The basic mechanical structure of the skeletal muscle machinery: One model for linking microscopic and macroscopic scales.

Measuring, analysing, and modelling muscle contraction has a long history. In consequence, some signature characteristics of skeletal muscle contraction have been found. On a microscopic level, these are the typical non-steady-state responses of the cross-bridge bindings to steps in force and length. On a macroscopic level, the force-velocity, enthalpy-velocity, and efficiency-velocity relations for concentric steady-state contractions are crucial characteristics. As these characteristics were repeatedly confirmed across animal species and sizes, they are expected to pinpoint basic physical properties of the mechanical structure that embodies the skeletal muscle machinery. The approach presented in this article explains, for the first time, these characteristics at both the microscopic and the macroscopic scale with one model and one set of parameters. According to expectation, this model is solely built on the basic mechanical structure of the muscular, contractile machinery. Its four mechanical elements represent the source of work, the serial elasticity, damping due to mechanical deformation, and damping due to the biochemical ATP hydrolysis in the energy conversion process. For explaining all mentioned non-steady-state and steady-state characteristics at once, the model requires, at maximum, ten parameters of which only three parameters representing damping properties plus one representing muscle-internal steady-state kinematics were free to be chosen. All other parameters were already fixed by literature knowledge of the geometrical structure and force characteristics of one cross-bridge. Amongst other results, we found that (i) the most reduced variant of the model is mathematically equivalent to a former version and (ii) the curvature parameter of the Hill relation can be interpreted as the ratio of strengths of the two modelled damping processes. This model approach not only unifies microscopic and macroscopic experimental findings, but further allows to interpret findings of molecular damping and elasticity and scaling of muscle properties, as discussed in this article.