Mechanical model of muscle contraction. 3. The orientation of the levers belonging to the myosin heads in working stroke follows the same uniform law in all half-sarcomeres of an isometrically stimulated fiber

Abstract

A myosin II head is modelled during the working stroke (WS) by three rigid segments articulated between them: the motor domain (S1a), the lever (S1b) and the rod (S2). Hypothesis 4 introduced in accompanying Paper 2 states that the lever of a WS head moves in a fixed plane where the position of S1b is characterized by the angle {theta}. This assumption allows the geometrization of a cross-bridge, i.e. the poly-articulated chain consisting of five rigid segments: the actin filament (Afil), S1a, S1b, S2, and the myosin filament (Mfil). The equations established in Paper 2 are operative to calculate the number of heads potentially in WS for a Mfil surrounded by six Afil. In addition, the value of the angles {theta} of the levers belonging to these WS heads is accessible. This census leads to an integer number (Np) of angular positions ({theta}i) distributed discretely between {theta}up and {theta}down, the two values that delimit {theta} during the WS. The number of Mfil per half-sarcomere (hs) is estimated between 400 and 2000 depending on the typology, figures that induce Gaussian variability for each of the Np values {theta}i calculated for a single Mfil. By summing the Gaussian Np densities and after normalization, we obtain a probability density (dG) of the continuous variable {theta} between {theta}up and {theta}down. The function dG is calculated for a random length of a hs between 1 and 1.1 m where the binding rate of the myosin heads is maximum. From this reference length, the hs is shortened 11 times with a step of 1 nm, i.e. a total of 11 nm. For each shortening, a count of the new {theta}i positions is performed, which leads to a new probability density dG. The classic statistical law that approximates these 12 distributions of {theta} is the Uniform law between {theta}up and {theta}down. Other conditions and values given to the data of the algorithmic procedure lead to a similar result, hence the formulation of hypothesis 5: the distribution of the angle {theta} follows an identical uniform law in all the hs of a muscle fiber stimulated in isometric conditions.