arXiv subjects

Jake McGrath

Publications and source records attributed to Jake McGrath.

4 recordsLinked to original sources

arXiv2026

Molecular-scale, nonlinear actomyosin binding dynamics drive population-scale adaptation and evolutionary convergence

Biological actuators -- from myosin motors to muscles -- follow Hill's model where a dimensionless parameter $\alpha$ captures the nonlinear coupling between contraction rate and force generation. Our prior work identified a characteristic $\alpha^* = 3.85 \pm 2.32$ across natural muscles and showed that $\alpha^*$ optimizes a power-efficiency tradeoff, potentially explaining its prevalence in nature. However, those results reflected short-term actuation tasks whereas phenotypic distributions in $\alpha$ emerge over evolutionary timescales. Here, we use numerical simulations of self-propelled agents to explore how nonlinear actomyosin actuation (parameterized by $\alpha$) shapes population dynamics. Agents of different $\alpha$ compete for resources and reproduce with slight mutations. Without mutations, resource availability drives populations in $\alpha$ toward distinct behaviors: under abundance or scarcity, specialized $\alpha$ survive. However, with mutations and selection, populations evolve toward distributions centered around the characteristic $\alpha^*$ observed in nature. Further, we show that the mutation rate $\delta$ governs a balance between adaptability and robustness: large $\delta$ generates instability and extinction, small $\delta$ prevents feedback, while intermediate $\delta$ enables long-term adaptability while remaining robust to short-term noise. Our results suggest that nonlinear actuation provides a general understanding of energy management in actomyosin systems across a wide range of timescales, ranging from the task-specific to evolutionary. These insights may guide the rational design of active materials with adaptive properties.

nlin.AO↗

arXiv2025

Commanding the Foul Shot: A New Ensemble of Free Throw Metrics

With the NBA's adoption of in-game limb tracking in 2023, Sony's Hawk-Eye system now captures high-resolution, 3D poses of players and the ball 60 times per second. Linking these data to key events opens a new era in NBA analytics. Here, we leverage a large dataset of 21,964 shot attempts from 72 NBA players to introduce a novel ensemble of metrics for evaluating free-throw shooting. Inspired by baseball analytics, we introduce command, which quantifies the quality of a free throw by measuring a shooter's accuracy and precision near the basket's bullseye. This metric recognizes that some makes (or misses) are better than others and captures a player's ability to execute quality attempts consistently. We demonstrate that command captures underlying skill more effectively than traditional make-or-miss statistics; early-season command predicts late-season success more reliably than traditional shooting percentage. To identify what drives command, we define launch-based metrics assessing consistency in release velocity, angle, and 3D position. Players with greater touch, i.e., more consistent launch dynamics, exhibit stronger command as they can reliably control their shot trajectory. Finally, we develop a physics model to identify the range of launch conditions that result in a make and to determine which launch conditions are most robust to small perturbations. This framework reveals ''safe'' launch regions and explains why certain players excel at free throws, providing actionable insights for player development.

stat.AP↗

arXiv2025

Control across scales: signals, information, and adaptive biological mechanical function

Biological systems perform an astonishing array of dynamical processes -- including development and repair, regulation, behavior and motor control, sensing and signaling, and adaptation, among others. Powered by the transduction of stored energy resources, these behaviors enable biological systems to regulate functions, achieve specific outcomes, and maintain stability far from thermodynamic equilibrium. These behaviors span orders of magnitude in length and time: from nanometer-scale molecular motors driving morphogenesis to kilometer-scale seasonal migrations, and from millisecond reflexes to millennia of evolutionary adaptations. While physical laws govern the dynamics of biological systems, they alone are insufficient to fully explain how living systems sense, decide, adapt, and, ultimately, control their dynamics. In this article, we argue that control theory provides a powerful, unifying framework for understanding how biological systems regulate dynamics to maintain stability across length and time scales far from equilibrium.

cond-mat.soft↗

arXiv2024

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

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.

physics.bio-ph↗