Mechanical model of muscle contraction. 1. Force-velocity relationship

The two parameters that determine the functionality of a skeletal muscle fiber are the tension (T) exerted at its two endpoints and the shortening speed (V), two mechanical characteristics. We established a relationship between T and V by developing a theoretical model of muscle contraction based on the swinging lever arm hypothesis. At the nanoscale, force and movement are generated by the myosin II heads during the working stroke (WS). The change in conformation of a myosin head during the WS is characterized by the rotation of the lever correlated to the linear displacement of the motor domain. The position of the lever is marked by the angle θ. The maximum variation of θ between the two limits θ up and θ down relating to the two positions up and down is usually given equal to 70°. When the angle θ is between θ up and θ down , the WS is triggered in three modes, fast, slow or very slow. During the isometric tetanus plateau, θ is uniformly distributed between the two angles θup and θ T separated by a usual difference of 50°. Consequently during isometric tetanus plateau there is a 20° interval between θ T and θ down where no head is found in WS. We link this absence to the slow detachment of the heads whose orientation of the levers is between θ T and θ down during the rise to the isometric tetanus plateau. The equation between T and V refers to these four occurrences: fast, slow or very slow initiations of the WS between θ up and θ down , then slow detachment between θ T and θ down . The equation is constructed from the geometric data of the myosin head and the time constants of the cross-bridge cycle reactions associated with these four events. The biphasic aspect of the curve is explained by the slow detachment that occurs only at very slow speeds. An additional term, derived from the viscosity present as soon as the velocity increases completes the equation. An adequate fit between the model and examples from the physiological literature is found (r 2 > 99%).