Striated muscle contraction requires intricate interactions of microstructures. The classic textbook assumption that myosin filaments are compressed at the meshed Z-disc during striated muscle fibre contraction conflicts with experimental evidence. For example, myosin filaments are too stiff to be compressed sufficiently by the muscular force, and, unlike compressed springs, the muscle fibres do not restore their resting length after contractions to short lengths. Further, the dependence of a fibre's maximum contraction velocity on sarcomere length is unexplained to date. In this paper, we present a structurally consistent model of sarcomere contraction that reconciles these findings with the well-accepted sliding filament and crossbridge theories. The few required model parameters are taken from the literature or obtained from reasoning based on structural arguments. In our model, the transition from hexagonal to tetragonal actin filament arrangement near the Z-disc together with a thoughtful titin arrangement enables myosin filament sliding through the Z-disc. This sliding leads to swivelled crossbridges in the adjacent half-sarcomere that dampen contraction. With no fitting of parameters required, the model predicts straightforwardly the fibre's entire force-length behaviour and the dependence of the maximum contraction velocity on sarcomere length. Our model enables a structurally and functionally consistent view of the contractile machinery of the striated fibre with possible implications for muscle diseases and evolution.
BackgroundAs motors of life, muscles convert chemical energy into mechanical energy and heat. Muscles transport substances within the body, stabilize the skeleton and enable locomotion. The first property characterizing the mechanical function of striated muscles to be described [1] was the active isometric force-length relationship (FLR). This property shows the maximal forces the striated muscle fibre can produce by electrical stimulation at different constant lengths. The classic FLR (figure 1, straight lines) [2] with its strikingly linear segments has been described not only up to the fibre level but also for the whole muscle [7,8]. Despite the fact that this relationship represents basic textbook knowledge for life science students, to date a convincing structural model explaining the shape of the entire FLR does not exist.According to the sliding filament [4,5] and crossbridge [6] theories, actin and myosin filaments slide relative to each other in response to forces generated by temporary crossbridges formed by myosin heads-projecting from the myosin filaments-and actin filaments. This yields straightforward geometric explanations for the plateau region and for the region of decreasing isometric force based on filament lengths ( figure 1, black lines) [2]. The slope change (figure 1, black circle) in the range of increasing isometric force (ascending limb) is typically related to myosin filaments hitting the Z-disc, a thinmeshed filament structure [9] defining the sarcomere bounda...