The calorimetric criterion for a two-state process revisited

The "calorimetric criterion" is one of the important experimental approache s for determining whether protein folding is an "all-or-none" two-state tra nsition (i.e., whether intermediates are present at equilibrium). The calor imetric criterion states that the equivalence of the "measured" calorimetri c enthalpy change and the effective two-state van't Hoff enthalpy change de monstrates that there is a two-stale transition. This paper addresses the e ssential question of whether the calorimetric criterion is a necessary and sufficient condition for a two-state process and shows that it is necessary but not sufficient by means of specific examples. Analysis of simple model s indicates that the heat capacity curve, regardless of whether ii originat es from a two-state process or not, can always be decomposed in such a way that the calorimetric criterion is satisfied. Exact results for a three-sta te model and a homopolymer tetramer demonstrate that the deviation from the calorimetric criterion is not simply related to the population of intermed iate states. Analysis of a three-helix bundle protein model, which has a tw o-state folding from a random coil to ordered (molten) globule, shows that the calorimetric criterion may not be satisfied if the standard linear inte rpolation of baselines (weighted or unweighted) is employed. A specific exa mple also suggests that the more recently introduced deconvolution method i s not necessarily better than the simple calorimetric criterion for disting uishing a two-state transition from a three-state transition. Although the calorimetric criterion is not a sufficient condition for a two-state proces s, it is likely to continue to be of practical utility, particularly when i ts results are shown to be consistent with those from other experimental me thods.