Meeting Abstract
Muscle contraction occurs in a densely packed lattice of thick and thin filaments with myosin motor molecules utilizing ATP to generate forces. During contraction, the thick and thin filaments slide relative to each other in the axial direction and, as our recent X-ray diffraction evidence suggests, those filaments also move radially. With the assumption that these filaments move in a fluid environment surrounding them, we asked how viscous forces may play a role in the mechanics and energetics of muscle contraction. To address this question we modeled the lattice of filaments and motor molecules using a spatially distributed system of singularities (stokeslets and potential doublets) that satisfy the Stokes equations and continuity. The model specifies filament spacing and size, myosin spacing and size, as well as sliding velocity. From that system we predict both flows and forces associated with contraction as a function of the axial and radial motions. Even with pure axial sliding, conservation of mass leads to radial flows throughout the filament lattice. Thus sliding motions contribute to flux of solutes (such as ADP and ATP) into an out of the filament lattice. Radial motions greatly amplify this flux. To our surprise, however, we find that the associated viscous forces exerted on motor molecules are quite modest: shear forces exerted by a thin filament on a myosin molecule account for less than 1% of the force that can be generated. We suggest that the energy lost by viscous stresses may be offset by the increased delivery of ATP.
