Roles of Local Non-equilibrium Free Energy in the Description of Biomolecules

TL;DR

This paper explores how local non-equilibrium free energy profiles relate to work and efficiency in biomolecular processes, verified through simulations of RNA translocation by ATPase motors, providing insights into molecular energetics.

Contribution

It demonstrates the practical application of non-equilibrium free energy theory to analyze biomolecular translocation processes, linking theory with simulation data.

Findings

RNA translocation efficiency ranges from 48% to 60% for most molecules

12% of molecules reach 80-100% efficiency

The theory helps quantify energy states of molecular sub-states

Abstract

When a system is in equilibrium, external perturbations yield a time series of non-equilibrium distributions, and recent experimental techniques give access to the non-equilibrium data that may contain critical information. Jinwoo and Tanaka (L. Jinwoo and H. Tanaka, Sci. Rep. 2015, 5, 7832) have provided mathematical proof that such a process's non-equilibrium free energy profile over a system's substates has Jarzynski's work as content, which spontaneously dissipates while molecules perform their tasks. Here we numerically verify this fact and give a practical example where we analyze a computer simulation of RNA translocation by a ring-shaped ATPase motor. By interpreting the cyclic process of substrate translocation as a series of quenching, relaxation, and second quenching, the theory gives how much individual sub-states of the ATPase motor have been energized until the end of the process. It turns out that the efficiency of RNA translocation is $48\sim 60\%$ for most molecules, but $12\%$ of molecules achieve $80\sim 100\%$ efficiency, which is consistent with the literature. This theory would be a valuable tool for extracting quantitative information about molecular non-equilibrium behavior from experimental observations.