Theoretical study of the competition between cell-cell and cell-matrix adhesions

Adhesions between neighboring cells or between cells and their surrounding tissue/matrix play a crucial role in a wide range of biological processes. In order to investigate the competitive mechanisms between cell-cell and cell-matrix adhesions, we here develop a theoretical framework for multiple interacting cells lying on a planar matrix coated with distributed ligands. This model allows us to study, from the viewpoints of energy and statistics, the effects of such physical mechanisms as binding energy of bonds, nonspecific interactions, elastic deformation of cell membranes, and mixing entropy. Our calculations show that cell-matrix adhesion cannot occur when the ligand density on the matrix is lower than a threshold value, and cell-cell adhesion does not happen for a high ligand density. Glycocalyx repulsion plays a more important role in cell-matrix adhesion than in cell-cell adhesion. In addition, it is found that the cell-cell adhesion density decreases as the number of cells increases.