Database algorithm for generating protein backbone and side-chain co-ordinates from a C alpha trace application to model building and detection of co-ordinate errors

Homology modeling by the ICM method

Five models have been built by the ICM method for the Comparative Modeling section of the Meeting on the Critical Assessment of Techniques for Protein Structure Prediction. The targets have homologous proteins with known three-dimensional structure with sequence identity ranging from 25 to 77%. After alignment of the target sequence with the related three-dimensional structure, the modeling procedure consists of two subproblems: side-chain prediction and loop prediction. The ICM method approaches these problems with the following steps: (1) a starting model is created based on the homologous structure with the conserved portion fixed and the nonconserved portion having standard covalent geometry and free torsion angles; (2) the Biased Probability Monte Carlo (BPMC) procedure is applied to search the subspaces of either all the nonconservative side-chain torsion angles or torsion angles in a loop backbone and surrounding side chains. A special algorithm was designed to generate low-energy loop deformations. The BPMC procedure globally optimizes the energy function consisting of ECEPP/3 and solvation energy terms. Comparison of the predictions with the NMR or crystallographic solutions reveals a high proportion of correctly predicted side chains. The loops were not correctly predicted because imprinted distortions of the backbone increased the energy of the near-native conformation and thus made the solution unrecognizable. Interestingly, the energy terms were found to be reliable and the sampling of conformational space sufficient. The implications of this finding for the strategies of future comparative modeling are discussed.

Confronting the problem of interconnected structural changes in the comparative modeling of proteins

Comparative models of three proteins have been built using a variety of computational methods, heavily supplemented by visual inspection. We consider the accuracy obtained to be worse than expected. A careful analysis of the models shows that a major reason for the poor results is the interconnectedness of the structural differences between the target proteins and the template structures they were modeled from. Side chain conformations are often determined by details of the structure remote in the sequence, and can be influenced by relatively small main chain changes. Almost all of the regions of substantial main chain conformational change interact with at least one other such region, so that they often cannot be modeled independently. Visual inspection is sometimes effective in correcting errors in sequence alignment and in spotting when an alternative template structure is more appropriate. We expect some improvements in the near future through the development of structure-based sequence alignment tools, side chain interconnectedness rotamer choice algorithms, and a better understanding of the context sensitivity of conformational features.

The use of position-specific rotamers in model building by homology

In this study we concentrate on replacing side chains as a subtask of model building by homology. Two problems arise. How to determine potential low energy rotamers? And how to avoid the combinatorial explosion that results from the combination of many residues for which multiple good rotamers are predicted? We attempt to solve these problems by choosing position-specific rather than generalized rotamers and by sorting the residues that have to be modelled as a function of their freedom in rotamer space. The practical advantages of our method are the quality of the models for cases of high backbone similarity, the small amount of human intervention needed, and the fact that the method automatically estimates the reliability with which each residue has been modeled. Other methods described in this issue are probably more suitable if large backbone rearrangements or loop insertions and deletions need to be modeled.

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 A RMS deviation (RMSD) with greater than 80% of the chi 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 A, the prediction on buried side chain is accurate with an RMS error of 1.8 A and approximately 70% of the chi angles correctly predicted. When the backbone RMSD is larger, in the range of 1.6-1.8 A, the prediction quality is still significantly better than random, with RMS error at 2.2 A on the buried side chains and 60% accuracy on chi 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 A), side-chain packing methods work well. When sequence identity is between 30-50%, reflecting a backbone RMS error of 1-2 A, 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 A), 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.

Repacking protein cores with backbone freedom: structure prediction for coiled coils

Progress in homology modeling and protein design has generated considerable interest in methods for predicting side-chain packing in the hydrophobic cores of proteins. Present techniques are not practically useful, however, because they are unable to model protein main-chain flexibility. Parameterization of backbone motions may represent a general and efficient method to incorporate backbone relaxation into such fixed main-chain models. To test this notion, we introduce a method for treating explicitly the backbone motions of alpha-helical bundles based on an algebraic parameterization proposed by Francis Crick in 1953 [Crick, F. H. C. (1953) Acta Crystallogr. 6, 685-689]. Given only the core amino acid sequence, a simple calculation can rapidly reproduce the crystallographic main-chain and core side-chain structures of three coiled coils (one dimer, one trimer, and one tetramer) to within 0.6-A root-mean-square deviations. The speed of the predictive method [approximately 3 min per rotamer choice on a Silicon Graphics (Mountain View, CA) 4D/35 computer] permits it to be used as a design tool.

Modeling mutations and homologous proteins

A protein sequence with at lease 40% identity to a known structure can now be modelled automatically, with an accuracy approaching that o fa low-resolution X-ray structure or a medium-resolution nuclear magnetic resonance structure. In general, these models have goods stereochemistry and an overall structural accuracy that is as high as the similarity between the template and the actual structure being predicted. As a result, the number of sequences that can be modelled is an order of magnitude larger then the number of experimentally determined protein structures. In addition, evaluation techniques are available that can estimated errors in different regions of the model. Thus, the number of applications where homology modelling is proving useful is growing rapidly.

Building proteins from C alpha coordinates using the dihedral probability grid Monte Carlo method

Dihedral probability grid Monte Carlo (DPG-MC) is a general-purpose method of conformational sampling that can be applied to many problems in peptide and protein modeling. Here we present the DPG-MC method and apply it to predicting complete protein structures from C alpha coordinates. This is useful in such endeavors as homology modeling, protein structure prediction from lattice simulations, or fitting protein structures to X-ray crystallographic data. It also serves as an example of how DPG-MC can be applied to systems with geometric constraints. The conformational propensities for individual residues are used to guide conformational searches as the protein is built from the amino-terminus to the carboxyl-terminus. Results for a number of proteins show that both the backbone and side chain can be accurately modeled using DPG-MC. Backbone atoms are generally predicted with RMS errors of about 0.5 A (compared to X-ray crystal structure coordinates) and all atoms are predicted to an RMS error of 1.7 A or better.

A self consistent mean field approach to simultaneous gap closure and side-chain positioning in homology modelling

A new computational procedure which simultaneously provides gap closure and side-chain positioning in homology modelling is described. It uses a database search scheme to generate fragments to model gaps, a rotamer library to define side-chain conformations, and iteratively refines a conformational matrix CM, such that its elements CM(i,j,o) and CM(i,j,k) give the probabilities that the backbone of residue i adopts the conformation described by fragment j and that its side-chain adopts the conformation of its possible rotamer k. Each residue experiences the average of all possible environments, weighted by their respective probabilities. The method converges, thereby deserving the name of 'self consistent mean field' approach.

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.

Cavities and packing at protein interfaces

An analysis of internal packing defects or "cavities" (both empty and water-containing) within protein structures has been undertaken and includes 3 cavity classes: within domains, between domains, and between protein subunits. We confirm several basic features common to all cavity types but also find a number of new characteristics, including those that distinguish the classes. The total cavity volume remains only a small fraction of the total protein volume and yet increases with protein size. Water-filled "cavities" possess a more polar surface and are typically larger. Their constituent waters are necessary to satisfy the local hydrogen bonding potential. Cavity-surrounding atoms are observed to be, on average, less flexible than their environments. Intersubunit and interdomain cavities are on average larger than the intradomain cavities, occupy a larger fraction of their resident surfaces, and are more frequently water-filled. We observe increased cavity volume at domain-domain interfaces involved with shear type domain motions. The significance of interfacial cavities upon subunit and domain shape complementarity and the protein docking problem, as well as in their structural and functional role in oligomeric proteins, will be discussed. The results concerning cavity size, polarity, solvation, general abundance, and residue type constituency should provide useful guidelines for protein modeling and design.

Homology modeling of the Abl-SH3 domain

A tertiary structure model of the Abl-SH3 domain is predicted by using homology modeling techniques coupled to molecular dynamics simulations. Two template proteins were used, Fyn-SH3 and Spc-SH3. The refined model was extensively checked for errors using criteria based on stereochemistry, packing, solvation free-energy, accessible surface areas, and contact analyses. The different checking methods do not totally agree, as each one evaluates a different characteristic of protein structures. Several zones of the protein are more susceptible to incorporating errors. These include residues 13, 15, 35, 39, 45, 46, 50, and 60. An interesting finding is that the measurement of the C alpha chirality correlated well with the rest of the criteria, suggesting that this parameter might be a good indicator of correct local conformation. Deviations of more than 4 degrees may be indicative of poor local structure.

The protein folding problem: finding a few minimums in a near infinite space

Folding a protein from only a knowledge of its amino acid sequence is a formidable many-body problem. Since it is computationally impossible to test all possible atomic conformations to determine the global minimum representing the compact state, methods need to be developed to sample only a small part of the configurational space and yet delineate the free energy optimum (or nearly so). This article largely reviews such techniques as applied by the authors and their colleagues.

Parser for protein folding units

General patterns of protein structural organization have emerged from studies of hundreds of structures elucidated by X-ray crystallography and nuclear magnetic resonance. Structural units are commonly identified by visual inspection of molecular models using qualitative criteria. Here, we propose an algorithm for identification of structural units by objective, quantitative criteria based on atomic interactions. The underlying physical concept is maximal interactions within each unit and minimal interaction between units (domains). In a simple harmonic approximation, interdomain dynamics is determined by the strength of the interface and the distribution of masses. The most likely domain decomposition involves units with the most correlated motion, or largest interdomain fluctuation time. The decomposition of a convoluted 3-D structure is complicated by the possibility that the chain can cross over several times between units. Grouping the residues by solving an eigenvalue problem for the contact matrix reduces the problem to a one-dimensional search for all reasonable trial bisections. Recursive bisection yields a tree of putative folding units. Simple physical criteria are used to identify units that could exist by themselves. The units so defined closely correspond to crystallographers' notion of structural domains. The results are useful for the analysis of folding principles, for modular protein design and for protein engineering.

A statistical analysis of side-chain conformations in proteins: comparison with ECEPP predictions

A comparison of the statistical distributions of side-chain conformations of 17 amino acids (Gly, Ala, and Pro excluded), observed in 63 nonhomologous globular proteins (covering 10,832 residues), is made with similar distributions calculated from the low-energy conformational states for the same amino acids (blocked with acetyl and N-methylamide groups at the N- and C-termini, respectively) obtained by Vásquez et al. [(1983), Macromolecules 16, 1043-1049] using the ECEPP/2 force field. Those residues (i) with linear side chains (Arg, Lys, Met, Cys, Ser), or those that are unbranched through the gamma-carbon atom (Glu, Gln) show good agreement, whereas (ii) those with side chains that are branched at C beta or C gamma show poor agreement with ECEPP calculations. A possible explanation for this is shown to be the greater tendency for side-chain atoms in class (ii) to interact with the backbone and/or adjacent side chains. Accordingly, ECEPP/3 calculations, carried out after elongating the backbone chain of the model peptide unit (by adding three Ala residues on each side of the central residue, and then blocking the termini as before), result in distributions that are often closer to the observed side-chain distributions. The implications of these results for the relative importance of short-range versus long-range interactions in determining protein structure are discussed.

A molecular dynamics approach for the generation of complete protein structures from limited coordinate data

Generation of full protein coordinates from limited information, e.g., the C alpha coordinates, is an important step in protein homology modeling and structure determination, and molecular dynamics (MD) simulations may prove to be important in this task. We describe a new method, in which the protein backbone is built quickly in a rather crude way and then refined by minimization techniques. Subsequently, the side chains are positioned using extensive MD calculations. The method is tested on two proteins, and results compared to proteins constructed using two other MD-based methods. In the first method, we supplemented an existing backbone building method with a new procedure to add side chains. The second one largely consists of available methodology. The constructed proteins are compared to the corresponding X-ray structures, which became available during this study, and they are in good agreement (backbone RMS values of 0.5-0.7 A, and all-atom RMS values of 1.5-1.9 A). This comparative study indicates that extensive MD simulations are able, to some extent, to generate details of the native protein structure, and may contribute to the development of a standardized methodology to predict reliably (parts of) protein structures when only partial coordinate data are available.

Knowledge-based protein modeling

Knowledge, both from the three-dimensional structures of homologous proteins and from the general analysis of protein structure, is of value in modeling a protein of known sequence but unknown structure. While many models are still constructed at least in part by manual methods on graphics devices, automated procedures have come into greater use. These procedures include those that assemble fragments of structure from other known structures and those that derive coordinates for the model from the satisfaction of restraints placed on atomic positions.

Homologous modeling of the lysosomal protective protein/carboxypeptidase L: structural and functional implications of mutations identified in galactosialidosis patients

The deficiency of the lysosomal protective protein/carboxypeptidase L (CARB L) causes the lysosomal storage disorder, galactosialidosis, characterized by neuraminidase and beta-galactosidase deficiencies in patients' cells. The three enzymes form a complex inside the lysosome, and the neuraminidase and beta-galactosidase deficiencies are secondary to CARB L deficiency. Sequence similarity and common enzymological properties suggest that the protomeric tertiary structure of CARB L is conserved within a family of serine carboxypeptidases which includes the yeast carboxypeptidase Y, killer expression I gene product and several plant carboxypeptidases. We used this homology to build a model of the CARB L structure based on the recently published X-ray atomic coordinates of the wheat carboxypeptidase II (CPDW-II) which shares 32% primary structure identity with CARB L. Small insertions and deletions were accommodated into the model structure by energy minimization using the DREIDING II force field. The C alpha atomic coordinates of the final CARB L model have a RMS shift of 1.01 A compared to the corresponding conserved residues in the CPDW-II template structure. The correct orientation of the homologous catalytic triad residues Ser150, His429 and Asp392, the potential energy calculations and the distribution of hydrophobic and hydrophillic residues in the structure all support the validity of the CARB L model. Most missense mutations identified in galactosialidosis patients were located in secondary structural elements except for the Tyr211-->Asn mutation which is in a loop. The other mutant residues have their side chains deeply buried in the central beta-sheet of the model structure except for the Phe412-->Val mutation which is located in the dimer interface. The predicted effects of specific mutations on CARB L structural stability correlates well with recently published transient expression studies of mutant CARB L (Shimmoto, M. et al., J. Clin. Invest., 91:2393-2399, 1993).

Finding the lowest free energy conformation of a protein is an NP-hard problem: proof and implications

The protein folding problem and the notion of NP-completeness and NP-hardness are discussed. A lattice model is suggested to capture the essence of protein folding. For this model we present a proof that finding the lowest free energy conformation belongs to the class of NP-hard problems. The implications of the proof are discussed and we suggest that the natural folding process cannot be considered as a search for the global free energy minimum. However, we suggest an explanation as to why, for many proteins, the native functional conformation may coincide with the lowest free energy conformation.

Calculation of protein backbone geometry from alpha-carbon coordinates based on peptide-group dipole alignment

An algorithm is proposed for the conversion of a virtual-bond polypeptide chain (connected C alpha atoms) to an all-atom backbone, based on determining the most extensive hydrogen-bond network between the peptide groups of the backbone, while maintaining all of the backbone atoms in energetically feasible conformations. Hydrogen bonding is represented by aligning the peptide-group dipoles. These peptide groups are not contiguous in the amino acid sequence. The first dipoles to be aligned are those that are both sufficiently close in space to be arranged in approximately linear arrays termed dipole paths. The criteria used in the construction of dipole paths are: to assure good alignment of the greatest possible number of dipoles that are close in space; to optimize the electrostatic interactions between the dipoles that belong to different paths close in space; and to avoid locally unfavorable amino acid residue conformations. The equations for dipole alignment are solved separately for each path, and then the remaining single dipoles are aligned optimally with the electrostatic field from the dipoles that belong to the dipole-path network. A least-squares minimizer is used to keep the geometry of the alpha-carbon trace of the resulting backbone close to that of the input virtual-bond chain. This procedure is sufficient to convert the virtual-bond chain to a real chain; in applications to real systems, however, the final structure is obtained by minimizing the total ECEPP/2 (empirical conformational energy program for peptides) energy of the system, starting from the geometry resulting from the solution of the alignment equations. When applied to model alpha-helical and beta-sheet structures, the algorithm, followed by the ECEPP/2 energy minimization, resulted in an energy and backbone geometry characteristic of these alpha-helical and beta-sheet structures. Application to the alpha-carbon trace of the backbone of the crystallographic 5PTI structure of bovine pancreatic trypsin inhibitor, followed by ECEPP/2 energy minimization with C alpha-distance constraints, led to a structure with almost as low energy and root mean square deviation as the ECEPP/2 geometry analog of 5PTI, the best agreement between the crystal and reconstructed backbone being observed for the residues involved in the dipole-path network.

A structural model for the nucleotide binding domains of the flavocytochrome b-245 beta-chain

NADPH is a system in phagocytic cells that generates O2- and hydrogen peroxide in the endocytic vacuole, both of which are important for killing of the engulfed microbe. Dysfunction of this oxidase results in the syndrome of chronic granulomatous disease, characterized by a profound predisposition to bacterial and fungal infections. A flavocytochrome b is the site of most of the mutations causing this syndrome. The FAD and NADPH binding sites have been located on the beta subunit of this molecule, the C-terminal half of which showed weak sequence similarity to other reductases, including the ferredoxin-NADP reductase (FNR) of known structure. This enabled us to build a model of the nucleotide binding domains of the flavocytochrome using this structure as a template. The model was built initially using a novel automatic modeling method based on distance-matrix projection and then refined using energy minimization with appropriate side-chain torsional constraints. The resulting model rationalized much of the observed sequence conservation and identified a large insertion as a potential regulatory domain. It confirms the inclusion of the neutrophil flavocytochrome b-245 (Cb-245) as a member of the FNR family of reductases and strongly supports its function as the proximal electron transporting component of the NADPH oxidase.

De novo and inverse folding predictions of protein structure and dynamics

In the last two years, the use of simplified models has facilitated major progress in the globular protein folding problem, viz., the prediction of the three-dimensional (3D) structure of a globular protein from its amino acid sequence. A number of groups have addressed the inverse folding problem where one examines the compatibility of a given sequence with a given (and already determined) structure. A comparison of extant inverse protein-folding algorithms is presented, and methodologies for identifying sequences likely to adopt identical folding topologies, even when they lack sequence homology, are described. Extension to produce structural templates or fingerprints from idealized structures is discussed, and for eight-membered beta-barrel proteins, it is shown that idealized fingerprints constructed from simple topology diagrams can correctly identify sequences having the appropriate topology. Furthermore, this inverse folding algorithm is generalized to predict elements of supersecondary structure including beta-hairpins, helical hairpins and alpha/beta/alpha fragments. Then, we describe a very high coordination number lattice model that can predict the 3D structure of a number of globular proteins de novo; i.e. using just the amino acid sequence. Applications to sequences designed by DeGrado and co-workers [Biophys. J., 61 (1992) A265] predict folding intermediates, native states and relative stabilities in accord with experiment. The methodology has also been applied to the four-helix bundle designed by Richardson and co-workers [Science, 249 (1990) 884] and a redesigned monomeric version of a naturally occurring four-helix dimer, rop. Based on comparison to the rop dimer, the simulations predict conformations with rms values of 3-4 A from native. Furthermore, the de novo algorithms can assess the stability of the folds predicted from the inverse algorithm, while the inverse folding algorithms can assess the quality of the de novo models. Thus, the synergism of the de novo and inverse folding algorithm approaches provides a set of complementary tools that will facilitate further progress on the protein-folding problem.

New programs for protein tertiary structure prediction

Prediction of protein tertiary structure remains an unsolved problem in molecular biology, but a solution to this problem is extremely important for protein engineering and rational drug design. Recent developments in motif recognition and side chain modeling present the prospect of nearly automatic model building for a large fraction of newly determined protein sequences. We review some of these new algorithms and present preliminary results of their application to the prediction of a structure for fasciclin III, a neural adhesion molecule from Drosophila.

PROGEN: an automated modelling algorithm for the generation of complete protein structures from the alpha-carbon atomic coordinates

A modelling algorithm (PROGEN) for the generation of complete protein atomic coordinates from only the alpha-carbon coordinates is described. PROGEN utilizes an optimal geometry parameter (OGP) database for the positioning of atoms for each amino acid of the polypeptide model. The OGP database was established by examining the statistical correlations between 23 different intra-peptide and inter-peptide geometric parameters relative to the alpha-carbon distances for each amino acid in a library of 19 known proteins from the Brookhaven Protein Database (BPDB). The OGP files for specific amino acids and peptides were used to generate the atomic positions, with respect to alpha-carbons, for main-chain and side-chain atoms in the modelled structure. Refinement of the initial model was accomplished using energy minimization (EM) and molecular dynamics techniques. PROGEN was tested using 60 known proteins in the BPDB, representing a wide spectrum of primary and secondary structures. Comparison between PROGEN models and BPDB crystal reference structures gave r.m.s.d. values for peptide main-chain atoms between 0.29 and 0.76 A, with a grand average of 0.53 A for all 60 models. The r.m.s.d. for all non-hydrogen atoms ranged between 1.44 and 1.93 A for the 60 polypeptide models. PROGEN was also able to make the correct assignment of cis- or trans-proline configurations in the protein structures examined. PROGEN offers a fully automatic building and refinement procedure and requires no special or specific structural considerations for the protein to be modelled.

Reconstruction of protein conformations from estimated positions of the C alpha coordinates

Protein C alpha coordinates are used to accurately reconstruct complete protein backbones and side-chain directions. This work employs potentials of mean force to align semirigid peptide groups around the axes that connect successive C alpha atoms. The algorithm works well for all residue types and secondary structure classes and is stable for imprecise C alpha coordinates. Tests on known protein structures show that root mean square errors in predicted main-chain and C beta coordinates are usually less than 0.3 A. These results are significantly more accurate than can be obtained from competing approaches, such as modeling of backbone conformations from structurally homologous fragments.

Successful prediction of the coiled coil geometry of the GCN4 leucine zipper domain by simulated annealing: comparison to the X-ray structure

The recently solved X-ray structure of the dimerization region ("leucine zipper") of the yeast transcriptional activator GCN4 (O'Shea, E.K., Klemm, J.D., Kim, P.S., Alber, T. Science 254:539-544, 1991) is compared to previously predicted models which had been obtained by a conformational search procedure employing simulated annealing without any knowledge of the crystal coordinates (Nilges, M., Brünger, A.T. Protein Eng. 4:649-659, 1991). During the course of the simulated annealing procedure, the models converged towards the X-ray structure. The averaged root mean square difference between the models and the X-ray structure is 1.26 and 1.75 A for backbone atoms and all nonhydrogen atoms at the dimerization interface, respectively. The local helix-helix crossing angle of the X-ray structure falls within the range predicted by the models; a slight unwinding of the coiled coil toward the N-terminal DNA-binding end of the dimerization region has been correctly predicted. Distance maps between the helices are largely identical. The region around asparagine 20 is asymmetric in the X-structure and in the models. Surface side chain dihedrals showed a large variation in the models although the chi 1, chi 2, chi 3, chi 4 3-fold dihedrals were correctly predicted in 69, 42, 43, and 44% of the cases, respectively. Phenomenological free energies of dimerization of the models show little correlation with the root mean square difference between the models and the X-ray structure.

Application of a directed conformational search for generating 3-D coordinates for protein structures from alpha-carbon coordinates

A directed conformational search algorithm using the program CONGEN (ref. 3), which samples backbone conformers, is described. The search technique uses information from the partially built structures to direct the search process and is tested on the problem of generating a full set of backbone Cartesian coordinates given only alpha-carbon coordinates. The method has been tested on six proteins of known structure, varying in size and classification, and was able to generate the original backbone coordinates with RMSs ranging from 0.30-0.87A for the alpha-carbons and 0.5-0.99A RMSs for the backbone atoms. Cis peptide linkages were also correctly identified. The procedure was also applied to two proteins available with only alpha-carbon coordinates in the Brookhaven Protein Data Bank; thioredoxin (SRX) and triacylglycerol acylhydrolase (TGL). All-atom models are proposed for the backbone of both these proteins. In addition, the technique was applied to randomized coordinates of flavodoxin to assess the effects of irregularities in the data on the final RMS. This study represents the first time a deterministic conformational search was used on such a large scale.

Comprehensive sequence analysis of the 182 predicted open reading frames of yeast chromosome III

With the completion of the first phase of the European yeast genome sequencing project, the complete DNA sequence of chromosome III of Saccharomyces cerevisiae has become available (Oliver, S. G., et al., 1992, Nature 357, 38-46). We have tested the predictive power of computer sequence analysis of the 176 probable protein products of this chromosome, after exclusion of six problem cases. When the results of database similarity searches are pooled with prior knowledge, a likely function can be assigned to 42% of the proteins, and a predicted three-dimensional structure to a third of these (14% of the total). The function of the remaining 58% remains to be determined. Of these, about one-third have one or more probable transmembrane segments. Among the most interesting proteins with predicted functions are a new member of the type X polymerase family, a transcription factor with an N-terminal DNA-binding domain related to GAL4, a "fork head" DNA-binding domain previously known only in Drosophila and in mammals, and a putative methyltransferase. Our analysis increased the number of known significant sequence similarities on chromosome III by 13, to now 67. Although the near 40% success rate of identifying unknown protein function by sequence analysis is surprisingly high, the information gap between known protein sequences and unknown function is expected to widen and become a major bottleneck of genome projects in the near future. Based on the experience gained in this test study, we suggest that the development of an automated computer workbench for protein sequence analysis must be an important item in genome projects.

Fast and simple Monte Carlo algorithm for side chain optimization in proteins: application to model building by homology

An unknown protein structure can be predicted with fair accuracy once an evolutionary connection at the sequence level has been made to a protein of known 3-D structure. In model building by homology, one typically starts with a backbone framework, rebuilds new loop regions, and replaces nonconserved side chains. Here, we use an extremely efficient Monte Carlo algorithm in rotamer space with simulated annealing and simple potential energy functions to optimize the packing of side chains on given backbone models. Optimized models are generated within minutes on a workstation, with reasonable accuracy (average of 81% side chain chi 1 dihedral angles correct in the cores of proteins determined at better than 2.5 A resolution). As expected, the quality of the models decreases with decreasing accuracy of backbone coordinates. If the back-bone was taken from a homologous rather than the same protein, about 70% side chain chi 1 angles were modeled correctly in the core in a case of strong homology and about 60% in a case of medium homology. The algorithm can be used in automated, fast, and reproducible model building by homology.

An ATPase domain common to prokaryotic cell cycle proteins, sugar kinases, actin, and hsp70 heat shock proteins

The functionally diverse actin, hexokinase, and hsp70 protein families have in common an ATPase domain of known three-dimensional structure. Optimal superposition of the three structures and alignment of many sequences in each of the three families has revealed a set of common conserved residues, distributed in five sequence motifs, which are involved in ATP binding and in a putative interdomain hinge. From the multiple sequence alignment in these motifs a pattern of amino acid properties required at each position is defined. The discriminatory power of the pattern is in part due to the use of several known three-dimensional structures and many sequences and in part to the "property" method of generalizing from observed amino acid frequencies to amino acid fitness at each sequence position. A sequence data base search with the pattern significantly matches sugar kinases, such as fuco-, glucono-, xylulo-, ribulo-, and glycerokinase, as well as the prokaryotic cell cycle proteins MreB, FtsA, and StbA. These are predicted to have subdomains with the same tertiary structure as the ATPase subdomains Ia and IIa of hexokinase, actin, and Hsc70, a very similar ATP binding pocket, and the capacity for interdomain hinge motion accompanying functional state changes. A common evolutionary origin for all of the proteins in this class is proposed.

Structure prediction and modelling

Cracking the second fundamental code of molecular biology (how the tertiary structure of a protein is determined by its amino acid sequence) remains an elusive goal. However, the impetus to establish credible approximations, if not a definitive solution to this relationship, has never been greater. In the past year significant progress has been made through a series of novel approaches. This review describes the most important developments and outlines how they can be usefully employed by those whose specialization lies outside the field.

Accurate modeling of protein conformation by automatic segment matching

Segment match modeling uses a data base of highly refined known protein X-ray structures to build an unknown target structure from its amino acid sequence and the atomic coordinates of a few of its atoms (generally only the C alpha atoms). The target structure is first broken into a set of short segments. The data base is then searched for matching segments, which are fitted onto the framework of the target structure. Three criteria are used for choosing a matching data base segment: amino acid sequence similarity, conformational similarity (atomic co-ordinates), and compatibility with the target structure (van der Waals' interactions). The new method works surprisingly well: for eight test proteins ranging in size from 46 to 323 residues, the all-atom root-mean-square deviation of the modeled structures is between 0.93 A and 1.73 A (the average is 1.26 A). Deviations of this magnitude are comparable with those found for protein co-ordinates before and after refinement against X-ray data or for co-ordinates of the same protein in different crystal packings. These results are insensitive to errors in the C alpha positions or to missing C alpha atoms: accurate models can be built with C alpha errors of up to 1 A or by using only half the C alpha atoms. The fit to the X-ray structures is improved significantly by building several independent models based on different random choices and then averaging co-ordinates; this novel concept has general implications for other modeling tasks. The segment match modeling method is fully automatic, yields a complete set of atomic co-ordinates without any human intervention and is efficient (14 s/residue on the Silicon Graphics 4D/25 Personal Iris workstation.

Optimal protocol and trajectory visualization for conformational searches of peptides and proteins

Conformational searches by molecular dynamics and different types of Monte Carlo or build-up methods usually aim to find the lowest-energy conformation. However, this is often misleading, as the energy functions used in conformational calculations are imprecise. For instance, though positions of local minima defined by the repulsive part of the Lennard-Jones potential are usually altered only slightly by functional modification, the relative depths of the minima could change significantly. Thus, the purpose of conformational searches and, correspondingly, performance criteria should be reformulated and appropriate methods found to extract different local minima from the search trajectory and allow visualization in the search space. Attempts at convergence to the lowest-energy structure should be replaced with efforts to visit a maximum number of different local energy minima with energies within a certain range. We use this quantitative criterion consistently to evaluate performances of different search procedures. To utilize information generated in the course of simulation, a "stack" of low energy conformations is created and stored. It keeps track of variables and visit numbers for the best representatives of different conformational families. To visualize the search, projection of multidimensional walks onto a principal plane defined by a set of reference structures is used. With Met-enkephalin as a structural example and a Monte Carlo procedure combined with energy minimization (MCM) as a basic search method, we analyzed the influence on search efficiency of different characteristics as temperature schedules, the step size for variable modification, constrained random step and response mechanisms to search difficulties. Simulated annealing MCM had comparable efficiency with MCM at constant and elevated temperature (about 600 K). Constraining the randomized choice of side-chain chi angles to optimal values (rotamers) on every MCM step did not improve, but rather worsened, the search efficiency. Two low-energy Met-enkephalin conformations with parallel Tyr1 and Phe4 rings, a gamma-turn around the Gly2 residue, and Phe4 and Met5 side-chains forming together a compact hydrophobic cluster were found and are suggested as possible structural candidates for interaction with a receptor or a membrane.

Evaluation of protein models by atomic solvation preference

Important properties of globular proteins, such as the stability of the folded state, depend sensitively on interactions with solvent molecules. An excluded volume approximation to protein-solvent interaction, the solvent contact model, was used to derive atomic solvation preference parameters from a database of known protein structures. The ability of solvation preference to discriminate between correct and incorrect three-dimensional structures for a given sequence, or to identify the correct sequence placement in a given structure, was tested. Backbone co-ordinates were taken from experimentally known structures or hypothetical models and side-chain conformations (in rotamer space) were optimized by an efficient Monte Carlo algorithm using simulated annealing and simple potential functions. Discrimination by solvation preference was very clear between deliberately misfolded and correct globular models as well as between native-like and non-native-like topologies of combinatorially generated myoglobin models. Due to its statistical nature, the evaluation works best on entire protein models, while the identification of incorrect parts of models is more difficult. In one case locally incorrect chain tracing in a crystal structure was identified. The method is computationally fast compared to methods based on surface area calculations and is recommended for use as a diagnostic tool in model building based on sequence similarity, in folding simulations and in protein design.

Stereochemical quality of protein structure coordinates

Methods have been developed to assess the stereochemical quality of any protein structure both globally and locally using various criteria. Several parameters can be derived from the coordinates of a given structure. Global parameters include the distribution of phi, psi and chi 1 torsion angles, and hydrogen bond energies. There are clear correlations between these parameters and resolution; as the resolution improves, the distribution of the parameters becomes more clustered. These features show a broad distribution about ideal values derived from high-resolution structures. Some structures have tightly clustered distributions even at relatively low resolutions, while others show abnormal scatter though the data go to high resolution. Additional indicators of local irregularity include proline phi angles, peptide bond planarities, disulfide bond lengths, and their chi 3 torsion angles. These stereochemical parameters have been used to generate measures of stereochemical quality which provide a simple guide as to the reliability of a structure, in addition to the most important measures, resolution and R-factor. The parameters used in this evaluation are not novel, and are easily calculated from structure coordinates. A program suite is currently being developed which will quickly check a given structure, highlighting unusual stereochemistry and possible errors.