The major challenge in modern research on protein folding is the development of an analytical theoretical model capable of calculating the quantities directly measured in both equilibrium and kinetic experiments. We have approached this problem experimentally by studying a small ultrafast folding protein, the 35-residue subdomain from the villin headpiece. This protein is the smallest naturally occurring protein that autonomously folds into a globular structure, so it should have one of the simplest protein folding mechanisms and therefore amenable to understanding in depth by theoretical models. Our theoretical approach is to calculate the experimentally measured quantities with a very simple Ising-like statistical mechanical model, originally developed to explain our results on the -hairpin from the protein GB1, and similar to models of Baker, Finkelstein and coworkers. The key simplifying feature of these models is that they only explicitly consider interactions between residues that are in contact in the native structure (the perfectly funneled energy landscape of Wolynes and Onuchic. These so-called Gō models have been remarkably successful in predicting both the number of stable states and folding rates for individual proteins, and have also had some success in predicting the relative effect on folding rates and equilibrium constants produced by site-directed mutants (Fersht values). However, up to now they have not been used to calculate what is actually measured experimentally.? ? In this work we analyze an extensive set of equilibrium and kinetic data on the villin subdomain. The equilbrium data consist of the excess heat capacity, tryptophan fluoresence quantum yield (QY) and natural circular dichroism spectrum (CD) as a function of temperature, while the kinetic data consist of the time course of the QY over a wide temperature range from laser temperature jump experiments (this work). These measured quantities are calculated using a coarse-grained version of the Ising-like model of Muoz, Henry, and Eaton. Relaxation rates are calculated by diffusion on a one-dimensional free energy surface using either the number of ordered resides or fraction of native contacts as reaction coordinates. We also analyze values for a number of mutants (this work) by calculating the change in relaxation rate resulting from the change in the free energy surface produced by the mutation. Our calculation of the kinetics as diffusion on a free energy surface with order parameters as reaction coordinates, an approach introduced by Wolynes and coworkers, is validated by solving the coupled differential equations for all 97,769 species of the model. The solution to the master equation demonstrates that the ensemble of species at the free energy barrier top are true transition state species as judged by their nearly equal probability of proceeding to the folded and unfolded states (p-fold ).? ? We also analyze the data in terms of a conventional chemical kinetics model and a model using an empirical free energy surface, similar to what has previously been done for other proteins by Gruebele and Muoz. For lack of a better term, we call this latter model a physical kinetics model since the progress curves are calculated as diffusion on a free energy surface. The chemical and physical kinetics models are not only helpful in the interpretation of the experimental results, but they also expose features that support the validity of the theoretical results. We believe that our analysis, using three very different types of models to interpret the data, represents the most comprehensive approach so far to understanding experimental protein folding results. ? ? Both the three-state and physical kinetics model explain the 100 ns phase as resulting from reconfiguration in the folded well. The theoretical model fits all of the experimental data. It explains the low phi values as resulting from an early transitions state, and yields the order in which the three alpha helices form. The success of the model supports the basic concept that sequences evolve not only to produce functional proteins, but also to produce a funneled energy landscape. It also suggests that the folding rates and mechanisms of protein folding are determined primarily by the topology of the fold.? ? We are also refining our Tertiary Two State model for allosteric inetractions, and are carrying out collaborative research with the group in Parma, Italy to test its theortical predictions.
| Godoy-Ruiz, Raquel; Henry, Eric R; Kubelka, Jan et al. (2008) Estimating free-energy barrier heights for an ultrafast folding protein from calorimetric and kinetic data. J Phys Chem B 112:5938-49 |
| Eaton, William A; Henry, Eric R; Hofrichter, James et al. (2007) Evolution of allosteric models for hemoglobin. IUBMB Life 59:586-99 |
| Cellmer, Troy; Henry, Eric R; Kubelka, Jan et al. (2007) Relaxation rate for an ultrafast folding protein is independent of chemical denaturant concentration. J Am Chem Soc 129:14564-5 |
