A twist in the lower 50 kDa subunit during catalysis (Coureux et al. https://doi.org/10.1038/nature01927) is the basis for torque at the site of weak association with actin. The change in direction of ATP hydrolysis when the catalytic site opens at two boundary conformations (coordinates) accelerates the myosin head. The torque from the momentum of the oscillating mass adds to the thermodynamic potential of the actin-associated state. The selective advantages are that the total energies of both the torque-dependent state and Hamiltonian are defined by Δ G ATP <0 per ATP and that the total energy is conserved over the two openings of the catalytic site per cycle. As momentum vanishes, the boundary coordinates constrain the changes in mechanical and thermodynamic potentials to the same time differential. The dwell time of weak association is an analytical solution to functions that maximize the thermodynamic potential and minimize the Hamiltonian path in the same differential. The derived dwell time is determined to be near π times the torque-free weak association constant (Boltzmann factor) when dwell time distributions from myosin IC and myosin VI are fit. This baseline dwell time can be enhanced by harmonic coupling with an optical trap or between heads. When the force diagram includes a spring element in the N-terminal domain of myosin I or the trailing head of myosin VI after the power stroke, the momentum that transfers depends on the difference between spring constants of the myosin and load. The torque from the momentum extends the dwell time until the coordinates of the catalytic site reach the boundary, which occurs at the beat frequency. The plot of the beat frequency as a function of increasing load matches the changes in dwell time measured for myosin I and myosin VI.
Henry G. Zot (Sun,) studied this question.