The interrelationships of side-chain and main-chain conformations in proteins

The accurate determination of a large number of protein structures by X-ray crystallography makes it possible to conduct a reliable statistical analysis of the distribution of the main-chain and side-chain conformational angles, how these are dependent on residue type, adjacent residue in the sequence, secondary structure, residue-residue interactions and location at the polypeptide chain termini. The interrelationship between the main-chain (phi, psi) and side-chain (chi 1) torsion angles leads to a classification of amino acid residues that simplify the folding alphabet considerably and can be a guide to the design of new proteins or mutational studies. Analyses of residues occurring with disallowed main-chain conformation or with multiple conformations shed some light on why some residues are less favoured in thermophiles.     

Refined crystal structure of troponin C from turkey skeletal muscle at 2.0 A resolution

The crystal structure of troponin C from turkey skeletal muscle has been refined at 2.0 A resolution (1 A = 0.1 nm). The resulting crystallographic R factor (R = sigma[[Fo[-[Fc[[/sigma[Fo[, where [Fo[ and [Fc[ are the observed and calculated structure factor amplitudes) is 0.155 for the 8054 reflections with intensities I greater than or equal to 2 sigma(I) within the 10 A to 2.0 A resolution range. With 66% of the residues in helical conformation, troponin C provides a good sample for helix analysis. The mean alpha-helix dihedral angles (phi, psi = -62 degrees, -42 degrees) agree with values observed for helical regions in other proteins. The helices are all curved and/or kinked. In particular, the 31 amino acid long inter-domain helix is smoothly curved, with a rather large radius of curvature of 137 A. Helix packing is different in the Ca2+-free domain (N-terminal) and the Ca2+-bound domain (C-terminal). The inter-helix angles for the two helix-loop-helix motifs in the regulatory domain are 133 degrees and 151 degrees, whereas the value for the two motifs in the C-terminal domain is 110 degrees, as observed in the EF-hands of parvalbumin. These differences affect the packing of the respective hydrophobic cores of each domain, in particular the disposition of aromatic rings. Pairwise arrangement of Ca2+-binding loops is common to both states, but the conformation is markedly different. Conversion of one to the other can be achieved by small cumulative changes of main-chain dihedral angles. The integrity of loop structure is maintained by numerous electrostatic interactions. Both salt bridges and carboxyl-carboxylate interactions are observed in TnC. There are more intramolecular (9) than intermolecular (1) salt bridges. Carboxyl-carboxylate interactions occur because the pH of the crystals is 5.0 and there is a multitude of aspartate and glutamate residues. One is intramolecular and four are intermolecular. Polar side-chain interactions occur more commonly with main-chain carbonyls and amides than with other polar side-chains. These interactions are mostly short range, and are similar to those observed in other proteins with one exception: negatively charged side-chains interact more frequently with main-chain carbonyl oxygen atoms. However, out of 19 such interactions, 10 involve oxygen atoms of the Ca2+ ligands. These unfavorable interactions are compensated by the favorable interactions with the Ca2+ ions and with main-chain amides. They are a trivial consequence of the tight fold of the Ca2+-binding loops.     

Rotamer strain energy in protein helices - quantification of a major force opposing protein folding

It is widely believed that the dominant force opposing protein folding is the entropic cost of restricting internal rotations. The energetic changes from restricting side-chain torsional motion are more complex than simply a loss of conformational entropy, however. A second force opposing protein folding arises when a side-chain in the folded state is not in its lowest-energy rotamer, giving rotameric strain. chi strain energy results from a dihedral angle being shifted from the most stable conformation of a rotamer when a protein folds. We calculated the energy of a side-chain as a function of its dihedral angles in a poly(Ala) helix. Using these energy profiles, we quantify conformational entropy, rotameric strain energy and chi strain energy for all 17 amino acid residues with side-chains in alpha-helices. We can calculate these terms for any amino acid in a helix interior in a protein, as a function of its side-chain dihedral angles, and have implemented this algorithm on a web page. The mean change in rotameric strain energy on folding is 0.42 kcal mol-1 per residue and the mean chi strain energy is 0.64 kcal mol-1 per residue. Loss of conformational entropy opposes folding by a mean of 1.1 kcal mol-1 per residue, and the mean total force opposing restricting a side-chain into a helix is 2.2 kcal mol-1. Conformational entropy estimates alone therefore greatly underestimate the forces opposing protein folding. The introduction of strain when a protein folds should not be neglected when attempting to quantify the balance of forces affecting protein stability. Consideration of rotameric strain energy may help the use of rotamer libraries in protein design and rationalise the effects of mutations where side-chain conformations change.     

A relational database of protein structures designed for flexible enquiries about conformation

A relational database of protein structure has been developed to enable rapid and flexible enquiries about the occurrence of many aspects of protein architecture. The coordinates of 294 proteins from the Brookhaven Data Bank have been processed by standard computer programs to generate many additional terms that quantify aspects of protein structure. These terms include solvent accessibility, main-chain and side-chain dihedral angles, and secondary structure. In a relational database, the information is stored in tables with columns holding the different terms and rows holding the different entries for the terms. The different relational base tables store the information about the protein coordinate set, the different chains in the protein, the amino acid residues and ligands, the atomic coordinates, the salt bridges, the hydrogen bonds, the disulphide bridges and the close tertiary contacts. The database was established under ORACLE management system. Enquiries are constructed in ORACLE using SQL (structured query language) which is simple to use and alleviates the need for extensive computer programs. A single table can be searched for entries that meet various criteria, e.g. all protein solved to better than a given resolution. The power of the database occurs when several tables, or the entries in a single table, are cross-correlated. For example the dihedral angles of proline in the fourth position in an alpha-helix in high resolution structures can be rapidly obtained. The structural database provides a powerful tool to obtain empirical rules about protein conformation. This database of protein structures is part of a joint project between Birkbeck College and Leeds University to establish an integrated data resource of protein sequences and structures (ISIS) that encodes the complex patterns of residues and coordinates that define protein conformation. The entire data resource (ISIS) will provide a system to guide all areas of protein modelling including structure prediction, site-directed mutagenesis and de novo protein design. The availability of ISIS is described in the paper.     

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.     

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.     

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.     

Side-chain conformation angles of amino acids: effect of temperature factor cut-off

The paper presents the analysis of the side-chain conformation angles of amino acids in 90% non-identical protein structures. The analysis has been carried out using 113,699 residues, which is higher compared to the previous studies. In the present study, one more quality check, namely, temperature factor cut-off, has been introduced in addition to resolution and R-factor cut-offs. Due to this, the present calculation reveals the approximate values for the minimum and the maximum of the three-rotameric states of chi1. In addition, the conformation angles chi2 and chi3 have been addressed with the improved data set. The results reported here could be of use in protein modeling.     

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.