# Modeling work-speed-accuracy trade-offs in a stochastic rotary machine

## TL;DR

This paper presents a minimal stochastic model of rotary molecular machines, analyzing work-speed-accuracy trade-offs, revealing bounds on performance, and discussing implications for biological systems like ATP synthase.

## Contribution

It introduces a simplified model capturing key dynamics of stochastic rotary machines and explores fundamental trade-offs, providing insights into biological efficiency.

## Key findings

- An upper bound on accuracy and work at specific speeds.
- Slow driving minimizes work-accuracy ratio.
- Accuracy decays at physiological rotation rates in F1-ATP synthase.

## Abstract

Molecular machines are stochastic systems that catalyze the energetic processes keeping living cells alive and structured. Inspired by the examples of F1-ATP synthase and the bacterial flagellum, we present a minimal model of an externally driven stochastic rotary machine. We explore the trade-offs of work, driving speed, and driving accuracy when changing driving strength, speed, and the underlying system dynamics. We find an upper bound on accuracy and work for a particular speed. Our results favor slow driving when tasked with minimizing the work-accuracy ratio and maximizing the rate of successful cycles. Finally, in the parameter regime mapping to the dynamics of F1-ATP synthase, we find a significant decay of driving accuracy at physiological rotation rates, raising questions about how ATP synthase achieves reasonable or even remarkable efficiency in vivo.