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

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