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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

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 θ. 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 θ of the levers belonging to these WS heads is accessible. This census leads to an integer number (Np) of angular positions (θi) distributed discretely between θup and θdown, the two values that delimit θ 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 θi calculated for a single Mfil. By summing the Gaussian Np densities and after normalization, we obtain a probability density (dG) of the continuous variable θ between θup and θdown. The function dG is calculated for a random length of a hs between 1 and 1.1 μm 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 θi positions is performed, which leads to a new probability density dG. The classic statistical law that approximates these 12 distributions of θ is the Uniform law between θup and θdown. 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 θ follows an identical uniform law in all the hs of a muscle fiber stimulated in isometric conditions.