Chemical denaturation:: Potential impact of undetected intermediates in the free energy of unfolding and m-values obtained from a two-state assumption

The chemical unfolding transition of a protein was simulated, including the presence of an intermediate (I) in equilibrium with the native (N) and unfolded (U) states. The calculations included free energies of unfolding, Delta G(u)(w), in the range of 1.4 kcal/mol to 10 kcal/mol and three different global m-values. The simulations included a broad range of equilibrium constants for the N <-> I process. The dependence of the N <-> I equilibrium on the concentration of denaturant was also included in the simulations. Apparent Delta G(u)(w) and m-values were obtained from the simulated unfolding transitions by fitting the data to a two-state unfolding process. The potential-errors were calculated for two typical experimental situations: 1) the unfolding is monitored by a physical property that does not distinguish between native and intermediate states (case 1), and 2) the physical property does not distinguish between intermediate and unfolded states (case II). The results obtained indicated that in the presence of an intermediate, and in both experimental situations, the free energy of unfolding and the m-values could be largely underestimated. The errors in Delta G(u)(w) and m-values do not depend on the m-values that characterize the global N <-> U transition. They are dependent on the equilibrium constant for the N <-> I transition and its characteristic m(1)-value. The extent of the underestimation increases for higher energies of unfolding. Including no random error in the simulations, it was estimated that the underestimation in Delta G(u)(w) could range between 25% and 35% for unfolding transitions of 3-10 kcal/mol (case I). In case II, the underestimation in Delta G(u)(w) could be even larger than in case I. In the same energy range, a 50% error in the m-value could also take place. The fact that most of the mutant proteins are characterized by both a lower m-value and a lower stability than the wild-type protein suggests that in some cases the results could have been underestimated due to the application of the two-state assumption.