Exploring structures in protein folding funnels with free energy functionals: the transition state ensemble.

We use free energy functionals that account for the partial ordering of residues in the transition state ensemble to characterize the free energy surfaces for fast folding proteins. We concentrate on chymotrypsin inhibitor and lambda-repressor. We show how the explicit cooperativity that can arise from many body forces, such as side-chain ordering or hydrophobic surface burial, determines the crossover from folding with a large delocalized nucleus and the specific small classical nucleus of the type envisioned in nucleation growth scenarios. We compare the structural correlations present in the transition state ensemble obtained from free energy functionals with those inferred from experiment using extrathermodynamic free energy relations for folding time obtained via protein engineering kinetics experiments. We also use the free energy functionals to examine both the size of barriers and multidimensional representations of the free energy profiles in order to address the question of appropriate reaction coordinates for folding.