Thermodynamic analysis of interactions between denaturants and protein surface exposed on unfolding: Interpretation of urea and guanidinium chloride m ‐values and their correlation with changes in accessible surface area (ASA) using preferential interaction coefficients and the local‐bulk domain model

A denaturant m ‐value is the magnitude of the slope of a typically linear plot of the unfolding free energy change ΔG° obs vs. molar concentration (C 3 ) of denaturant. For a given protein, the guanidinium chloride (GuHCl) m ‐value is approximately twice as large as the urea m ‐value. Myers et al. (Protein Sci 1995;4:2138–2148) found that experimental m ‐values for protein unfolding in both urea and GuHCl are proportional to ΔASA   corr max , the calculated maximum amount of protein surface exposed to water in unfolding, corrected empirically for the effects of disulfide crosslinks: (urea m ‐value/ΔASA   corr max ) = 0.14±0.01 cal M −1 Å −2 and (GuHCl m ‐value/ΔASA   corr max ) = 0.28±0.03 cal M −1 Å −2 . The observed linearity of plots of ΔG° obs vs. C 3 indicates that the difference in preferential interaction coefficients ΔΓ 3 characterizing the interactions of these solutes with denatured and native protein surface is approximately proportional to denaturant concentration. The proportionality of m ‐values to ΔASA   corr maxindicates that the corresponding ΔΓ 3 are proportional to ΔASA   corr maxat any specified solute concentration. Here we use the local‐bulk domain model of solute partitioning in the protein solution (Courtenay et al., Biochemistry 2000;39:4455–4471) to obtain a novel quantitative interpretation of denaturant m ‐values. We deduce that the proportionality of m ‐value to ΔASA   corr maxresults from the proportionality of B   1 0(the amount of water in the local domain surrounding the protein surface exposed upon unfolding) to ΔASA   corr max . We show that both the approximate proportionality of ΔΓ 3 to denaturant concentration and the residual dependence of ΔΓ 3 /m 3 (where m 3 is molal concentration) on denaturant concentration are quantitatively predicted by the local‐bulk domain model if the molal‐scale solute partition coefficient K P and water‐solute exchange stoichiometry S 1,3 are independent of solute concentration. We obtain K P,urea = 1.12±0.01 and K P,GuHCl = 1.16±0.02 (or K P,GuH+ ≅ 1.48), values which will be useful to characterize the effect of accumulation of those solutes on all processes in which the water‐accessible area of unfolded protein surface changes. We demonstrate that the local‐bulk domain analysis of an m ‐value plot justifies the use of linear extrapolation to estimate (≲ 5% error) the stability of the native protein in the absence of denaturant (ΔG   o o ), with respect to a particular unfolded state. Our surface area calculations indicate that published m ‐values/ΔASA ratios for unfolding of alanine‐based α‐helical oligopeptides by urea and GuHCl exceed the corresponding m ‐value/ΔASA ratios for protein unfolding by approximately fourfold. We propose that this difference originates from the approximately fourfold difference (48% vs. 13%) in the contribution of polar backbone residues to ΔASA of unfolding, a novel finding which supports the long‐standing but not universally accepted hypothesis that urea and guanidinium cation interact primarily with backbone amide groups. We propose that proteins which exhibit significant deviations from the average m ‐value/ΔASA ratio will be found to exhibit significant deviations from the expected amount and/or average composition of the surface exposed on unfolding. Proteins 2000;41:72–85. © 2000 Wiley‐Liss, Inc.