Nonlinear Elasticity of a Crossbridge in Sarcomere Lattice

Abstract

Crossbridge elasticity is an essential determinant of strain dependent transition rates in the actomyosin cycle. Recent estimates of myosin stiffness range from 1.5 to 3.2pN/nm and are much larger than most previous estimates used in sliding filament models. These higher stiffnesses limit thermally-induced motions on unattached myosin heads, affect transition rates associated with power stroke and narrow the parabolic parts of energy landscapes. This in turn raises the energy barriers between actomyosin states reducing the probability of strain dependent transitions between them. Estimates of crossbridge stiffness derived from a study of its parts (S2, the lever arm, the “neck region”) could be helpful in informing this issue. We used the known atomic structures of crossbridge components in molecular dynamic simulations (CHARMM) to estimate the elasticity of the individual components. We then used nonlinear finite element analysis to estimate the crossbridge stiffness under a range of tensile and compressive forces in the context of the 3-D sarcomere lattice. Using estimated axial and lateral stiffnesses for S2 (of 60 pN/nm, and 0.01 pN/nm respectively), and a bending stiffness S1 of 3 pN/nm, we computed force displacement relationships for crossbridges under tension and in compression. As expected, crossbridge stiffness under tension was slightly below 3 pN/nm at any force. In contrast, stiffness under compression falls about 3-fold at 1 pN, and more than an order of magnitude at forces exceeding 3-4 pN. Consequently, the energy landscape is asymmetric and skewed toward negative crossbridge strains. Our data agree well with recent measurements of nonlinear cross-bridge compliance (Kaya et al., Science 329:686-688) and quantitatively define departures from these measurements in terms of azimuthal departures of the S1-S2 plane from the axial axis of myosin filament and increased inter-filament lattice spacings.Supported by: R01s AR048776 and DC 011528.