Mathematical Modeling of the Effect of Cell Mobility and Active Intercellular Interactions on the Sorting of the Cells of Two Types in the Cultures of Biological Tissues

The cell motion is at the bottom of many biological phenomena. An important role in controlling cell motions is played by active stresses developing in biological tissues as a result of mechanical intercellular interactions. An investigation of the evolution of the mixtures of cells of different types forming cell aggregates shows that active intercellular force interactions lead to the spatial separation of the cells of different types, or the cell sorting. Within the framework of the continuum model of biological media [24] (the cells of different types are regarded as separate phases), in this study we investigate the effect of the parameters characterizing various mechanisms of the development of
active intercellular stresses, as well as adhesion and cell mobility, on the process of the sorting of cells of two types that form an aggregate of spherical shape at the initial moment of time. It is shown that the sufficient condition for the sorting of cells of different types and the formation of a sharp boundary between the regions occupied by these cells is the absence of contracting interactions between the cells of different phases under the condition of asymmetry of the initial distributions of their concentrations or asymmetry of the parameters characterizing the development of active stresses in different phases. It is shown that the cells of the phase, where active contracting intercellular interactions are stronger (at the same values of the other parameters and the same initial distributions of phase concentrations for different cell phases), strive to occupy the central region of a spheroid. At the same time, the cells of the other phase, where the contracting interactions are weaker, are displaced to the periphery. An increase in the parameter characterizing cell repulsion leads to the displacement of this cell phase toward the periphery. Beside the active interaction forces, the cell motions can be controlled by both passive mechanical properties of the medium and the cell mobility. The asymmetry of the interphase distributions of these parameters can lead to the situation, when the cells that possess the greater contracting interactions will be displaced toward the cell spheroid periphery and surround the cells, the interaction between which is weaker