We use a Helfrich-type model to simulate the dynamics of cell membranes accounting for elastic properties, which are associated with bending and line tension. We couple this to active processes of actin polymerization which has a force generating role during cell motility, which requires polarization to distinguish between the cell front and the rear. Our model to characterize cell polarity is based on a Turing-type instability within a reaction-diffusion model accounting for different diffusion properties for membrane-bound proteins and proteins within the cytoplasm and kinetic processes of attachment and detachment at and from the cell membrane. A phase-field type model is used for efficient computational studies using adaptive finite elements within the high performance computing toolbox AMDiS.
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