The sliding filament model of muscle contraction. II. The energetic and dynamical predictions of a quantum mechanical transducer model

A theoretical model of a molecular energy transducing unit designed for the production of mechanical work is constructed and its consequences examined and compared with the experimentally determined myothermal and dynamic properties of vertebrate striated muscle. The model rests on a number of independent assumptions which include: the almost instantaneous generation of mechanical force by the occurrence of a radiationless transition between vibronic states of the transducer (crossbridge) at a point of potential energy surface crossing; transmission of this force to the load via the active sites on the thin filament by means of non-bonding repulsive forces, no energy being required for detachment; “detachment” consists of a second radiationless transition at a lower energy point than the first force generating transition, the energy difference appearing largely as work. The method of force generation completely avoids problems such as the “force-rate dilemma” which occur repeatedly in any discussion where state populations are near-Boltzmann and also leads without further arbitrary assumptions to such concepts as “attached but non force-producing states” and strongly position dependent “attachment” and “detachment” rate constants since these can only be appreciable near potential energy surface crossings. The kinetics and energetics of a transducer of this type operating cyclically and converting ATP → ADP + P_i are considered and shown to lead to length-tension and energetic behaviour very similar to that exhibited by vertebrate striated muscle, both for contraction and stretching. The existence of a limiting tension for stretching is predicted by the model as is the decrease of the rate of enthalpy release rate below the isometric value. At the limiting tension the rate of enthalpy release by the transducers is virtually zero, as observed. However, the stretching only inhibits the ATP hydrolysis, the cyclic synthesis from ADP and work being impossible with this model. The response to rapid length step changes automatically contains the asymmetry observed experimentally (with respect to lengthening and shortening) and arbitrary assumptions over and above those giving adequate explanation of the steady-state properties are not required. The asymmetry arises mainly as a consequence of the non-bonded pushing action of the crossbridges. This same assumption predicts the occurrence of an asymmetric thermoelastic ratio for active muscle with respect to stretching and contraction. The quantitative aspects of the model are satisfactory as it simultaneously reconciles the numerical magnitudes of macroscopic quantities such as isometric tension, maximum contraction velocity, limiting tension sustainable on stretching, isometric heat rate and resting heat rate with molecular parameters such as the filament and crossbridge periodicities, molecular vibrational relaxation rates, recurrence times for the radiationless transitions occurring, etc. This is achieved without any parameter optimization and only a very much smaller number of unknown parameters than the number of observed results accounted for. Many of the entities occurring in the model cycle (vibronic states of crossbridges, ATP, etc.) appear to be in one-to-one correspondence with many of the kinetic entities postulated to account for the biochemical kinetic results obtained for the actomyosin ATPase system in vitro. Finally, the rigor state has to be viewed in a different way from the conventional one; on the basis that the present model states which are part of the contraction cycle but sparsely populated during the latter (and hence are of chemical kinetic but not dynamical importance) are heavily populated during the rigor state. The mechanical properties of the rigor state would then be determined by these molecular states which would be very short-lived during the contraction cycle. If this is correct the rigor state could yield much more information about inaccessible parts of the contraction cycle than is presently supposed. The model leads one to expect a rather different response to quick length step changes in the rigor state from that of the active state, in contrast to current interpretations in terms of a large number of attached crossbridges, unable to detach due to the absence of ATP.