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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 θ. 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 . 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 θup and θdown, the two boundaries framing the angle θ 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 , on the one hand, and between MB and TA, on the other hand, is performed. This algorithmic optimization leads to theoretical values of θup and θdown equal to +28° (−28°) and −42° (+42°) respectively with a variability of ±5° in a hs on the right (left), data in accordance with the commonly accepted experimental values for vertebrate muscle fibers.