A Cellular Potts Model simulating cell migration on and in matrix environments

Cell migration on and through extracellular matrix plays a critical role in a wide variety of physiological and pathological phenomena, and in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix- or cell-derived biophysical parameters, such as matrix fiber orientation, gap size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migratory phenotype on both two-dimensional substrates and within three-dimensional environments, in a close comparison with experimental evidence. As distinct features of our approach, the cells are represented by compartmentalized discrete objects, differentiated in the nucleus and in the cytosolic region, while the extracellular matrix is composed of a fibrous mesh and of a homogeneous fluid. Our model provides a strong correlation of the directionality of migration with the topological ECM distribution and, further, a biphasic dependence of migration on the matrix density, and in part adhesion, in both two-dimensional and three-dimensional settings. Moreover, we demonstrate that the directional component of cell movement is strongly correlated with the topological distribution of the ECM fibrous network. In the three-dimensional networks, we also investigate the effects of the matrix mechanical microstructure, observing that, at a given distribution of fibers, cell motility has a subtle bimodal relation with the elasticity of the scaffold. Finally, cell locomotion requires deformation of the cell’s nucleus and/or cell-derived proteolysis of steric fibrillar obstacles within rather rigid matrices characterized by small pores, not, however, for sufficiently large pores. In conclusion, we here propose a mathematical modeling approach that serves to characterize cell migration as a biological phenomen in health, disease and tissue engineering applications. The research that led to the present paper was partially supported by a grant of the group GNFM of INdAM