Toward a unified theory of muscle contraction. II: predictions with the mean-field approximation

The contractile behavior of a single half-sarcomere has been calculated from the lattice model with dimeric myosin and extensible filaments, using the model cycle with two working strokes, explicit Pi-release transitions and faster binding for the second head of the dimer. The mean-field approximation is used to generate independent state probabilities for myosin heads, assuming that the positional symmetry of actin filaments in the half-sarcomere is preserved. This model predicts absolute values of the active tension, stiffness and ATPase of fast fibers and their variation with shortening velocity, the phase-2 tension response to a length-release step and the transient tension rise during ramp stretching, in reasonable agreement with experimental data for frog muscle. It accounts for three observations beyond the reach of traditional models: (i) with elastically stiff myosin, a two-stroke model explains the rate of rapid tension recovery as a function of step size, (ii) slow Pi release from A.M.ADP.Pi after the first stroke generates the flat tension response observed after rapid recovery from a small release step, (iii) a discrete lattice model generates undamped oscillations in the isotonic length response to a force step, as observed when the sarcomeres are highly ordered. The discrete lattice also generates length-dependent oscillations in the tension-length curve and the tension response to ramp shortening, which may be smoothed out if lattice symmetry is broken.