Journal of the American Chemical Society ARTICLE Figure 6. Two-dimensional projections of the free-energy surface as a function of MHP and hydrophobic core compactness (as captured by the sum of the distances between the three core phenylalanines) as calculated for (a) the native ensemble (ﬁve simulations), (b) the ensemble containing all combinations with four carbonylations events (35 simulations), and (c) the fully carbonylated ensemble (ﬁve simulations). Only the last 25 ns of each simulation were used to calculate the free-energy maps. The ellipses are centered at the average values of MHP and ∑dPhe for the three populations, with the major and minor semiaxes equal to the standard deviations of the distributions. The relative free energies were calculated as F = kT ln P, where P is the probability of occurrence of a given state, as seen in our simulations. well with octanol/water partition factors for amino acid side- chain analogues (Figure 5a), a widely used measure of amino acid hydrophobicity. In agreement with our TI result discussed above, the intrinsic hydrophobicity of Lys and Arg residues increases dramatically upon carbonylation. In terms of MHP weights, converting Lys to Asa or Arg to Gsa is similar to mutating them to highly hydrophobic leucine and valine, respectively (Figure 5b). In fact, the similarity between Asa and Leu, and Gsa and Val, respectively, extends to other basic physicochemical properties as well (SI Table S1). The effect of carbonylating Pro to Gsa is less dramatic, albeit still resulting in a net increase in hydrophobicity (Figure 5b). In addition to increasing hydrophobicity, carbonylation also results in charge neutralization when it comes to Lys and Arg residues, and both of these effects potentially increase the intrinsic aggregability of the affected proteins.43 45 To analyze this more closely, we have used the MHP approach to characterize the hydrophobicity of a protein surface and compare it with the degree of the protein’s structural integrity. In particular, we have studied the projections of the free energy surface for native and fully carbonylated forms of villin head- piece, as well as for an intermediate including all combinations with four carbonylated residues, using MHP, phenylalanine core compactness, and rmsd from the experimental NMR structure as order parameters (Figure 6 and SI Figure S2). Note that free energy projections using MHP as an order parameter were ﬁrst used by Polyansky and Zagrovic in the context of protein phosphorylation (manuscript in preparation). These free energy maps clearly demonstrate that surface hydrophobicity and the fraction of partially unfolded, aggregation-prone structures increase as the level of carbonylation increases. However, this analysis also shows that compact and structurally native-like, yet signiﬁcantly hydrophobic structures are present to a high degree in ensembles with moderate levels of carbonylation (Figure 6b). This is a direct consequence of the fact that Asa and Gsa are signiﬁcantly more hydrophobic compared with Lys and Arg, respectively, which at moderate levels of carbonylation may not be enough to unfold the molecules but is enough to increase their surface hydrophobicity. On the other hand, only unfolded structures with high surface hydrophobicity are populated in the fully carbonylated ensemble (Figure 6c and SI Figure S2). Taken together, these results suggest that carbonylation increases Figure 7. Aggregability versus carbonylation. (a) Distribution of changes in aggregability upon 27 single-point mutations in six known proteins causing amyloidogenic disease and in one model protein. Red arrows represent the estimation of aggregability change upon Lys (left arrow, ln(νmut/νwt) = 3.37 ( 0.73) and Arg (right arrow, ln(νmut/νwt) = 3.85 ( 0.73) carbonylation, calculated using eq 5. The error bars show standard deviation around zero calculated for the change in R-helix and β-sheet propensities for all proteins used by Chiti et al.43 (b) Site-speciﬁc intrinsic aggregation propensity, Zagg, for the native (solid black line) and three carbonylated villin headpiece molecules (only single carbo- nylation hits: Arg15 to Gsa, the lightest gray dotted line; Pro22 to Gsa, dark gray solid line; and Lys31 to Asa, the darkest gray dashed line). surface hydrophobicity through unfolding, but it does so also just by itself by modifying the physicochemical properties of the affected residues, which consequently may lead to an increase in aggregability. To put this on a quantitative footing, we have used the model of Chiti et al.43 to estimate the expected change in the aggrega- tion rate of an unstructured protein as a consequence of a single- point “mutation” induced by carbonylation (i.e., Lys to Asa or Arg to Gsa conversion). Changes in aggregability for these two 7021 dx.doi.org/10.1021/ja110577e |J. Am. Chem. Soc. 2011, 133, 7016–7024