A discontinuously coupled network of phase oscillators replicate actomyosin cooperation

Abstract

Groups of non-processive myosin motors exhibit complex and non-linear behaviors when binding to actin. These operate at larger scales and time frames than an individual motor, indicating the presence of a strong cooperative disposition. Limits in contemporary microscopy prevent verification of motor-filament binding dynamics, whilst mathematical models rely on continuum abstractions in which cooperativity is implicit and individual motor behavior cannot be separated from the behaviour of the whole. Understanding the fundamental interactions driving the emergent behaviour in actomyosin therefore remains an open question. Here we suggest that the diversity of empirically observed in-vitro oscillations can be explained by a minimal Kuramoto-style phase oscillator model of actomyosin, where cooperativity is orchestrated by the actomyosin geometry and mechanical environment. The model mirrors the irregular and regular saw-tooth oscillations present in in-vitro actomyosin and sarcomeric SPOC experiments with only adjustments of the external mechanical environment, and despite the models simplicity. Actomyosin-like behaviour thus arises as a generic property of the discontinuous mechanical coupling in an incommensurate architecture, rather than specific to molecular motor reaction kinetics. We demonstrate a range of synchronising behaviours arising from the cooperative motor dynamics that, once synchronised, are stable over a large range of external forces. These synchronising behaviours arise from the cooperative motor dynamics that, once synchronised, are stable over a large range of external forces. The nature of the synchronisation patterns allow recruitment of rotors as the external force increases, reducing variance in the backbones velocity. This is a demonstration of morphological control. Due to interest in this behaviour in contemporary robotics, we build a physical experiment, using electric motors to power our oscillators. Using the experiment we verify both the organisational and control properties of the system. This demonstrates non-biological motors can cooperate similarly to biological motors when working within an actomyosin geometry, suggesting that the actomyosin complex may not depend on motor-specific qualities to achieve its biological function. These findings offer novel insights into synchronising networks of oscillators and have potential applications in emulating actomyosin-like behaviors within contemporary robotics using non-biological motors.