Chemotaxis, signal relaying and aggregation morphology

Nanjundiah, Vidyanand

doi:10.1016/0022-5193(73)90149-5

Cited by 251 publications

(140 citation statements)

References 22 publications

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“…As to its problems, we note Nanjundiah [72] who writes of the logistic form " …even this fails at both, very small and very large concentrations" (p. 67 in [72]). By inspection, the dynamics of movement are dominated by the taxis term as v → 0, whereas realistically a low signal concentration would not be expected to elicit a significant chemotactic response.…”

Section: (M2) Signal-dependent Sensitivitymentioning

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: (M2) Signal-dependent Sensitivitymentioning

confidence: 99%

A user’s guide to PDE models for chemotaxis

2008

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“…The purpose of the present paper is to study blowup mechanism for a system of parabolic equations. It arises in mathematical biology to describe the chemotactic feature of slime molds.We take the form proposed by Nanjundiah [20], simplifying the one previously given by Keller and Segel [14]. It is stated as follows, where u = u (x, t) and v = v(x, t) stand the density of slime molds and the concentration chemical substances secreted by them, respectively:…”

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confidence: 99%

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confidence: 99%

“…We take the form proposed by Nanjundiah [20], simplifying the one previously given by Keller and Segel [14]. It is stated as follows, where u = u(x, t) and v = v(x, t) stand the density of slime molds and the concentration chemical substances secreted by them, respectively: The first equation describes the conservation of mass; the effect of diffusion, Vn, and that of chemotaxis, uVv, are competing for u to vary.…”

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confidence: 99%

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Parabolic system of chemotaxis: Blowup in a finite and the infinite time

Senba¹,

Suzuki²

2001

Methods and Applications of Analysis

138

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1. Introduction. The purpose of the present paper is to study blowup mechanism for a system of parabolic equations. It arises in mathematical biology to describe the chemotactic feature of slime molds.We take the form proposed by Nanjundiah [20], simplifying the one previously given by Keller and Segel [14]. It is stated as follows, where u = u (x, t) and v = v(x, t) stand the density of slime molds and the concentration chemical substances secreted by them, respectively:

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“…Since then, a number of variations of the Keller-Segel model have attracted the attention of many mathematicians, and the focused issue was the boundedness or blow-up of the solutions ( [5,7,9,10,39,20]). The striking feature of Keller-Segel models is the possibility of blow-up of solutions in a finite (or infinite) time (see, e.g., [1,9,18,39]), which strongly depends on the space dimension. Moreover, some recent studies have shown that the blow-up of solutions can be inhibited by the nonlinear diffusion (see Ishida et al [11] Winkler et al [1,27,36,40]) and the (generalized) logistic damping (see Li and Xiang [14], Tello and Winkler [31], Wang et al [33], Zheng et al [48]).…”

Section: Introductionmentioning

confidence: 99%