Testing the Physical Theory of Folding as Diffusive Motion over an Energy Landscape using Transition Path Analysis of Single-Molecule Folding Trajectories

Abstract

Biomolecular folding is a notoriously complex process, owing to the many degrees of freedom involved. The physical picture of folding features a diffusive search over a multi-dimensional energy landscape in conformational space for the minimum-energy structure. Although widely accepted, this picture has not yet been fully tested experimentally, by measuring the folding landscape for different molecules and showing that the statistics of the conformational dynamics matches what is expected for diffusion over these landscapes. Using optical tweezers to measure the folding trajectories of single nucleic acids and proteins at high resolution, we applied a framework for testing the dynamics of the motion based on the conditional transition-path probability, and compared the results to expectations for diffusion over the energy landscapes measured by force spectroscopy of the same molecules. The conditional probability for being on a reactive transition path, calculated directly from records of the molecular extension, was compared to the probability expected for ideal diffusion over a one-dimensional energy landscape based on the committor function. Applying this method to simple DNA hairpins with varied sequence, we found good agreement, indicating that folding is indeed described quantitatively by diffusion across the measured landscapes. The same result was found for the protein PrP, showing that even the formation of complex tertiary structures are well-described by the energy landscape theory.