Journal of the American Chemical Society ARTICLE Figure 5. Molecular hydrophobicity potential (MHP) values of native and carbonylated residues. (a) Comparison of the calculated MHP values with the hydrophobicity scale based on free energy of partitioning between aqueous phase and octanol.43 Large black diamonds represent carbonylable and carbonylated residues Lys, Arg, Pro, Asa, and Gsa, while small gray diamonds represent standard amino acid residues. The regression line (calculated 2 without Asa and Gsa residues) with R = 0.825 shows that the calculated values correlate well with hydrophobicity scale for standard amino acid residues. (b) Calculated MHP values for all native and carbonylated residues (black bars, carbonylable and carbonylated residues; gray bars, other native residues). For all three structural measures of foldedness (rmsd, core compactness, and R-helicity), an ensemble of structures with a given number of carbonylated residues (regardless of their type or position) was deﬁned to be unfolded if the average value of the measure in question, reduced by its standard deviation, was greater that its average over the ﬁve native trajectories, increased by its respective standard deviation (e.g., if rmsdcarb σrmsdcarb > rmsdnat þ σrmsdnat). According to this deﬁnition, signiﬁcant unfolding (i.e., rmsdcarb σrmsdcarb > 3.6 Å, ∑dPhecarb σ∑dPhecarb > 20.5 Å, and NRcarb þ σNRcarb < 20.6) was observed for (1) simulations in the KR set with Arg15 and at least four Lys residues carbonylated according to R-helicity and core compact- ness, and in simulations with Arg15 and at least two Lys residues carbonylated according to rmsd; (2) simulations in the KP set with Pro22 and at least four Lys residues carbonylated according to R-helicity, and simulations with Pro22 and at least three Lys residues carbonylated according to rmsd; and (3) simulations in the KRP set with Arg15, Pro22, and at least three Lys residues carbonylated according to R-helicity and core compactness, and in simulations with Arg15, Pro22, and at least one Lys residue carbonylated according to rmsd. When it comes to conforma- tional entropy, our results suggest that there is a sizable increase in conformational entropy after complete carbonyla- tion (approximately 1 J K 1 mol 1 per atom). While this increase is consistent with unfolding of the protein, its absolute magnitude could be aﬀected by the sampling employed. On the whole, our results suggest that globular proteins like villin head- piece likely remain structurally stable upon carbonylation, unless the carbonylation level is high. Moreover, these results suggest that the type and the position of the aﬀected residues do make a diﬀerence in terms of the extent of structural damage caused. These ﬁndings are further corroborated by the analysis of the average pairwise rmsd between diﬀerent simulated trajectories exhibiting varying levels and types of carbonylation (Figure 4). According to this analysis, ensembles with ﬁve or more carbo- nylated residues are by-and-large non-native-like, and further- more their unfolded ensembles are largely mutually diﬀerent when it comes to structure. In order to estimate to what extent carbonylation of diﬀerent residues aﬀects protein stability, we used a simple, two-state model with the diﬀerence in free energy between the folded and the unfolded states of villin headpiece represented as ΔGf-u. We assumed that carbonylation of each residue acts independently and that carbonylation of each Lys residue has the same thermodynamic eﬀect. Using these assumptions, the total change in the free energy of stabilization of villin headpiece upon carbonylation, ΔΔGcarb, can be expressed as ΔΔGcarb ¼ nK ΔΔGK þ nR ΔΔGR þ nPΔΔGP 2 ð Þ where ΔΔGK, ΔΔGR, and ΔΔGP are free energy changes upon carbonylation of individual Lys, Arg, and Pro residues, respec- tively, and nK, nR, and nP are the numbers of carbonylated Lys, Arg, and Pro residues, respectively. According to this, when the villin headpiece unfolds, and ΔΔGcarb > ΔGf-u ΔΔGcarb < ΔGf-u when the molecule remains in the native conformation upon carbonylation. We used our simulated data and traces given in Figure 3a c, together with the deﬁnition of foldedness given above, to determine whether a given ensemble of structures is folded or unfolded. For example, one inequality, derived using core compactness as a reporter of the state of the villin headpiece (folded or unfolded), is 5ΔΔGK þ ΔΔGP < ΔGf-u Using the same approach, we derived 19 additional inequal- ities using rmsd, core compactness, and R-helicity criteria (see SI for details). This system of inequalities has no unique solution, partly because diﬀerent structural measures that were used are not necessarily mutually consistent when it comes to the deﬁni- tion of foldedness. However, it was possible to ﬁnd an approx- imate solution using numerical approaches (see SI for details). Average values over 1136 variations of ΔΔGK, ΔΔGR, and ΔΔGP values that fulﬁlled the maximal 16 out of 20 inequalities are ΔΔGK = 0.13ΔGf-u, ΔΔGR = 0.54ΔGf-u and ΔΔGP = 0.13ΔGf-u. In other words, carbonylation of Arg15 has by far the largest eﬀect on the protein’s stability, while the eﬀect of carbonylating Lys and Pro residues is markedly smaller. Effect of Carbonylation on Protein Aggregability. Since hydrophobicity is one of the most dominant properties that determines aggregability, we have compared the hydrophobi- city (related to aggregability) of native Lys, Arg, and Pro residues and their carbonylated counterparts, Asa and Gsa, using the MHP approach42 (Figure 5). MHP values correlate 7020 dx.doi.org/10.1021/ja110577e |J. Am. Chem. Soc. 2011, 133, 7016–7024 3 ð Þ 4 ð Þ 5 ð Þ