The dead-end elimination theorem and its use in protein side-chain positioning

Branch-and-terminate: a combinatorial optimization algorithm for protein design

BACKGROUND

Several deterministic and stochastic combinatorial optimization algorithms have been applied to computational protein design and homology modeling. As structural targets increase in size, however, it has become necessary to find more powerful methods to address the increased combinatorial complexity.

RESULTS

We present a new deterministic combinatorial search algorithm called 'Branch-and-Terminate' (B&T), which is derived from the Branch-and-Bound search method. The B&T approach is based on the construction of an efficient but very restrictive bounding expression, which is used for the search of a combinatorial tree representing the protein system. The bounding expression is used both to determine the optimal organization of the tree and to perform a highly effective pruning procedure named 'termination'. For some calculations, the B&T method rivals the current deterministic standard, dead-end elimination (DEE), sometimes finding the solution up to 21 times faster. A more significant feature of the B&T algorithm is that it can provide an efficient way to complete the optimization of problems that have been partially reduced by a DEE algorithm.

CONCLUSIONS

The B&T algorithm is an effective optimization algorithm when used alone. Moreover, it can increase the problem size limit of amino acid sidechain placement calculations, such as protein design, by completing DEE optimizations that reach a point at which the DEE criteria become inefficient. Together the two algorithms make it possible to find solutions to problems that are intractable by either algorithm alone.

Improvement of side-chain modeling in proteins with the self-consistent mean field theory method based on an analysis of the factors influencing prediction

With the objective of improving side-chain conformation prediction, we have analyzed the influence of various factors on prediction by the Self-Consistent Mean Field Theory method, applied to a set of high resolution x-ray protein structure models. These factors may be classed as variations in the mean field optimization protocol, variations in the potential energy function, and variations in rotamer library completeness. We have developed an optimization protocol that consistently reached lower mean field conformational free energies than two other protocols. This protocol led to an important improvement in prediction. We observed a major improvement in prediction with two more detailed van der Waals parameter sets, which we found to be due mainly to the introduction of scaling of 1-4 interactions. In a comparison of two knowledge-based rotamer libraries of considerably different size, we observed an unexpected decrease in prediction with an increase in library completeness. However, when we introduced a torsion potential term in the potential energy function, we found an important increase in average prediction and in the prediction of almost all residue types with a more complete rotamer set. The two knowledge-based rotamer libraries now became equivalent in terms of average prediction. The results we obtained in an analysis of the effect of the introduction of an additional electrostatic term in the potential energy function were largely inconclusive. However, we found a small increase in average prediction for an electrostatic potential term with a fixed dielectric constant of 15. The combined effect of all the factors we analyzed in this study resulted in average prediction accuracies of 79.9% for X1, 68.1% for X1 + 2, and 1.590 A for global rms deviation (RMSD); the corresponding values for core residues were 88.2%, 78.6%, and 1.171 A. These values represent improvements in average prediction of 6.5% for X1, 9.1% for X1 + 2, and 0.163 A for global RMSD over the original conditions; the corresponding improvements in the core were 5.9%, 9.0%, and 0.180 A, respectively.

Guiding a docking mode by phage display: selection of correlated mutations at the staphylokinase-plasmin interface

During co-evolution of interacting proteins, functionally disruptive mutations on one side of the interface may be compensated by local amino acid changes on the other to restore binding affinity. This information can be useful for geometry-based docking approaches by reducing the translational and rotational space available to the proteins. Here, we demonstrate that correlated mutations at a protein-protein interface can be rapidly identified by selecting a phage-displayed library of a randomly mutated component of the complex for complementation of mutations that decreased binding in the interacting partner. This approach was used to deduce the binding mode of staphylokinase (Sak), a 15.5 kDa "indirect" plasminogen activator on microplasmin (microPli), the 28 kDa serine protease domain of plasmin. Biopanning indicated that residues Arg94 and Gly174 in microPli are located in close proximity to Glu75 and the Glu88:Ile128 pair in Sak, respectively. The coupled mutations Glu94<-->Lys75 reversed and Gly174<-->Lys88:Val128 introduced a salt bridge, whereby the binding affinities (with coupling energies of 1.8 to 2.3 kcal mol-1, respectively) and the plasminogen activation ability of the mutated complexes were partially restored. These findings suggested a unique docking mode of Sak at the western rim of the active-site cleft of microPli, that is in agreement with the structure of the Sak-microPli complex as recently derived by other methods.

Validation of NMR side-chain conformations by packing calculations

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

Computational protein design

A 'protein design cycle', involving cycling between theory and experiment, has led to recent advances in rational protein design. A reductionist approach, in which protein positions are classified by their local environments, has aided development of an appropriate energy expression. The computational principles and practicalities of the protein design cycle are discussed.

Knowledge-based structure prediction of MHC class I bound peptides: a study of 23 complexes

BACKGROUND

The binding of T-cell antigenic peptides to MHC molecules is a prerequisite for their immunogenicity. The ability to identify binding peptides based on the protein sequence is of great importance to the rational design of peptide vaccines. As the requirements for peptide binding cannot be fully explained by the peptide sequence per se, structural considerations should be taken into account and are expected to improve predictive algorithms. The first step in such an algorithm requires accurate and fast modeling of the peptide structure in the MHC-binding groove.

RESULTS

We have used 23 solved peptide-MHC class I complexes as a source of structural information in the development of a modeling algorithm. The peptide backbones and MHC structures were used as the templates for prediction. Sidechain conformations were built based on a rotamer library, using the 'dead end elimination' approach. A simple energy function selects the favorable combination of rotamers for a given sequence. It further selects the correct backbone structure from a limited library. The influence of different parameters on the prediction quality was assessed. With a specific rotamer library that incorporates information from the peptide sidechains in the solved complexes, the algorithm correctly identifies 85% (92%) of all (buried) sidechains and selects the correct backbones. Under cross-validation, 70% (78%) of all (buried) residues are correctly predicted and most of all backbones. The interaction between peptide sidechains has a negligible effect on the prediction quality.

CONCLUSIONS

The structure of the peptide sidechains follows from the interactions with the MHC and the peptide backbone, as the prediction is hardly influenced by sidechain interactions. The proposed methodology was able to select the correct backbone from a limited set. The impairment in performance under cross-validation suggests that, currently, the specific rotamer library is not satisfactorily representative. The predictions might improve with an increase in the data.

High-resolution protein design with backbone freedom

Recent advances in computational techniques have allowed the design of precise side-chain packing in proteins with predetermined, naturally occurring backbone structures. Because these methods do not model protein main-chain flexibility, they lack the breadth to explore novel backbone conformations. Here the de novo design of a family of alpha-helical bundle proteins with a right-handed superhelical twist is described. In the design, the overall protein fold was specified by hydrophobic-polar residue patterning, whereas the bundle oligomerization state, detailed main-chain conformation, and interior side-chain rotamers were engineered by computational enumerations of packing in alternate backbone structures. Main-chain flexibility was incorporated through an algebraic parameterization of the backbone. The designed peptides form alpha-helical dimers, trimers, and tetramers in accord with the design goals. The crystal structure of the tetramer matches the designed structure in atomic detail.

Protein sidechain conformer prediction: a test of the energy function

BACKGROUND

Homology modeling is an important technique for making use of the rapidly increasing number of protein sequences in the absence of structural information. The major problems in such modeling, once the alignment has been made, concern the positions of loops and the orientations of sidechains. Although progress has been made in recent years for sidechain prediction, current methods appear to have a limit on the order of 70% in their accuracy. It is important to have an understanding of this limitation, which for energy-based methods could arise from inaccuracies of the potential function.

RESULTS

A test of the CHARMM function for sidechain prediction was performed. To eliminate the multiple-residue search problem, the minimum energy positions of individual sidechains in ten proteins were calculated in the presence of all other sidechains in their crystal orientations. This test provides a necessary condition that any energy function useful for sidechain placement must satisfy. For chi1 x chi2 rotations, the accuracies were 77.4% and 89.5%, respectively, and in the presence of crystal waters were 86.5% and 94.9%, respectively. If there was an error, the crystal structure usually corresponded to an alternative local minimum on the calculated energy map. Prediction accuracy correlated with the size of the energy gap between primary and secondary minima.

CONCLUSIONS

The results indicate that the errors in current sidechain prediction schemes cannot be attributed to the potential energy function per se. The test used here establishes a necessary condition that any proposed energy-based sidechain prediction method, as well as many statistically based methods, must satisfy.

Predicting structural effects in HIV-1 protease mutant complexes with flexible ligand docking and protein side-chain optimization

We present a computational approach for predicting structures of ligand-protein complexes and analyzing binding energy landscapes that combines Monte Carlo simulated annealing technique to determine the ligand bound conformation with the dead-end elimination algorithm for side-chain optimization of the protein active site residues. Flexible ligand docking and optimization of mobile protein side-chains have been performed to predict structural effects in the V32I/I47V/V82I HIV-1 protease mutant bound with the SB203386 ligand and in the V82A HIV-1 protease mutant bound with the A77003 ligand. The computational structure predictions are consistent with the crystal structures of these ligand-protein complexes. The emerging relationships between ligand docking and side-chain optimization of the active site residues are rationalized based on the analysis of the ligand-protein binding energy landscape.

Exploring the conformational space of protein side chains using dead-end elimination and the A* algorithm

We describe an algorithm which enables us to search the conformational space of the side chains of a protein to identify the global minimum energy combination of side chain conformations as well as all other conformations within a specified energy cutoff of the global energy minimum. The program is used to explore the side chain conformational energy surface of a number of proteins, to investigate how this surface varies with the energy model used to describe the interactions within the system and the rotamer library. Enumeration of the rotamer combinations enables us to directly evaluate the partition function, and thus calculate the side chain contribution to the conformational entropy of the folded protein. An investigation of these conformations and the relationships between them shows that most of the conformations near to the global energy minimum arise from changes in side chain conformations that are essentially independent; very few result from a concerted change in conformation of two or more residues. Some of the limitations of the approach are discussed.

Pairwise calculation of protein solvent-accessible surface areas

BACKGROUND

The tractability of many algorithms for determining the energy state of a system depends on the pairwise nature of an energy expression. Some energy terms, such as the standard implementation of the van der Waals potential, satisfy this criterion whereas others do not. One class of important potentials that are not pairwise involves benefits and penalties for burying hydrophobic and/or polar surface areas. It has been found previously that, in some cases, a pairwise approximation to these surface areas correlates with the true surface areas. We set out to generalize the applicability of this approximation.

RESULTS

We develop a pairwise expression with one scalable parameter that closely reproduces both the true buried and the true exposed solvent-accessible surface areas. We then refit our previously published coiled-coil stability data to give solvation parameters of 26 cal/mol A2 favoring hydrophobic burial and 100 cal/mol A2 opposing polar burial.

CONCLUSIONS

An accurate pairwise approximation to calculate exposed and buried protein solvent-accessible surface area is achieved.

Computer search algorithms in protein modification and design

The computer-aided design of protein sequences requires efficient search algorithms to handle the enormous combinatorial complexity involved. A variety of different algorithms have now been applied with some success. The choice of algorithm can influence the representation of the problem in several important ways--the discreteness of the configuration, the types of energy terms that can be used and the ability to find the global minimum energy configuration. The use of dead end elimination to design the complete sequence for a small protein motif and the use of genetic and mean-field algorithms to design hydrophobic cores for proteins represent the major themes of the past year.

Helical protein design

It is now possible to design small proteins capable of folding into compact structures with well-packed cores. Given the present state of knowledge of protein folding and design, it is possible to extract a set of engineering guidelines that may assist in future de novo protein design.

Design, structure and stability of a hyperthermophilic protein variant

Here we report the use of an objective computer algorithm in the design of a hyperstable variant of the Streptococcal protein Gbeta1 domain (Gbeta1). The designed seven-fold mutant, Gbeta1-c3b4, has a melting temperature in excess of 100 degrees C and an enhancement in thermodynamic stability of 4.3 kcal mol(-1) at 50 degrees C over the wild-type protein. Gbeta1-c3b4 maintains the Gbeta1 fold, as determined by nuclear magnetic resonance spectroscopy, and also retains a significant level of binding to human IgG in qualitative comparisons with wild type. The basis of the stability enhancement appears to have multiple components including optimized core packing, increased burial of hydrophobic surface area, more favorable helix dipole interactions, and improvement of secondary structure propensity. The design algorithm is able to model such complex contributions simultaneously using empirical physical/chemical potential functions and a combinatorial optimization algorithm based on the dead-end elimination theorem. Because the design methodology is based on general principles, there is the potential of applying the methodology to the stabilization of other unrelated protein folds.

Evolving catalytic antibodies in a phage-displayed combinatorial library

In vitro affinity maturation for evolving catalytic antibodies has been demonstrated by generating a diverse repertoire of the appropriate complementarity-determining regions on a phage surface. Phage display is followed by a selection based on binding to an altered antigen that was not used at the time of immunization, and provides variants with new catalytic activity and substrate specificity. This library format reduces the time needed to isolate the desired catalytic antibody fragments to under 2 weeks.

De novo protein design: towards fully automated sequence selection

Several groups have applied and experimentally tested systematic, quantitative methods to protein design with the goal of developing general design algorithms. We have sought to expand the range of computational protein design by developing quantitative design methods for residues of all parts of a protein: the buried core, the solvent exposed surface, and the boundary between core and surface. Our goal is an objective, quantitative design algorithm that is based on the physical properties that determine protein structure and stability and which is not limited to specific folds or motifs. We chose the betabetaalpha motif typified by the zinc finger DNA binding module to test our design methodology. Using previously published sequence scoring functions developed with a combined experimental and computational approach and the Dead-End Elimination theorem to search for the optimal sequence, we designed 20 out of 28 positions in the test motif. The resulting sequence has less than 40% homology to any known sequence and does not contain any metal binding sites or cysteine residues. The resulting peptide, pda8d, is highly soluble and monomeric and circular dichroism measurements showed it to be folded with a weakly cooperative thermal unfolding transition. The NMR solution structure of pda8d was solved and shows that it is well-defined with a backbone ensemble rms deviation of 0. 55 A. Pda8d folds into the desired betabetaalpha motif with well-defined elements of secondary structure and tertiary organization. Superposition of the pda8d backbone to the design target is excellent, with an atomic rms deviation of 1.04 A.

De novo protein design: fully automated sequence selection

The first fully automated design and experimental validation of a novel sequence for an entire protein is described. A computational design algorithm based on physical chemical potential functions and stereochemical constraints was used to screen a combinatorial library of 1.9 x 10(27) possible amino acid sequences for compatibility with the design target, a betabetaalpha protein motif based on the polypeptide backbone structure of a zinc finger domain. A BLAST search shows that the designed sequence, full sequence design 1 (FSD-1), has very low identity to any known protein sequence. The solution structure of FSD-1 was solved by nuclear magnetic resonance spectroscopy and indicates that FSD-1 forms a compact well-ordered structure, which is in excellent agreement with the design target structure. This result demonstrates that computational methods can perform the immense combinatorial search required for protein design, and it suggests that an unbiased and quantitative algorithm can be used in various structural contexts.

Probing the role of packing specificity in protein design

By using a protein-design algorithm that quantitatively considers side-chain packing, the effect of specific steric constraints on protein design was assessed in the core of the streptococcal protein G beta1 domain. The strength of packing constraints used in the design was varied, resulting in core sequences that reflected differing amounts of packing specificity. The structural flexibility and stability of several of the designed proteins were experimentally determined and showed a trend from well-ordered to highly mobile structures as the degree of packing specificity in the design decreased. This trend both demonstrates that the inclusion of specific packing interactions is necessary for the design of native-like proteins and defines a useful range of packing specificity for the design algorithm. In addition, an analysis of the modeled protein structures suggested that penalizing for exposed hydrophobic surface area can improve design performance.

Coupling backbone flexibility and amino acid sequence selection in protein design

Using a protein design algorithm that considers side-chain packing quantitatively, the effect of explicit backbone motion on the selection of amino acids in protein design was assessed in the core of the streptococcal protein G beta 1 domain (G beta 1). Concerted backbone motion was introduced by varying G beta 1's supersecondary structure parameter values. The stability and structural flexibility of seven of the redesigned proteins were determined experimentally and showed that core variants containing as many as 6 of 10 possible mutations retain native-like properties. This result demonstrates that backbone flexibility can be combined explicitly with amino acid side-chain selection and that the selection algorithm is sufficiently robust to tolerate perturbations as large as 15% of G beta 1's native supersecondary structure parameter values.

Dead-end based modeling tools to explore the sequence space that is compatible with a given scaffold

The dead-end elimination algorithm has proven to be a powerful tool in protein homology modeling since it allows one to determine rapidly the global minimum-energy conformation (GMEC) of an arbitrarily large collection of side chains, given fixed backbone coordinates. After introducing briefly the necessary background, we focus on logic arguments that increase the efficacy of the dead-end elimination process. Second, we present new theoretical considerations on the use of the dead-end elimination method as a tool to identify sequences that are compatible with a given scaffold structure. Third, we initiate a search for properties derived from the computed GMEC structure to predict whether a given sequence can be well packed in the core of a protein. Three properties will be considered: the nonbonded energy, the accessible surface area, and the extent by which the GMEC side-chain conformations deviate from a locally optimal conformation.

Automated design of the surface positions of protein helices

Using a protein design algorithm that quantitatively considers side-chain interactions, the design of surface residues of alpha helices was examined. Three scoring functions were tested: a hydrogen-bond potential, a hydrogen-bond potential in conjunction with a penalty for uncompensated burial of polar hydrogens, and a hydrogen-bond potential in combination with helix propensity. The solvent exposed residues of a homodimeric coiled coil based on GCN4-p1 were designed by using the Dead-End Elimination Theorem to find the optimal amino acid sequence for each scoring function. The corresponding peptides were synthesized and characterized by circular dichroism spectroscopy and size exclusion chromatography. The designed peptides were dimeric and nearly 100% helical at 1 degree C, with melting temperatures from 69-72 degrees C, over 12 degrees C higher than GCN4-p1, whereas a random hydrophilic sequence at the surface positions produced a peptide that melted at 15 degrees C. Analysis of the designed sequences suggests that helix propensity is the key factor in sequence design for surface helical positions.

Three-dimensional structure of staphylokinase, a plasminogen activator with therapeutic potential

The three-dimensional structure of staphylokinase has been determined at 1.8 A. The puntative site of interaction with plasminogen was identified and epitopes were mapped.

Prediction of protein side-chain rotamers from a backbone-dependent rotamer library: a new homology modeling tool

Modeling by homology is the most accurate computational method for translating an amino acid sequence into a protein structure. Homology modeling can be divided into two sub-problems, placing the polypeptide backbone and adding side-chains. We present a method for rapidly predicting the conformations of protein side-chains, starting from main-chain coordinates alone. The method involves using fewer than ten rotamers per residue from a backbone-dependent rotamer library and a search to remove steric conflicts. The method is initially tested on 299 high resolution crystal structures by rebuilding side-chains onto the experimentally determined backbone structures. A total of 77% of chi1 and 66% of chi(1 + 2) dihedral angles are predicted within 40 degrees of their crystal structure values. We then tested the method on the entire database of known structures in the Protein Data Bank. The predictive accuracy of the algorithm was strongly correlated with the resolution of the structures. In an effort to simulate a realistic homology modeling problem, 9424 homology models were created using three different modeling strategies. For prediction purposes, pairs of structures were identified which shared between 30% and 90% sequence identity. One strategy results in 82% of chi1 and 72% chi(1 + 2) dihedral angles predicted within 40 degrees of the target crystal structure values, suggesting that movements of the backbone associated with this degree of sequence identity are not large enough to disrupt the predictive ability of our method for non-native backbones. These results compared favorably with existing methods over a comprehensive data set.

Novel knowledge-based mean force potential at atomic level

We present a new approach at the atomic level for the development of knowledge-based mean force potentials (MFPs) that can be used in fold recognition, ab initio structure prediction, comparative modelling and molecular recognition. Our method is based on atom-type definitions, raising the total frequency of the pairwise distributions and leading to very accurate and specific distance-dependent energy functions. Forty different heavy atom types were defined depending on their bond connectivity, chemical nature and location level (side-chain or backbone). Using this approach it has been possible to obtain average frequencies of pairwise contacts about 15 times higher than the ones obtained using the classic way of one heavy atom definition for each amino acid (i.e. alpha-carbon, beta-carbon, virtual centroid or virtual beta-carbon co-ordinates). In this paper we use this approach to develop a MFP that can be used in fold recognition and we compare it with a classic MFP at the amino acid level compiled from the alpha-carbon distances between the different amino acid pairs. Both potentials involve all the pairwise contacts extracted from a non-redundant folds database of 180 protein chains with a sequence identity threshold of 25%. The pairwise energy functions of the MFP at the atomic level have a deep and very well defined minimum for each pairwise interaction, in contrast to the same curves obtained from the MFP developed at the amino acid level, which generally have multiple minima with similar depth. Our results also show that this MFP is able to produce very similar energy profiles for couples of proteins that share a very low sequence identity but are closely related at the structural level. When these profiles are plotted considering the structure-structure alignment, they are mostly superimposed, showing a correlation with the structure-structure similarity. In the same test, the MFP at the amino acid level fails to produce similar profiles. We suggest that using this MFP at the atomic level in the last stages of fold recognition or threading, when some candidates are available, can improve the sequence-structure alignments and, therefore, the final models. We also discuss the possibility of using this approach in the development of new MFPs to be used in ab initio structure prediction, comparative modelling and molecular recognition procedures.

Trematode myoglobins, functional molecules with a distal tyrosine

The myoglobins of two trematodes, Paramphistomum epiclitum and Isoparorchis hypselobagri, were isolated to homogeneity. The native molecules are monomeric with Mr 16,000-17,000 and pI 6.5-7.5. In each species, at least four different globin isoforms occur. Primary structure was determined at the protein level. The globin chains contain 147 amino acid residues. Although major determinants of the globin fold are conserved, characteristic substitutions are present. A Tyr residue occurs at the helical positions B10 and E7 (distal position). This is confirmed by NMR measurements (Zhang, W., Rashid, K. A., Haque, M., Siddiqi, A. H., Vinogradov, S. N., Moens, L. & La Mar, G. N. (1997) J. Biol. Chem. 272, 3000-3006). A distal Tyr normally provokes oxidation of the iron atom and the inability to bind oxygen, whereas a Tyr-B10 is indicative for a high oxygen affinity. In contrast, trematode myoglobins are functional molecules with a high oxygen affinity. Molecular modeling predicts two possible positions for the aromatic ring of Tyr-E7: one being outside the heme pocket making it freely accessible to the ligand and one within the heme pocket potentially able to form a second hydrogen bond with the iron-bound oxygen. A hydrogen bond between Tyr-B10 and the bound oxygen as in the Ascaris hemoglobin is predicted as well. The predicted structure may explain the high oxygen affinity of the trematode myoglobins.

All in one: a highly detailed rotamer library improves both accuracy and speed in the modelling of sidechains by dead-end elimination

BACKGROUND

About a decade ago, the concept of rotamer libraries was introduced to model sidechains given known mainchain coordinates. Since then, several groups have developed methods to handle the challenging combinatorial problem that is faced when searching rotamer libraries. To avoid a combinatorial explosion, the dead-end elimination method detects and eliminates rotamers that cannot be members of the global minimum energy conformation (GMEC). Several groups have applied and further developed this method in the fields of homology modelling and protein design.

RESULTS

This work addresses at the same time increased prediction accuracy and calculation speed improvements. The proposed enhancements allow the elimination of more than one-third of the possible rotameric states before applying the dead-end elimination method. This is achieved by using a highly detailed rotamer library allowing the safe application of an energy-based rejection criterion without risking the elimination of a GMEC rotamer. As a result, we gain both in modelling accuracy and in computational speed. Being completely automated, the current implementation of the dead-end elimination prediction of protein sidechains can be applied to the modelling of sidechains of proteins of any size on the high-end computer systems currently used in molecular modelling. The improved accuracy is highlighted in a comparative study on a collection of proteins of varying size for which score results have previously been published by multiple groups. Furthermore, we propose a new validation method for the scoring of the modelled structure versus the experimental data based upon the volume overlap of the predicted and observed sidechains. This overlap criterion is discussed in relation to the classic RMSD and the frequently used +/- 40 degrees window in comparing chi 1 and chi 2 angles.

CONCLUSIONS

We have shown that a very detailed library allows the introduction of a safe energy threshold rejection criterion, thereby increasing both the execution speed and the accuracy of the modelling program. We speculate that the current method will allow the sidechain prediction of medium-sized proteins and complex protein interfaces involving up to 150 residues on low-end desktop computers.

Protein folding: the endgame

The last stage of protein folding, the "endgame," involves the ordering of amino acid side-chains into a well defined and closely packed configuration. We review a number of topics related to this process. We first describe how the observed packing in protein crystal structures is measured. Such measurements show that the protein interior is packed exceptionally tightly, more so than the protein surface or surrounding solvent and even more efficiently than crystals of simple organic molecules. In vitro protein folding experiments also show that the protein is close-packed in solution and that the tight packing and intercalation of side-chains is a final and essential step in the folding pathway. These experimental observations, in turn, suggest that a folded protein structure can be described as a kind of three-dimensional jigsaw puzzle and that predicting side-chain packing is possible in the sense of solving this puzzle. The major difficulty that must be overcome in predicting side-chain packing is a combinatorial "explosion" in the number of possible configurations. There has been much recent progress towards overcoming this problem, and we survey a variety of the approaches. These approaches differ principally in whether they use ab initio (physical) or more knowledge-based methods, how they divide up and search conformational space, and how they evaluate candidate configurations (using scoring functions). The accuracy of side-chain prediction depends crucially on the (assumed) positioning of the main-chain. Methods for predicting main-chain conformation are, in a sense, not as developed as that for side-chains. We conclude by surveying these methods. As with side-chain prediction, there are a great variety of approaches, which differ in how they divide up and search space and in how they score candidate conformations.

Animal membrane receptors and adhesive molecules

This review summarizes some important data, principles, opinions, commentaries, and modern methodology concerning the receptor structure, interactions, signaling and receptor-mediated cell functions. Three sections give a brief overview of the signaling synergy, multivariant signaling, and some reactions in phosphorylation networks. A concise report about the cytotoxic reaction of NK cells represents an example of multistage recognition reaction, involving differently acting receptors, changes in affinities of cell-cell interactions, and secretion of regulatory and cytotoxic molecules. Some interesting trends in receptor engineering, including antibody molecules as a special receptor phenomenon are mentioned in the final section.

A distant evolutionary relationship between bacterial sphingomyelinase and mammalian DNase I

The three-dimensional structure of bacterial sphingomyelinase (SMase) was predicted using a protein fold recognition method; the search of a library of known structures showed that the SMase sequence is highly compatible with the mammalian DNase I structure, which suggested that SMase adopts a structure similar to that of DNase I. The amino acid sequence alignment based on the prediction revealed that, despite the lack of overall sequence similarity (less than 10% identity), those residues of DNase I that are involved in the hydrolysis of the phosphodiester bond, including two histidine residues (His 134 and His 252) of the active center, are conserved in SMase. In addition, a conserved pentapeptide sequence motif was found, which includes two catalytically critical residues, Asp 251 and His 252. A sequence database search showed that the motif is highly specific to mammalian DNase I and bacterial SMase. The functional roles of SMase residues identified by the sequence comparison were consistent with the results from mutant studies. Two Bacillus cereus SMase mutants (H134A and H252A) were constructed by site-directed mutagenesis. They completely abolished their catalytic activity. A model for the SMase-sphingomyelin complex structure was built to investigate how the SMase specifically recognizes its substrate. The model suggested that a set of residues conserved among bacterial SMases, including Trp 28 and Phe 55, might be important in the substrate recognition. The predicted structural similarity and the conservation of the functionally important residues strongly suggest a distant evolutionary relationship between bacterial SMase and mammalian DNase I. These two phosphodiesterases must have acquired the specificity for different substrates in the course of evolution.

Prediction and evaluation of side-chain conformations for protein backbone structures

A common approach to protein modeling is to propose a backbone structure based on homology or threading and then to attempt to build side chains onto this backbone. A fast algorithm using the simple criteria of atomic overlap and overall rotamer probability is proposed for this purpose. The method was first tested in the context of exhaustive searches of side chain configuration space in protein cores and was then applied to all side chains in 49 proteins of known structure, using simulated annealing to sample space. The latter procedure obtains the correct rotamer for 57% and the correct chi 1 value for 74% of the 6751 residues in the sample. When low-temperature Monte-Carlo simulations are initiated from the results of the simulated-annealing processes, consensus configurations are obtained which exhibit slightly more accurate predictions. The Monte-Carlo procedure also allows converged side chain entropies to be calculated for all residues. These prove to be accurate indicators of prediction reliability. For example, the correct rotamer is obtained for 79% and the correct chi 1 value is obtained for 84% of the half of the sample residues exhibiting the lowest entropies. Side chain entropy and predictability are nearly completely uncorrelated with solvent-accessible area. Some precedents for and implications of this observation are discussed.

A structural explanation for the twilight zone of protein sequence homology

Homology modeling of protein structures as a function of sequence breaks down at the twilight zone limit of sequence identity between the template and target proteins. Our results suggest that protein sequences that have diverged from a common ancestor beyond the twilight zone may adopt side-chain interactions that are very different from those endowed by the ancestral sequence.

Protein design automation

We have conceived and implemented a cyclical protein design strategy that couples theory, computation, and experimental testing. The combinatorially large number of possible sequences and the incomplete understanding of the factors that control protein structure are the primary obstacles in protein design. Our protein design automation algorithm objectively predicts protein sequences likely to achieve a desired fold. Using a rotamer description of the side chains, we implemented a fast discrete search algorithm based on the Dead-End Elimination Theorem to rapidly find the globally optimal sequence in its optimal geometry from the vast number of possible solutions. Rotamer sequences were scored for steric complementarity using a van der Waals potential. A Monte Carlo search was then executed, starting at the optimal sequence, in order to find other high-scoring sequences. As a test of the design methodology, high-scoring sequences were found for the buried hydrophobic residues of a homodimeric coiled coil based on GCN4-p1. The corresponding peptides were synthesized and characterized by CD spectroscopy and size-exclusion chromatography. All peptides were dimeric and nearly 100% helical at 1 degree C, with melting temperatures ranging from 24 degrees C to 57 degrees C. A quantitative structure activity relation analysis was performed on the designed peptides, and a significant correlation was found with surface area burial. Incorporation of a buried surface area potential in the scoring of sequences greatly improved the correlation between predicted and measured stabilities and demonstrated experimental feedback in a complete design cycle.

Modeling side-chain conformation

Over the past few years, a number of methods for the calculation of side-chain conformations in proteins have been described. More recent studies have considered the effect of combinatorial packing, derivations from idealized rotameric structures and, to a limited extent, backbone flexibility on the quality and efficiency of calculations of protein side-chain conformation. Although further work is needed to address the issue of backbone displacements, the recent progress solves the packing problem to a significant degree. This opens the way for fruitful incorporation of these methods into general procedures for homology modeling and studies of ligand-protein interactions.

Testing homology modeling on mutant proteins: predicting structural and thermodynamic effects in the Ala98-->Val mutants of T4 lysozyme

BACKGROUND

Current approaches to homology modeling predict how amino acid substitutions will alter a protein's structure, primarily by modeling sidechain conformations upon essentially immobile backbone frameworks. However, recent crystal structures of T4 lysozyme mutants reveal significant shifts of the mainchain and other potentially serious problems for sidechain rotamer-based modeling. This paper evaluates the accuracy of structural and thermodynamic predictions from two common sidechain modeling approaches to measure errors caused by the fixed-backbone approximation.

RESULTS

Tested on a series of T4 lysozyme mutants, this sidechain rotamer library approach did not handle mainchain shifts well, correctly predicting the sidechain conformations of only two of six mutants. By contrast, allowing sidechains to move more flexibly appeared to compensate for the rigidity of the mainchain and gave reasonably accurate coordinate predictions (rms errors of 0.5-1.0 A for each mutated sidechain), better on average than 90% of possible conformations. The calculated packing energies correlated well with experimental stabilities (r2 = 0.81) and correctly captured the cooperative interactions of several neighboring mutations.

CONCLUSIONS

Mutant modeling can be relatively accurate despite the fixed-backbone approximation. Mainchain shifts (0.2-0.5 A) cause increased sidechain coordinate errors of 0.1-0.8 A, torsional errors of 10-30 degrees, and exaggerated strain energy for overpacked mutants, compared with the same calculations performed with the correct mutant backbones.

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.

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.