Validity of Hill's Equation in an Artificial Actomyosin Streaming System
The rotation of an actomyosin motor (9,11), assembled from blades, one side onto which F-actin of uniform polarity was attached, suspended in a solution of heavy meromyosin (HMM), was modelled as due to sliding of HMM over the margins of the blades, whereby the work resulting from ATPase activity is used for pushing bulk fluid containing HMM from the leading surface of the blade over the force-generating filaments to the back surface, which leads to increased sliding velocity. The amount of HMM contributing to force-generation is divided into one component perpendicular to the filaments, which is diffusion-limited and regulated by a component parallel to the filaments, represented by the movement of the bulk fluid, the supply of new HMM and the observable velocity of rotation of the blade. Using Hill's equation (6) which essentially states that the product of a virtual force and a virtual velocity is constant within the range of observable forces and velocities, the force can be expressed as velocity, giving a simple first order differential equation. A solution to this equation can be fitted to the observed data with physically meaningful constants in terms of mass, viscosity, the force-velocity constant and a constant expressing the quality of the preparation. Control experiments were performed, using fixed blades. In these experiments, bulk flow around the margins did not increase as a result of ATPase activity and no movement or streaming was observed. The results show that Hill's equation may be applicable to streaming caused by actomyosin irrespective of its confinement to skeletal muscle and independently of preferred molecular model, and leads to several verify-able predictions.
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