Topological and geometrical quantities in active cellular structures

Wenzel, Dennis; Praetorius, Simon; Voigt, Axel

doi:10.1063/1.5085766

Cited by 24 publications

(23 citation statements)

References 49 publications

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“…In the latter two descriptions, a phase field distinguishes the two phases (the interior and the exterior of the cell), where either the zero contour of the phase field determines the position of the membrane, or there is a gradual variation of the different physical quantities across the interface [227]. Phase-field models have also been used for multi-cellular systems [228,229], as for collective cell migration [230] (for a review about physical models for collective cell motility see [231]) and tissues [232,233], see also Box 4. Alternatively, microscopic models with explicit membrane and self-propelled (pulling or pushing) filaments can be employed [234,235]. This approach incorporates fluctuations of the internal structure, persistent and random-walk-like motion, and shape changes in response to external conditions.…”

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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“…n is the second central moment of the distribution of n, and γ is a constant that may decrease as σ 2 n increases [44,45], or may be independent of σ 2 n [46]. This relation has been commonly used to explore the topology of tessellations and arrangements in cellular assemblies [40,47,48]. In the case of homeostatic MDCK-II tissues, irrespective of the conditions in which they were grown, all tissues show the same linear dependence (Fig.…”

Section: Universal Topology Of Homeostatic Statesmentioning

confidence: 99%

On the mechanical regulation of epithelial tissue homeostasis

Kaliman

Hubert

Wollnik

et al. 2021

Preprint

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Despite recent efforts to understand homeostasis in epithelial tissues, there are many unknowns surrounding this steady state. It is considered to be regulated by mechanoresponse, but unlike for single cells, this remains heavily debated for tissues. Here, we show that changes in matrix stiffness induce a non-equilibrium transition from tubular to squamous Madin-Darby Canine Kidney II tissues. Nonetheless, despite different cell morphologies and densities, all homeostatic tissues display equivalent topologies, which, hence, must be actively targeted and regulated. On the contrary, the mechanoresponse induces dramatic changes in the large-scale organization of the colonies. On stiff gels, this yields an unreported cooperative state of motile cells displaying higher densities than in the arrested homeostatic state. This suggests a more complex relation between cell density and motility than previously anticipated. Our results unequivocally relate the mechanosensitive properties of individual cells to the evolving macroscopic structures, an effect that could be important for understanding the emergent pathologies of living tissues.

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“…We model a monolayer of cells using a coarse-grained, phase-field approach that resolves individual cells and the forces between them, but not the internal machinery of the cell. The phase-field method for a single cell is considered in [29][30][31][32]; it has been used to study the contact inhibition of locomotion and collisions in binary cell systems [24,33], collective cell migration [34][35][36], the effect of the stiffness mismatch between single cancer cells and normal cells in metastasis [37] and the role of cell overlaps in the solid-liquid transition of a cell sheet [38].…”

Section: The Phase-field Modelmentioning

confidence: 99%

Active inter-cellular forces in collective cell motility

Zhang

Mueller

Doostmohammadi

et al. 2020

J. R. Soc. Interface.

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The collective behaviour of confluent cell sheets is strongly influenced both by polar forces, arising through cytoskeletal propulsion, and by active inter-cellular forces, which are mediated by interactions across cell-cell junctions. We use a phase-field model to explore the interplay between these two contributions and compare the dynamics of a cell sheet when the polarity of the cells aligns to (i) their main axis of elongation, (ii) their velocity and (iii) when the polarity direction executes a persistent random walk. In all three cases, we observe a sharp transition from a jammed state (where cell rearrangements are strongly suppressed) to a liquid state (where the cells can move freely relative to each other) when either the polar or the inter-cellular forces are increased. In addition, for case (ii) only, we observe an additional dynamical state, flocking (solid or liquid), where the majority of the cells move in the same direction. The flocking state is seen for strong polar forces, but is destroyed as the strength of the inter-cellular activity is increased.

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Topological and geometrical quantities in active cellular structures

Cited by 24 publications

References 49 publications

Computational models for active matter

Computational models for active matter

On the mechanical regulation of epithelial tissue homeostasis

Active inter-cellular forces in collective cell motility

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