title: Existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium.
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.
authors.affiliation: CIMS, New York University, 251 Mercer Street, New York, NY, 10012, USA. angelika.manhart@cims.nyu.edu.|Faculty of Mathematics, University of Vienna, Oskar-Morgenstern Platz 1, 1090, Vienna, Austria. angelika.manhart@cims.nyu.edu.
authors.forename: Angelika
authors.initials: A
authors.lastname: Manhart
authors.affiliation: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern Platz 1, 1090, Vienna, Austria.
authors.forename: Christian
authors.initials: C
authors.lastname: Schmeiser
mesh_terms: D008841:Actin Cytoskeleton / Q000378:metabolism; D008954:Models, Biological; D058105:Polymerization; D011554:Pseudopodia / Q000502:physiology*
keywords: Actin; Lamellipodium; Lyapunov function