Actin-Myosin Spatial Patterns from a Simplified Isotropic Viscoelastic Model

Abstract

F-actin networks are involved in cell mechanical processes ranging from motility to endocytosis. The mesoscale architecture of assemblies of individual F-actin polymers that gives rise to micrometer-scale rheological properties is poorly understood, despite numerous in vivo and vitro studies. In vitro networks have been shown to organize into spatial patterns when spatially confined, including dense spherical shells inside spherical emulsion droplets. Here we develop a simplified model of an isotropic, compressible, viscoelastic material continually assembling and disassembling. We demonstrate that spherical shells emerge naturally when the strain relaxation rate (corresponding to internal network reorganization) is slower than the disassembly rate (corresponding to F-actin depolymerization). These patterns are consistent with recent experiments, including a collapse of shells to a central high-density focus of F-actin when either assembly or disassembly is reduced with drugs. Our results demonstrate how complex spatio-temporal patterns can emerge without spatially distributed force generation, polar alignment of F-actin polymers, or spatially nonuniform regulation of F-actin by upstream biochemical networks.

Cytoskeletal Symmetry Breaking and Chirality: From Reconstituted Systems to Animal Development

“…It posits that interfacial polymerization can trigger an instability which induces spontaneous symmetry breaking [106]. In the light of work from the Schwille group [99] and the model of Lewis et al [107], myosin-mediated actin fragmentation or viscous/elastic stress originating from turnover/de-polymerization might also be possible explanations for spontaneous symmetry breaking observed experimentally in the ActA system.…”

“…Strikingly, inhibition of either polymerization or de-polymerization leads to collapse of vortices while fusion of two droplets with vortices leads to re-organization of the two halos into one that scales to the size of the droplet [108]. These observations have led to the development of a mathematical model that can explain this emergent phenomenon: Lewis et al, using an isotropic viscoelastic model, show that these dissipative structures can emerge from the viscoelasticity of the system when rearrangements in the actomyosin network are slower than the disassembly rate while not requiring a specific polarity of its constituents [107]. Thus, unlike in the microtubule-motor examples above, polarity sorting does not seem to contribute to formation of mesoscopic structures in this case [60][61][62].…”

Intracellular Fluid Mechanics: Coupling Cytoplasmic Flow with Active Cytoskeletal Gel

“…Similar continuous models introduced later considered both elastoviscous (springs and dashpots in parallel, hence the actin network does not flow on long timescales) (Gracheva & Othmer 2004, Larripa & Mogilner 2006, viscoelastic (springs and dashpots in series, hence the actin network flows on long timescales) (Kruse et al 2006, Rubinstein et al 2009, purely elastic (Rubinstein et al 2005), and purely viscous (Barnhart et al 2015, Carlsson 2011, Recho et al 2013) models of the crawling cells. An insightful illustration that viscoelastic effects can lead to nontrivial patterns in the actomyosin continuum was given by Lewis et al (2014), who showed that in the emerging pattern in a contractile gel, one region can be dominated by viscous and another by elastic forces.…”

Towards Design of Self‐Organizing Biomimetic Systems

“…One interaction site of the actomyosin system with other functional modules is the energy‐depending (ATP) network contraction. Since previous actin models lacked an ATP dependent contractility, a spatially distributed model needed to be derived including viscoelastic material properties and a novel formulation for the active contractile stress, which models the dependency of cluster formation on a medium ATP concentration, according to experimental observations in synthetic minimal actin cortices . A further interaction side of the actomyosin cortex is the energy depending polymerization of actin filaments.…”

“…The oscillating behavior of the positioner system defines an attachment site for the division subsystem in the spatial center of the system . It is assumed that the division is caused by a protein ring, which is regarded as a viscoelastic and contractile gel and described by a continuous model adapted from actin models . In the original publications, the models of the functional modules were treated as isolated systems.…”