| Typical skeletal muscle experiments show a region on the force-length diagram where total tension decreases with length. From the perspective of materials science such softening of the mechanical response suggests localization instability which however has not been demonstrated by direct observations. Even though it has been long debated that the factor preventing catastrophic instability is passive elasticity, the conclusive mathematical analysis apparently has never been carried out. In this study we address the problem from the energetical point of view and associate stable configurations of the activated muscle with local minima of the total energy. As we show the crucial role in stabilizing the muscle on the descending limb of the tension-length curve is played by the non-uniform distribution of sarcomere lengths which in our model is not a mere outcome of dynamics but is a result of a collective interaction of sarcomeres. The non-uniform equilibrium microstructures are shown to exhibit quasi-periodic patterns on the microscale which are practically undistinguishable from the homogeneous deformation on the macroscale. The variation of the degree of nonuniformity with elongation is shown to follow the so-called devil's staircase pattern which is a typical feature of the behavior of the modulated phases in solid-state physics. Overall, our analysis of a lumped model of the muscle has shown that the energy landscape of the fully tetanized fiber is “wiggly”, exhibiting multiple metastable states. The possibility of a variety of evolutionary paths in such a landscape creates a potential for history dependence, which, in turn, explains the mysteries of the permanent extra tension after stretch and the associated deficit of tension after shortening. |
