# Molecular free energy profiles from force spectroscopy experiments by inversion of observed committors

## TL;DR

This paper investigates how force probe size and linker properties influence the accuracy of molecular free energy barriers derived from single-molecule force spectroscopy using committor inversion, employing a 2D diffusion model.

## Contribution

It introduces a 2D framework to analyze the impact of probe and linker characteristics on free energy profile extraction via committor inversion.

## Key findings

- The probe size significantly affects the measured activation barrier.
- Linker stiffness and diffusion anisotropy alter the committor-based barrier estimates.
- The study delineates the validity range of committor inversion in force spectroscopy.

## Abstract

In single-molecule force spectroscopy experiments, a biomolecule is attached to a force probe via polymer linkers, and the total extension -- of molecule plus apparatus -- is monitored as a function of time. In a typical unfolding experiment at constant force, the total extension jumps between two values that correspond to the folded and unfolded states of the molecule. For several biomolecular systems the committor, which is the probability to fold starting from a given extension, has been used to extract the molecular activation barrier (a technique known as "committor inversion"). In this work, we study the influence of the force probe, which is much larger than the molecule being measured, on the activation barrier obtained by committor inversion. We use a two-dimensional framework in which the diffusion coefficient of the molecule and of the pulling device can differ. We systematically study the free energy profile along the total extension obtained from the committor, by numerically solving the Onsager equation and using Brownian dynamics simulations. We analyze the dependence of the extracted barrier on the linker stiffness, molecular barrier height, and diffusion anisotropy, and thus, establish the range of validity of committor inversion. Along the way, we showcase the committor of 2-dimensional diffusive models and illustrate how it is affected by barrier asymmetry and diffusion anisotropy.