Modeling Thick Filament Activation Suggests a Molecular Basis for Force Depression

Abstract

ABSTRACTMultiscale models aiming to connect muscle’s molecular and cellular function have been difficult to develop, in part, due to a lack of self-consistent multiscale data. To address this gap, we measured the force response from single skinned rabbit psoas muscle fibers to ramp shortenings and step stretches performed on the plateau region of the force-length relationship. We isolated myosin from the same muscles and, under similar conditions, performed single molecule and ensemble measurements of myosin’s ATP-dependent interaction with actin using laser trapping and in vitro motility assays. We fit the fiber data by developing a partial differential equation model that includes thick filament activation, whereby an increase in force on the thick filament pulls myosin out of an inhibited state. The model also includes a series elastic element and a parallel elastic element. This parallel elastic element models a titin-actin interaction proposed to account for the increase in isometric force following stretch (residual force enhancement). By optimizing the model fit to a subset of our fiber measurements, we specified seven unknown parameters. The model then successfully predicted the remainder of our fiber measurements and also our molecular measurements from the laser trap and in vitro motility. The success of the model suggests that our multiscale data are self-consistent and can serve as a testbed for other multiscale models. Moreover, the model captures the decrease in isometric force observed in our muscle fibers after active shortening (force depression), suggesting a molecular mechanism for force depression, whereby a parallel elastic element combines with thick filament activation to decrease the number of cycling cross-bridges.SIGNIFICANCEConnecting the molecular and cellular scales of muscle contraction would assist in, e.g., the treatment of genetic muscle diseases, the development of heart drugs, and the design of prostheses. The history dependence of muscle contraction, having no clear molecular basis, has remained an obstacle in making this connection for the seventy years since its discovery. We measured the force- and motion-generating capacity of rabbit psoas muscle from the scale of single molecules to single cells. We developed a mathematical model that, when fit to some of the cellular measurements, predicted the remaining cellular measurements and also the molecular measurements. The model’s ability to capture muscle’s history dependence suggests a unified description of muscle contraction from the molecular to cellular scale.