Introduction to Models of Cell Motility

Deng, Youyuan; Levine, Herbert

doi:10.1007/978-3-030-98606-3_7

Cited by 2 publications

(3 citation statements)

References 116 publications

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“…To amplify (and exploit) this scale separation, we set D v = 1 (as in [1]) and D u = ε2 , where ε is a small parameter that can be taken arbitrary small. Furthermore, we assume that our spatial domain is no longer periodic but instead unbounded 6 . This transforms the PDE model (1.1) into…”

Section: B Analysismentioning

confidence: 99%

“…In absence of a signal, the formation of pseudopods happens at random places on the cell membrane, resulting in random motion. In contrast, when a cell senses a chemical signal, it can concentrate the random protrusions at the side of the cell where the signal comes from, leading to movement in the direction of the signal [6]. As cells are small, the difference in signal strength between the front and the back of the cell (the gradient) is small as well.…”

Section: Introductionmentioning

confidence: 99%

“…As cells are small, the difference in signal strength between the front and the back of the cell (the gradient) is small as well. Furthermore, the cell can only use discrete points at the membrane where the receptors are to estimate the direction of the signal [6]. Therefore, one of the [1].…”

Section: Introductionmentioning

confidence: 99%

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Waves in a Stochastic Cell Motility Model

Hamster¹,

Heijster²

2023

Preprint

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In Bhattacharya et al. (Science Advances, 2020), a set of chemical reactions involved in the dynamics of actin waves in cells was studied. Both at the microscopic level, where the individual chemical reactions are directly modelled using Gillespie-type algorithms, and on a macroscopic level where a deterministic reactiondiffusion equation arises as the large-scale limit of the underlying chemical reactions. In this work, we derive, and subsequently study, the related mesoscopic stochastic reaction-diffusion system, or Chemical Langevin Equation, that arises from the same set of chemical reactions. We explain how the stochastic patterns that arise from this equation can be used to understand the experimentally observed dynamics from Bhattacharya et al. In particular, we argue that the mesoscopic stochastic model better captures the microscopic behaviour than the deterministic reaction-diffusion equation, while being more amenable for mathematical analysis and numerical simulations than the microscopic model.

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Section: B Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Waves in a Stochastic Cell Motility Model

Hamster¹,

Heijster²

2023

Preprint

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Waves in a Stochastic Cell Motility Model

Hamster

Heijster

2023

Bull Math Biol

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In Bhattacharya et al. (Sci Adv 6(32):7682, 2020), a set of chemical reactions involved in the dynamics of actin waves in cells was studied at two levels. The microscopic level, where the individual chemical reactions are directly modelled using Gillespie-type algorithms, and on a macroscopic level where a deterministic reaction–diffusion equation arises as the large-scale limit of the underlying chemical reactions. In this work, we derive, and subsequently study, the related mesoscopic stochastic reaction–diffusion system, or chemical Langevin equation, that arises from the same set of chemical reactions. We explain how the stochastic patterns that arise from this equation can be used to understand the experimentally observed dynamics from Bhattacharya et al. In particular, we argue that the mesoscopic stochastic model better captures the microscopic behaviour than the deterministic reaction–diffusion equation, while being more amenable for mathematical analysis and numerical simulations than the microscopic model.

show abstract

Introduction to Models of Cell Motility

Cited by 2 publications

References 116 publications

Waves in a Stochastic Cell Motility Model

Waves in a Stochastic Cell Motility Model

Waves in a Stochastic Cell Motility Model

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