Protein folding using fragment assembly and physical energy function

We perform a systematic study of the effects of sequence-independent backbone interactions and sequence-dependent side-chain interactions on protein folding using fragment assembly and physical energy function. Structures for ten proteins belonging to various structural classes are predicted only with Lennard-Jones interaction between backbone atoms. We find nativelike structures for beta proteins, suggesting that for proteins in this class, the global tertiary structures can be determined mainly by sequence-independent backbone interactions. On the other hand, for alpha proteins, nonlocal hydrophobic side-chain interaction is also required to obtain nativelike structures.     

Quantum chemical quantification of weakly polar interaction energies in the TC5b miniprotein

The tertiary structure of the TC5b miniprotein is stabilized by inter-residue interactions of the Trp-cage, which is composed of a Tyr and several Pro residues surrounding a central Trp residue. The interactions include Ar-Ar (aromatic side-chain-aromatic side-chain), Ar-NH (aromatic side-chain-backbone amide), and CH-pi (aromatic side-chain-aliphatic hydrogen) interactions. In the present work, the strength of the weakly polar interactions found in the TC5b miniprotein was quantified using all of the available 38 NMR structures (1L2Y) from the Protein Data Bank with DFT quantum chemical calculations at the BHandHLYP/cc-pVTZ level of theory and molecular fragmentation with capping of the partial structures. The energies of interaction between the individual residues of the Trp-cage range between -5.85+/-1.41 and -21.30+/-0.88 kcal mol(-1), leading to a significant total structural stabilization energy of -52.13+/-2.56 kcal mol(-1) of which about 50% is from the weakly polar interactions. Furthermore, the strengths of the individual weakly polar interactions are between -2.32+/-0.17 and -2.93+/-0.12 kcal mol(-1) for the CH-pi interactions, between -2.48+/-0.97 and -3.09+/-1.02 kcal mol(-1) for the Ar-NH interaction and -2.74+/-1.06 kcal mol(-1) for the Ar-Ar interaction.     

Development of novel statistical potentials describing cation-pi interactions in proteins and comparison with semiempirical and quantum chemistry approaches

Novel statistical potentials derived from known protein structures are presented. They are designed to describe cation-pi and amino-pi interactions between a positively charged amino acid or an amino acid carrying a partially charged amino group and an aromatic moiety. These potentials are based on the propensity of residue types to be separated by a certain spatial distance or to have a given relative orientation. Several such potentials, describing different kinds of correlations between residue types, distances, and orientations, are derived and combined in a way that maximizes their information content and minimizes their redundancy. To test the ability of these potentials to describe cation-pi and amino-pi systems, we compare their energies with those computed with the CHARMM molecular mechanics force field and with quantum chemistry calculations at the Hartree-Fock level (HF) and at the second order of the M?ller-Plesset perturbation theory (MP2). The latter calculations are performed in the gas phase and in acetone, in order to mimic the average dielectric constant of protein environments. The energies computed with the best of our statistical potentials and with gas-phase HF or MP2 show correlation coefficients up to 0.96 when considering one side-chain degree of freedom in the statistical potentials and up to 0.94 when using a totally simplified model excluding all side-chain degrees of freedom. These potentials perform as well as, or better than, the CHARMM molecular mechanics force field that uses a much more detailed protein representation. The good performance of our cation-pi statistical potentials suggests their utility in protein structure and stability prediction and in protein design.     

Modelling of carbohydrate–aromatic interactions: <Emphasis Type="Italic">ab initio </Emphasis>energetics and force field performance

Summary Aromatic amino acid residues are often present in carbohydrate-binding sites of proteins. These binding sites are characterized by a placement of a carbohydrate moiety in a stacking orientation to an aromatic ring. This arrangement is an example of CH/π interactions. Ab initio interaction energies for 20 carbohydrate–aromatic complexes taken from 6 selected ultra-high resolution X-ray structures of glycosidases and carbohydrate-binding proteins were calculated. All interaction energies of a pyranose moiety with a side chain of an aromatic residue were calculated as attractive with interaction energy ranging from −2.8 to −12.3 kcal/mol as calculated at the MP2/6-311+G(d) level. Strong attractive interactions were observed for a wide range of orientations of carbohydrate and aromatic ring as present in selected X-ray structures. The most attractive interaction was associated with apparent combination of CH/π interactions and classical H-bonds. The failure of Hartree–Fock method (interaction energies from +1.0 to −6.9 kcal/mol) can be explained by a dispersion nature of a majority of the studied complexes. We also present a comparison of interaction energies calculated at the MP2 level with those calculated using molecular mechanics force fields (OPLS, GROMOS, CSFF/CHARMM, CHEAT/CHARMM, Glycam/AMBER, MM2 and MM3). For a majority of force fields there was a strong correlation with MP2 values. RMSD between MP2 and force field values were 1.0 for CSFF/CHARMM, 1.2 for Glycam/AMBER, 1.2 for GROMOS, 1.3 for MM3, 1.4 for MM2, 1.5 for OPLS and to 2.3 for CHEAT/CHARMM (in kcal/mol). These results show that molecular mechanics approximates interaction energies very well and support an application of molecular mechanics methods in the area of glycochemistry and glycobiology.     

Intrinsic energy landscapes of amino acid side-chains

Amino acid side-chain conformational properties influence the overall structural and dynamic properties of proteins and, therefore, their biological functions. In this study, quantum mechanical (QM) potential energy surfaces for the rotation of side-chain χ(1) and χ(2) torsions in dipeptides in the alphaR, beta, and alphaL backbone conformations were calculated. The QM energy surfaces provide a broad view of the intrinsic conformational properties of each amino acid side-chain. The extent to which intrinsic energetics dictates side-chain orientation was studied through comparisons of the QM energy surfaces with χ(1) and χ(2) free energy surfaces from probability distributions obtained from a survey of high resolution crystal structures. In general, the survey probability maxima are centered in minima of the QM surfaces as expected for sp(3) (or sp(2) for χ(2) of Asn, Phe, Trp, and Tyr) atom centers with strong variations between amino acids occurring in the energies of the minima indicating intrinsic differences in rotamer preferences. High correlations between the QM and survey data were found for hydrophobic side-chains except Met, suggesting minimal influence of the protein and solution environments on their conformational distributions. Conversely, low correlations for polar or charged side-chains indicate a dominant role of the environment in stabilizing conformations that are not intrinsically favored. Data also link the presence of off-rotamers in His and Trp to favorable interactions with the backbone. Results also suggest that the intrinsic energetics of the side-chains of Phe and Tyr may play important roles in protein folding and stability. Analyses on whether intrinsic side-chain energetics can influence backbone preference identified a strong correlation for residues in the alphaL backbone conformation. It is suggested that this correlation reflects the intrinsic instability of the alphaL backbone such that assumption of this backbone conformation is facilitated by intrinsically favorable side-chain conformations. Together our results offer a broad overview of the conformational properties of amino acid side-chains and the QM data may be used as target data for force field optimization.     

Differential ordering of the protein backbone and side chains during protein folding revealed by site-specific recombinant infrared probes

The time scale for ordering of the polypeptide backbone relative to the side chains is a critical issue in protein folding. The interplay between ordering of the backbone and ordering of the side chains is particularly important for the formation of β-sheet structures, as the polypeptide chain searches for the native stabilizing cross-strand interactions. We have studied these issues in the N-terminal domain of protein L9 (NTL9), a model protein with mixed α/β structure. We have developed a general approach for introducing site-specific IR probes for the side chains (azide) and backbone ((13)C═(18)O) using recombinant protein expression. Temperature-jump time-resolved IR spectroscopy combined with site-specific labeling enables independent measurement of the respective backbone and side-chain dynamics with single residue resolution. We have found that side-chain ordering in a key region of the β-sheet structure occurs on a slower time scale than ordering of the backbone during the folding of NTL9, likely as a result of the transient formation of non-native side-chain interactions.     

A united-residue force field for off-lattice protein-structure simulations. I. Functional forms and parameters of long-range side-chain interaction potentials from protein crystal data

A two-stage procedure for the determination of a united-residue potential designed for protein simulations is outlined. In the first stage, the long-range and local-interaction energy terms of the total energy of a polypeptide chain are determined by analyzing protein-crystal data and averaging the all-atom energy surfaces. In the second stage (described in the accompanying article), the relative weights of the energy terms are optimized so as to locate the native structures of selected test proteins as the lowest energy structures. The goal of the work in the present study is to parameterize physically reasonable functional forms of the potentials of mean force for side-chain interactions. The potentials are of both radial and anisotropic type. Radial potentials include the Lennard-Jones and the shifted Lennard-Jones potential (with the shift parameter independent of orientation). To treat the angular dependence of side-chain interactions, three functional forms of the potential that were designed previously to describe anisotropic systems are evaluated: Berne-Pechukas (dilated Lennard-Jones); Gay-Berne (shifted Lennard-Jones with orientation-dependent shift parameters); and Gay-Berne-Vorobjev (the same as the preceding one, but with one more set of variable parameters). These functional forms were used to parameterize, within a short-distance range, the potentials of mean force for side-chain pair interactions that are related by the Boltzmann principle to the pair correlation functions determined from protein-crystal data. Parameter determination was formulated as a generalized nonlinear least-squares problem with the target function being the weighted sum of squares of the differences between calculated and “experimental” (i.e., estimated from protein-crystal data) angular, radial-angular, and radial pair correlation functions, as well as contact free energies. A set of 195 high-resolution nonhomologous structures from the Protein Data Bank was used to calculate the “experimental” values. The contact free energies were scaled by the slope of the correlation line between side-chain hydrophobicities, calculated from the contact free energies, and those determined by Fauchere and Pliška from the partition coefficients of amino acids between water and n-octanol. The methylene group served to define the reference contact free energy corresponding to that between the glycine methylene groups of backbone residues. Statistical analysis of the goodness of fit revealed that the Gay-Berne-Vorobjev anisotropic potential fits best to the experimental radial and angular correlation functions and contact free energies and therefore represents the free-energy surface of side-chain-side-chain interactions most accurately. Thus, its choice for simulations of protein structure is probably the most appropriate. However, the use of simpler functional forms is recommended, if the speed of computations is an issue. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 849–873, 1997     

Hydrogen-bond cooperativity, vibrational coupling, and dependence of helix stability on changes in amino acid sequence in small 3 10-helical peptides. A density functional theory study

Five pentapeptides, GGGGG, GAGGG, GVGGG, GLGGG, and GIGGG, have been completely optimized in the 3(10)-helical and open beta-strand conformations at the B3LYP/D95 level. The energies of the helices relative to the beta-strands vary from -2.1 to -3.6 kcal and depend on the amino acid residue sequence. The energies of substituting A, V, L, or I for G in the second position are also presented. Vibrational analyses were performed on the optimized structures. Vibrational coupling through the individual H-bond chains of the helices is confirmed to be stronger than that through space or through the covalent bonds. The cooperative interactions of the H-bonds are evident from both the structures and the coupling of the amide I, amide II, and N-H vibrations.     

Quantitation of the nearest-neighbour effects of amino acid side-chains that restrict conformational freedom of the polypeptide chain using reversed-phase liquid chromatography of synthetic model peptides with L- and D-amino acid substitutions

Side-chain backbone interactions (or "effects") between nearest neighbours may severely restrict the conformations accessible to a polypeptide chain and thus represent the first step in protein folding. We have quantified nearest-neighbour effects (i to i+1) in peptides through reversed-phase liquid chromatography (RP-HPLC) of model synthetic peptides, where L- and D-amino acids were substituted at the N-terminal end of the peptide sequence, adjacent to a L-Leu residue. These nearest-neighbour effects (expressed as the difference in retention times of L- and D-peptide diastereomers at pHs 2 and 7) were frequently dramatic, depending on the type of side-chain adjacent to the L-Leu residue, albeit such effects were independent of mobile phase conditions. No nearest-neighbour effects were observed when residue i is adjacent to a Gly residue. Calculation of minimum energy conformations of selected peptides supported the view that, whether a L- or D-amino acid is substituted adjacent to L-Leu, its orientation relative to this bulky Leu side-chain represents the most energetically favourable configuration. We believe that such energetically favourable, and different, configurations of L- and D-peptide diastereomers affect their respective interactions with a hydrophobic stationary phase, which are thus quantified by different RP-HPLC retention times. Side-chain hydrophilicity/hydrophobicity coefficients were generated in the presence of these nearest-neighbour effects and, despite the relative difference in such coefficients generated from peptides substituted with L- or D-amino acids, the relative difference in hydrophilicity/hydrophobicity between different amino acids in the L- or D-series is maintained. Overall, our results demonstrate that such nearest-neighbour effects can clearly restrict conformational space of an amino acid side-chain in a polypeptide chain.     

Tri-peptide reference structures for the calculation of relative solvent accessible surface area in protein amino acid residues

Relative amino acid residue solvent accessibility values allow the quantitative comparison of atomic solvent-accessible surface areas in different residue types and physical environments in proteins and in protein structural alignments. Geometry-optimised tri-peptide structures in extended solvent-exposed reference conformations have been obtained for 43 amino acid residue types at a high level of quantum chemical theory. Significant increases in side-chain solvent accessibility, offset by reductions in main-chain atom solvent exposure, were observed for standard residue types in partially geometry-optimised structures when compared to non-minimised models built from identical sets of proper dihedral angles abstracted from the literature. Optimisation of proper dihedral angles led most notably to marked increases of up to 54% in proline main-chain atom solvent accessibility compared to literature values. Similar effects were observed for fully-optimised tri-peptides in implicit solvent. The relief of internal strain energy was associated with systematic variation in N, C^α and C^β atom solvent accessibility across all standard residue types. The results underline the importance of optimisation of ‘hard’ degrees of freedom (bond lengths and valence bond angles) and improper dihedral angle values from force field or other context-independent reference values, and impact on the use of standardised fixed internal co-ordinate geometry in sampling approaches to the determination of absolute values of protein amino acid residue solvent accessibility. Quantum chemical methods provide a useful and accurate alternative to molecular mechanics methods to perform energy minimisation of peptides containing non-standard (chemically modified) amino acid residues frequently present in experimental protein structure data sets, for which force field parameters may not be available. Reference tri-peptide atomic co-ordinate sets including hydrogen atoms are made freely available.     

New-generation amber united-atom force field

We have developed a new-generation Amber united-atom force field for simulations involving highly demanding conformational sampling such as protein folding and protein-protein binding. In the new united-atom force field, all hydrogens on aliphatic carbons in all amino acids are united with carbons except those on Calpha. Our choice of explicit representation of all protein backbone atoms aims at minimizing perturbation to protein backbone conformational distributions and to simplify development of backbone torsion terms. Tests with dipeptides and solvated proteins show that our goal is achieved quite successfully. The new united-atom force field uses the same new RESP charging scheme based on B3LYP/cc-pVTZ//HF/6-31g** quantum mechanical calculations in the PCM continuum solvent as that in the Duan et al. force field. van der Waals parameters are empirically refitted starting from published values with respect to experimental solvation free energies of amino acid side-chain analogues. The suitability of mixing new point charges and van der Waals parameters with existing Amber covalent terms is tested on alanine dipeptide and is found to be reasonable. Parameters for all new torsion terms are refitted based on the new point charges and the van der Waals parameters. Molecular dynamics simulations of three small globular proteins in the explicit TIP3P solvent are performed to test the overall stability and accuracy of the new united-atom force field. Good agreements between the united-atom force field and the Duan et al. all-atom force field for both backbone and side-chain conformations are observed. In addition, the per-step efficiency of the new united-atom force field is demonstrated for simulations in the implicit generalized Born solvent. A speedup around two is observed over the Duan et al. all-atom force field for the three tested small proteins. Finally, the efficiency gain of the new united-atom force field in conformational sampling is further demonstrated with a well-known toy protein folding system, an 18 residue polyalanine in distance-dependent dielectric. The new united-atom force field is at least a factor of 200 more efficient than the Duan et al. all-atom force field for ab initio folding of the tested peptide.     

Gas-phase models of gamma turns: effect of side-chain/backbone interactions investigated by IR/UV spectroscopy and quantum chemistry

The conformations of laser-desorbed jet-cooled short peptide chains Ac-Phe-Xxx-NH2 (Xxx=Gly, Ala, Val, and Pro) have been investigated by IR/UV double resonance spectroscopy and density-functional-theory (DFT) quantum chemistry calculations. Singly gamma-folded backbone conformations (betaL-gamma) are systematically observed as the most stable conformers, showing that in these two-residue peptide chains, the local conformational preference of each residue is retained (betaL for Phe and gamma turn for Xxx). Besides, beta turns are also spontaneously formed but appear as minor conformers. The theoretical analysis suggests negligible inter-residue interactions of the main conformers, which enables us to consider these species as good models of gamma turns. In the case of valine, two similar types of gamma turns, differing by the strength of their hydrogen bond, have been found both experimentally and theoretically. This observation provides evidence for a strong flexibility of the peptide chain, whose minimum-energy structures are controlled by side-chain/backbone interactions. The qualitative conformational difference between the present species and the reversed sequence Ac-Xxx-Phe-NH2 is also discussed.     

Quasiracemic crystallization as a tool to assess the accommodation of noncanonical residues in nativelike protein conformations

Quasiracemic crystallization has been used to obtain high-resolution structures of two variants of the villin headpiece subdomain (VHP) that contain a pentafluorophenylalanine (F(5)Phe) residue in the hydrophobic core. In each case, the crystal contained the variant constructed from l-amino acids and the native sequence constructed from d-amino acids. We were motivated to undertake these studies by reports that racemic proteins crystallize more readily than homochiral forms and the prospect that quasiracemic crystallization would enable us to determine whether a polypeptide containing a noncanonical residue can closely mimic the tertiary structure of the native sequence. The results suggest that quasiracemic crystallization may prove to be generally useful for assessing mimicry of naturally evolved protein folding patterns by polypeptides that contain unnatural side-chain or backbone subunits.     

The effect of aqueous solvation upon alpha-helix formation for polyalanines

The incremental free energies of aqueous solution for acetyl(ala)NNH2 in its extended unfolded and alpha-helical conformations are compared using the SM5.2 solvation method of Cramer and Truhlar. A combination of density functional theory (DFT) at the B3LYP/D95(d,p) and AM1 has been employed using the ONIOM method. The incremental solvation energies of alpha-helical structures are very similar for both ONIOM and AM1 optimized structures as these structures do not significantly change upon solution. However, the conformations of the unfolded peptides change from extended beta-strand to polyproline II conformations upon aqueous solution. The incremental solvation free energy per residue of the polyproline II structure is about 2 kcal/mol/residue greater than that for the alpha-helix, representing an upper limit for the difference between the solvation energies. However, most of this difference disappears when the energy required to distort the optimized gas-phase extended beta-strand structure to the optimized polyproline II solution structure is included in the analysis, leaving an estimated difference in incremental solvation free energy of 0.3-0.5 kcal/mol favoring the unfolded structure. The solution structure sacrifices the stability derived from the intramolecular C5 H-bonds for more favorable interactions with the aqueous solvent.     

Investigating Ugi/Passerini Multicomponent Reactions for the Site-Selective Conjugation of Native Trastuzumab**

Site-selective modification of proteins has been the object of intense studies over the past decades, especially in the therapeutic field. Prominent results have been obtained with recombinant proteins, for which site-specific conjugation is made possible by the incorporation of particular amino acid residues or peptide sequences. In parallel, methods for the site-selective and site-specific conjugation of native and natural proteins are starting to thrive, allowing the controlled functionalization of various types of amino acid residues. Pursuing the efforts in this field, we planned to develop a new type of site-selective method, aiming at the simultaneous conjugation of two amino acid residues. We reasoned that this should give higher chances of developing a site-selective strategy compared to the great majority of existing methods that solely target a single residue. We opted for the Ugi four-centre three-component reaction to implement this idea, with the aim of conjugating the side-chain amine and carboxylate groups of two neighbouring lysine and aspartate/glutamate. Herein, we show that this strategy can give access to valuable antibody conjugates bearing several different payloads; furthermore, the approach limits the potential conjugation sites to only six on the model antibody trastuzumab.     

Fine grained sampling of residue characteristics using molecular dynamics simulation

In a fine-grained computational analysis of protein structure, we investigated the relationships between a residue's backbone conformations and its side-chain packing as well as conformations. To produce continuous distributions in high resolution, we ran molecular dynamics simulations over a set of protein folds (dynameome). In effect, the dynameome dataset samples not only the states well represented in the PDB but also the known states that are not well represented in the structural database. In our analysis, we characterized the mutual influence among the backbone ?,ψ angles with the first side-chain torsion angles (χ₁) and the volumes occupied by the side-chains. The dependencies of these relationships on side-chain environment and amino acids are further explored. We found that residue volumes exhibit dependency on backbone 2° structure conformation: side-chains pack more densely in extended β-sheet than in α-helical structures. As expected, residue volumes on the protein surface were larger than those in the interior. The first side-chain torsion angles are found to be dependent on the backbone conformations in agreement with previous studies, but the dynameome dataset provides higher resolution of rotamer preferences based on the backbone conformation. All three gauche^?, gauche⁺, and trans rotamers show different patterns of ?,ψ dependency, and variations in χ₁ value are skewed from their canonical values to relieve the steric strains. By demonstrating the utility of dynameomic modeling on the native state ensemble, this study reveals details of the interplay among backbone conformations, residue volumes and side-chain conformations.     

Ab initio studies of the conformers and conformational distribution of the gaseous hydroxyamino acid threonine

Systematic and extensive conformational search has been performed to characterize the gas-phase threonine structures. A total of 1296 unique trial structures were generated by allowing for all combinations of internal single-bond rotamers. All the trial structures were optimized at the B3LYP/6-311G* level of the theory and then subjected to further optimization at the B3LYP/6-311++G** level. A total of 71 conformers were found and their rotational constants, dipole moments, zero-point vibrational energies, harmonic frequencies and vertical ionization energies of all the conformers were determined. Single-point energies were also calculated at the MP2/6-311G(2df,p) and B3LYP/6-311G(2df,p) levels. Characteristic H-bonding types were classified and listed for all the conformers. The conformational distributions of gaseous threonine at various temperatures were calculated.     

A united-residue force field for off-lattice protein-structure simulations. II. Parameterization of short-range interactions and determination of weights of energy terms by Z-score optimization

Continuing our work on the determination of an off-lattice united-residue force field for protein-structure simulations, we determined and parameterized appropriate functional forms for the local-interaction terms, corresponding to the rotation about the virtual bonds (U_tor), the bending of virtual-bond angles (U_b), and the energy of different rotameric states of side chains (U_rot). These terms were determined by applying the Boltzmann principle to the distributions of virtual-bond torsional and virtual-bond angles and side-chain rotameric states, respectively, calculated from a data base of 195 high-resolution nonhomologous proteins. The complete energy function was constructed by combining the individual energy terms with appropriate weights. The weights were determined by optimizing the so-called Z-score value (which is the normalized difference between the energy of the native structure and the mean energy of non-native structures) of the histidine-containing phosphocarrier protein from Streptococcus faecalis (1PTF; an 88-residue α + β protein). To accomplish this, a database of C^α patterns was created using high-resolution nonhomologous protein structures from the Protein Data Bank, and the distributions of energy components of 1PTF were obtained by threading its sequence through ∼500 randomly chosen C^α-patterns from the X-ray structures in the PDB, followed by energy minimization, with the energy function incorporating initially guessed weights. The resulting minimized energies were used to optimize the Z-score value of 1PTF as a function of the weights of the various energy terms, and the new weights were used to generate new energy-component distributions. The process was iterated, until the weights used to generate the distributions and the optimized weights were self-consistent. The potential function with the weights of the various energy terms obtained by optimizing the Z-score value for 1PTF was found to locate the native structures of other test proteins (within an average RMS deviation of 3 Å): calcium-binding protein (4ICB), ubiquitin (1UBQ), α-spectrin (1SHG), major cold-shock protein (1MJC), and cytochrome b₅ (3B5C) (which included α and β structures) as distinctively lowest in energy in similar threading experiments. © 1997 by John Wiley & Sons, Inc. J Comput Chem 18: 874–887, 1997     

Energetic determinants of oligomeric state specificity in coiled coils

The coiled coil is one of the simplest and best-studied protein structural motifs, consisting of two to five helices wound around each other. Empirical rules have been established on the tendency of different core sequences to form a certain oligomeric state but the physical forces behind this specificity are unclear. In this work, we model four sequences onto the structures of dimeric, trimeric, tetrameric, and pentameric coiled coils. We first examine the ability of an effective energy function (EEF1.1) to discriminate the correct oligomeric state for a given sequence. We find that inclusion of the translational, rotational, and side-chain conformational entropy is necessary for discriminating the native structures from their misassembled counterparts. The decomposition of the effective energy into residue contributions yields theoretical values for the oligomeric propensity of different residue types at different heptad positions. We find that certain calculated residue propensities are general and consistent with existing rules. For example, leucine at d favors dimers, leucine at a favors tetramers or pentamers, and isoleucine at a favors trimers. Other residue propensities are sequence context dependent. For example, glutamine at d favors trimers in one context and pentamers in another. Charged residues at e and g positions usually destabilize higher oligomers due to higher desolvation. Nonpolar residues at these positions confer pentamer specificity when combined with certain residues at positions a and d. Specifically, the pair Leua-Alag' or the inverse was found to stabilize the pentamer. The small energy gap between the native and misfolded counterparts explains why a few mutations at the core sites are sufficient to induce a change in the oligomeric state of these peptides. A large number of possible experiments are suggested by these results.