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      Large-scale simulations of biological cell sorting driven by differential adhesion follow diffusion-limited domain coalescence regime

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      PLoS Computational Biology
      Public Library of Science

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          Abstract

          Cell sorting, whereby a heterogeneous cell mixture segregates and forms distinct homogeneous tissues, is one of the main collective cell behaviors at work during development. Although differences in interfacial energies are recognized to be a possible driving source for cell sorting, no clear consensus has emerged on the kinetic law of cell sorting driven by differential adhesion. Using a modified Cellular Potts Model algorithm that allows for efficient simulations while preserving the connectivity of cells, we numerically explore cell-sorting dynamics over very large scales in space and time. For a binary mixture of cells surrounded by a medium, increase of domain size follows a power-law with exponent n = 1/4 independently of the mixture ratio, revealing that the kinetics is dominated by the diffusion and coalescence of rounded domains. We compare these results with recent numerical studies on cell sorting, and discuss the importance of algorithmic differences as well as boundary conditions on the observed scaling.

          Author summary

          Cell sorting describes the spontaneous segregation of identical cells in biological tissues. This phenomenon is observed during development or organ regeneration in a variety of biological systems. Minimization of the total surface energy of a tissue, in which adhesion strengh between homotypic and heterotypic cells are different, is one of the mechanisms that explain cell sorting. This mechanism is then similar to the one that drives demixing of two immiscible fluids. Because of the high sensibility of this process to finite-size and finite-time effects, no clear consensus has emerged on the scaling law of cell sorting driven by differential adhesion. Using an efficient numerical code, we were able to investigate this scaling law on very large binary mixtures of cells. We show that on long times, cell sorting obeys a universal power law, which is independent of the mixture ratio and boundary conditions.

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          Most cited references36

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          Emerging modes of collective cell migration induced by geometrical constraints.

          The role of geometrical confinement on collective cell migration has been recognized but has not been elucidated yet. Here, we show that the geometrical properties of the environment regulate the formation of collective cell migration patterns through cell-cell interactions. Using microfabrication techniques to allow epithelial cell sheets to migrate into strips whose width was varied from one up to several cell diameters, we identified the modes of collective migration in response to geometrical constraints. We observed that a decrease in the width of the strips is accompanied by an overall increase in the speed of the migrating cell sheet. Moreover, large-scale vortices over tens of cell lengths appeared in the wide strips whereas a contraction-elongation type of motion is observed in the narrow strips. Velocity fields and traction force signatures within the cellular population revealed migration modes with alternative pulling and/or pushing mechanisms that depend on extrinsic constraints. Force transmission through intercellular contacts plays a key role in this process because the disruption of cell-cell junctions abolishes directed collective migration and passive cell-cell adhesions tend to move the cells uniformly together independent of the geometry. Altogether, these findings not only demonstrate the existence of patterns of collective cell migration depending on external constraints but also provide a mechanical explanation for how large-scale interactions through cell-cell junctions can feed back to regulate the organization of migrating tissues.
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            Corrections to late-stage behavior in spinodal decomposition: Lifshitz-Slyozov scaling and Monte Carlo simulations

            David Huse (1986)
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              Simulation of biological cell sorting using a two-dimensional extended Potts model.

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                Author and article information

                Contributors
                Role: ConceptualizationRole: Data curationRole: Formal analysisRole: Funding acquisitionRole: InvestigationRole: MethodologyRole: Project administrationRole: ResourcesRole: SoftwareRole: SupervisionRole: ValidationRole: VisualizationRole: Writing – original draftRole: Writing – review & editing
                Role: Editor
                Journal
                PLoS Comput Biol
                PLoS Comput Biol
                plos
                PLoS Computational Biology
                Public Library of Science (San Francisco, CA USA )
                1553-734X
                1553-7358
                August 2021
                16 August 2021
                : 17
                : 8
                : e1008576
                Affiliations
                [001] Université de Paris, CNRS, UMR 7057, Matière et Systèmes Complexes (MSC), Paris, France
                The University of Melbourne Melbourne School of Psychological Sciences, AUSTRALIA
                Author notes

                The authors have declared that no competing interests exist.

                Author information
                https://orcid.org/0000-0002-6619-1466
                Article
                PCOMPBIOL-D-20-02142
                10.1371/journal.pcbi.1008576
                8389523
                34398883
                d8f3c622-309c-4e5c-b4b1-d1a9361cdca1
                © 2021 Marc Durand

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 29 November 2020
                : 6 July 2021
                Page count
                Figures: 7, Tables: 0, Pages: 13
                Funding
                The author received no specific funding for this work.
                Categories
                Research Article
                Physical Sciences
                Materials Science
                Materials
                Mixtures
                Physical Sciences
                Mathematics
                Applied Mathematics
                Algorithms
                Research and Analysis Methods
                Simulation and Modeling
                Algorithms
                Engineering and Technology
                Signal Processing
                Autocorrelation
                Research and Analysis Methods
                Mathematical and Statistical Techniques
                Statistical Methods
                Autocorrelation
                Physical Sciences
                Mathematics
                Statistics
                Statistical Methods
                Autocorrelation
                Physical Sciences
                Physics
                Condensed Matter Physics
                Surface Energy
                Biology and Life Sciences
                Cell Biology
                Cell Motility
                Research and Analysis Methods
                Simulation and Modeling
                Physical Sciences
                Mathematics
                Algebra
                Algebraic Geometry
                Physical Sciences
                Physics
                Classical Mechanics
                Motion
                Velocity
                Custom metadata
                vor-update-to-uncorrected-proof
                2021-08-26
                The source code and data used to produce the results and analyses presented in this manuscript are available on OSF at link https://doi.org/10.17605/OSF.IO/NVYBR.

                Quantitative & Systems biology
                Quantitative & Systems biology

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