Complex patterns formed by motile cells of Escherichia coli

Budrene, Elena O.; Berg, Howard C.

doi:10.1038/349630a0

Cited by 528 publications

(456 citation statements)

References 17 publications

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“…A number of models have been developed based on systems of equations similar to (1) that successfully capture many key features of the lifecycle [38,44]. Understanding bacterial pattern formation has also benefited from modelling: certain bacteria, including E. coli and S. typhimurium, can be induced to form a variety of spatial patterns when provided a suitable environment [11,12,108]. Mathematical models indicate a chemotactic process in which cells produce an auto-attractant may underlie this patterning ( [101,108], see also [68]).…”

Section: Derivation and Applications Of Chemotaxis Modelsmentioning

confidence: 99%

A user’s guide to PDE models for chemotaxis

2008

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Mathematical modelling of chemotaxis (the movement of biological cells or organisms in response to chemical gradients) has developed into a large and diverse discipline, whose aspects include its mechanistic basis, the modelling of specific systems and the mathematical behaviour of the underlying equations. The Keller-Segel model of chemotaxis (Keller and Segel in J Theor Biol 26:399-415, 1970; 30:225-234, 1971) has provided a cornerstone for much of this work, its success being a consequence of its intuitive simplicity, analytical tractability and capacity to replicate key behaviour of chemotactic populations. One such property, the ability to display "auto-aggregation", has led to its prominence as a mechanism for self-organisation of biological systems. This phenomenon has been shown to lead to finite-time blow-up under certain formulations of the model, and a large body of work has been devoted to determining when blow-up occurs or whether globally existing solutions exist. In this paper, we explore in detail a number of variations of the original Keller-Segel model. We review their formulation from a biological perspective, contrast their patterning properties, summarise key results on their analytical properties and classify their solution form. We conclude with a brief discussion and expand on some of the outstanding issues revealed as a result of this work.

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Section: Derivation and Applications Of Chemotaxis Modelsmentioning

confidence: 99%

A user’s guide to PDE models for chemotaxis

2008

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“…The study of peritrichously flagellated bacteria such as E. coli has received considerable attention [31,12,68,13,24,14,15,74,16,76,79,29]. However, many bacterial strains such as Pseudomonas aeruginosa have a single flagellum at one end of a rodshaped body or a pair of flagella, one at each end [91,39].…”

Section: Introductionmentioning

confidence: 99%

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

Hsu

Dillon

2009

Bull. Math. Biol.

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We introduce a 3D model for a motile rod-shaped bacterial cell with a single polar flagellum which is based on the configuration of a monotrichous type of bacteria such as Pseudomonas aeruginosa. The structure of the model bacterial cell consists of a cylindrical body together with the flagellar forces produced by the rotation of a helical flagellum. The rod-shaped cell body is composed of a set of immersed boundary points and elastic links. The helical flagellum is assumed to be rigid and modeled as a set of discrete points along the helical flagellum and flagellar hook. A set of flagellar forces are applied along this helical curve as the flagellum rotates. An additional set of torque balance forces are applied on the cell body to induce counter-rotation of the body and provide torque balance. The three dimensional Navier-Stokes equations for incompressible fluid are used to described the fluid dynamics of the coupled fluid-microorganism system using Peskin's immersed boundary method. A study of numerical convergence is presented along with simulations of a single cell and the interaction of two model cells.

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“…In the case of bacterial chemotaxis, such patterns are often observed in petri dishes (Budrene and Berg, 1991;Ben-Jacob et al, 1994Berg, 1996). Indeed pattern formation models have generally been based on K-S models.…”

Section: Pattern Formation and Bacterial Chemotaxismentioning

confidence: 99%

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis I: The Single Cell

Tindall¹,

et al. 2008

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We review the application of mathematical modeling to understanding the behavior of populations of chemotactic bacteria. The application of continuum mathematical models, in particular generalized Keller-Segel models, is discussed along with attempts to incorporate the microscale (individual) behavior on the macroscale, modeling the interaction between different species of bacteria, the interaction of bacteria with their environment, and methods used to obtain experimentally verified parameter values. We allude briefly to the role of modeling pattern formation in understanding collective behavior within bacterial populations. Various aspects of each model are discussed and areas for possible future research are postulated.

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Complex patterns formed by motile cells of Escherichia coli

Cited by 528 publications

References 17 publications

A user’s guide to PDE models for chemotaxis

A user’s guide to PDE models for chemotaxis

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

Overview of Mathematical Approaches Used to Model Bacterial Chemotaxis I: The Single Cell

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