A kinetic model of muscle contraction and its oscillatory characteristics

Abstract

A set of five differential equations has been found which gives a satisfactory account of the isotonic and isometric properties of striated muscle. Four of these differential equations give an equally satisfactory account of the results of length-drive experiments with sinusoidal variation of length. In this case, the fifth equation (of motion) is redundant. These sets of equations predict a number of results not yet measured relating to the superposition of oscillatory length changes on isotonic contraction. The equations predict correctly the variation of tension with time when the amplitude of the driven oscillation increases beyond the region where it can be treated as a perturbation, and the deviation of the mean tension per cycle from the steady-state tension for isotonic contraction with superimposed oscillations in length or velocity. The equations can be derived rigorously from a more complex set of eight equations which themselves are formulated from the basic principles of chemical physics, the theory of molecular force fields and radiationless transitions. The reduced model may be consistent with many other molecular theories and its predictive success does not prove the correctness or otherwise of the level 1 assumptions of the seven-state theory. By the same token, macroscopic mechanical experiments of the type presently carried out cannot give information on level 1 questions such as the existence or otherwise of 'binding' of crossbridges to the thin filament. The experimental kinetic results can be described with or without this assumption. The theory needs considerable development in so far as it does not consider elastic elements at all at present, nor have detailed conclusions yet been extracted from the equations for the case of stretching, except for isotonic steady states where agreement is encouraging.