Validation of NMR side-chain conformations by packing calculations

The precision and accuracy of protein structures determined by nuclear magnetic resonance (NMR) spectroscopy depend on the completeness of input experimental data set. Typically, rather than a single structure, an ensemble of up to 20 equally representative conformers is generated and routinely deposited in the Protein Database. There are substantially more experimentally derived restraints available to define the main-chain coordinates than those of the side chains. Consequently, the side-chain conformations among the conformers are more variable and less well defined than those of the backbone. Even when a side chain is determined with high precision and is found to adopt very similar orientations among all the conformers in the ensemble, it is possible that its orientation might still be incorrect. Thus, it would be helpful if there were a method to assess independently the side-chain orientations determined by NMR. Recently, homology modeling by side-chain packing algorithms has been shown to be successful in predicting the side-chain conformations of the buried residues for a protein when the main-chain coordinates and sequence information are given. Since the main-chain coordinates determined by NMR are consistently more reliable than those of the side-chains, we have applied the side-chain packing algorithms to predict side-chain conformations that are compatible with the NMR-derived backbone. Using four test cases where the NMR solution structures and the X-ray crystal structure of the same protein are available, we demonstrate that the side-chain packing method can provide independent validation for the side-chain conformations of NMR structures. Comparison of the side-chain conformations derived by side-chain packing prediction and by NMR spectroscopy demonstrates that when there is agreement between the NMR model and the predicted model, on average 78% of the time the X-ray structure also concurs. While the side-chain packing method can confirm the reliable residue conformations in NMR models, more importantly, it can also identify the questionable residue conformations with an accuracy of 60%. This validation method can serve to increase the confidence level for potential users of structural models determined by NMR.     

The use of side-chain packing methods in modeling bacteriophage repressor and cro proteins.

In recent years, it has been repeatedly demonstrated that the coordinates of the main-chain atoms alone are sufficient to determine the side-chain conformations of buried residues of compact proteins. Given a perfect backbone, the side-chain packing method can predict the side-chain conformations to an accuracy as high as 1.2 Å RMS deviation (RMSD) with greater than 80% of the χ angles correct. However, similarly rigorous studies have not been conducted to determine how well these apply, if at all, to the more important problem of homology modeling per se. Specifically, if the available backbone is imperfect, as expected for practical application of homology modeling, can packing constraints alone achieve sufficiently accurate predictions to be useful? Here, by systematically applying such methods to the pairwise modeling of two repressor and two cro proteins from the closely related bacteriophages 434 and P22, we find that when the backbone RMSD is 0.8 Å, the prediction on buried side chain is accurate with an RMS error of 1.8 Å and approximately 70% of the χ angles correctly predicted. When the backbone RMSD is larger, in the range of 1.6–1.8 Å, the prediction quality is still significantly better than random, with RMS error at 2.2 Å on the buried side chains and 60% accuracy on χ angles. Together these results suggest the following rules-of-thumb for homology modeling of buried side chains. When the sequence identity between the modeled sequence and the template sequence is >50% (or, equivalently, the expected backbone RMSD is <1 Å), side-chain packing methods work well. When sequence identity is between 30–50%, reflecting a backbone RMS error of 1–2 Å, it is still valid to use side-chain packing methods to predict the buried residues, albeit with care. When sequence identity is below 30% (or backbone RMS error greater than 2 Å), the backbone constraint alone is unlikely to produce useful models. Other methods, such as those involving the use of database fragments to reconstruct a template backbone, may be necessary as a complementary guide for modeling.     

Energy minimization method using automata network for sequence and side-chain conformation prediction from given backbone geometry

Globular proteins have high packing densities as a result of residue side chains in the core achieving a tight, complementary packing. The internal packing is considered the main determinant of native protein structure. From that point of view, we present here a method of energy minimization using an automata network to predict a set of amino acid sequences and their side-chain conformations from a desired backbone geometry for de novo design of proteins. Using discrete side-chain conformations, that is, rotamers, the sequence generation problem from a given backbone geometry becomes one of combinatorial problems. We focused on the residues composing the interior core region and predicted a set of amino acid Sequences and their side-chain conformations only from a given backbone geometry. The kinds of residues were restricted to six hydrophobic amino acids (Ala, Ile, Met, Leu, Phe, and Val) because the core regions are almost always composed of hydrophobic residues. The obtained sequences were well packed as was the native sequence. The method can be used for automated sequence generation in the de novo design of proteins. © 1994 Wiley-Liss, Inc.     

The role played by environmental residues on sidechain torsional angles within homologous families of proteins: A new method of sidechain modeling

We investigated the conservation of sidechain conformation for each residue within a homologous family of proteins in the Protein Data Bank (PDB) and performed sidechain modeling using this information. The information was represented by the probability of conserved sidechain torsional angles obtained from many families of proteins, and these were calculated for a pair of residues at topologically equivalent positions as a result of structural alignment. Probabilities were obtained for a pair of same amino acids and for a pair of different amino acids. The correlation between environmental residues and the fluctuation of probability was examined for the pair of same amino acid residues, and the simple probability was calculated for the pair of different amino acids. From the results on the same amino acid pairs, 17 amino acids, except for Ala, Gly, and Pro, were divided into two types: those that were influenced and those that were not influenced by the environmental residues. From results on different amino acid pairs, a replacement between large residues, such as Trp, Phe, and Tyr, was performed assuming conservation of their torsional angles within a homologous family of proteins. We performed sidechain modeling for 11 known proteins from their native and modeled backbones, respectively. With the native backbones, the percentage of the χ₁ angle correct within 30° was found to be 67% and 80% for all and core residues, respectively. With the modeled backbones, the percentage of the correct χ₁ angle was found to be 60% and 72% for all and core residues, respectively. To estimate an upper limit on the accuracy for predicting sidechain conformations, we investigated the probability of conserved sidechain torsional angles for highly similar proteins having > 90% sequence identity and <2.5-Å X-ray resolution. In those proteins, 83% of the sidechain conformations were conserved for the χ₁ angle. Proteins 31:355–369, 1998. © 1998 Wiley-Liss, Inc.     

Configurational-bias sampling technique for predicting side-chain conformations in proteins

Prediction of side-chain conformations is an important component of several biological modeling applications. In this work, we have developed and tested an advanced Monte Carlo sampling strategy for predicting side-chain conformations. Our method is based on a cooperative rearrangement of atoms that belong to a group of neighboring side-chains. This rearrangement is accomplished by deleting groups of atoms from the side-chains in a particular region, and regrowing them with the generation of trial positions that depends on both a rotamer library and a molecular mechanics potential function. This method allows us to incorporate flexibility about the rotamers in the library and explore phase space in a continuous fashion about the primary rotamers. We have tested our algorithm on a set of 76 proteins using the all-atom AMBER99 force field and electrostatics that are governed by a distance-dependent dielectric function. When the tolerance for correct prediction of the dihedral angles is a <20 degrees deviation from the native state, our prediction accuracies for chi1 are 83.3% and for chi1 and chi2 are 65.4%. The accuracies of our predictions are comparable to the best results in the literature that often used Hamiltonians that have been specifically optimized for side-chain packing. We believe that the continuous exploration of phase space enables our method to overcome limitations inherent with using discrete rotamers as trials.     

Side-chain entropy and packing in proteins.

What role does side-chain packing play in protein stability and structure? To address this question, we compare a lattice model with side chains (SCM) to a linear lattice model without side chains (LCM). Self-avoiding configurations are enumerated in 2 and 3 dimensions exhaustively for short chains and by Monte Carlo sampling for chains up to 50 main-chain monomers long. This comparison shows that (1) side-chain degrees of freedom increase the entropy of open conformations, but side-chain steric exclusion decreases the entropy of compact conformations, thus producing a substantial entropy that opposes folding; (2) there is a side-chain “freezing” or ordering, i.e., a sharp decrease in entropy, near maximum compactness; and (3) the different types of contacts among side chains (s) and main-chain elements (m) have different frequencies, and the frequencies have different dependencies on compactness. mm contacts contribute significantly only at high densities, suggesting that main-chain hydrogen bonding in proteins may be promoted by compactness. The distributions of mm, ms, and ss contacts in compact SCM configurations are similar to the distributions in protein structures in the Brookhaven Protein Data Bank. We propose that packing in proteins is more like the packing of nuts and bolts in a jar than like the pairwise matching of jigsaw puzzle pieces.     

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.     

The dominant role of side-chain backbone interactions in structural realization of amino acid code. ChiRotor: a side-chain prediction algorithm based on side-chain backbone interactions

The basic differences between the 20 natural amino acid residues are due to differences in their side-chain structures. This characteristic design of protein building blocks implies that side-chain-side-chain interactions play an important, even dominant role in 3D-structural realization of amino acid codes. Here we present the results of a comparative analysis of the contributions of side-chain-side-chain (s-s) and side-chain-backbone (s-b) interactions to the stabilization of folded protein structures within the framework of the CHARMm molecular data model. Contrary to intuition, our results suggest that side-chain-backbone interactions play the major role in side-chain packing, in stabilizing the folded structures, and in differentiating the folded structures from the unfolded or misfolded structures, while the interactions between side chains have a secondary effect. An additional analysis of electrostatic energies suggests that combinatorial dominance of the interactions between opposite charges makes the electrostatic interactions act as an unspecific folding force that stabilizes not only native structure, but also compact random conformations. This observation is in agreement with experimental findings that, in the denatured state, the charge-charge interactions stabilize more compact conformations. Taking advantage of the dominant role of side-chain-backbone interactions in side-chain packing to reduce the combinatorial problem, we developed a new algorithm, ChiRotor, for rapid prediction of side-chain conformations. We present the results of a validation study of the method based on a set of high resolution X-ray structures.     

Studies on the conformation of amino acids. X. Conformations of norvalyl, leucyl and aromatic side groups in a dipeptide unit

Backbone-side group conformations of amino acid residues including one or two δ-carbons in the side group have been investigated. Conformational energies of norvalyl, leucyl, phenylalanyl, tyrosyl, tryptophenyl, and histidinyl side groups in a dipeptide unit have been calculated by using classical energy expressions. The side group conformations about the C^α—C^β and C^β—C^γ bonds are restricted to specific values of the respective rotational angles. Thus, most favourable positions of γ- and δ-atoms of a linear side-chain (norvalyl) are restricted to (γ_I, δ_II) (γ_II, δ_I), (γ_II, δ_II), (γ_III, δ_II), and (γ_III, δ_III), whereas those of the side-chain branching at a sp³ γ-atom (leueyl) are further restricted. It is also shown that there is a definite correlation between the orientations of the two peptide planes and that of the planar group of the aromatic side chain of phenylalanyl type residues. The studies bring out an important fact that while the γ-atoms have definite and characteristic effects on the backbone rotational angles ? and ψ, the δ atoms and beyond have no effects on the preferred ? and ψ values. Thus, the preferred backbone conformations are independent of the preferred side group conformations beyond the γ-atom and vice versa. The observed ?, ψ, χ¹, and χ² values of amino acids, simple peptides, and of the three protein molecules lysozyme, myoglobin, and chymotrypsin have been compared with the theoretical predictions, and the agreement is found to be excellent.     

On the role of the crystal environment in determining protein side-chain conformations

The role of crystal packing in determining the observed conformations of amino acid side-chains in protein crystals is investigated by (1) analysis of a database of proteins that have been crystallized in different unit cells (space group or unit cell dimensions) and (2) theoretical predictions of side-chain conformations with the crystal environment explicitly represented. Both of these approaches indicate that the crystal environment plays an important role in determining the conformations of polar side-chains on the surfaces of proteins. Inclusion of the crystal environment permits a more sensitive measurement of the achievable accuracy of side-chain prediction programs, when validating against structures obtained by X-ray crystallography. Our side-chain prediction program uses an all-atom force field and a Generalized Born model of solvation and is thus capable of modeling simple packing effects (i.e. van der Waals interactions), electrostatic effects, and desolvation, which are all important mechanisms by which the crystal environment impacts observed side-chain conformations. Our results are also relevant to the understanding of changes in side-chain conformation that may result from ligand docking and protein-protein association, insofar as the results reveal how side-chain conformations change in response to their local environment.     

Accuracy of side-chain prediction upon near-native protein backbones generated by ab initio folding methods

The ab initio folding problem can be divided into two sequential tasks of approximately equal computational complexity: the generation of native-like backbone folds and the positioning of side chains upon these backbones. The prediction of side-chain conformation in this context is challenging, because at best only the near-native global fold of the protein is known. To test the effect of displacements in the protein backbones on side-chain prediction for folds generated ab initio, sets of near-native backbones (≤ 4 Å Cα RMS error) for four small proteins were generated by two methods. The steric environment surrounding each residue was probed by placing the side chains in the native conformation on each of these decoys, followed by torsion-space optimization to remove steric clashes on a rigid backbone. We observe that on average 40% of the χ1 angles were displaced by 40° or more, effectively setting the limits in accuracy for side-chain modeling under these conditions. Three different algorithms were subsequently used for prediction of side-chain conformation. The average prediction accuracy for the three methods was remarkably similar: 49% to 51% of the χ1 angles were predicted correctly overall (33% to 36% of the χ1+2 angles). Interestingly, when the inter-side-chain interactions were disregarded, the mean accuracy increased. A consensus approach is described, in which side-chain conformations are defined based on the most frequently predicted χ angles for a given method upon each set of near-native backbones. We find that consensus modeling, which de facto includes backbone flexibility, improves side-chain prediction: χ1 accuracy improved to 51–54% (36–42% of χ1+2). Implications of a consensus method for ab initio protein structure prediction are discussed. Proteins 33:204–217, 1998. © 1998 Wiley-Liss, Inc.     

The reconstruction of side-chain conformations from protein Cα coordinates

A model of nine proteins including side-chain atoms have been built from the known C^α coordinates and amino acid sequences using a Monte Carlo Protein Building Annealing method. The Cartesian coordinates for the side-chain atoms were established with bond lengths and angles selected randomly from within previously determined ranges. A simulated annealing technique is used to generate some 300 structures with differing side-chain conformations. The atomic coordinates of the backbone atoms are fixed during the simulated annealing process. The coordinates of the side-chain atoms of 300 low energy conformations are averaged to obtain a mean structure that is minimized with the C^α atoms constrained to their position in the x-ray structure using the OPLS/AMBER force field with the GB/SA water model. The rms deviation of the main-chain atoms (without C^β) compared with the corresponding crystal structures is in the range 0.20–0.64 Å. The rms deviation of the side-chain atoms is between 1.72 and 2.71 Å and for all atoms is between 1.19 and 1.99 Å. The method is insensitive to random errors in the C^α positions and the computational requirement is modest. © 1997 John Wiley & Sons, Inc.     

Rotamer Dynamics: Analysis of Rotamers in Molecular Dynamics Simulations of Proteins

Given by χ torsional angles, rotamers describe the side-chain conformations of amino acid residues in a protein based on the rotational isomers (hence the word rotamer). Constructed rotamer libraries, based on either protein crystal structures or dynamics studies, are the tools for classifying rotamers (torsional angles) in a way that reflect their frequency in nature. Rotamer libraries are routinely used in structure modeling and evaluation. In this perspective article, we would like to encourage researchers to apply rotamer analyses beyond their traditional use. Molecular dynamics (MD) of proteins highlight the in silico behavior of molecules in solution and thus can identify favorable side-chain conformations. In this article, we used simple computational tools to study rotamer dynamics (RD) in MD simulations. First, we isolated each frame in the MD trajectories in separate Protein Data Bank files via the cpptraj module in AMBER. Then, we extracted torsional angles via the Bio3D module in R language. The classification of torsional angles was also done in R according to the penultimate rotamer library. RD analysis is useful for various applications such as protein folding, study of rotamer-rotamer relationship in protein-protein interaction, real-time correlation between secondary structures and rotamers, study of flexibility of side chains in binding site for molecular docking preparations, use of RD as guide in functional analysis and study of structural changes caused by mutations, providing parameters for improving coarse-grained MD accuracy and speed, and many others. Major challenges facing RD to emerge as a new scientific field involve the validation of results via easy, inexpensive wet-lab methods. This realm is yet to be explored.     

Relating side-chain mobility in proteins to rotameric transitions: Insights from molecular dynamics simulations and NMR

The dynamic aspect of proteins is fundamental to understanding protein stability and function. One of the goals of NMR studies of side-chain dynamics in proteins is to relate spin relaxation rates to discrete conformational states and the timescales of interconversion between those states. Reported here is a physical analysis of side-chain dynamics that occur on a timescale commensurate with monitoring by ²H spin relaxation within methyl groups. Motivated by observations made from tens-of-nanoseconds long MD simulations on the small protein eglin c in explicit solvent, we propose a simple molecular mechanics-based model for the motions of side-chain methyl groups. By using a Boltzmann distribution within rotamers, and by considering the transitions between different rotamer states, the model semi-quantitatively correlates the population of rotamer states with ‘model-free’ order parameters typically fitted from NMR relaxation experiments. Two easy-to-use, analytical expressions are given for converting S²_axis’ values (order parameter for C–CH₃ bond) into side-chain rotamer populations. These predict that S²_axis’ values below 0.8 result from population of more than one rotameric state. The relations are shown to predict rotameric sampling with reasonable accuracy on the ps–ns timescale for eglin c and are validated for longer timescales on ubiquitin, for which side-chain residual dipolar coupling (RDC) data have been collected.     

Classification of amino acid spin systems using PFG HCC(CO)NH-TOCSY with constant-time aliphatic 13C frequency labeling

Summary We have developed a useful strategy for identifying amino acid spin systems and side-chain carbon resonance assignments in small ¹⁵N-, ¹³C-enriched proteins. Multidimensional constant-time pulsed field gradient (PFG) HCC(CO)NH-TOCSY experiments provide side-chain resonance frequency information and establish connectivities between sequential amino acid spin systems. In PFG HCC(CO)NH-TOCSY experiments recorded with a properly tuned constant-time period for frequency labeling of aliphatic ¹³C resonances, phases of cross peaks provide information that is useful for identifying spin system types. When combined with ¹³C chemical shift information, these patterns allow identification of the following spin system types: Gly, Ala, Thr, Val, Leu, Ile, Lys, Arg, Pro, long-type (i.e., Gln, Glu and Met), Ser, and AMX-type (i.e., Asp, Asn, Cys, His, Phe, Trp and Tyr).     

1H and 13C nmr studies of cyclic and linear dipeptides containing threonyl,seryl, aspartyl,and histidyl residues

The side-chain conformations of D - orL - Thr, D - or L -Ser, L -Asp, and L - His residues in cyclic and linear dipeptides in D₂O or in DMSO-d₆ are deduced from vicinal (¹H,¹H) and (¹³C, ¹H) coupling constants. Vicinal (¹³C, ¹³C) coupling constants strongly depend on substituents and cannot be used without a more sound analysis. In cyclic dipeptides, the Thr and Ser side chains are folded above the DKP ring, with χ¹ near 60°. The L -Asp side chain interacts more specifically with peptide bonds (χ¹ near 300°). The L - His side chain is more flexible and its conformation depends on the proximity of a second side chain and on solute-solvent interactions. In all cases, this side chain is not completely folded. In linear dipeptides, the conformation of a C-terminal L -His residue is mainly influenced by the end carboxylic group. On the other hand, a N-terminal L -His residue interacts more easily with a neighboring L -Asp residue. In aqueous solution, the imidazole pK_a depends on the proximity of terminal and lateral charged groups but does not reveal any specific interaction in cyclic dipeptides. A comparison between the conformations of cyclic peptides observed in solution, in the crystalline state and calculated by empirical methods, allows one to point out the discriminating role of the packing in crystals, and of solute-solvent interactions in solution.     

Protein side-chain resonance assignment and NOE assignment using RDC-defined backbones without TOCSY data

One bottleneck in NMR structure determination lies in the laborious and time-consuming process of side-chain resonance and NOE assignments. Compared to the well-studied backbone resonance assignment problem, automated side-chain resonance and NOE assignments are relatively less explored. Most NOE assignment algorithms require nearly complete side-chain resonance assignments from a series of through-bond experiments such as HCCH-TOCSY or HCCCONH. Unfortunately, these TOCSY experiments perform poorly on large proteins. To overcome this deficiency, we present a novel algorithm, called Nasca (NOE Assignment and Side-Chain Assignment), to automate both side-chain resonance and NOE assignments and to perform high-resolution protein structure determination in the absence of any explicit through-bond experiment to facilitate side-chain resonance assignment, such as HCCH-TOCSY. After casting the assignment problem into a Markov Random Field (MRF), Nasca extends and applies combinatorial protein design algorithms to compute optimal assignments that best interpret the NMR data. The MRF captures the contact map information of the protein derived from NOESY spectra, exploits the backbone structural information determined by RDCs, and considers all possible side-chain rotamers. The complexity of the combinatorial search is reduced by using a dead-end elimination (DEE) algorithm, which prunes side-chain resonance assignments that are provably not part of the optimal solution. Then an A* search algorithm is employed to find a set of optimal side-chain resonance assignments that best fit the NMR data. These side-chain resonance assignments are then used to resolve the NOE assignment ambiguity and compute high-resolution protein structures. Tests on five proteins show that Nasca assigns resonances for more than 90% of side-chain protons, and achieves about 80% correct assignments. The final structures computed using the NOE distance restraints assigned by Nasca have backbone RMSD 0.8–1.5 Å from the reference structures determined by traditional NMR approaches.     

Extending the accuracy limits of prediction for side-chain conformations

Current techniques for the prediction of side-chain conformations on a fixed backbone have an accuracy limit of about 1.0-1.5 A rmsd for core residues. We have carried out a detailed and systematic analysis of the factors that influence the prediction of side-chain conformation and, on this basis, have succeeded in extending the limits of side-chain prediction for core residues to about 0.7 A rmsd from native, and 94 % and 89 % of chi(1) and chi(1+2 ) dihedral angles correctly predicted to within 20 degrees of native, respectively. These results are obtained using a force-field that accounts for only van der Waals interactions and torsional potentials. Prediction accuracy is strongly dependent on the rotamer library used. That is, a complete and detailed rotamer library is essential. The greatest accuracy was obtained with an extensive rotamer library, containing over 7560 members, in which bond lengths and bond angles were taken from the database rather than simply assuming idealized values. Perhaps the most surprising finding is that the combinatorial problem normally associated with the prediction of the side-chain conformation does not appear to be important. This conclusion is based on the fact that the prediction of the conformation of a single side-chain with all others fixed in their native conformations is only slightly more accurate than the simultaneous prediction of all side-chain dihedral angles.     

Conformation of cyclic dipeptides from empirical energy calculations

Empirical energy calculations on cyclo-Gly-X with X- Phe, Tyr, Val, and Leu as a function of the side-chain torsion angles χ indicate that the conformation of minimum energy are characterized by χ₁ = 60°, χ² = 90° for Phe and Try, χ¹ = ?60° for Val and χ¹ = ?60°, χ² = 180° and χ¹ = 60° and χ² = 150° for Leu. The minimum energy conformation of cyclo-Gly-Phe and cyclo-Gly-Val have the side chains of Phe and Val stacked over the poperazinedione ring as suggested by NMR and found for cyclo-Gly-Tyr crystal structure. In contrast, the Leu side chain is expected to exist in an extended or a quasi-folded form.     

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.