Mechanical model of muscle contraction. 6. Calculations of the tension exerted by a skeletal fiber during a shortening staircase

Abstract

Accompanying Paper 1 tests a theoretical relationship between force and shortening velocity of a muscle fiber without justifying its validity. Paper 2 determines the kinematics and dynamics of a myosin II head during the working stroke (WS). Paper 3 imposes the Uniform law as a density representative of the orientation of the levers belonging to the WS heads. By support of these works, Papers 4 and 5 put into equation the evolution of the tension during the four phases of a length step. The present paper closes all six articles by imposing two tasks on itself. The first purpose is to apply the theoretical elements developed for a length step to a succession of identical length steps, otherwise known as shortening staircase. With the values of the geometric and temporal parameters assigned to a myosin head in Papers 1 to 5, a correct adjustment is established between the theoretical tension deduced from our model and the experimental tension published in 1997 by a team of Italian researchers relating to nine shortening staircases performed on the same fiber. In particular, we obtain the equation of the tension reached at the time end of the step (T*) which remains constant step by step as soon as the shortening of a half-sarcomere exceeds 17 nm. The second objective is to find and explain the equation of the Force-Velocity curve introduced ex abrupto into Paper 1: by decreasing the size and duration of the steps, the staircase tends towards a constant slope line corresponding to a continuous speed shortening. By applying the methods of infinitesimal calculus to the different formulations leading to T*, we deduce the Force-Velocity relationship (see Supplement S6.L). And the circle is complete.