Force-velocity and tension transient measurements from Drosophila jump muscle reveal the necessity of both weakly-bound cross-bridges and series elasticity in models of muscle contraction

Abstract

Muscle contraction is a fundamental biological process where molecular interactions between the myosin molecular motor and actin filaments result in contraction of a whole muscle, a process spanning size scales differing in eight orders of magnitude. Since unique behavior is observed at every scale in between these two extremes, to fully understand muscle function it is vital to develop multi-scale models. Based on simulations of classic measurements of muscle heat generation as a function of work, and shortening rate as a function of applied force, we hypothesize that a model based on molecular measurements must be modified to include a weakly-bound interaction between myosin and actin in order to fit measurements at the muscle fiber or whole muscle scales. This hypothesis is further supported by the model's need for a weakly-bound state in order to qualitatively reproduce the force response that occurs when a muscle fiber is rapidly stretched a small distance. We tested this hypothesis by measuring steady-state force as a function of shortening velocity, and the force transient caused by a rapid length step in Drosophila jump muscle fibers. Then, by performing global parameter optimization, we quantitatively compared the predictions of two mathematical models, one lacking a weakly-bound state and one with a weakly-bound state, to these measurements. Both models could reproduce our force-velocity measurements, but only the model with a weakly-bound state could reproduce our force transient measurements. However, neither model could concurrently fit both measurements. We find that only a model that includes weakly-bound cross-bridges with force-dependent detachment and an elastic element in series with the cross-bridges is able to fit both of our measurements. This result suggests that the force response after stretch is not a reflection of distinct steps in the cross-bridge cycle, but rather arises from the interaction of cross-bridges with a series elastic element. Additionally, the model suggests that the curvature of the force-velocity relationship arises from a combination of the force-dependence of weakly- and strongly-bound cross-bridges. Overall, this work presents a minimal cross-bridge model that has predictive power at the fiber level.

Keywords: Multi-scale modeling; Muscle mechanics; Myosin; Stretch-activation; Weak binding.