title: Actomyosin contraction, aggregation and traveling waves in a treadmilling actin array.
abstract: We use perturbation theory to derive a continuum model for the dynamic actomyosin bundle/ring in the regime of very strong crosslinking. Actin treadmilling is essential for contraction. Linear stability analysis and numerical solutions of the model equations reveal that when the actin treadmilling is very slow, actin and myosin aggregate into equidistantly spaced peaks. When treadmilling is significant, actin filament of one polarity are distributed evenly, while filaments of the opposite polarity develop a shock wave moving with the treadmilling velocity. Myosin aggregates into a sharp peak surfing the crest of the actin wave. Any actomyosin aggregation diminishes contractile stress. The easiest way to maintain higher contraction is to upregulate the actomyosin turnover which destabilizes nontrivial patterns and stabilizes the homogeneous actomyosin distributions. We discuss the model's implications for the experiment.
authors.affiliation: Courant Inst. of Math. Sciences, New York University, 251 Mercer St, New York, NY 10012.
authors.forename: Dietmar
authors.initials: D
authors.lastname: Oelz
authors.affiliation: Courant Inst. of Math. Sciences, New York University, 251 Mercer St, New York, NY 10012; Department of Biology, New York University.
authors.forename: Alex
authors.initials: A
authors.lastname: Mogilner
keywords: constriction ring; continuum model; myosin contraction