Mapping the energy landscape of biomolecules using single molecule force correlation spectroscopy (FCS): Theory and applications

TL;DR

This paper introduces a theoretical framework called force correlation spectroscopy (FCS) to map the energy landscape of proteins by analyzing folding and unfolding times during controlled stretching and relaxation cycles, providing insights into protein dynamics.

Contribution

The paper develops a new theory of FCS that incorporates tension propagation and relaxation dynamics to better characterize protein energy landscapes.

Findings

FCS can resolve unfolding and folding kinetics.

Simulation data validate the FCS approach.

Parameters of the energy landscape are extracted successfully.

Abstract

In the current AFM experiments the distribution of unfolding times, P(t), is measured by applying a constant stretching force f_s from which the apparent unfolding rate is obtained. To describe the complexity of the underlying energy landscape requires additional probes that can incorporate the dynamics of tension propagation and relaxation of the polypeptide chain upon force quench. We introduce a theory of force correlation spectroscopy (FCS) to map the parameters of the energy landscape of proteins. In the FCS the joint distribution, P(T,t) of folding and unfolding times is constructed by repeated application of cycles of stretching at constant fs, separated by release periods T during which the force is quenched to f_q<f_s. During the release period, the protein can collapse to a manifold of compact states or refold. We show that P(T,t) can be used to resolve the kinetics of unfolding as well as formation of native contacts and to extract the parameters of the energy landscape using chain extension as the reaction coordinate and P(T,t). We illustrate the utility of the proposed formalism by analyzing simulations of unfolding-refolding trajectories of a coarse-grained protein S1 with beta-sheet architecture for several values of f_s, T and f_q=0. The simulations of stretch-relax trajectories are used to map many of the parameters that characterize the energy landscape of S1.