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The aim of this work is to gain understanding of how the inner components of certain non-muscle actomyosin bundles, specifically cytokinesis constriction rings, but also stress fibers and the keratocyte rear bundle, 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.

Typically existing studies suggest that local asymmetry is provided by either actin or myosin patterning, or by an involved mechanism which favors contraction. Alternatively it is also suggested that actin depolymerization provides contractile force.

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 and to come up with a minimum set of modeling assumptions which allow to simulate the observed ring constriction. 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 thus allowing myosin-II to effectively contract the cytokinesis ring.