Reconstructing folding energy landscapes from splitting probability analysis of single-molecule trajectories

Abstract

Structural self-assembly in biopolymers, such as proteins and nucleic acids, involves a diffusive search for the minimumenergy state in a conformational free-energy landscape. The likelihood of folding proceeding to completion, as a function of the reaction coordinate used to monitor the transition, can be described by the splitting probability, p fold (x). P fold encodes information about the underlying energy landscape, and it is often used to judge the quality of the reaction coordinate. Here, we show how p fold can be used to reconstruct energy landscapes from single-molecule folding trajectories, using force spectroscopy measurements of single DNA hairpins. Calculating p fold (x) directly from trajectories of the molecular extension measured for hairpins fluctuating in equilibrium between folded and unfolded states, we inverted the result expected from diffusion over a 1D energy landscape to obtain the implied landscape profile. The results agreed well with the landscapes reconstructed by established methods, but, remarkably, without the need to deconvolve instrumental effects on the landscape, such as tether compliance. The same approach was also applied to hairpins with multistate folding pathways. The relative insensitivity of the method to the instrumental compliance was confirmed by simulations of folding measured with different tether stiffnesses. This work confirms that the molecular extension is a good reaction coordinate for these measurements, and validates a powerful yet simple method for reconstructing landscapes from single-molecule trajectories.