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Continuum Modeling of Cell Sorting within a Plane Layer with Account for the Possible Separation of the Boundaries of the Regions Occupied by Cells of Two Different Types

Abstract

In aggregates formed by cells of different types, the phenomenon of their sorting is observed: as a result of cell interactions, structures develop in which cells of one type can form a compact mass surrounded by cells of another type. The physical mechanisms underlying the sorting process are still the subject of discussion. We have previously proposed a continuum model of a biological continuum formed by two actively interacting cell phases and a fluid. Based on this model, a model problem of redistribution of cells of two types, which fill an infinite plane layer, was considered under the assumption that the continuums modeling two cell populations are bounded by a common outer boundary. In the proposed study, a similar problem is formulated and investigated, taking into account the possible relative displacement of surfaces that bound cells of different types. This formulation allows us to describe the formation and propagation of fronts separating regions that differ in the concentrations of cell phases. The behavior of solutions is studied depending on the dimensionless parameters characterizing active intercellular interactions. The participation of these mechanisms in the formation of new cellular structures was analyzed numerically. It has been shown that, in a wide range of parameters, cells with stronger contracting active interactions tend to occupy the central region, displacing cells with weaker contracting interactions to the periphery. The novel formulation is physically more adequate and allows us to expand the range of parameters in which a stable result is achieved.

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Funding

The study was supported financially by the Russian Foundation for Basic Research (project no. 20-01-00329) and the State Program АААА-А19-119012990119-3.

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Correspondence to S. A. Logvenkov or A. A. Stein.

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Logvenkov, S.A., Stein, A.A. Continuum Modeling of Cell Sorting within a Plane Layer with Account for the Possible Separation of the Boundaries of the Regions Occupied by Cells of Two Different Types. Fluid Dyn 57, 221–233 (2022). https://doi.org/10.1134/S0015462822030090

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  • DOI: https://doi.org/10.1134/S0015462822030090

Keywords:

  • cell systems
  • active media
  • biological morphogenesis