Mechanical model of muscle contraction 2. Kinematic and dynamic aspects of a myosin II head during the working stroke

The condition of a myosin II head during which force and movement are generated is commonly referred to as Working Stroke (WS). During the WS, the myosin head is mechanically modelled by 3 two by two articulated segments, the motor domain (S1a) strongly fixed to an actin molecule, the lever (S1b) on which a motor moment is exerted, and the rod (S2) pulling the myosin filament (Mfil). When the half-sarcomere (hs) is shortened or lengthened by a few nanometers, it is assumed that the lever of a myosin head in WS state moves in a fixed plane including the longitudinal axis of the actin filament (Afil). As a result, the 5 rigid segments, i.e. Afil, S1a, S1b, S2 and Mfil, follow deterministic and configurable trajectories. The orientation of S1b in the fixed plane is characterized by the angle {theta}. After deriving the geometric equations singularizing the WS state, we obtain an analytical relationship between the hs shortening velocity (u) and the angular velocity of the lever [Formula]. The principles of classical mechanics applied to the 3 solids, S1a, S1b and S2, lead to a relationship between the motor moment exerted on the lever (MB) and the tangential force dragging the actin filament (TA). We distinguish {theta}up and {theta}down, the two boundaries framing the angle {theta} during the WS, relating to up and down conformations. With the usual data assigned to the cross-bridge elements, a linearization procedure of the relationships between u and [Formula], on the one hand, and between MB and TA, on the other hand, is performed. This algorithmic optimization leads to theoretical values of {theta}up and {theta}down equal to +28{degrees} (-28{degrees}) and -42{degrees} (+42{degrees}) respectively with a variability of {+/-}5{degrees} in a hs on the right (left), data in accordance with the commonly accepted experimental values for vertebrate muscle fibers.