Exploring protein-folding ensembles: a variable-barrier model for the analysis of equilibrium unfolding experiments

Recent theoretical and experimental results point to the existence of small barriers to protein folding. These barriers can even be absent altogether, resulting in a continuous folding transition (i.e., downhill folding). With small barriers, the detailed properties of folding ensembles may become accessible to equilibrium experiments. However, further progress is hampered because folding experiments are interpreted with chemical models (e.g., the two-state model), which assume the existence of well defined macrostates separated by arbitrarily high barriers. Here we introduce a phenomenological model based on the classical Landau theory for critical transitions. In this physical model the height of the thermodynamic free energy barrier and the general properties of the folding ensemble are directly obtained from the experimental data. From the analysis of differential scanning calorimetry data alone, our model identifies the presence of a significant (>35 kJ/mol) barrier for the two-state protein thioredoxin and the absence of a barrier for BBL, a previously characterized downhill folding protein. These results illustrate the potential of our approach for extracting the general features of protein ensembles from equilibrium folding experiments.