Моделирование сортировки двух типов клеток в клеточном сфероиде с учетом подвижности границ областей, занятых клетками разных типов

Известия РАН. Механика жидкости и газа. 2022. № 6. С. 101–115.

Logvenkov S. A.

The cultivation of cell aggregates obtained by mixing cells of different types, in particular
embryonic ones, leads to their sorting, i.e., the formation of cell structures that are characterized by
the spatial separation of large groups of cells of different types, separated from each other by well
observed boundaries. Typical are cell structures in which a compact mass of cells of one type is surrounded
by cells of another type. In the present study, the problem of redistribution of the densities of
two types of cells that form a cell spheroid is formulated and investigated. The problem formulation
uses the previously proposed continuum model of a biological continuum [Logvenkov S.A., Stein A.A.
Fluid Dynamics 2022. V. 57, No. 3, P. 221] formed by two actively interacting cell phases and a fluid.
Problems are solved that use two types of boundary conditions taking into account the possible movement
of the outer boundaries of areas occupied by cells of different types: in one case, both boundaries
are considered to coincide, and in the other, the possibility of their independent movement is allowed.
The influence of local and nonlocal laws of development of active intercellular interactions on the
sorting process is studied. The properties of the solutions are analyzed for both problem formulations.
It is shown that solutions of the problem with two independently moving boundaries describe more
adequately the phenomenon of sorting, when cells with stronger contracting active interactions tend
to occupy the central region, displacing cells with weaker contracting interactions. Solutions of the
problem with two boundaries are more stable relative to perturbations of the initial conditions. For
describing this process, both nonlocal and local models can be used.

Keywords: клеточные системы, cell systems, active media, biological morphogenesis, активные среды, биологическое формообразование