Mathematical models of intracellular mobility

A review of mathematical models describing various autowave and fountain protoplasm flows in amoeboid cells (amoebs, leukocytes, cancer cells, etc..) is presented. The active force in such flows is generated by actomyosin interactions. These models are the systems of nonlinear partial differential equations. Qualitative analysis of the models is realized and results of computer experiments are presented. The ways to design more advanced amoeboid motility models taking the migration on a surface in the presence of external stimuli into account are shown.