A major challenge to advancing our understanding of how proteins fold is the development of an analytical theoretical model capable of calculating the quantities directly measured in both equilibrium and kinetic experiments. That is, we require a partition function to predict thermodynamic properties and a master equation to predict kinetic properties. To this end we have been developing an Ising-like model, with the major input being the contact map of the native structure. This model has been remarkably successful in quantitatively accounting for a wide range of data for the 35-residue subdomain from the villin headpiece, the smallest naturally occurring protein that autonomously folds into a globular structure (see Kubelka et al., PNAS 2008;Cellmer et al., PNAS 2008, Cellmer et al., PNAS 2011). These data include, heat capacity, tryptophan fluorescence quantum yield (QY), and natural circular dichroism spectrum (CD) as a function of temperature in both denaturants and viscogens, while the kinetic data consist of time courses of the QY from nanosecond laser temperature jump experiments as a function of temperature, denaturant concentration, and viscosity. Anticipating the next generation of folding experiments, consisting of measurements of transition paths in single molecule FRET experiments (see annual report on single molecule experiments), we are carrying out stochastic kinetic to make closer connections to molecular dynamics simulations. Advances in computing have enabled microsecond all-atom molecular-dynamics trajectories of protein folding that can be used to compare with and test critical assumptions of theoretical models. We show that recent simulations by the Shaw group are consistent with a key assumption of our Ising-like theoretical model that native structure grows in only a few regions of the amino acid sequence as folding progresses. The distribution of mechanisms predicted by simulating the master equation of this native-centric model for the benchmark villin subdomain with only two adjustable thermodynamic parameters and one temperature-dependent kinetic parameter is remarkably similar to the distribution in the molecular-dynamics trajectories.

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Cellmer, Troy; Henry, Eric R; Hofrichter, James et al. (2008) Measuring internal friction of an ultrafast-folding protein. Proc Natl Acad Sci U S A 105:18320-5
Kubelka, Jan; Henry, Eric R; Cellmer, Troy et al. (2008) Chemical, physical, and theoretical kinetics of an ultrafast folding protein. Proc Natl Acad Sci U S A 105:18655-62