Theory for protein folding cooperativity: helix bundles.

We present a theory for protein folding stability and cooperativity for helix bundle proteins. We treat the individual helices with a Schellman-Zimm-Bragg-like approach, using nucleation and propagation quantities, and we treat the hydrophobic and van der Waals contacts between the helices as a binding equilibrium. Predictions are in good agreement with experiments on both thermal and urea-induced transitions of (1) molecules that can undergo single helix-to-coil transitions for various chain lengths and (2) three-helix-bundle proteins A and alpha3C. The present model addresses a problem raised by Kaya and Chan that proteins fold more cooperatively than previous models predict. The present model correctly predicts the experimentally observed two-state cooperativities, DeltaH(van't Hoff)/DeltaH(cal) approximately 1, for helix-bundle proteins. The predicted folding cooperativity is greater than that of helix formation alone, or collapse alone, because of the nonlinear coupling between the tertiary interactions and the helical interactions.