Complex regimes of the contractile activity in amoeboid cell.
Laser diagnostics of intracellular flows and
mathematical models
A.V. Priezzhev 
, Yu.M. Romanovsky , D.A. Pavlov 
, V.A. Teplov 
Department of Physics, M.V. Lomonosov State University, Moscow;
Department of Computational Mathematics and Cybernetics,
M.V. Lomonosov State University, Moscow;
Institute of Theoretical and Experimental Biophysics RAS,
Pushchino, Moscow Region
The motility of amoeboid cells is defined by autowave processes, which are caused by interaction of actomyosin based contractile apparatus and intracellular protoplasmic flows. We give a review of the experimental evidences on autowave motility, which have been obtained by a variety of techniques, among them optic probing. The potentialities of laser doppler microscope in order to determine the values of parameters used in the mathematical models is discussed. One- and two-dimensional models of autowave motility in Physarum plasmodium are presented, which respectively describe the ectoplasm contraction waves and shuttle endoplasm streaming in plasmodial strand and the complex autowave processes in plasmodial sheet. The models are systems of the partial differential equations connecting the deformation of cortical layers, the active stress and the concentration of calcium ions. Conditions of autowave excitation have been found. Increasing a parameter determining the positive feedback loop one can obtain with the help of computer calculations different autowave regimes: from quasi-garmonic standing wave to rotate waves with quasi-stochastic automodulation. Model solutions are discussed for the case of non-uniform parameter distribution that is characteristic of the directed movement of amoeboid cells.
The work is supported by research grant N 94-04-12233Í from Russian Foundation for Basic Investigations.