Transition Path Times for the Folding of Nucleic Acids and Proteins Determined from Experimentally-Reconstructed Energy Landscape Profiles

Abstract

The transition path time for a folding reaction describes the time spent during the structural transition itself. In terms of the standard picture of folding as diffusion over a configurational free-energy landscape, it is the time required to cross over the barrier. Transition times are very brief and hence challenging to measure directly, but they may also be found indirectly from the shape of the landscape. We investigated the transition time for various nucleic acids and proteins by reconstructing the folding energy landscape profiles from high-resolution single-molecule force spectroscopy measurements using optical tweezers. Studying DNA hairpins, we first showed that landscapes reconstructed from the inverse Boltzmann transform of the extension probability distribution could be used to determine the diffusion constant for barrier crossing, D, via Kramers theory and the observed folding rates, before finding the transition time, τtp. We next showed that the same results could be found from a landscape parameterization obtained by fitting the distribution of unfolding forces, and applied this method to estimate τtp for several RNA pseudoknots and a riboswitch aptamer. Finally, we estimated τtp in the protein PrP both from the energy landscape reconstructed by the Hummer-Szabo formalism and from the landscape parameterization using unfolding force distributions. All the molecules had τtp on the order of 1-10 µs.