Prediction of protein side-chain conformation by packing optimization

We have developed a rapid and completely automatic method for prediction of protein side-chain conformation, applying the simulated annealing algorithm to optimization of side-chain packing (van der Waals) interactions. The method directly attacks the combinatorial problem of simultaneously predicting many residues' conformation, solving in 8 to 12 hours problems for which the systematic search would require over 10(300) central processing unit years. Over a test set of nine proteins ranging in size from 46 to 323 residues, the program's predictions for side-chain atoms had a root-mean-square (r.m.s.) deviation of 1.77 A overall versus the native structures. More importantly, the predictions for core residues were especially accurate, with an r.m.s. value of 1.25 A overall: 80 to 90% of the large hydrophobic side-chains dominating the internal core were correctly predicted, versus 30 to 40% for most current methods. The predictions' main errors were in surface residues poorly constrained by packing and small residues with greater steric freedom and hydrogen bonding interactions, which were not included in the program's potential function. van der Waals interactions appear to be the supreme determinant of the arrangement of side-chains in the core, enforcing a unique allowed packing that in every case so far examined matches the native structure.     

Improved side-chain prediction accuracy using an ab initio potential energy function and a very large rotamer library

Accurate prediction of the placement and comformations of protein side chains given only the backbone trace has a wide range of uses in protein design, structure prediction, and functional analysis. Prediction has most often relied on discrete rotamer libraries so that rapid fitness of side-chain rotamers can be assessed against some scoring function. Scoring functions are generally based on experimental parameters from small-molecule studies or empirical parameters based on determined protein structures. Here, we describe the NCN algorithm for predicting the placement of side chains. A predominantly first-principles approach was taken to develop the potential energy function incorporating van der Waals and electrostatics based on the OPLS parameters, and a hydrogen bonding term. The only empirical knowledge used is the frequency of rotameric states from the PDB. The rotamer library includes nearly 50,000 rotamers, and is the most extensive discrete library used to date. Although the computational time tends to be longer than most other algorithms, the overall accuracy exceeds all algorithms in the literature when placing rotamers on an accurate backbone trace. Considering only the most buried residues, 80% of the total residues tested, the placement accuracy reaches 92% for chi(1), and 83% for chi(1 + 2), and an overall RMS deviation of 1 A. Additionally, we show that if information is available to restrict chi(1) to one rotamer well, then this algorithm can generate structures with an average RMS deviation of 1.0 A for all heavy side-chains atoms and a corresponding overall chi(1 + 2) accuracy of 85.0%.     

Analysis of the relationship between side-chain conformation and secondary structure in globular proteins

The relationship between the preferred side-chain dihedral angles and the secondary structure of a residue was examined. The structures of 61 proteins solved to a resolution of 2.0 A (1 A = 0.1 nm) or better were analysed using a relational database to store the information. The strongest feature observed was that the chi 1 distribution for most side-chains in an alpha-helix showed an absence of the g- conformation and a shift towards the t conformation when compared to the non-alpha/beta structures. The exceptions to this tendency were for short polar side-chains that form hydrogen bonds with the main-chain which prefer g+. Shifts in the chi 1 preferences for residues in the beta-sheet were observed. Other side-chain dihedral angles (chi 2, chi 3, chi 4) were found to be influenced by the main-chain. This paper presents more accurate distributions for the side-chain dihedral angles which were obtained from the increased number of proteins determined to high resolution. The means and standard deviations for chi 1 and chi 2 angles are presented for all residues according to the secondary structure of the main-chain. The means and standard deviations are given for the most popular conformations for side-chains in which chi 3 and chi 4 rotations affect the position of C atoms.     

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.     

The penultimate rotamer library

All published rotamer libraries contain some rotamers that exhibit impossible internal atomic overlaps if built in ideal geometry with all hydrogen atoms. Removal of uncertain residues (mainly those with B-factors >/=40 or van der Waals overlaps >/=0.4 A) greatly improves the clustering of rotamer populations. Asn, Gln, or His side chains additionally benefit from flipping of their planar terminal groups when required by atomic overlaps or H-bonding. Sensitivity to skew and to the boundaries of chi angle bins is avoided by using modes rather than traditional mean values. Rotamer definitions are listed both as the modal values and in a preferred version that maximizes common atoms between related rotamers. The resulting library shows significant differences from previous ones, differences validated by considering the likelihood of systematic misfitting of models to electron density maps and by plotting changes in rotamer frequency with B-factor. Few rotamers now show atomic overlaps in ideal geometry; those overlaps are relatively small and can be understood in terms of bond angle distortions compensated by favorable interactions. The new library covers 94.5% of examples in the highest quality protein data with 153 rotamers and can make a significant contribution to improving the accuracy of new structures. Proteins 2000;40:389-408.     

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.     

A consistent set of statistical potentials for quantifying local side-chain and backbone interactions

The frequencies of occurrence of atom arrangements in high-resolution protein structures provide some of the most accurate quantitative measures of interaction energies in proteins. In this report we extend our development of a consistent set of statistical potentials for quantifying local interactions between side-chains and the polypeptide backbone, as well as nearby side-chains. Starting with phi/psi/chi1 propensities that select for optimal interactions of the 20 amino acid side-chains with the 2 flanking peptide bonds, the following 3 new terms are added: (1) a distance-dependent interaction between the side-chain at i and the carbonyl oxygens and amide protons of the peptide units at i +/- 2, i +/- 3, and i +/- 4; (2) a distance-dependent interaction between the side-chain at position i and side-chains at positions i + 1 through i + 4; and (3) an orientation-dependent interaction between the side-chain at position i and side-chains at i + 1 through i + 4. The relative strengths of these 4 pseudo free energy terms are estimated by the average information content of each scoring matrix and by assessing their performance in a simple fragment threading test. They vary from -0.4 - -0.5 kcal/mole per residue for phi/psi/chi1 propensities to a range of -0.15 - -0.6 kcal/mole per residue for each of the other 3 terms. The combined energy function, containing no interactions between atoms more than 4 residues apart, identifies the correct structural fragment for randomly selected 15 mers over 40% of the time, after searching through 232,000 alternative conformations. For 14 out of 20 sets of all-atom Rosetta decoys analyzed, the native structure has a combined score lower than any of the 1700-1900 decoy conformations. The ability of this energy function to detect energetically important details of local structure is demonstrated by its power to distinguish high-resolution crystal structures from NMR solution structures.     

Protonate3D: assignment of ionization states and hydrogen coordinates to macromolecular structures

A new method, called Protonate3D, is presented for the automated prediction of hydrogen coordinates given the 3D coordinates of the heavy atoms of a macromolecular structure. Protonate3D considers side-chain "flip," rotamer, tautomer, and ionization states of all chemical groups, ligands, and solvent, provided suitable templates are available in a parameter file. The energy model includes van der Waals, Coulomb, solvation, rotamer, tautomer, and titration effects. The results of computational validation experiments suggest that Protonate3D can accurately predict the location of hydrogen atoms in macromolecular structures.     

High-resolution solution structure of reduced French bean plastocyanin and comparison with the crystal structure of poplar plastocyanin

The three-dimensional solution structure of reduced (CuI) plastocyanin from French bean leaves has been determined by distance geometry and restrained molecular dynamics methods using constraints obtained from 1H n.m.r. (nuclear magnetic resonance) spectroscopy. A total of 1244 experimental constraints were used, including 1120 distance constraints, 103 dihedral angle constraints and 21 hydrogen bond constraints. Stereospecific assignments were made for 26 methylene groups and the methyls of 11 valines. Additional constraints on copper co-ordination were included in the restrained dynamics calculations. The structures are well defined with average atomic root-mean-square deviations from the mean of 0.45 A for all backbone heavy atoms and 1.08 A for side-chain heavy atoms. French bean plastocyanin adopts a beta-sandwich structure in solution that is similar to the X-ray structure of reduced poplar plastocyanin; the average atomic root-mean-square difference between 16 n.m.r. structures and the X-ray structure is 0.76 A for all backbone heavy atoms. The conformations of the side-chains that constitute the hydrophobic core of French bean plastocyanin are very well defined. Of 47 conserved residues that populate a single chi 1 angle in solution, 43 have the same rotamer in the X-ray structure. Many surface side-chains adopt highly preferred conformations in solution, although the 3J alpha beta coupling constants often indicate some degree of conformational averaging. Some surface side-chains are disordered in both the solution and crystal structures of plastocyanin. There is a striking correlation between measures of side-chain disorder in solution and side-chain temperature factors in the X-ray structure. Side-chains that form a distinctive acidic surface region, believed to be important in binding other electron transfer proteins, appear to be disordered. Fifty backbone amide protons form hydrogen bonds to carbonyls in more than 60% of the n.m.r. structures; 45 of these amide protons exchange slowly with solvent deuterons. Ten hydrogen bonds are formed between side-chain and backbone atoms, eight of which are correlated with decreased proton exchange. Of the 60 hydrogen bonds formed in French bean plastocyanin, 56 occur in the X-ray structure of the poplar protein; two of the missing hydrogen bonds are absent as a result of mutations. It appears that molecular dynamics refinement of highly constrained n.m.r. structures allows accurate prediction of the pattern of hydrogen bonding.     

Protein-protein docking predictions for the CAPRI experiment

We predicted structures for all seven targets in the CAPRI experiment using a new method in development at the time of the challenge. The technique includes a low-resolution rigid body Monte Carlo search followed by high-resolution refinement with side-chain conformational changes and rigid body minimization. Decoys (approximately 10(6) per target) were discriminated using a scoring function including van der Waals and solvation interactions, hydrogen bonding, residue-residue pair statistics, and rotamer probabilities. Decoys were ranked, clustered, manually inspected, and selected. The top ranked model for target 6 predicted the experimental structure to 1.5 A RMSD and included 48 of 65 correct residue-residue contacts. Target 7 was predicted at 5.3 A RMSD with 22 of 37 correct residue-residue contacts using a homology model from a known complex structure. Using a preliminary version of the protocol in round 1, target 1 was predicted within 8.8 A although few contacts were correct. For targets 2 and 3, the interface locations and a small fraction of the contacts were correctly identified.     

Computing van der Waals energies in the context of the rotamer approximation

The rotamer approximation states that protein side-chain conformations can be described well using a finite set of rotational isomers. This approximation is often applied in the context of computational protein design and structure prediction to reduce the complexity of structural sampling. It is an effective way of reducing the structure space to the most relevant conformations. However, the appropriateness of rotamers for sampling structure space does not imply that a rotamer-based energy landscape preserves any of the properties of the true continuous energy landscape. Specifically, because the energy of a van der Waals interaction can be very sensitive to small changes in atomic separation, meaningful van der Waals energies are particularly difficult to calculate from rotamer-based structures. This presents a problem for computational protein design, where the total energy of a given structure is often represented as a sum of precalculated rigid rotamer self and pair contributions. A common way of addressing this issue is to modify the van der Waals function to reduce its sensitivity to atomic position, but excessive modification may result in a strongly nonphysical potential. Although many different van der Waals modifications have been used in protein design, little is known about which performs best, and why. In this paper, we study 10 ways of computing van der Waals energies under the rotamer approximation, representing four general classes, and compare their performance using a variety of metrics relevant to protein design and native-sequence repacking calculations. Scaling van der Waals radii by anywhere from 85 to 95% gives the best performance. Linearizing and capping the repulsive portion of the potential can give additional improvement, which comes primarily from getting rid of unrealistically large clash energies. On the other hand, continuously minimizing individual rotamer pairs prior to evaluating their interaction works acceptably in native-sequence repacking, but fails in protein design. Additionally, we show that the problem of predicting relevant van der Waals energies from rotamer-based structures is strongly nonpairwise decomposable and hence further modifications of the potential are unlikely to give significant improvement.     

Distributions of water around amino acid residues in proteins

The atomic co-ordinates from 16 high-resolution (less than or equal to 1.7 A = 0.1 nm), non-homologous proteins have been used to study the distributions of water molecule sites around the 20 different amino acid residues. The proportion of residues whose main-chain atoms are in contact with water molecules was fairly constant (between 40% and 60%), irrespective of the nature of the side-chain. However, the proportion of residues whose side-chain atoms were in contact with water molecules showed a clear (inverse) correlation with the hydrophobicity of the residue, being as low as 14% for leucine and isoleucine but greater than 80% for asparagine and arginine. Despite the problems in determining accurate water molecule sites from X-ray diffraction data and the complexity of the protein surface, distinct non-random distributions of water molecules were found. These hydration patterns are consistent with the expected stereochemistry of the potential hydrogen-bonding sites on the polar side-chains. The water molecules around apolar side-chains lie predominantly at van der Waals' contact distances, but most of these have a primary, shorter contact with a neighbouring polar atom. Further analysis of these distributions, combined with energy minimization techniques, should lead to improved modelling of protein structures, including their primary shells of hydration.     

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.     

An analysis of incorrectly folded protein models. Implications for structure predictions

Proteins with homologous amino acid sequences have similar folds and it has been assumed that an unknown three-dimensional structure can be obtained from a known homologous structure by substituting new side-chains into the polypeptide chain backbone, followed by relatively small adjustment of the model. To examine this approach of structure prediction and, more generally, to isolate the characteristics of native proteins, we constructed two incorrectly folded protein models. Sea-worm hemerythrin and the variable domain of mouse immunoglobulin K-chain, two proteins with no sequence homology, were chosen for study; the former is composed of a bundle of four alpha-helices and the latter consists of two 4-stranded beta-sheets. Using an automatic computer procedure, hemerythrin side-chains were substituted into the immunoglobulin domain and vice versa. The structures were energy-minimized with the program CHARMM and the resulting structures compared with the correctly folded forms. It was found that the incorrect side-chains can be incorporated readily into both types of structures (alpha-helices, beta-sheets) with only small structural adjustments. After constrained energy-minimization, which led to an average atomic co-ordinate shift of no more than 0.7 to 0.9 A, the incorrectly folded models arrived at potential energy values comparable to those of the correct structures. Detailed analysis of the energy results shows that the incorrect structures have less stabilizing electrostatic, van der Waals' and hydrogen-bonding interactions. The difference is particularly pronounced when the electrostatic and van der Waals' energy terms are calculated by modified equations that include an approximate representation of solvent effects. The incorrectly folded structures also have a significantly larger solvent-accessible surface and a greater fraction of non-polar side-chain atoms exposed to solvent. Examination of their interior shows that the packing of side-chains at the secondary structure interfaces, although corresponding to sterically allowed conformations, deviates from the characteristics found in normal proteins. The analysis of incorrectly folded structures has made it clear that the absence of bad non-bonded contacts, though necessary, is not sufficient to demonstrate the validity of model-built structures and that modeling of homologous structures has to be accompanied by a thorough quantitative evaluation of the results. Further, certain features that characterize native proteins are made evident by their absence in misfolded models.     

Molecular conformation of ascidiacyclamide, a cytotoxic cyclic peptide from Ascidian: X-ray analyses of its free form and solvate crystals.

In order to investigate the conformational variation of ascidiacyclamide, a cytotoxic cyclic peptide from marine tunicate Ascidian, single crystals were prepared from ethanol and aqueous ethanol solutions as its free form (crystal I) and H2O/0.5 C2H5OH solvate (crystal II), respectively, and were determined by the x-ray diffraction method. Crystal I showed a pseudo C2-symmetric saddle-shaped rectangular conformation. Similar conformations were also observed in crystal II, where there were two crystallographically independent C2-symmetric molecules (named Mol-A and -B) per asymmetric unit. Mol-A and -B included H2O and H2O/C2H5OH solvents within their ring structures, respectively. These water and ethanol molecules were located on the crystallographic dyad axes, and were stabilized by the van der Waals contacts (including hydrogen bonds) with the polar-ring N atoms and nonpolar D-Val side-chain atoms. The conformational characteristics of ascidiacyclamide and its fluctuation/variation were discussed based on the present and previously reported x-ray results.     

Side-chain conformational entropy in protein unfolded states

The largest force disfavoring the folding of a protein is the loss of conformational entropy. A large contribution to this entropy loss is due to the side-chains, which are restricted, although not immobilized, in the folded protein. In order to accurately estimate the loss of side-chain conformational entropy that occurs upon folding it is necessary to have accurate estimates of the amount of entropy possessed by side-chains in the ensemble of unfolded states. A new scale of side-chain conformational entropies is presented here. This scale was derived from Monte Carlo computer simulations of small peptide models. It is demonstrated that the entropies are independent of host peptide length. This new scale has the advantage over previous scales of being more precise with low standard errors. Better estimates are obtained for long (e.g., Arg and Lys) and rare (e.g., Trp and Met) side-chains. Excellent agreement with previous side-chain entropy scales is achieved, indicating that further advancements in accuracy are likely to be small at best. Strikingly, longer side-chains are found to possess a smaller fraction of the theoretical maximum entropy available than short side-chains. This indicates that rotations about torsions after chi(2) are significantly affected by side-chain interactions with the polypeptide backbone. This finding invalidates previous assumptions about side-chain-backbone interactions. Proteins 2000;40:443-450.     

Structure-function relationships of a membrane pore forming toxin revealed by reversion mutagenesis

Cyt2Aa1 is a haemolytic membrane pore forming toxin produced by Bacillus thuringiensis subsp. kyushuensis. To investigate membrane pore formation by this toxin, second-site revertants of an inactive mutant toxin Cyt2Aa1-I150A were generated by random mutagenesis using error-prone PCR. The decrease in side chain length caused by the replacement of isoleucine by alanine at position 150 in the alphaD-beta4 loop results in the loss of important van der Waals contacts that exist in the native protein between I150 and K199 and L203 on alphaE. 28 independent revertants of I150A were obtained and their relative toxicity can be explained by the position of the residue in the structure and the effect of the mutation on side-chain interactions. Analysis of these revertants revealed that residues on alphaA, alphaB, alphaC, alphaD and the loops between alphaA and alphaB, alphaD and beta5, beta6 and beta7 are important in pore formation. These residues are on the surface of the molecule suggesting that they may participate in membrane binding and toxin oligomerization. Changing the properties of the amino acid side-chains of these residues could affect the conformational changes required to transform the water-soluble toxin into the membrane insertion competent state.     

Side-chain conformations in an unfolded protein: chi1 distributions in denatured hen lysozyme determined by heteronuclear 13C, 15N NMR spectroscopy.

Using a 13C and 15N-labelled sample, multi-dimensional heteronuclear NMR techniques have been carried out to characterise hen lysozyme denatured in 8 M urea at pH 2.0. The measurement of 3J(C',Cgamma) and 3J(N,Cgamma) coupling constants has enabled side-chain chi1 torsion angle populations to be probed in the denatured polypeptide chain. Analysis of the coupling constant data has allowed the relative populations of the three staggered rotamers about chi1 to be defined for 51 residues. The amino acids can broadly be divided into five classes that show differing side-chain conformational preferences in the denatured state. These range from a strong preference for the -60 degrees chi1 rotamer for methionine and leucine (74-79 % population) to a favouring of the +60 degrees chi1 rotamer for threonine (67 % population). The differences in behaviour reflect the steric and electrostatic characteristics of the side-chains concerned. A close agreement is seen between the chi1 populations calculated from the experimental coupling constant data and predictions from the statistical model for a random coil that uses the chi1 torsion angle distributions in a data base of native protein structures. Short-range interactions therefore dominate in determining the local conformational properties of side-chains in a denatured protein. Deviations are, however, observed for many of the aromatic residues involved in hydrophobic clusters within the denatured protein. For these residues the effects of additional non-local interactions in the clusters presumably play a major role in determining the chi1 preferences.     

Constrained geometric simulation of diffusive motion in proteins

We describe a new computational method, FRODA (framework rigidity optimized dynamic algorithm), for exploring the internal mobility of proteins. The rigid regions in the protein are first determined, and then replaced by ghost templates which are used to guide the movements of the atoms in the protein. Using random moves, the available conformational phase space of a 100 residue protein can be well explored in approximately 10-100 min of computer time using a single processor. All of the covalent, hydrophobic and hydrogen bond constraints are maintained, and van der Waals overlaps are avoided, throughout the simulation. We illustrate the results of a FRODA simulation on barnase, and show that good agreement is obtained with nuclear magnetic resonance experiments. We additionally show how FRODA can be used to find a pathway from one conformation to another. This directed dynamics is illustrated with the protein dihydrofolate reductase.