Taxis equations for amoeboid cells

Erban, Radek; Othmer, Hans G.

doi:10.1007/s00285-007-0070-1

Cited by 58 publications

(50 citation statements)

References 52 publications

(124 reference statements)

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“…Most motile bacteria move by the use of one or more flagella and are able to swim in a viscous fluid environment [85]. Alternative forms of bacterial motility include gliding in myxobacteria [96,104,52,40] and the complex swimming mechanisms of spirochaetes [25,105]. Bacterial swarming on surfaces is also facilitated by flagella [58].…”

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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Section: Introductionmentioning

confidence: 99%

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

Hsu

Dillon

2009

Bull. Math. Biol.

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“…excitation, adaptation times and turning frequency) with coefficients in the macroscopic partial differential equation (1) [14,15,34,35]. Similar questions for models of eukaryotic cells have also been addressed in [16,35]. In Section 3, we will assume fast signal transduction and simplify the model by eliminating the signal transduction variables, thus we do not specify the explicit form of f here.…”

Section: A Velocity Jump Model For Bacterial Chemotaxis Incorporatingmentioning

confidence: 99%

Travelling Waves in Hyperbolic Chemotaxis Equations

et al. 2010

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Mathematical models of bacterial populations are often written as systems of partial differential equations for the densities of bacteria and concentrations of extracellular (signal) chemicals. This approach has been employed since the seminal work of Keller and Segel in the 1970s [Keller and Segel, J. Theor. Biol., 1971]. The system has been shown to permit travelling wave solutions which correspond to travelling band formation in bacterial colonies, yet only under specific criteria, such as a singularity in the chemotactic sensitivity function as the signal approaches zero. Such a singularity generates infinite macroscopic velocities which are biologically unrealistic. In this paper, we formulate a model that takes into consideration relevant details of the intracellular processes while avoiding the singularity in the chemotactic sensitivity. We prove the global existence of solutions and then show the existence of travelling wave solutions both numerically and analytically.

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“…The influence of S, the density of the chemical substance, is highlighted in the notation T [S]. One could follow this model in [3][4][5][8][9][10]13,[15][16][17]21].…”

Section: T [S](t X V → V)f (T X V ) Dv − λ[S](t V X)f (T V X)mentioning

confidence: 99%

One-dimensional chemotaxis kinetic model

tabar

2010

Nonlinear Differ. Equ. Appl.

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Abstract. In this paper, we study a variation of the equations of a chemotaxis kinetic model and investigate it in one dimension. In fact, we use fractional diffusion for the chemoattractant in the Othmar-Dunbar-Alt system (Othmer in J Math Biol 26(3): 1988). This version was exhibited in Calvez in Amer Math Soc, pp [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62] 2007 for the macroscopic well-known Keller-Segel model in all space dimensions. These two macroscopic and kinetic models are related as mentioned in Bournaveas, Ann Inst H Poincaré

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Taxis equations for amoeboid cells

Cited by 58 publications

References 52 publications

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

Travelling Waves in Hyperbolic Chemotaxis Equations

One-dimensional chemotaxis kinetic model

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