Single muscle fiber contraction is dictated by inter-sarcomere dynamics

This paper presents first results from a study where we developed a generic framework for analysing inter-sarcomere dynamics. Our objective is to find an accurate description of a muscle as a linear motor composed of parallel and series coupled subunits. The quality of theoretical models can be tested through their ability to predict experimental observations. With the current method we have found rigorous mathematical explanations for mechanisms such as sarcomere popping, extra tension and homogenization. These phenomena have been observed for many years in single fibers experiments, yet have never been completely understood in terms of a mechanical model. Now they can be explained on a theoretical basis. Interestingly, rather simplistic descriptions of each of the various molecular components in the sarcomere (actin-myosin cross-bridges, titin and contributions from passive elastic components) are sufficient to predict these behaviors. The complexity of a real muscle fiber is addressed through rigorous coupling of the single component models in a system of differential equations. We examine the properties of the differential equations, based on a down-stripped model, which permits the derivation of analytical solutions. They suggest that the contraction characteristics of inter-connected sarcomeres are essentially dictated by the initial distribution of the sarcomeres on the force-length curve and their starting velocities. The complete model is applied to show the complexity of inter-sarcomere dynamics of activated fibers in stretch-release experiments with either external force or length control. Seemingly contradictory and unexpected observations from single fiber experiments, which have hitherto been discussed with the argument of uncontrollable biological variability, turn out to be a consistent set of possible fiber responses. They result from a convolution of multiple relatively simple rules each of them defining a certain characteristics of the single sarcomere.