Bayesian estimates of free energies from nonequilibrium work data in the presence of instrument noise

TL;DR

This paper introduces a Bayesian method to accurately estimate free energy differences from nonequilibrium work data, accounting for instrument noise, and demonstrates its application to single-molecule experiments with optical tweezers.

Contribution

The paper develops a Bayesian formalism that corrects for instrument noise in free energy estimates from non-equilibrium work measurements, enhancing analysis of single-molecule experiments.

Findings

Fast, far-from-equilibrium measurements have less noise and yield more accurate free energy estimates.

The Bayesian method effectively compensates for instrument noise in experimental data.

Application to RNA hairpin experiments demonstrates improved free energy estimation.

Abstract

The Jarzynski equality and the fluctuation theorem relate equilibrium free energy differences to non-equilibrium measurements of the work. These relations extend to single-molecule experiments that have probed the finite-time thermodynamics of proteins and nucleic acids. The effects of experimental error and instrument noise have not previously been considered. Here, we present a Bayesian formalism for estimating free-energy changes from non-equilibrium work measurements that compensates for instrument noise and combines data from multiple driving protocols. We reanalyze a recent set of experiments in which a single RNA hairpin is unfolded and refolded using optical tweezers at three different rates. Interestingly, the fastest and farthest-from-equilibrium measurements contain the least instrumental noise, and therefore provide a more accurate estimate of the free energies than a few slow, more noisy, near-equilibrium measurements. The methods we propose here will extend the scope of single-molecule experiments; they can be used in the analysis of data from measurements with AFM, optical, and magnetic tweezers.