Transport models for chemotactic cell populations based on individual cell behavior

Rivero, Mercedes; Tranquillo, Robert T.; Buettner, Helen M.; Lauffenburger, Douglas A.

doi:10.1016/0009-2509(89)85098-5

Cited by 201 publications

(198 citation statements)

References 35 publications

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“…In by far the majority of applications a constant diffusion coefficient is assumed, yet it is far more likely that this term should depend nonlinearly on the signal concentration and/or the cell density, as can be seen from derivations of Keller-Segel type systems through the various approaches mentioned in the introduction [15,45,80,92,95,96]. An explicit example is given in the formulation of the density-dependent chemotactic sensitivity models above, where a diffusion coefficient of the form D(u) = D (q − uq u ) was derived.…”

Section: (M5) Nonlinear Diffusionmentioning

confidence: 99%

“…A number of authors dating back to Patlak [86] in the 1950s have derived models for chemotaxis based on a more realistic description of individual cell migration (see also [2,76]). Rivero et al [92] (1 + κv) 2 for the case of the flagella bacteria Escherichia coli. Notice also that their derivation resulted in a nonlinear signal-dependent diffusion coefficient.…”

Section: (M6) Saturating Signal Productionmentioning

confidence: 99%

“…We base the model on that proposed in [92] for E. coli, however, we greatly simplify their model by assuming a constant cell diffusion and a chemotactic component that depends only on the signal gradient and a single regularisation parameter. We extend the model to a higher dimensional version, however, we note that this has not been derived in detail.…”

Section: (M6) Saturating Signal Productionmentioning

confidence: 99%

See 2 more Smart Citations

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: (M5) Nonlinear Diffusionmentioning

confidence: 99%

Section: (M6) Saturating Signal Productionmentioning

confidence: 99%

Section: (M6) Saturating Signal Productionmentioning

confidence: 99%

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A user’s guide to PDE models for chemotaxis

2008

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“…On fitting the model to the experimental findings of Dahlquist et al, they found that by including expressions for two receptors with different affinities, as part of the chemotactic coefficient, they were able to account for the difference in cell velocities across a range of attractant concentrations. Ford and Cummings (1992) compared each of the models of Alt (1980), Segel (1977) and Rivero et al (1989) and considered the various relationships between each model. They noted that Alt's three-dimensional model can be reduced to one dimension when the attractant gradient is assumed to vary in only one spatial dimension and the run times are distributed according to a Poisson distribution.…”

Section: (T X θ) = β 0 (S(t X) S(t − T X − T Cθ))mentioning

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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“…Experiments with Dtrg mutant show no change in swimming speed with varying concentrations of the non-metabolizable analogue, suggesting that sensing plays a role in the observed variation of swimming speed. These results indicate that variation in swimming speed will play a role in the chemotactic response of the cells when exposed to gradients since the drift velocity is known to be a linear function of the swimming speed (Rivero et al 1989). Thus, the focus of the current study is to investigate the role of swimming speed on the drift velocity of bacteria in gradients of 2Dg and quantify the contribution of swimming speed variation towards the enhancement of net drift.…”

Section: Introductionmentioning

confidence: 97%

Variation of swimming speed enhances the chemotactic migration of Escherichia coli

et al. 2015

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Studies on chemotaxis of Escherichia coli have shown that modulation of tumble frequency causes a net drift up the gradient of attractants. Recently, it has been demonstrated that the bacteria is also capable of varying its runs speed in uniform concentration of attractant. In this study, we investigate the role of swimming speed on the chemotactic migration of bacteria. To this end, cells are exposed to gradients of a non-metabolizable analogue of glucose which are sensed via the Trg sensor. When exposed to a gradient, the cells modulate their tumble duration, which is accompanied with variation in swimming speed leading to drift velocities that are much higher than those achieved through the modulation of the tumble duration alone. We use an existing intra-cellular model developed for the Tar receptor and incorporate the variation of the swimming speed along with modulation of tumble frequency to predict drift velocities close to the measured values. The main implication of our study is that E. coli not only modulates the tumble frequency, but may also vary the swimming speed to affect chemotaxis and thereby efficiently sample its nutritionally rich environment.

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Transport models for chemotactic cell populations based on individual cell behavior

Cited by 201 publications

References 35 publications

A user’s guide to PDE models for chemotaxis

A user’s guide to PDE models for chemotaxis

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

Variation of swimming speed enhances the chemotactic migration of Escherichia coli

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