Non-native interactions in the unfolded state affect native protein stability. (a) Schematic diagram of the equilibrium between the natively folded and the unfolded (non-native, or denatured) states. Selected exposed and buried residues are marked by circles. A simplistic view of cooperative folding envisages all conformations in the unfolded ensemble to be open, with negligible residue-residue contact, as exemplified by the chain on the right. (b) Double-mutant cycles (DMC) in square-lattice models are simulated using different hypothetical interaction schemes to explore a range of native specificity – from the HP model (s = 0), which allows for non-native interactions , to the Gō model (s = 1), which precludes them (the Gō model was formulated originally by Nobuhiro Gō and co-workers in 1975 and favors only native interactions). Native specificity is the ability of a set of interactions to discriminate against non-native attractions and is indicated here by the parameter s. Hydrophobic (H) and polar (P) residues are drawn, respectively, as black and white circles. The wild-type sequence has H at both mutation sites (red and blue). Two single mutants and one double mutant that preserve the wild-type native structure (which is shown on the left) are created by changing either one or both of these sites to P. Depicted on the right are three example unfolded conformations (in an ensemble of around 6 million) that have (from top to bottom) no, one, and two contacts involving the mutation sites. The plot on the left shows how the free energy of folding (ΔG) of the wild type (black curve) and the mutants (red, blue, and magenta curves) as well as the coupling energy ΔΔGint (green curve) depend on the native specificity parameter s. Results are presented for model contact energy ε = -5 kBT, where kB is the Boltzmann constant and T is absolute temperature. Free energies are in units of kBT.
Chan and Zhang Journal of Biology 2009 8:27 doi:10.1186/jbiol126