A theory on auto-oscillation and contraction in striated muscle

It is widely accepted that muscle cells take either force-generating or relaxing state in an all-or-none fashion through the so-called excitation-contraction coupling. On the other hand, the membrane-less contractile apparatus takes the third state, i.e., the auto-oscillation (SPOC) state, at the activation level that is intermediate between full activation and relaxation. Here, to explain the dynamics of all three states of muscle, we construct a novel theoretical model based on the balance of forces not only parallel but also perpendicular to the long axis of myofibrils, taking into account the experimental fact that the spacing of myofilament lattice changes with sarcomere length and upon contraction. This theory presents a phase diagram composed of several states of the contractile apparatus and explains the dynamic behavior of SPOC, e.g., periodical changes in sarcomere length with the saw-tooth waveform. The appropriate selection of the constant of the molecular friction due to the cross-bridge formation can explain the difference in the SPOC periods observed under various activating conditions and in different muscle types, i.e., skeletal and cardiac. The theory also predicts the existence of a weak oscillation state at the boundary between SPOC and relaxation regions in the phase diagram. Thus, the present theory comprehensively explains the characteristics of auto-oscillation and contraction in the contractile system of striated muscle.