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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
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.