Microscale velocity-dependent unbinding generates a macroscale performance-efficiency tradeoff in actomyosin systems

Abstract

Myosin motors are fundamental biological actuators, powering diverse mechanical tasks in eukaryotic cells via ATP hydrolysis. Recent work revealed that myosin's velocity-dependent detachment rate can bridge actomyosin dynamics to macroscale Hill muscle predictions. However, the influence of this microscale unbinding, which we characterize by a dimensionless parameter $\alpha$, on macroscale energetic flows-such as power consumption, output and efficiency-remains elusive. Here we develop an analytical model of myosin dynamics that relates unbinding rates $\alpha$ to energetics. Our model agrees with published in-vivo muscle data and, furthermore, uncovers a performance-efficiency tradeoff governed by $\alpha$. To experimentally validate the tradeoff, we build HillBot, a robophysical model of Hill's muscle that mimics nonlinearity. Through HillBot, we decouple $\alpha$'s concurrent effect on performance and efficiency, demonstrating that nonlinearity drives efficiency. We compile 136 published measurements of $\alpha$ in muscle and myoblasts to reveal a distribution centered at $\alpha^* = 3.85 \pm 2.32$. Synthesizing data from our model and HillBot, we quantitatively show that $\alpha^*$ corresponds to a class of generalist actuators that are both relatively powerful and efficient, suggesting that the performance-efficiency tradeoff underpins the prevalence of $\alpha^*$ in nature. We leverage these insights and propose a nonlinear variable-impedance protocol to shift along a performance-efficiency axis in robotic applications.