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.     

Improved side-chain modeling for protein-protein docking

Success in high-resolution protein-protein docking requires accurate modeling of side-chain conformations at the interface. Most current methods either leave side chains fixed in the conformations observed in the unbound protein structures or allow the side chains to sample a set of discrete rotamer conformations. Here we describe a rapid and efficient method for sampling off-rotamer side-chain conformations by torsion space minimization during protein-protein docking starting from discrete rotamer libraries supplemented with side-chain conformations taken from the unbound structures, and show that the new method improves side-chain modeling and increases the energetic discrimination between good and bad models. Analysis of the distribution of side-chain interaction energies within and between the two protein partners shows that the new method leads to more native-like distributions of interaction energies and that the neglect of side-chain entropy produces a small but measurable increase in the number of residues whose interaction energy cannot compensate for the entropic cost of side-chain freezing at the interface. The power of the method is highlighted by a number of predictions of unprecedented accuracy in the recent CAPRI (Critical Assessment of PRedicted Interactions) blind test of protein-protein docking methods.     

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 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.     

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 jigsaw puzzle model: search for conformational specificity in protein interiors

The jigsaw puzzle model postulates that the predominant factor relating primary sequence to three-dimensional fold lies in the stereospecific packing of interdigitating side-chains within densely packed protein interiors. An attempt has been made to check the validity of the model by means of a surface complementarity function. Out of a database of 100 highly resolved protein structures the contacts between buried hydrophobic residues (Leu, Ile, Val, Phe) and their neighbours have been categorized in terms of the extent of side-chain surface area involved in a contact (overlap) and their steric fit (Sm). The results show that the majority of contacts between a buried residue and its immediate neighbours (side-chains) are of high steric fit and in the case of extended overlap at least one of the angular parameters characterizing interresidue geometry to have pronounced deviation from a random distribution, estimated by chi(2). The calculations thus tend to support the "jigsaw puzzle" model in that 75-85% of the contacts involving hydrophobic residues are of high surface complementarity, which, coupled to high overlap, exercise fairly stringent constraints over the possible geometrical orientations between interacting residues. These constraints manifest in simple patterns in the distributions of orientational angles. Approximately 60-80% of the buried side-chain surface packs against neighbouring side-chains, the rest interacting with main-chain atoms. The latter partition of the surface maintains an equally high steric fit (relative to side-chain contacts) emphasizing a non-trivial though secondary role played by main-chain atoms in interior packing. The majority of this class of contacts, though of high complementarity, is of reduced overlap. All residues whether hydrophobic or polar/charged show similar surface complementarity measures upon burial, indicating comparable competence of all amino acids in packing effectively with their atomic environments. The specificity thus appears to be distributed over the entire network of contacts within proteins. The study concludes with a proposal to classify contacts as specific and non-specific (based on overlap and fit), with the former perhaps contributing more to the specificity between sequence and fold than the latter.     

Core side-chain packing and backbone conformation in Lpp-56 coiled-coil mutants

Native proteins exhibit precise geometric packing of atoms in their hydrophobic interiors. Nonetheless, controversy remains about the role of core side-chain packing in specifying and stabilizing the folded structures of proteins. Here we investigate the role of core packing in determining the conformation and stability of the Lpp-56 trimerization domain. The X-ray crystal structures of Lpp-56 mutants with alanine substitutions at two and four interior core positions reveal trimeric coiled coils in which the twist of individual helices and the helix-helix spacing vary significantly to achieve the most favored superhelical packing arrangement. Introduction of each alanine "layer" into the hydrophobic core destabilizes the superhelix by 1.4 kcal mol(-1). Although the methyl groups of the alanine residues pack at their optimum van der Waals contacts in the coiled-coil trimer, they provide a smaller component of hydrophobic interactions than bulky hydrophobic side-chains to the thermodynamic stability. Thus, specific side-chain packing in the hydrophobic core of coiled coils are important determinants of protein main-chain conformation and stability.     

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.     

Determinants of protein side-chain packing.

The problem of protein side-chain packing for a given backbone trace is investigated using 3 different prediction models. The first requires an exhaustive search of all possible combinations of side-chain conformers, using the dead-end elimination theorem. The second considers only side-chain-backbone interactions, whereas the third neglects side-chain-backbone interactions and instead keeps side-chain-side-chain interactions. Predictions of side-chain conformations for 11 proteins using all 3 models show that removal of side-chain-side-chain interactions does not cause a large decrease in the prediction accuracy, whereas the model having only side-chain-side-chain interactions still retains a significant level of accuracy. These results suggest that the 2 classes of interactions, side-chain-backbone and side-chain-side-chain, are consistent with each other and work concurrently to stabilize the native conformations. This is confirmed by analyses of energy spectra of the side-chain conformations derived from the fourth prediction model, the Independent model, which gives almost the same quality of the prediction as the dead-end elimination. The analyses indicate that the 2 classes of interactions simultaneously increase the energy difference between the native and nonnative conformations.     

Statistical and conformational analysis of the electron density of protein side chains

Protein side chains make most of the specific contacts between proteins and other molecules, and their conformational properties have been studied for many years. These properties have been analyzed primarily in the form of rotamer libraries, which cluster the observed conformations into groups and provide frequencies and average dihedral angles for these groups. In recent years, these libraries have improved with higher resolution structures and using various criteria such as high thermal factors to eliminate side chains that may be misplaced within the crystallographic model coordinates. Many of these side chains have highly non-rotameric dihedral angles. The origin of side chains with high B-factors and/or with non-rotameric dihedral angles is of interest in the determination of protein structures and in assessing the prediction of side chain conformations. In this paper, using a statistical analysis of the electron density of a large set of proteins, it is shown that: (1) most non-rotameric side chains have low electron density compared to rotameric side chains; (2) up to 15% of chi1 non-rotameric side chains in PDB models can clearly be fit to density at a single rotameric conformation and in some cases multiple rotameric conformations; (3) a further 47% of non-rotameric side chains have highly dispersed electron density, indicating potentially interconverting rotameric conformations; (4) the entropy of these side chains is close to that of side chains annotated as having more than one chi(1) rotamer in the crystallographic model; (5) many rotameric side chains with high entropy clearly show multiple conformations that are not annotated in the crystallographic model. These results indicate that modeling of side chains alternating between rotamers in the electron density is important and needs further improvement, both in structure determination and in structure prediction.     

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.     

OPUS-PSP: an orientation-dependent statistical all-atom potential derived from side-chain packing

Here we report an orientation-dependent statistical all-atom potential derived from side-chain packing, named OPUS-PSP. It features a basis set of 19 rigid-body blocks extracted from the chemical structures of all 20 amino acid residues. The potential is generated from the orientation-specific packing statistics of pairs of those blocks in a non-redundant structural database. The purpose of such an approach is to capture the essential elements of orientation dependence in molecular packing interactions. Tests of OPUS-PSP on commonly used decoy sets demonstrate that it significantly outperforms most of the existing knowledge-based potentials in terms of both its ability to recognize native structures and consistency in achieving high Z-scores across decoy sets. As OPUS-PSP excludes interactions among main-chain atoms, its success highlights the crucial importance of side-chain packing in forming native protein structures. Moreover, OPUS-PSP does not explicitly include solvation terms, and thus the potential should perform well when the solvation effect is difficult to determine, such as in membrane proteins. Overall, OPUS-PSP is a generally applicable potential for protein structure modeling, especially for handling side-chain conformations, one of the most difficult steps in high-accuracy protein structure prediction and refinement.     

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.     

Conformational behavior of poly-N5-(3-hydroxypropyl)-L-glutamine in water-methanol mixtures studied by 13C Nmr and CD spectroscopy

The helix–coil transition of poly-N⁵-(3-hydroxypropyl)-L -glutamine (PHPLG) has been studied in methanol–water by CD and cmr spectroscopy. For polydisperse PHPLG, two separate peaks arising from residues in helical and random-coil conformations are observed during the transition for both main-chain carbons. These results are discussed and compared to those observed in the case of a polymer sample obtained by racemization of PHPLG in 0.1 M NaOH and of PHPLG samples of controlled molecular weight and dispersity. The dominant influence of the molecular-weight heterogeneity on the double-peak phenomenon has been verified. The linewidths and chemical shift of the ¹³C resonances are discussed in terms of side-chain–main-chain interactions and side-chain solvation.     

Residue-specific side-chain packing determines the backbone dynamics of transmembrane model helices

The transmembrane domains (TMDs) of membrane-fusogenic proteins contain an overabundance of β-branched residues. In a previous effort to systematically study the relation among valine content, fusogenicity, and helix dynamics, we developed model TMDs that we termed LV-peptides. The content and position of valine in LV-peptides determine their fusogenicity and backbone dynamics, as shown experimentally. Here, we analyze their conformational dynamics and the underlying molecular forces using molecular-dynamics simulations. Our study reveals that backbone dynamics is correlated with the efficiency of side-chain to side-chain van der Waals packing between consecutive turns of the helix. Leu side chains rapidly interconvert between two rotameric states, thus favoring contacts to its i±3 and i±4 neighbors. Stereochemical restraints acting on valine side chains in the α-helix force both β-substituents into an orientation where i,i±3 interactions are less favorable than i,i±4 interactions, thus inducing a local packing deficiency at VV3 motifs. We provide a quantitative molecular model to explain the relationship among chain connectivity, side-chain mobility, and backbone flexibility. We expect that this mechanism also defines the backbone flexibility of natural TMDs.     

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.     

Comparison of protein-protein interactions in serine protease-inhibitor and antibody-antigen complexes: implications for the protein docking problem

The protein-protein interaction energy of 12 nonhomologous serine protease-inhibitor and 15 antibody-antigen complexes is calculated using a molecular mechanics formalism and dissected in terms of the main-chain vs. side-chain contribution, nonrotameric side-chain contributions, and amino acid residue type involvement in the interface interaction. There are major differences in the interactions of the two types of protein-protein complex. Protease-inhibitor complexes interact predominantly through a main-chain-main-chain mechanism while antibody-antigen complexes interact predominantly through a side-chain-side-chain or a side-chain-main-chain mechanism. However, there is no simple correlation between the main-chain-main-chain interaction energy and the percentage of main-chain surface area buried on binding. The interaction energy is equally effected by the presence of nonrotameric side-chain conformations, which constitute approximately 20% of the interaction energy. The ability to reproduce the interface interaction energy of the crystal structure if original side-chain conformations are removed from the calculation is much greater in the protease-inhibitor complexes than the antibody-antigen complexes. The success of a rotameric model for protein-protein docking appears dependent on the extent of the main-chain-main-chain contribution to binding. Analysis of (1) residue type and (2) residue pair interactions at the interface show that antibody-antigen interactions are very restricted with over 70% of the antibody energy attributable to just six residue types (Tyr > Asp > Asn > Ser > Glu > Trp) in agreement with previous studies on residue propensity. However, it is found here that 50% of the antigen energy is attributable to just four residue types (Arg = Lys > Asn > Asp). On average just 12 residue pair interactions (6%) contribute over 40% of the favorable interaction energy in the antibody-antigen complexes, with charge-charge and charge/polar-tyrosine interactions being prominent. In contrast protease inhibitors use a diverse set of residue types and residue pair interactions.     

Entropy Hotspots for the Binding of Intrinsically Disordered Ligands to a Receptor Domain

Proline-rich motifs (PRMs) are widely used for mediating protein-protein interactions with weak binding affinities. Because they are intrinsically disordered when unbound, conformational entropy plays a significant role for the binding. However, residue-level differences of the entropic contribution in the binding of different ligands remain not well understood. We use all-atom molecular dynamics simulation and the maximal information spanning tree formalism to analyze conformational entropy associated with the binding of two PRMs, one from the Abl kinase and the other from the nonstructural protein 1 of the 1918 Spanish influenza A virus, to the N-terminal SH3 (nSH3) domain of the CrkII protein. Side chains of the stably folded nSH3 experience more entropy change upon ligand binding than the backbone, whereas PRMs involve comparable but heterogeneous entropy changes among the backbone and side chains. In nSH3, two conserved nonpolar residues forming contacts with the PRM experience the largest side-chain entropy loss. In contrast, the C-terminal charged residues of PRMs that form polar contacts with nSH3 experience the greatest side-chain entropy loss, although their “fuzzy” nature is attributable to the backbone that remains relatively flexible. Thus, residues that form high-occupancy contacts between nSH3 and PRM do not reciprocally contribute to entropy loss. Furthermore, certain surface residues of nSH3 distal to the interface with PRMs gain entropy, indicating a nonlocal effect of ligand binding. Comparing between the PRMs from cAbl and nonstructural protein 1, the latter involves a larger side-chain entropy loss and forms more contacts with nSH3. Consistent with experiments, this indicates stronger binding of the viral ligand at the expense of losing the flexibility of side chains, whereas the backbone experiences less entropy loss. The entropy “hotspots” as identified in this study will be important for tuning the binding affinity of various ligands to a receptor.     

An evaluvation of discrete and continuum search techniques for conformational analysis of side chains in proteins

Methodology for calculation of side-chain conformations in proteins is evaluated. The role and impact of corrections to idealized rotameric structures are considered, by incorporating methods for torsional optimization into rotamer-packing algorithms. Off-rotamer corrections given by continuum torsional optimization improve, over simpler rotamer-packing procedures, the accuracy with which the conformations of side chains of buried amino acids can be predicted. The analogy between protein side-chain calculations and spin systems is explored by adapting spin simulation methods to side-chain packing algorithms. Implementations of mean-field and heat-bath algorithms for side-chain packing are described and their performance tested. The procedures introduced here address the combinatorial problem in an efficient and reasonably effective manner, as evidenced by analysis of their convergence properties. Application of refined protocols yields overall prediction accuracies of 80% for χ¹ and 68percnt; for χ^1,2 pairs for a test set of 60 proteins, using a 40° cutoff to define correct placement. For buried amino acids (defined as having less than 30% relative solvent accessibility) the prediction accuracies increase to 88percnt; for χ¹ and 79percnt; for χ^1,2 pairs. The influence of the form of the potential energy function is studied by comparing results obtained with 12-6 and 9-6 potentials. The 9-6 form leads to more accurate results. Detailed comparison with previous work is presented, and the effect of combinatorial packing steps is shown to be important for all but the smallest proteins. © 1995 John Wiley & Sons, Inc.