Myosin driven contraction of random actin arrays is promoted by the combined effect of treadmilling and cross-linker proteins

Department of Mathematics

University of California, Davis

The aim of this modeling study is to gain understanding of how the inner components of certain non-muscle actomyosin bundles, specifically cytokinesis constriction rings, interact in order to effectuate contraction. It is generally accepted that the force generated by myosin-II thick filaments interspersed within the disordered ring-shaped bundle of actin filaments largely contributes to the observed contraction. Yet, randomly placed myosin-II is expected to contract or to expand its vicinity with equal probability. Hence some sort of asymmetry which favors contraction is usually stipulated. Our approach is to formulate a detailed microscopic ODE-model for the dynamics of a network of cross-linked actin filaments interspersed with myosin-II motor proteins. The result of our numerical experiments is that a disordered bundle of actin filaments tends to contract if the positioning of myosin-II binding sites has a bias towards the pointed ends of actin filaments. Furthermore we found based on simulations that actin treadmilling in combination with actin cross-linking has the potential to provide this kind of bias. Taking into account a net-loss of F-Actin by depolymerization and severing respectively we are able to reproduce a steady rate of convergence and the experimentally observed scaling invariance of the time of contraction with respect to the initial ring radius.