Mechanism of selection of side-chain rotamers in α-helices

In this study, a possible mechanism of selection of side-chain rotamers based on the rotamer distributions in known coiled-coil proteins is suggested. According to this mechanism, interhelical hydrophobic, polar, and packing interactions bring alpha-helices closer to each other and this effect squeezes side chains out of the helix-helix interface. As a result, in dimeric coiled coils and long alpha-alpha-hairpins where alpha-helices are packed in a face-to-face manner, most side chains occupying the a-positions have t-rotamers and those in the d-positions g(-)-rotamers. In tetramers, where alpha-helices are packed side-by-side, most side chains in the a-positions adopt g(-)-rotamers and those in the d-positions t-rotamers.     

Side-chain rotamers in protein alpha-alpha-hairpins and a mechanism of their selection

The observed features of side-chain rotamer distributions in protein alpha-alpha-hairpins are described. It was found that in left-turned alpha-alpha-hairpins most side chains occupying d-positions have t-rotamers and those in g-positions g- -rotamers. In right-turned alpha-alpha-hairpins, most side chains in a-positions adopt g- -rotamers and those in e-positions t-rotamers. Analysis of these features enables us to conclude that selection of side-chain rotamers in alpha-alpha-hairpins depends on both the type of the alpha-helix packing and the residue position. The observed features can be explained taking into account the squeezing mechanism according to which interhelical interactions bring alpha-helices closer to each other and this effect squeezes side chains out of the helix-helix interface and as a result they adopt unique conformations.     

Role of the structural context in selection of hydrophobic side-chain rotamers in a- and d-positions of α-helices

It was demonstrated for the first time that the distribution of side-chain rotamers in the a-and d-positions of α-helices of coiled-coil (cc) proteins follows a certain trend, rather then being random. For instance, most side chains adopt t rotamers in the a-positions and g^? rotamers in the d-positions of helical dimers. Vice versa, most side chains adopt g^? rotamers in the a-positions and t rotamers in the d-positions of tetramers. It was concluded that selection of the side-chain rotamers depends on the packing of α-helices and, consequently, depends on the structural context.     

Side-chain rotamers in protein α-α hairpins and a mechanism of their selection

Several regularities were observed for the distribution of side-chain rotamers in α-α hairpins of globular proteins. In left-turned α-α hairpins, most side chains adopt t rotamers in d-positions and g^? rotamers in g-positions. In right-turned α-α hairpins, most side-chains adopt g^? rotamers in a-positions and t rotamers in e-positions. Analysis of these regularities suggested that selection of the side-chain conformation in α-α hairpins depends on two main factors, the mode of α-helix packing and the positions of side chains in α-helices. The regularities were explained by the squeezing mechanism: interhelical interactions bring the α-helices close together so that the side chains are squeezed out of the helix-helix interface and adopt unique conformations.     

Rotamer libraries and probabilities of transition between rotamers for the side chains in protein-protein binding

Conformational changes in the side chains are essential for protein-protein binding. Rotameric states and unbound- to-bound conformational changes in the surface residues were systematically studied on a representative set of protein complexes. The side-chain conformations were mapped onto dihedral angles space. The variable threshold algorithm was developed to cluster the dihedral angle distributions and to derive rotamers, defined as the most probable conformation in a cluster. Six rotamer libraries were generated: full surface, surface noninterface, and surface interface-each for bound and unbound states. The libraries were used to calculate the probabilities of the rotamer transitions upon binding. The stability of amino acids was quantified based on the transition maps. The noninterface residues' stability was higher than that of the interface. Long side chains with three or four dihedral angles were less stable than the shorter ones. The transitions between the rotamers at the interface occurred more frequently than on the noninterface surface. Most side chains changed conformation within the same rotamer or moved to an adjacent rotamer. The highest percentage of the transitions was observed primarily between the two most occupied rotamers. The probability of the transition between rotamers increased with the decrease of the rotamer stability. The analysis revealed characteristics of the surface side-chain conformational transitions that can be utilized in flexible docking protocols.     

IRECS: a new algorithm for the selection of most probable ensembles of side-chain conformations in protein models

We introduce a new algorithm, IRECS (Iterative REduction of Conformational Space), for identifying ensembles of most probable side-chain conformations for homology modeling. On the basis of a given rotamer library, IRECS ranks all side-chain rotamers of a protein according to the probability with which each side chain adopts the respective rotamer conformation. This ranking enables the user to select small rotamer sets that are most likely to contain a near-native rotamer for each side chain. IRECS can therefore act as a fast heuristic alternative to the Dead-End-Elimination algorithm (DEE). In contrast to DEE, IRECS allows for the selection of rotamer subsets of arbitrary size, thus being able to define structure ensembles for a protein. We show that the selection of more than one rotamer per side chain is generally meaningful, since the selected rotamers represent the conformational space of flexible side chains. A knowledge-based statistical potential ROTA was constructed for the IRECS algorithm. The potential was optimized to discriminate between side-chain conformations of native and rotameric decoys of protein structures. By restricting the number of rotamers per side chain to one, IRECS can optimize side chains for a single conformation model. The average accuracy of IRECS for the chi1 and chi1+2 dihedral angles amounts to 84.7% and 71.6%, respectively, using a 40 degrees cutoff. When we compared IRECS with SCWRL and SCAP, the performance of IRECS was comparable to that of both methods. IRECS and the ROTA potential are available for download from the URL http://irecs.bioinf.mpi-inf.mpg.de.     

Three-dimensional structure of proteolytic fragment 163-231 of bacterioopsin determined from nuclear magnetic resonance data in solution.

546 NOESY cross-peak volumes were measured in the two-dimensional NOESY spectrum of proteolytic fragment 163-231 of bacterioopsin in organic solution. These data and 42 detected hydrogen bonds were applied for determining the peptide spatial structure. The fold of the polypeptide chain was determined by local structure analysis, a distance geometry approach and systematic search for energetically allowed side-chain rotamers which are consistent with experimental NOESY cross-peak volumes. The effective rotational correlation time of 6 ns for the molecule was evaluated from optimization of the local structure to meet NOE data and from the dependence on mixing time of the NiH/Ci alpha H cross-peak volumes of the residues in alpha-helical conformation. The resulting structure has two well defined alpha-helical regions, 168-191 and 198-227, with root-mean-square deviation 44 pm and 69 pm, respectively, between the backbone atoms in 14 final energy refined conformations. The alpha-helices correspond to transmembrane segments F and G of bacteriorhodopsin. The segment F contains proline 186, which introduces a kink of about 25 degrees with a disruption of the hydrogen bond with the NH group of the following residue. The segments are connected by a flexible loop region 192-197. Torsion angles chi 1 are unequivocally defined for 62% of side chains in the alpha-helices but half of them differ from electron cryo-microscopy (ECM) model of bacteriorhodopsin, apparently because of the low resolution of ECM. Nevertheless, the F and G segments can be packed as in the ECM model and with side-chain conformations consistent with all NMR data in solution.     

Statistical and energetic analysis of side-chain conformations in oligopeptides

The distributions of side-chain conformations in 258 crystal structures of oligopeptides have been analyzed. The sample contains 321 residues having side chains that extend beyond the C beta atom. Statistically observed preferences of side-chain dihedral angles are summarized and correlated with stereochemical and energetic constraints. The distributions are compared with observed distributions in proteins of known X-ray structures and with computed minimum-energy conformations of amino acid derivatives. The distributions are similar in all three sets of data, and they appear to be governed primarily by intraresidue interactions. In side chains with no beta-branching, the most important interactions that determine chi 1 are those between the C gamma H2 group and atoms of the neighboring peptide groups. As a result, the g- conformation (chi 1 congruent to -60 degrees) occurs most frequently for rotation around the C alpha-C beta bond in oligopeptides, followed by the t conformation (chi 1 congruent to 180 degrees), while the g+ conformation (chi 1 congruent to 60 degrees) is least favored. In residues with beta-branching, steric repulsions between the C gamma H2 or C gamma H3 groups and backbone atoms govern the distribution of chi 1. The extended (t) conformation is highly favored for rotation around the C beta-C gamma and C gamma-C delta bonds in unbranched side chains, because the t conformer has a lower energy than the g+ and g- conformers in hydrocarbon chains. This study of the observed side-chain conformations has led to a refinement of one of the energy parameters used in empirical conformational energy computations.     

Identification of amino acids involved in protein structural uniqueness: implication for de novo protein design

Structural uniqueness is characteristic of native proteins and is essential to express their biological functions. The major factors that bring about the uniqueness are specific interactions between hydrophobic residues and their unique packing in the protein core. To find the origin of the uniqueness in their amino acid sequences, we analyzed the distribution of the side chain rotational isomers (rotamers) of hydrophobic amino acids in protein tertiary structures and derived deltaS(contact), the conformational-entropy changes of side chains by residue-residue contacts in each secondary structure. The deltaS(contact) values indicate distinct tendencies of the residue pairs to restrict side chain conformation by inter-residue contacts. Of the hydrophobic residues in alpha-helices, aliphatic residues (Leu, Val, Ile) strongly restrict the side chain conformations of each other. In beta-sheets, Met is most strongly restricted by contact with Ile, whereas Leu, Val and Ile are less affected by other residues in contact than those in alpha-helices. In designed and native protein variants, deltaS(contact) was found to correlate with the folding-unfolding cooperativity. Thus, it can be used as a specificity parameter for designing artificial proteins with a unique structure.     

Protein recognition motifs: design of peptidomimetics of helix surfaces

Helices represent one of the most common recognition motifs in proteins. The design of nonpeptidic scaffolds, such as the 3,2',2'-tris-substituted terphenyl, that can imitate the side-chain orientation along one face of an alpha-helix potentially provides an effective means to modulate helix-recognition functions. Here, based on theoretical arguments, we described novel alpha-helix mimetics which are more effective than the terphenyl at constraining the aryl-aryl torsion angles to those associated with structures suitable for mimicking the alpha-helical twist for side-chain orientation and for superimposing the side chains of residues i, i + 3 or i + 4, i + 7 when compared with the alpha-beta side-chain vectors of the regular alpha-helix with an improved root mean square deviation (RMSD) of approximately 0.5 A. In addition, this study suggests that rotamer distributions around the C(alpha)--C(beta) bonds of these helix mimetics are similar to those of alpha-helices, except that these rotamer distributions show an approximately 60 degrees shift compared to those of alpha-helices when the mimetic axis is superimposed upon the helix axis. This change in rotamer orientation complicates mimicry of the helix surface.     

Side-chain flexibility in protein-ligand binding: the minimal rotation hypothesis

The goal of this work is to learn from nature about the magnitudes of side-chain motions that occur when proteins bind small organic molecules, and model these motions to improve the prediction of protein-ligand complexes. Following analysis of protein side-chain motions upon ligand binding in 63 complexes, we tested the ability of the docking tool SLIDE to model these motions without being restricted to rotameric transitions or deciding which side chains should be considered as flexible. The model tested is that side-chain conformational changes involving more atoms or larger rotations are likely to be more costly and less prevalent than small motions due to energy barriers between rotamers and the potential of large motions to cause new steric clashes. Accordingly, SLIDE adjusts the protein and ligand side groups as little as necessary to achieve steric complementarity. We tested the hypothesis that small motions are sufficient to achieve good dockings using 63 ligands and the apo structures of 20 different proteins and compared SLIDE side-chain rotations to those experimentally observed. None of these proteins undergoes major main-chain conformational change upon ligand binding, ensuring that side-chain flexibility modeling is not required to compensate for main-chain motions. Although more frugal in the number of side-chain rotations performed, this model substantially mimics the experimentally observed motions. Most side chains do not shift to a new rotamer, and small motions are both necessary and sufficient to predict the correct binding orientation and most protein-ligand interactions for the 20 proteins analyzed.     

Side-chain conformations in 4-alpha-helical bundles.

The distribution of the chi(1), chi(2) dihedral angles in a dataset consisting of 12 unrelated 4-alpha-helical bundle proteins was determined and qualitatively compared with that observed in globular proteins. The analysis suggests that the 4-alpha-helical bundle motif could occasionally impose steric constraints on side chains: (i) the side-chain conformations are limited to only a subset of the conformations observed in globular proteins and for some amino acids they are sterically more constrained than those in helical regions of globular proteins; (ii) aspartic acid and asparagine occasionally adopt rotamers that have not been previously reported for globular or helical proteins; (iii) some rotamers of tyrosine and isoleucine are predominantly or exclusively associated with hydrophobic core positions (a, d); (iv) mutations in the hydrophobic core occur preferentially between residue types which among other physicochemical properties also share a predominant rotamer.     

Structures of N-termini of helices in proteins.

We have surveyed 393 N-termini of alpha-helices and 156 N-termini of 3(10)-helices in 85 high resolution, non-homologous protein crystal structures for N-cap side-chain rotamer preferences, hydrogen bonding patterns, and solvent accessibilities. We find very strong rotamer preferences that are unique to N-cap sites. The following rules are generally observed for N-capping in alpha-helices: Thr and Ser N-cap side chains adopt the gauche - rotamer, hydrogen bond to the N3 NH and have psi restricted to 164 +/- 8 degrees. Asp and Asn N-cap side chains either adopt the gauche - rotamer and hydrogen bond to the N3 NH with psi = 172 +/- 10 degrees, or adopt the trans rotamer and hydrogen bond to both the N2 and N3 NH groups with psi = 1-7 +/- 19 degrees. With all other N-caps, the side chain is found in the gauche + rotamer so that the side chain does not interact unfavorably with the N-terminus by blocking solvation and psi is unrestricted. An i, i + 3 hydrogen bond from N3 NH to the N-cap backbone C = O in more likely to form at the N-terminus when an unfavorable N-cap is present. In the 3(10)-helix Asn and Asp remain favorable N-caps as they can hydrogen bond to the N2 NH while in the trans rotamer; in contrast, Ser and Thr are disfavored as their preferred hydrogen bonding partner (N3 NH) is inaccessible. This suggests that Ser is the optimum choice of N-cap when alpha-helix formation is to be encouraged while 3(10)-helix formation discouraged. The strong energetic and structural preferences found for N-caps, which differ greatly from positions within helix interiors, suggest that N-caps should be treated explicitly in any consideration of helical structure in peptides or proteins.     

Boltzmann-type distribution of side-chain conformation in proteins

We analyze packing imperfections in globular proteins as reflected in deviations of torsion angles from the equilibrium values for the isolated side chains. The distribution of conformations of methionine and lysine residues in a database of high-resolution structures is compared with energies of model compounds calculated with high-level quantum-mechanics. The distribution of the C-C and C-S torsion angles (chi(3)) correlates well with the Boltzmann factor of the torsion energy, exp(-betaE) of the model compounds C(2)H(5)-C(2)H(5) and C(2)H(5)-S-CH(3). An exponential relation was again found between the relative occurrence of g+, g- and t conformations for C(alpha)-C(beta) bonds in long side chains and the energy differences of rotamers of alpha-amino n-butyric acid, when dependence on backbone conformation was taken into account. The distribution of all 27 rotamers of methionine was correlated with the energy differences between the model's rotamers, corrected for clashes with nearby residues, the correlation being good for a set with backbone in the beta-conformation, but less clear for backbone alpha-conformation. In all correlations, the value of the coefficient beta corresponds to a temperature of circa 300 K. These results can be interpreted with a model that considers the structure of a folded protein as resulting from packing imperfectly complementary parts, with a requirement of an overall low energy. Compromises are required to optimize the fit of nonbonded contacts with surrounding groups, and side chains assume conformations away from the energy minimum. An exponential distribution is a most probable distribution, and this can be established easily under conditions other than thermal equilibrium.     

Packed protein bilayers in the 0.90 A resolution structure of a designed alpha helical bundle.

A 12-residue peptide designed to form an alpha-helix and self-associate into an antiparallel 4-alpha-helical bundle yields a 0.9 A crystal structure revealing unanticipated features. The structure was determined by direct phasing with the "Shake-and-Bake" program, and contains four crystallographically distinct 12-mer peptide molecules plus solvent for a total of 479 atoms. The crystal is formed from nearly ideal alpha-helices hydrogen bonded head-to-tail into columns, which in turn pack side-by-side into sheets spanning the width of the crystal. Within each sheet, the alpha-helices run antiparallel and are closely spaced (9-10 A center-to-center). The sheets are more loosely packed against each other (13-14 A between helix centers). Each sheet is amphiphilic: apolar leucine side chains project from one face, charged lysine and glutamate side chains from the other face. The sheets are stacked with two polar faces opposing and two apolar faces opposing. The result is a periodic biomaterial composed of packed protein bilayers, with alternating polar and apolar interfaces. All of the 30 water molecules in the unit cell lie in the polar interface or between the stacked termini of helices. A section through the sheet reveals that the helices packed at the apolar interface resemble the four-alpha-helical bundle of the design, but the helices overhang parts of the adjacent bundles, and the helix crossing angles are less steep than intended (7-11 degrees rather than 18 degrees).     

Improved modeling of side-chain--base interactions and plasticity in protein--DNA interface design

Combinatorial sequence optimization for protein design requires libraries of discrete side-chain conformations. The discreteness of these libraries is problematic, particularly for long, polar side chains, since favorable interactions can be missed. Previously, an approach to loop remodeling where protein backbone movement is directed by side-chain rotamers predicted to form interactions previously observed in native complexes (termed "motifs") was described. Here, we show how such motif libraries can be incorporated into combinatorial sequence optimization protocols and improve native complex recapitulation. Guided by the motif rotamer searches, we made improvements to the underlying energy function, increasing recapitulation of native interactions. To further test the methods, we carried out a comprehensive experimental scan of amino acid preferences in the I-AniI protein-DNA interface and found that many positions tolerated multiple amino acids. This sequence plasticity is not observed in the computational results because of the fixed-backbone approximation of the model. We improved modeling of this diversity by introducing DNA flexibility and reducing the convergence of the simulated annealing algorithm that drives the design process. In addition to serving as a benchmark, this extensive experimental data set provides insight into the types of interactions essential to maintain the function of this potential gene therapy reagent.     

Using quantum mechanics to improve estimates of amino acid side chain rotamer energies

Amino acid side chains adopt a discrete set of favorable conformations typically referred to as rotamers. The relative energies of rotamers partially determine which side chain conformations are more often observed in protein structures and accurate estimates of these energies are important for predicting protein structure and designing new proteins. Protein modelers typically calculate side chain rotamer energies by using molecular mechanics (MM) potentials or by converting rotamer probabilities from the protein database (PDB) into relative free energies. One limitation of the knowledge‐based energies is that rotamer preferences observed in the PDB can reflect internal side chain energies as well as longer‐range interactions with the rest of the protein. Here, we test an alternative approach for calculating rotamer energies. We use three different quantum mechanics (QM) methods (second order Møller‐Plesset (MP2), density functional theory (DFT) energy calculation using the B3LYP functional, and Hartree‐Fock) to calculate the energy of amino acid rotamers in a dipeptide model system, and then use these pre‐calculated values in side chain placement simulations. Energies were calculated for over 36,000 different conformations of leucine, isoleucine, and valine dipeptides with backbone torsion angles from the helical and strand regions of the Ramachandran plot. In a subset of cases these energies differ significantly from those calculated with standard molecular mechanics potentials or those derived from PDB statistics. We find that in these cases the energies from the QM methods result in more accurate placement of amino acid side chains in structure prediction tests. Proteins 2008. © 2007 Wiley‐Liss, Inc.     

Side chain burial and hydrophobic core packing in protein folding transition states

A critical step in the folding pathway of globular proteins is the formation of a tightly packed hydrophobic core. Several mutational studies have addressed the question of whether tight packing interactions are present during the rate-limiting step of folding. In some of these investigations, substituted side chains have been assumed to form native-like interactions in the transition state when the folding rates of mutant proteins correlate with their native-state stabilities. Alternatively, it has been argued that side chains participate in nonspecific hydrophobic collapse when the folding rates of mutant proteins correlate with side-chain hydrophobicity. In a reanalysis of published data, we have found that folding rates often correlate similarly well, or poorly, with both native-state stability and side-chain hydrophobicity, and it is therefore not possible to select an appropriate transition state model based on these one-parameter correlations. We show that this ambiguity can be resolved using a two-parameter model in which side chain burial and the formation of all other native-like interactions can occur asynchronously. Notably, the model agrees well with experimental data, even for positions where the one-parameter correlations are poor. We find that many side chains experience a previously unrecognized type of transition state environment in which specific, native-like interactions are formed, but hydrophobic burial dominates. Implications of these results to the design and analysis of protein folding studies are discussed.     

Determination of intrinsic hydrophilicity/hydrophobicity of amino acid side chains in peptides in the absence of nearest-neighbor or conformational effects

Understanding the hydrophilicity/hydrophobicity of amino acid side chains in peptides/proteins is one the most important aspects of biology. Though many hydrophilicity/hydrophobicity scales have been generated, an "intrinsic" scale has yet to be achieved. "Intrinsic" implies the maximum possible hydrophilicity/hydrophobicity of side chains in the absence of nearest-neighbor or conformational effects that would decrease the full expression of the side-chain hydrophilicity/hydrophobicity when the side chain is in a polypeptide chain. Such a scale is the fundamental starting point for determining the parameters that affect side-chain hydrophobicity and for quantifying such effects in peptides and proteins. A 10-residue peptide sequence, Ac-X-G-A-K-G-A-G-V-G-L-amide, was designed to enable the determination of the intrinsic values, where position X was substituted by all 20 naturally occurring amino acids and norvaline, norleucine, and ornithine. The coefficients were determined by reversed-phase high-performance liquid chromatography using six different mobile phase conditions involving different pH values (2, 5, and 7), ion-pairing reagents, and the presence and absence of different salts. The results show that the intrinsic hydrophilicity/hydrophobicity of amino acid side chains in peptides (proteins) is independent of pH, buffer conditions, or whether C(8) or C(18) reversed-phase columns were used for 17 side chains (Gly, Ala, Cys, Pro, Val, nVal, Leu, nLeu, Ile, Met, Tyr, Phe, Trp, Ser, Thr, Asn, and Gln) and dependent on pH and buffer conditions, including the type of salt or ion-pairing reagent for potentially charged side chains (Orn, Lys, His, Arg, Asp, and Glu).