2016/04/10 by Leonid Berlyand, Berlyand, Leonid, Mykhailo Potomkin +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Cellular Mechanics and Interactions #FOS: Mathematics #Solidification and crystal growth phenomena
paper · pdf · doi:10.48550/arxiv.1604.02749
openalex publication_date 2016/04/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This letter is concerned with asymptotic analysis of a PDE model for motility\nof a eukaryotic cell on a substrate. This model was introduced in [1], where it\nwas shown numerically that it successfully reproduces experimentally observed\nphenomena of cell-motility such as a discontinuous onset of motion and shape\noscillations. The model consists of a parabolic PDE for a scalar phase-field\nfunction coupled with a vectorial parabolic PDE for the actin filament network\n(cytoskeleton). We formally derive the sharp interface limit (SIL), which\ndescribes the motion of the cell membrane and show that it is a volume\npreserving curvature driven motion with an additional nonlinear term due to\nadhesion to the substrate and protrusion by the cytoskeleton. In a 1D model\nproblem we rigorously justify the SIL, and, using numerical simulations,\nobserve some surprising features such as discontinuity of interface velocities\nand hysteresis. We show that nontrivial traveling wave solutions appear when\nthe key physical parameter exceeds a certain critical value and the potential\nin the equation for phase field function possesses certain asymmetry.\n