Transition-Path Probability as a Test of Reaction-Coordinate Quality Reveals DNA Hairpin Folding Is a One-Dimensional Diffusive Process

Chemical reactions are typically described in terms of progress along a reaction coordinate. However, the quality of reaction coordinates for describing reaction dynamics is seldom tested experimentally. We applied a framework for gauging reaction coordinate quality based on transition path analysis to experimental data for the first time, looking at folding trajectories of single DNA hairpin molecules measured under tension applied by optical tweezers. The conditional probability for being on a reactive transition path was compared with the probability expected for ideal diffusion over a ID energy landscape based on the committor function. Analyzing measurements and simulations of hairpin folding where end-to-end extension is the reaction coordinate, after accounting for instrumental effects on the analysis, we found good agreement between transition-path and committor analyses for model two state hairpins, demonstrating that folding is well described by 1D diffusion. This work establishes transition-path analysis as a powerful new tool for testing experimental reaction-coordinate quality.