Meeting Abstract
Muscle contraction is mediated by myosin motors that derive their energy from ATP hydrolysis. Recent research suggests that diffusion may be limiting in the exceedingly crowded lattice of thick and thin filaments. Additionally, conservation of mass implies that, for constant lattice spacing, axial and radial fluid motion must necessarily accompany periodic lengthening and shortening of the sarcomere. We asked if such flow augments the rate of ATP supply inside the sarcomere. To address this question we developed a continuum model for the diffusion-convection equation in the sarcomere, with a time-dependent flow field driven by sinusoidal sarcomere contractions. By comparing the concentration gradient of ATP along the sarcomere radius with and without convection, we find that radial flows improve ATP replenishment in the sarcomere center over diffusion alone. After the first, second, and third contraction cycles, convection improves ATP concentrations by up to 81.9%, 30.8% and 19.2% respectively. After many (>200) cycles, the difference approaches zero as the system reaches an equilibrium state. These results pertain to constant extra-sarcomeric concentrations. If, however, those concentrations are time-dependent, flow will always lead to increased substrate availability. Our results indicate that, in addition to driving axial forces, the flow induced by shortening sarcomeres can augment ATP delivery, potentially offsetting the costs associated with viscous shearing.
