Relationships between the temperature dependence of solvent denaturation and the denaturant dependence of protein stability curves

We have used a simple binding model to consider how the thermodynamics of denaturant-protein interactions might influence the shape of protein stability curves (free energy change as a function of temperature), and how these effects translate into a temperature dependence of the apparent m-value (sensitivity of unfolding free energy to denaturant). We find that for an exothermic binding reaction with no binding heat capacity increment, increasing denaturant concentrations produces an apparent increase in curvature in the protein stability curve, giving rise to an increase in the heat capacity increment of unfolding. Similar increases are seen if the binding heat capacity increment is taken as positive. However, for a negative binding heat capacity increment, increasing denaturant concentrations decreases the curvature of the stability curve, giving rise to a decrease in the heat capacity of unfolding. At very high denaturant concentrations (above which the heat capacity of denaturation becomes negative) the stability curve becomes dimpled, showing two separate maxima rather than one. These three models result in very different temperature dependencies of apparent m-values. For urea-induced unfolding of the ankyrin-domain of the Drosophila Notch protein, we find a dependence of experimental m-values on temperature that is similar to that produced by a negative binding heat capacity increment. This temperature dependence is consistent with the observed decrease in heat capacity of unfolding as denaturant is added.