Abstract
A model for the dynamics of actin filament ends along the leading edge of the lamellipodium is analyzed. It contains accounts of nucleation by branching, of deactivation by capping, and of lateral flow along the leading edge by polymerization. A nonlinearity arises from a Michaelis–Menten type modeling of the branching process. For branching rates large enough compared to capping rates, the existence and stability of nontrivial steady states is investigated. The main result is exponential convergence to nontrivial steady states, proven by investigating the decay of an appropriate Lyapunov functional.
Highlights
The lamellipodium is a thin protrusion, developing when biological cells spread on flat surfaces
Concerning the geometry, two different situations will be considered: for cells surrounded by a lamellipodium, the leading edge is described as a one-dimensional interval with a periodicity assumption, where the two ends are identified
In this paper we derived, discussed and analyzed a mathematical model for the density of actin filament ends along the leading edge of a lamellipodium, a submodel of the filament based lamellipodium model (FBLM) (Manhart et al 2015, 2016; Oelz and Schmeiser 2010)
Summary
The lamellipodium is a thin protrusion, developing when biological cells spread on flat surfaces. Concerning the geometry, two different situations will be considered: for cells surrounded by a lamellipodium, the leading edge is described as a one-dimensional interval with a periodicity assumption, where the two ends are identified This situation applies mostly to stationary spreading cells and has been observed in several types of cells, such as fish keratocytes (Yam et al 2007), mouse fibroblasts (Symons and Mitchison 1991) or T cells (Hui et al 2012). It is shown that a transcritical bifurcation away from the zero steady state occurs, when the ratio between the branching rate and the capping rate exceeds a critical value This local result is extended in two special situations: In the case of the periodic leading edge, existence of a nontrivial steady state is proven far from the bifurcation point, if the lateral flow speed is almost constant.
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