Mechanical model of muscle contraction. 4. Theoretical calculations of the tension during the isometric tetanus plateau and the tension exerted at the end of phase 1 of a length step

Abstract

AbstractHypothesis 4 presented in accompanying Paper 2 states that the lever of a myosin II head in working stroke (WS) moves in a fixed plane, the orientation of the lever being defined by the angle θ. From this conjecture can be deduced the hypothesis 5 developed in accompanying Paper 3: the distribution of θ is identical and uniform in each half-sarcomere (hs) of a muscle fiber stimulated under isometric conditions. We propose a sixth hypothesis that establishes a linear relationship between the θ angle and the motor moment (ℳ) exerted on the lever. These three hypotheses lead to calculations of the tension during isometric tetanus plateau (T0) and the tension applied at the end of phase 1 of a length step when the only internal actions are the forces of elastic origin produced by the myosin heads in WS (T1Elas). However, the T1Elas values are higher than those observed experimentally. The model introduces the presence of viscosity as the seventh hypothesis. The internal actions resulting from the coupling of the elasticity of the WS heads and the viscosity make it possible to explain all the observed phenomena that contribute to the phase 1 of a length step. An adequate adjustment between the theoretical tension from the model (T1) and the tension representative of the end of phase 1 exposed in examples from the physiological literature is proven (r2 > 98%). Other parameters such as stiffness (e), compliance (C) and strain (Y) are deduced; their investigation enables the construction of an analytical “nanoscope” by means of which the uniform density of θ is explored. The equations for T0, T1, e, C and Y explain and predict the influence of factors such as the duration of phase 1, the initial length of the sarcomere, the concentration of calcium, the presence of an inhibitor, the tension rise to the isometric tetanus plateau, relaxation after tetanization or shortening at constant speed. The results obtained during a slack-test are indicated by the model, the slack of the fiber being interpreted as an event of purely viscous origin.