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.

Nonequilibrium physics in biology

“…Similarly, they are generic properties of active elastic materials with stress-dependent motor regulation (Günther and Kruse, 2007;Radszuweit et al, 2013) or in presence of turnover (Dierkes et al, 2014). In combination with filament treadmilling, motors can also generate waves in actomyosin bundles (Oelz and Mogilner, 2016;Torres et al, 2010;Wollrab et al, 2016) as were observed in cytokinetic rings in fission yeast (Wollrab et al, 2016). Lateral waves observed during the spreading of fibroblasts (Doebereiner et al, 2006;Giannone et al, 2004) have been proposed to result from cytoskeleton-membrane interactions (Gholami et al, 2012;Shlomovitz and Gov, 2007;Zimmermann et al, 2010).…”

­Back-to-back mechanisms drive actomyosin ring closure during Drosophila embryo cleavage

“…To our knowledge, this is the first example where sequential and separable mechanisms of varying Myosin-2 dependencies drive one ring closure event. Adding to what is already known from other cell types, actomyosin rings seem to combine mechanisms in all possible ways, where constriction may be powered by a single mechanism or by multiple mechanisms that either overlap at the same time or occur in sequence (Neujahr et al, 1997;Zang et al, 1997;Lord et al, 2005;Reichl et al, 2008;Burkel et al, 2012;Ma et al, 2012;Mendes Pinto et al, 2012Mishra et al, 2013;Davies et al, 2014;Oelz and Mogilner, 2016). Per contractile event, different combinations of mechanisms may have evolved to meet specific mechanical requirements, to increase robustness, or, as suggested here, to tune the kinetics of ring closure.…”

Protein Friction and Filament Bending Facilitate Contraction of Disordered Actomyosin Networks

“…These models use simplified representations of individual network components, and track how they evolve over time. Agent-based models enable detailed description of the mechanics on a microscopic scale, and can subsequently be used to develop accurate continuum models [23].…”