Force-velocity relationship and biochemical-to-mechanical energy conversion by the sarcomere

Abstract

The intracellular control mechanism leading to the well-known linear relationship between energy consumption by the sarcomere and the generated mechanical energy is analyzed here by coupling calcium kinetics with cross-bridge cycling. A key element in the control of the biochemical-to-mechanical energy conversion is the effect of filament sliding velocity on cross-bridge cycling. Our earlier studies have established the existence of a negative mechanical feedback mechanism whereby the rate of cross-bridge turnover from the strong, force-generating conformation to the weak, non-force-generating conformation is a linear function of the filament sliding velocity. This feedback allows the analytic derivation of the experimentally established Hill's equation for the force-velocity relationship. Moreover, it allows us to derive the transient length response to load clamps and the transient force response to sarcomere shortening at constant velocity. The results are in agreement with experimental studies. The mechanical feedback regulates the generated power, maintains the linear relationship between energy liberated by the actomyosin-ATPase and the generated mechanical energy, and determines the efficiency of biochemical-to-mechanical energy conversion. The mechanical feedback defines three elements of the mechanical energy: 1) external work done; 2) pseudopotential energy, required for cross-bridge recruitment; and 3) energy dissipation caused by the viscoelastic property of the cross bridge. The last two elements dissipate as heat.

Adaptive control of cardiac contraction to changes in loading: from theory of sarcomere dynamics to whole-heart function

“…Qη is proportional to the square of velocity, and thus negligible at physiological shortening velocities encountered in the functioning heart [25,28]. Thus, Eq.…”

“…The SCC [23,24,27,28,30,42], schematically presented in Fig. 1, is based on coupling the kinetics of calcium binding to troponin with XB cycling dynamics.…”

“…1. 2. The rate of XB turnover from the strong to weak conformation (g), representing the XB-weakening rate, is determined by the XB strain rate or filamentshortening velocity [24,28,29,42]. This negative feedback is the mechanical feedback, since a mechanical quantity (velocity) determines the rate of XB turnover from the strong to the weak biochemical conformations.…”

“…An increase in sarcomeric-shortening velocity increases the rate of XB weakening and decreases the time over which the XB generates power. The stipulation that the rate of XB weakening is a linear function of V is based on the finding that a linear dependence is essential and sufficient for the analytical derivation of Hill's well-established force-velocity relationship [24,28,42].…”

“…Opening the parentheses and rearranging provides the general equation for energy conversion [24,28,42]:…”