A curvilinear Model Approach: Actin Cortex Clustering Due to ATP-induced Myosin Pulls

Abstract

The actomyosin cortex is involved in a range of many cellular processes like cell division, motility or shaping. To obtain this variety of functionalities the membrane-bound actin mesh has to be reconstituted by the motor protein myosin. But little is known about the underlying mechanism, which control the different tasks. An underlying in vitro study of a synthetic actomyosin cortex has shown that the cortex organizes into spatial clusters for certain ATP concentrations. Here we develop a curvilinear model that captures the viscoelastic material behavior and the kinetics of the myosin cross bridge. Further, we suggest a formulation for the active contractile stress produced by the motor protein myosin. We demonstrate that the spatial pattern generated by the curvilinear model is consistent with the experimental observations, including mesh clustering due to contractile forces and an absence of contraction for low and high ATP concentrations. Additionally we show that the cluster positioning can be tuned by the ATP-gradient.

Symmetry Breaking and Emergence of Directional Flows in Minimal Actomyosin Cortices

“…F-actin, cross-linked by myosin II molecules, forms a mesh-like cortex, causing an active viscoelastic material behavior with a rheological property combination of the Maxwell and Kelvin-Voigt models [30] considered in the momentum equation [31] (Supplemental Equation (S14)). To model force generation according to the myosin cross-bridge sub-model, the active stress was developed from a stress term of our previous study [32] considering the observed medium ATP-dependency of myosin pulls in MACs [20]. The distributed reaction network is described by a system of partial differential equations (PDEs) assuming diffusion (G D , G T , ATP) or combined convection and diffusion flux (A, A M , M) (Supplemental Equations (S1)-(S6)).…”

Symmetry Breaking and Emergence of Directional Flows in Minimal Actomyosin Cortices

“…S14). To model force generation according to the myosin cross-bridge sub-model, the active stress was developed from a stress term of our previous study (32) considering the observed medium ATPdependency of myosin pulls in MACs (20). The distributed reaction network is described by a system of partial differential equations (PDEs) assuming diffusion (GD, GT, ATP) or combined convection and diffusion flux (A, AM, M) (Supplement Eq.…”

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.…”