Equilibrium binding energies from fluctuation theorems and force spectroscopy simulations

TL;DR

This paper demonstrates how fluctuation theorems and force spectroscopy simulations can accurately determine equilibrium binding energies and free energy profiles in a particle-substrate system, with potential experimental applications.

Contribution

It introduces a methodology combining Brownian dynamics, fluctuation theorems, and umbrella sampling to extract binding energies and substrate potentials from non-equilibrium simulations.

Findings

Jarzynski and Crooks theorems effectively estimate free energy differences.

Pulling rate influences the accuracy of free energy measurements.

Umbrella sampling provides equilibrium escape probabilities for various potentials.

Abstract

Brownian dynamics simulations are used to study the detachment of a particle from a substrate. Although the model is simple and generic, we attempt to map its energy, length and time scales onto a specific experimental system, namely a bead that is weakly bound to a cell and then removed by an optical tweezer. The external driving force arises from the combined optical tweezer and substrate potentials, and thermal fluctuations are taken into account by a Brownian force. The Jarzynski equality and Crooks' fluctuation theorem are applied to obtain the equilibrium free energy difference between the final and initial states. To this end, we sample non--equilibrium work trajectories for various tweezer pulling rates. We argue that this methodology should also be feasible experimentally for the envisioned system. Furthermore, we outline how the measurement of a whole free energy profile would allow the experimentalist to retrieve the unknown substrate potential by means of a suitable deconvolution. The influence of the pulling rate on the accuracy of the results is investigated, and umbrella sampling is used to obtain the equilibrium probability of particle escape for a variety of trap potentials.