The relation between force developed and energy liberated in an isometric twitch

Abstract

The development of force in muscular contraction requires a proportional expenditure of energy, and any quantitative theory of contraction must involve the constant of the proportion. In an isometric twitch the energy liberated, as well as the force developed, varies with muscle length; but over a wide range of lengths the ratio $Pl_{0}/H$ is nearly constant $(P=\text{force developed},l_{0}=\text{standard resting length},H=\text{energy liberated})$. Its actual value depends on the extensibility of the arrangements for recording force; when these were made as inextensible as possible, a value of about 10.3 was obtained. This is still rather too small, because of the compliance of the muscle itself, tendons, etc.; if this compliance could be eliminated the value would be about 13. In striated muscle the ultimate unit of length is the sarcomere. In order to develop a force of 1 dyne in the length of one sarcomere the energy required is about $2\times 10^{-5}$ $\text{erg}$; or, assuming that the energy is derived from the splitting and neutralization of $\text{ATP}$ and/or creatine phosphate, the number of molecules split is about $2.4\times 10^{7}$.