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

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.

arXiv comment8 pages

References in corpus (19)

• A nonequilibrium equality for free energy differences
• The Entropy Production Fluctuation Theorem and the Nonequilibrium Work Relation for Free Energy Differences
• Equilibrium free energy differences from nonequilibrium measurements: a master equation approach
• Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies
• Path ensembles averages in systems driven far-from-equilibrium
• The Nonequilibrium Thermodynamics of Small Systems
• Single-molecule experiments in biological physics: methods and applications
• Rare events and the convergence of exponentially averaged work values
• An experimental test of the Jarzynski equality in a mechanical experiment
• A "fast growth" method of computing free energy differences
• On practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example
• Work probability distribution in systems driven out of equilibrium
• On the work distribution for the adiabatic compression of a dilute classical gas
• Equilibrium free energies from fast-switching trajectories with large time steps
• Probing molecular free energy landscapes by periodic loading
• Optimal estimates of free energies from multi-state nonequilibrium work data
• Work distribution functions in polymer stretching experiments
• Work probability distribution in single molecule experiments
• Periodically driven stochastic un- and refolding transitions of biopolymers

Cited by in corpus (28)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• The length of time's arrow
• Optimized free energies from bidirectional single-molecule force spectroscopy
• A geometric approach to optimal nonequilibrium control: Minimizing dissipation in nanomagnetic spin systems
• Near-optimal protocols in complex nonequilibrium transformations
• Thermodynamic geometry of minimum-dissipation driven barrier crossing
• Far-from-Equilibrium Measurements of Thermodynamic Length
• Optimal estimators and asymptotic variances for nonequilibrium path-ensemble averages
• Quantum superposition of thermodynamic evolutions with opposing time's arrows
• Measurement of work in single-molecule experiments
• A unified, geometric framework for nonequilibrium protocol optimization
• Heat dissipation and fluctuations in a driven quantum dot
• Non-Equilibrium Evolution Thermodynamics Theory
• Polymer-mediated entropic forces between scale-free objects
• Nonequilibrium thermodynamics at the microscale: Work relations and the second law
• Fluctuation relations to calculate protein redox potentials from molecular dynamics simulations
• Measuring the convergence of Monte Carlo free energy calculations
• Waste-recycling Monte Carlo with optimal estimates: application to free energy calculations in alloys
• Exact Nonequilibrium Work Generating Function for a Small Classical System
• Posterior probability and fluctuation theorem in stochastic processes
• Substructure and Boundary Modeling for Continuous Action Recognition
• Density-Dependent Analysis of Nonequilibrium Paths Improves Free Energy Estimates
• Accurate estimation of dynamical quantities for nonequilibrium nanoscale system
• Bayesian Multistate Bennett Acceptance Ratio Methods
• Contact geometry and quantum thermodynamics of nanoscale steady states
• Regularized Bayesian calibration and scoring of the WD-FAB IRT model improves predictive performance over marginal maximum likelihood
• Non-Uniform Convergence in Moment Expansions of Integral Work Relations
• The Limits of Inference in Complex Systems: When Stochastic Models Become Indistinguishable