From mechanical folding trajectories to intrinsic energy landscapes of biopolymers

TL;DR

This paper develops a rigorous theoretical method to extract the intrinsic energy landscapes of biopolymers from single-molecule laser optical tweezer experiments, accounting for experimental fluctuations and noise, validated through simulations and applied to real data.

Contribution

The authors introduce a novel approach to reconstruct intrinsic folding energy landscapes from experimental trajectories, overcoming handle and bead effects in optical tweezer measurements.

Findings

Accurately extracts intrinsic free energy profiles from simulated data.

Quantitatively agrees with simulations for a coiled-coil protein.

Successfully applies to experimental data, independent of trap parameters.

Abstract

In single molecule laser optical tweezer (LOT) pulling experiments a protein or RNA is juxtaposed between DNA handles that are attached to beads in optical traps. The LOT generates folding trajectories under force in terms of time-dependent changes in the distance between the beads. How to construct the full intrinsic folding landscape (without the handles and the beads) from the measured time series is a major unsolved problem. By using rigorous theoretical methods---which account for fluctuations of the DNA handles, rotation of the optical beads, variations in applied tension due to finite trap stiffness, as well as environmental noise and the limited bandwidth of the apparatus---we provide a tractable method to derive intrinsic free energy profiles. We validate the method by showing that the exactly calculable intrinsic free energy profile for a Generalized Rouse Model, which mimics the two-state behavior in nucleic acid hairpins, can be accurately extracted from simulated time series in a LOT setup regardless of the stiffness of the handles. We next apply the approach to trajectories from coarse grained LOT molecular simulations of a coiled-coil protein based on the GCN4 leucine zipper, and obtain a free energy landscape that is in quantitative agreement with simulations performed without the beads and handles. Finally, we extract the intrinsic free energy landscape from experimental LOT measurements for the leucine zipper, which is independent of the trap parameters.