The physical bases of cell movement. The mechanisms of self-organisation of amoeboid motility

Structure formation and autowave processes in active media far from equilibrium are the subject of special division of the theory of nonlinear dynamic systems. In the present review the protoplasm of amoeboid cells is considered as an active medium, in which gel-like structures continuously assemble and disassemble. Local parts of these structures also spontaneously contract and relax, causing rather complex circular or shuttle-type flows of sol-like protoplasm. We consider several mathematical models of the resulting movements, wherein dissipative structures and the autowave processes multually generate each other. The main quantitative features of the protoplasm dynamics in Physarum plasmodium are consistent with a model that postulates the existence of positive feedback between a local deformation and the free calcium level controlling the network contraction. The potentialities of different physical methods used to determine the values of parameters in the mathematical models are discussed.