Asymptotic stability of contraction-driven cell motion

Modeling the interplay of mechanosensitive adhesion and membrane tension for polarization and shape determination in crawling cells

“…2D, where it is found to have a weak but destabilizing effect on the system. This finding is qualitatively consistent with previous contraction-driven cell motility models and with various experimental observations [33,56,57].…”

The numerical solution of the free-boundary cell motility problem

“…Authors of [23] hypothesized the existence of stable traveling wave solutions for the (2)-( 6) free-boundary problem, which could be a confirmation of the applicability of the presented model for cell motility mechanism. We digitized the actomyosin distribution and shape of moving keratocyte cells observed in [30] and used it as an initial condition of the described dynamic system (Fig.…”

“…The current work is based on the two-dimensional couple model described by the system of PDEs in the field of the dynamic domain Ω(t) with free boundary ∂Ω(t) for eukaryotic cells on substrates [23]. The key components of this model are Darcy's law, which describes the overloaded motion of the cytoskeleton of the active gel, and the Young-Laplace equation for pressure and velocity with an elastic nonlocal resistance force that depends on the area of a cell.…”

“…Compared to the initial statement of the problem the myosin density in (2) has been replaced by the normalizing function Q(m) = 1−e −m 1+e −m . The explicit derivation of the equation system of the model can be found in [23]- [25].…”

“…Here the condition ( 25) guaranties elimination of the first order residual (see (23)) and the condition (26) guarantees no additional multiplier for the ∆φ term in the right-hand side of (27).…”