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Protoplasmic droplets of the slime mold Physarum polycephalum develop various contraction patterns during their development.
We present a model of these droplets that incorporates the important chemical and mechanical aspects of the cell in a physiogical
realistic way. To account for the cell mechanics we consider the protoplasm as a two-phase incompressible medium consisting
of an active elastic gel and a fluid sol phase. We write the elastic equations for the gel, describing the dynamics of deformations,
and a hydrodynamic equation for the sol in a regime of large Reynolds numbers. A Calcium oscillator which dynamics is governed
by a reaction-diffusion-advection equation generates the mechanical stresses.
For small deformations an approximative model involving global coupling was derived and analyzed [1]. Numerical simulations using
the FEM technique in one and two dimensions are performed and confirm the theoretical predictions. Furthermore simulations of the
full model are compared with experimentally observed spatiotemporal contraction patterns. For certain cases we find a qualitative
agreement between the patterns of the model and the experimental results.
[1] "A model for oscillations and pattern formation in protoplasmic droplets of Physarum polycephalum", Eur. Phys. J. Special Topics 191, 159-172 (2010) |
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