A Mechanochemical Model for the Steady and Transient Contractions of the Skeletal Muscle

Abstract

A mechanochemical model for muscle contraction was presented which consisted of three subsystems: the regulatory mechanism of contraction by Ca ion, the cross-bridge cycle coupled with actin-myosin interaction and the dynamics of contraction with an external load. It was assumed that both the rate constant of the cross-bridge cycle and the net force of the cross-bridge were linear functions of the sliding velocity. Most parameters in the model were determined from the experimental data, but several were estimated by simulation techniques. The model adequately described the force-load-velocity relation, the rates of energy and heat output as well as some basic mechanical properties of muscle. Not only the steady-state contraction but also the twitch response could be explained by the model. Time courses of tension and shortening during isometric and isotonic twitches were calculated by the model on a digital computer. The calculated curves agreed satisfactorily with the experimental ones obtained from the frog semitendinosus muscle. The rate of tension rise of the isometric twitch was shown to attain the peak at nearly the same time as does the calculated Ca concentration curve.

A Mathematical Model of the Dynamic Force–length Relationship of Skeletal Muscle Operating on Ascending and Descending Limbs

“…First, ST enhancement was found for sarcomere lengths beyond the myo lament overlap [11]. Second, our simulation study suggested that F corresponded to the number of active cross-bridges [12].…”

“…This is because our SL/ ST model is macroscopic. Introduction of the molecular mechanism of muscle contraction may be necessary in the future, for constructing a model of cross-bridge cycling between myo laments [12].…”

Calcium model for mammalian skeletal muscle

“…For such an approach it is necessary to realise a model that is based upon physiologically recognisable component processes. Presently available models for skeletal muscle, in which activation processes are implemented, are not sufficiently extensive for this purpose (ASHLEY and MOISESCU, 1972;AKAZAWA et al, 1976;HATZE, 1977;RADU et al, 1974) or are based on obsolete data (TAYLOR, 1969). Such extensive models are also lacking for cardiac muscle, although a related approach such as ours is sometimes taken (BASSINGTHWAIGHTE and REUTER, 1972;KAUFMANN et al, 1974;TSATURYAN and IZAKOV, 1978;MARKHASIN and MIL'SHTEIN, 1979;VAN DEN BROEK, 1979).…”

Force-velocity relation and contractility in striated muscles.

“…Although many kinetic models have been developed in order to explain gross filament sliding from local molecular events, few of them have dealt with the molecular mechanism of Hill's characteristic equation [1,11]. In particular, AKAZAWA's model [1] successfully explains not only Hill's constants in the steadystate contraction but also the dynamic and energetic properties of isometric and isotonic twitches.…”

“…In particular, AKAZAWA's model [1] successfully explains not only Hill's constants in the steadystate contraction but also the dynamic and energetic properties of isometric and isotonic twitches. Four states (except for the resting state) were considered in the cross-bridge cycle: state 1) is an activation phase of a site on the thin filament through the binding of Ca ion to troponin, state 2) is a force-generating phase by the action of the cross-bridge attached to the thin filament, state 3) is a sliding phase by movement of the cross-bridge, and state 4) is a detachment phase of the cross-bridge.…”