Polymer principles of protein calorimetric two-state cooperativity.

The experimental calorimetric two-state criterion requires the van't Hoff enthalpy DeltaH(vH) around the folding/unfolding transition midpoint to be equal or very close to the calorimetric enthalpy DeltaH(cal) of the entire transition. We use an analytical model with experimental parameters from chymotrypsin inhibitor 2 to elucidate the relationship among several different van't Hoff enthalpies used in calorimetric analyses. Under reasonable assumptions, the implications of these DeltaH(vH)'s being approximately equal to DeltaH(cal) are equivalent: Enthalpic variations among denatured conformations in real proteins are much narrower than some previous lattice-model estimates, suggesting that the energy landscape theory "folding to glass transition temperature ratio" T(f) /T(g) may exceed 6.0 for real calorimetrically two-state proteins. Several popular three-dimensional lattice protein models, with different numbers of residue types in their alphabets, are found to fall short of the high experimental standard for being calorimetrically two-state. Some models postulate a multiple-conformation native state with substantial pre-denaturational energetic fluctuations well below the unfolding transition temperature, or predict a significant post-denaturational continuous conformational expansion of the denatured ensemble at temperatures well above the transition point, or both. These scenarios either disagree with experiments on protein size and dynamics, or are inconsistent with conventional interpretation of calorimetric data. However, when empirical linear baseline subtractions are employed, the resulting DeltaH(vH)/DeltaH(cal)'s for some models can be increased to values closer to unity, and baseline subtractions are found to correspond roughly to an operational definition of native-state conformational diversity. These results necessitate a re-assessment of theoretical models and experimental interpretations.