Investigation of cell repackaging processes in epithelial sheets in silico: part II. Tissue development under conditions of different boundaries

The paper presents a comprehensive analysis of cell repacking processes in epithelial tis-sues, conducted using an advanced mathematical model of epithelial tissue evolution. The model is discrete and based on a vertex mathematical framework. The proposed mathematical model incorporates key processes of real tissues, such as cell division, intercalation, chemomechanical interaction, and the redistribution of chemical signals. This allows for accounting for the influence of mechanical and chemical factors in epithelial morphogenesis. The study focuses on cell re-packing processes under various conditions. Namely, during the fusion of a cell mass developing within another tissue; the development of epithelial tissue under elastic and rigid boundaries; the development of epithelial tissue under non-uniform processes of division and intercalation; and during cell migration within the tissue. Comprehensive numerical modeling was performed, re-vealing patterns of morphogenetic transformations in epithelial structures. Critical parameters of intercalation ensuring optimal redistribution of mechanical stresses during tissue fusion were established. It was also found that the key factor in the described dynamics is not so much the change in the energy landscape but the level of local cell motility at the boundary between the two tissues. Fundamental differences in the distribution of shear stresses during tissue growth under rigid and elastic boundaries were identified. A qualitative comparison of our results with the results of clinical studies available in the literature shows satisfactory agreement. It is demon-strated that cell division modes (activation and inhibition) significantly affect the energy balance of the system. It was revealed that under conditions of inhibited cell division, the process of tis-sue relaxation directly associated with cell division is absent, leading to a gradual accumulation of mechanical stresses. This, in turn, can have consequences for its morphogenesis, stability, and response to external stimuli. Furthermore, a comparative analysis revealed characteristic features of amoeboid and mesenchymal types of cell migration. The obtained results are signifi-cant for understanding the fundamental mechanisms of morphogenesis, tissue regeneration, and the development of pathological processes, and can also be used in tissue engineering and the development of therapeutic approaches.