| Abstract: |
| The way that cells move is key to the creation and development of most organisms on earth. Consequently a deeper understanding of cell motility is likely to have significant applications to medicine.
The aim of this work is to implement an efficient numerical method to study cell deformation and movement. The model we employ considers the actomyosin filament network as a viscoelastic and contractile gel. The mechanical properties are modeled with with a force balancing equation for displacement. This is coupled to two reaction-diffusion equations describing the actin and myosin biochemical dynamics. We carry out linear stability analysis to determine key bifurcation parameters and find analytical solutions close to bifurcation points. We then use a finite element scheme to produce numerical solutions in 2 and 3 dimensions.
We see that the solutions predicted from linear stability theory are replicated in the early stages of movement. Subsequently we see significant deformations, some of which are consistent with shapes found in experiments. The model we describe could be thought of as the initial deformation which leads to movement. |
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