Reconstructing folding energy landscape profiles from nonequilibrium pulling curves with an inverse Weierstrass integral transform.

The energy landscapes that drive structure formation in biopolymers are difficult to measure. Here we validate experimentally a novel method to reconstruct landscape profiles from single-molecule pulling curves using an inverse Weierstrass transform (IWT) of the Jarzysnki free-energy integral. The method was applied to unfolding measurements of a DNA hairpin, replicating the results found by the more-established weighted histogram (WHAM) and inverse Boltzmann methods. Applying both WHAM and IWT methods to reconstruct the folding landscape for a RNA pseudoknot having a stiff energy barrier, we found that landscape features with sharper curvature than the force probe stiffness could not be recovered with the IWT method. The IWT method is thus best for analyzing data from stiff force probes such as atomic force microscopes.

Determining intrachain diffusion coefficients for biopolymer dynamics from single-molecule force spectroscopy measurements.

The conformational diffusion coefficient for intrachain motions in biopolymers, D, sets the timescale for structural dynamics. Recently, force spectroscopy has been applied to determine D both for unfolded proteins and for the folding transitions in proteins and nucleic acids. However, interpretation of the results remains unsettled. We investigated how instrumental effects arising from the force probes used in the measurement can affect the value of D recovered via force spectroscopy. We compared estimates of D for the folding of DNA hairpins found from measurements of rates and energy landscapes made using optical tweezers with estimates obtained from the same single-molecule trajectories via the transition path time. The apparent D obtained from the rates was much lower than the result found from the same data using transition time analysis, reflecting the effects of the mechanical properties of the force probe. Deconvolution of the finite compliance effects on the measurement allowed the intrinsic value to be recovered. These results were supported by Brownian dynamics simulations of the effects of force-probe compliance and bead size.