis for mesoderm formation is set forth. The blastula being essentially a hollow sphere, we assume that the induction mechanism in an embryo at the blastula stage can be simulated by diffusion-reaction processes on spherical surfaces. A model is constructed for the simple case when the source is held constant with respect to time, the decay proportional to the concentration and the diffusion coefficient a constant. From simulation we find a (best) value for the decay constant to be 6 x 10(-5)/sec and for the diffusion constant to be 0.24 x 10(-6) cm2/sec. The relation between the parameters is derived from an analytic solution for the diffusion process on a spherical surface with a continuously producing point source and the concentration proportional to the decay. The form and regulative properties of the steady concentration gradient are discussed.

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“…Although the direction needs not to be biased towards the negative terminal, longer mean free path this way with respect to the opposite results the current. Max Delbruck in 1970s thought what chemoattractant gradient controls is the same: how frequently bacteria tumbles [ 178 ]. Along the gradient, bacteria tumble more frequently moving downhill (i.e.…”

Section: What Feature Of a Morphogen Gradient Provides Positional Inf...mentioning

confidence: 99%

Patterning principles of morphogen gradients

Simsek

Özbudak

2022

Open Biol.

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Metazoan embryos develop from a single cell into three-dimensional structured organisms while groups of genetically identical cells attain specialized identities. Cells of the developing embryo both create and accurately interpret morphogen gradients to determine their positions and make specific decisions in response. Here, we first cover intellectual roots of morphogen and positional information concepts. Focusing on animal embryos, we then provide a review of current understanding on how morphogen gradients are established and how their spans are controlled. Lastly, we cover how gradients evolve in time and space during development, and how they encode information to control patterning. In sum, we provide a list of patterning principles for morphogen gradients and review recent advances in quantitative methodologies elucidating information provided by morphogens.

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Mathematical Aspects of Bacterial Chemotaxis

Cited by 15 publications

References 0 publications

A traveling-wave solution for bacterial chemotaxis with growth

A traveling-wave solution for bacterial chemotaxis with growth

A diffusion model for mesoderm induction in amphibian embryos

Patterning principles of morphogen gradients

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