A new view of the radial geometry in muscle: myofilament lattice spacing controls force production and energy storage.

Abstract

Muscle is highly organized in both the axial direction and the radial direction, or the direction of contraction and the direction orthogonal to it. As muscle generates force, it does so in both the axial and radial directions. Lattice spacing, which is the radial spacing between its contractile filaments, increases as muscle shortens. Historically, the effects of these processes have not been accounted for in our conceptual or mathematical models of muscle contraction. We develop a computational model of the half-sarcomere that is fully three dimensional and thus replicates the processes which occur in muscle's radial direction. This model employs a novel cross-bridge model which uses multiple springs, both extensional and angular. Where prior cross-bridge models use a change in rest length to generate force, our multi-spring model uses a lever arm mechanism similar to myosin's. Using this model and experiments with isolated skinned muscle, we show that changes in lattice spacing increase the slope of the length tension curve by more than 20%. The length-tension curve describes the relationship between a muscle's sarcomere lengths and the maximum force which it can generate. The length-tension curve has been attributed to changing degrees of the overlap of thick and thin filaments as sarcomere length varies. A steep slope on the length-tension curve is necessary for passive stability of muscular systems, such as cardiac muscle, which operate at short sarcomere lengths. These systems rely on the small length changes which accompany a new load to tailor the force produced for the new load. Without the steeper slope produced by varying lattice spacings, an external mechanism of force regulation would be necessary to provide system stability. Additional model results show that substantial energy is stored in deformation of the cross-bridges during maximum activation, more than twice that which is stored in deformation of the thick and thin filaments. This energy is highly correlated with force produced in the radial direction, itself of the same order of magnitude as the axial force produced. These relative levels of axial and radial forces are themselves a confirmation of previous experimental measurements of radial force. The stored energy may play a role in powering rapid, one-off explosive movements such as prey striking by Mantis shrimp and tongue extension in toads.