How Valid Are Denaturant-Induced Unfolding Free Energy Measurements? Level of Conformance to Common Assumptions over an Extended Range of Ribonuclease A Stability

A thermodynamic cycle is used to explore a host of assumptions, conditions, and criteria which must be met for evaluation of authentic unfolding free energy changes. The thermodynamic cycle involves measurement of the unfolding free energy change (delta GzeroN-U) for RNase A at a reference pH, along with determination of the titration free energy changes for the native and unfolded species over an extended pH range. From these free energy changes, delta GzeroN-U at any pH in the range can be predicted and compared with delta GzeroN-U determined by use of the linear extrapolation method (LEM). Good agreement is found between predicted and determined free energy changes covering a broad range of protein stability changes (5 kcal/mol), pH (pH from 3 to 8.5), and lengths of linear extrapolation (C1/2 values from 2.4 to 7.7 M urea). The agreement between predicted and LEM-determined delta GzeroN-U values demonstrates (1) that delta GzeroN-U determined by the LEM is a function of state; i.e., it has the properties of additivity and independence of pathway required of an authentic free energy quantity; (2) the ability to obtain delta GzeroN-U values which are in agreement with the free energy change predicted by the cycle is independent of the length of linear extrapolation; and (3) the two-state assumption holds over an extensive pH range. The fact that the pH titration curve of unfolded RNase A in 6 M GdnHCl could be used in accurately predicting urea-induced delta GzeroN-U values shows that the unfolded ensemble in 6 M GdnHCl is thermodynamically identical to urea-unfolded RNase A as far as the pH dependence of protein stability is concerned. Urea-induced and GdnHCl-induced RNase A delta GzeroN-U values at pH 3 were found not to agree with one another, but this appears to be due to the inability to control the salt effect of GdnHCl on the native state of RNase A. These results provide strong evidence that the LEM applied to urea-induced unfolding of RNase A results in reliable free energy changes that meet a number of essential criteria for authentic thermodynamic quantities. The titration method is important in its own right in providing a means for evaluating the pH dependence of two-state protein unfolding free energy changes which does not require analysis of denaturant-induced unfolding transitions.