Gamma estimator of Jarzynski equality for recovering binding energies from noisy dynamic data sets

Zhifeng Kuang,Patrick B Dennis,Daniel J Oliver,Rajesh R Naik,Carole C Perry,Kristi M Singh

doi:10.1038/s41467-020-19233-7

Abstract

A fundamental problem in thermodynamics is the recovery of macroscopic equilibrated interaction energies from experimentally measured single-molecular interactions. The Jarzynski equality forms a theoretical basis in recovering the free energy difference between two states from exponentially averaged work performed to switch the states. In practice, the exponentially averaged work value is estimated as the mean of finite samples. Numerical simulations have shown that samples having thousands of measurements are not large enough for the mean to converge when the fluctuation of external work is above 4 kBT, which is easily observable in biomolecular interactions. We report the first example of a statistical gamma work distribution applied to single molecule pulling experiments. The Gibbs free energy of surface adsorption can be accurately evaluated even for a small sample size. The values obtained are comparable to those derived from multi-parametric surface plasmon resonance measurements and molecular dynamics simulations.

Highlights

A fundamental problem in thermodynamics is the recovery of macroscopic equilibrated interaction energies from experimentally measured single-molecular interactions
Based on small experimental sample sizes, those rare trajectories having small work values may be collected or may be lost, so divergent results may be obtained so that extreme caution must be exercised in estimating the free energy using the average Jarzynski equality (JE) estimator
When the Gaussian work distribution approximation has been proven to be in the regime of near-equilibrium, where the work fluctuation is about kBT, we have demonstrated that the Gaussian work distribution estimator gives nonphysical results when the work fluctuation is much greater than kBT

Summary

Introduction

A fundamental problem in thermodynamics is the recovery of macroscopic equilibrated interaction energies from experimentally measured single-molecular interactions. The Jarzynski equality forms a theoretical basis in recovering the free energy difference between two states from exponentially averaged work performed to switch the states. The values obtained are comparable to those derived from multi-parametric surface plasmon resonance measurements and molecular dynamics simulations. Are two commonly used label-free techniques to quantify protein adsorption energies on surfaces. These techniques monitor realtime adsorption and desorption processes of analyte flowing through a channel and binding to a target. A long-standing problem is to recover the macroscopically observed ΔG from experimentally measured single-molecule interactions[6,7]

Methods

Results

Conclusion