Theoretical analysis of power‐law stress relaxation and calcium‐dependent passive mechanics in cardiac muscle

This study investigates the passive viscoelastic properties of cardiac muscle by introducing a theoretical model that explains the observed power-law kinetics of murine cardiac trabeculae passive stress decay. The model accounts for two parallel processes contributing to passive mechanics: an elastic component and a viscoelastic component designed to simulate stress/strain-mediated unfolding of serial domains in the titin molecule. Under stress, serial globular domains within the elastic region of the titin molecule reversibly unfold. This unfolding phenomenon contributes to both hysteresis (a lag in stress between loading and unloading) and preconditioning effects in simulated mechanics. Experimental evidence indicates that stress relaxation in cardiac muscle follows a power law and that the muscle's non-linear stress-strain relationship and hysteresis behaviour are calcium-dependent. To analyse these phenomena, we simulate the apparent viscous element as a mesoscopic-scale ensemble of chains, each composed of serial globular domains that unfold in a stress-dependent manner. The observed increase in passive tension with increased Ca²⁺ concentration is attributed to Ca²⁺-mediated: (1) PEVK attachment to actin; (2) stiffening of the proximal element; and (3) stabilization of folded conformations of serial domains in the titin chain. Although the model was developed to represent the behaviour of titin, it equivalently represents any contributing process involving a linked series of domains that undergo stress-mediated unfolding. By providing a unified basis for the observed viscoelastic and preconditioning effects, calcium dependency, and power-law stress relaxation phenomena, this study offers a novel theoretical basis for understanding and simulating the role of titin in striated muscle mechanics. KEY POINTS: Passive stress relaxation of cardiac muscle follows a power-law decay, a phenomenon that is explained using a theoretical model of dynamic unfolding of globular domains along polymer chain. The theoretical model simulates the behaviour of titin, a giant sarcomere protein linking myosin thick filaments to the Z disk and providing passive restoring force during muscle stretch. The theoretical model is able to account the observed effects of Ca²⁺ on the effective viscoelastic passive mechanics of cardiac muscle. This model provides a theoretical basis for understanding passive viscocelastic properties and titin's role in striated muscle mechanics.