Computational approaches to substrate-based cell motility

Ziebert, Falko; Aranson, Igor S.

doi:10.1038/npjcompumats.2016.19

Cited by 80 publications

(82 citation statements)

References 169 publications

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“…The major technical challenge for a continuum modeling of cell migration is the presence of a moving boundary and the nonlinear and nonlocal coupling of cytoskeletal dynamics to a moving and deformable membrane. Various continuum models for cell motility on substrates have been employed [219,[222][223][224][225][226]. Commonly, three different modeling approaches have been used: sharp-interface models, in which the interface is represented by a curve that moves with some velocity, level set methods, and diffuse-interface models.…”

Section: Cell Motility Modelsmentioning

confidence: 99%

Computational models for active matter

et al. 2020

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A variety of computational models have been developed to describe active matter at different length and time scales. The diversity of the methods and the challenges in modeling active matterranging from molecular motors and cytoskeletal filaments over artificial and biological swimmers on microscopic to groups of animals on macroscopic scales-mainly originate from their out-ofequilibrium character, multiscale nature, nonlinearity, and multibody interactions. In the present review, various modeling approaches and numerical techniques are addressed, compared, and differentiated to illuminate the innovations and current challenges in understanding active matter. The complexity increases from minimal microscopic models of dry active matter toward microscopic models of active matter in fluids. Complementary, coarse-grained descriptions and continuum models are elucidated. Microscopic details are often relevant and strongly affect collective behaviors, which implies that the selection of a proper level of modeling is a delicate choice, with simple models emphasizing universal properties and detailed models capturing specific features. Finally, current approaches to further advance the existing models and techniques to cope with real-world applications, such as complex media and biological environments, are discussed.2

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Section: Cell Motility Modelsmentioning

confidence: 99%

Computational models for active matter

et al. 2020

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“…Many aspects of cell motility have been extensively modeled, ranging from the biochemistry and physics of actin-polymerization-based protrusion [2,3], to the importance of cytoskeleton mechanics [4–6], to a wide variety of internal mechanisms for determining a cell’s orientation [7–9]. Many of these aspects of the modeling of eukaryotic cell shape and motility have been reviewed in two recent papers [10,11]. …”

Section: Introductionmentioning

confidence: 99%

Crawling and turning in a minimal reaction-diffusion cell motility model: Coupling cell shape and biochemistry

et al. 2017

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We study a minimal model of a crawling eukaryotic cell with a chemical polarity controlled by a reaction-diffusion mechanism describing Rho GTPase dynamics. The size, shape, and speed of the cell emerge from the combination of the chemical polarity, which controls the locations where actin polymerization occurs, and the physical properties of the cell, including its membrane tension. We find in our model both highly persistent trajectories, in which the cell crawls in a straight line, and turning trajectories, where the cell transitions from crawling in a line to crawling in a circle. We discuss the controlling variables for this turning instability and argue that turning arises from a coupling between the reaction-diffusion mechanism and the shape of the cell. This emphasizes the surprising features that can arise from simple links between cell mechanics and biochemistry. Our results suggest that similar instabilities may be present in a broad class of biochemical descriptions of cell polarity.

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“…A deformable finite domain R with a positive control parameter inside and a negative one outside can be elegantly implemented by the so-called phase field method. This approach, originally developed for solidification processes [37] has been applied in recent years to many soft matter [38] and biological problems [39], for instance droplets and vesicles in flows [40] or cell motility [41]. It is a well-adapted approach to self-consistently describe deformable and/or moving boundaries.…”

Section: Coupling Of Stripe Patterns To Deformable Domain Boundariesmentioning

confidence: 99%

Nonlinear patterns shaping the domain on which they live

2020

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Nonlinear stripe patterns in two spatial dimensions break the rotational symmetry and generically show a preferred orientation near domain boundaries, as described by the famous Newell-Whitehead-Segel (NWS) equation. We first demonstrate that, as a consequence, stripes favour rectangular over quadratic domains. We then investigate the effects of patterns 'living' in deformable domains by introducing a model coupling a generalized Swift-Hohenberg model to a generic phase field model describing the domain boundaries. If either the control parameter inside the domain (and therefore the pattern amplitude) or the coupling strength ('anchoring energy' at the boundary) are increased, the stripe pattern self-organizes the domain on which it 'lives' into anisotropic shapes. For smooth phase field variations at the domain boundaries, we simultaneously find a selection of the domain shape and the wave number of the stripe pattern. This selection shows further interesting dynamical behavior for rather steep variations of the phase field across the domain boundaries. The here-discovered feedback between the anisotropy of a pattern and its orientation at boundaries is relevant e.g. for shaken drops or biological pattern formation during development.

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Computational approaches to substrate-based cell motility

Cited by 80 publications

References 169 publications

Computational models for active matter

Computational models for active matter

Crawling and turning in a minimal reaction-diffusion cell motility model: Coupling cell shape and biochemistry

Nonlinear patterns shaping the domain on which they live

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