Is it always possible to distinguish two- and three-state systems by evaluating the van't Hoff enthalpy?

Many small globular proteins are traditionally classified as thermodynamical two-state systems, i.e., the protein is either in the native, active state (folded) or in the denatured state (unfolded). We challenge this view and show that there may exist (protein) systems for which a van't Hoff analysis of experimental data cannot determine whether the system corresponds to two or three thermodynamical states when only temperatures in a narrow temperature region around the transition are considered. We generalize a widely employed two-state protein folding model to include a third, transition state. For this three-state system we systematically study the deviation of the calorimetric enthalpy (heat of transition) from the van't Hoff enthalpy, a measure of the two-stateness of a transition. We show that under certain conditions the heat capacity of the three-state system can be almost indistinguishable from the heat capacity for the two-state system over a broad temperature interval. The consequence may be that some three-state (or even more than three-states) systems have been misinterpreted as two-state systems when the conclusion is drawn solely upon the van't Hoff enthalpy. These findings are important not only for proteins, but also for the interpretation of thermodynamical systems in general.