Measurement of work in single-molecule experiments

TL;DR

This paper investigates the errors in free energy estimates in single-molecule experiments using fluctuation relations, highlighting the impact of experimental parameters and validating findings with simulations and DNA hairpin experiments.

Contribution

It quantifies the error introduced when using subsystem work instead of total work in free energy calculations, providing theoretical estimates validated by experiments.

Findings

Error can reach up to 100% depending on experimental conditions.

Theoretical estimates match numerical simulations and experimental data.

Bandwidth and number of experiments significantly affect free energy accuracy.

Abstract

A main goal of single-molecule experiments is to evaluate equilibrium free energy differences by applying fluctuation relations to repeated work measurements along irreversible processes. We quantify the error that is made in a free energy estimate by means of the Jarzynski equality when the accumulated work expended on the whole system (including the instrument) is erroneously replaced by the work transferred to the subsystem consisting of the sole molecular construct. We find that the error may be as large as 100%, depending on the number of experiments and on the bandwidth of the data acquisition apparatus. Our theoretical estimate is validated by numerical simulations and pulling experiments on DNA hairpins using optical tweezers.