Knowledge-based potentials for proteins.

Knowledge based potentials and energy functions are extracted from a number of databases of known protein structures. Recent developments have shown that this type of potential is successful in many areas of protein structure research. Among these are quality assessment and error recognition of folds and the prediction of unknown structures by fold-recognition techniques.

Who solved the protein folding problem?

For the third time, techniques for the prediction of three-dimensional structures of proteins were critically assessed in a worldwide blind test. Steady progress is undeniable. How did this happen and what are the implications?

Helmholtz free energy of peptide hydrogen bonds in proteins.

We estimate the Helmholtz free energy of peptide hydrogen bonds in native protein structures as a function of spatial separation between donor and acceptor atoms. The resulting potential function has a deep narrow well at H-bond contact but bond formation is hindered by a barrier and the net change in free energy is close to zero. The barrier provides a molecular lock mechanism acting as a kinetic trap. Once formed, H-bonds keep protein chains in a precise orientation. However, bond formation requires energy input and opposes protein folding. In contrast, the free energy functions of most side-chain interactions have no energy barriers. They lack spatial precision but free energy differences of contact formation are substantial. These interactions drive folding and stabilize structures but precision is mediated and maintained by H-bonds.

Calculation of conformational ensembles from potentials of mean force. An approach to the knowledge-based prediction of local structures in globular proteins.

We present a prototype of a new approach to the folding problem of polypeptide chains. This approach is based on the analysis of known protein structures. It derives the energy potentials for the atomic interactions of all amino acid residue pairs as a function of the distance between the involved atoms. These potentials are then used to calculate the energies of all conformations that exist in the data base with respect to a given sequence. Then, by using only the most stable conformations, clusters of the most probable conformations for the given sequence are obtained. To discuss the results properly we introduce a new classification of segments based on their conformational stability. Special care is taken to allow for sparse data sets. The use of the method is demonstrated in the discussion of the identical oligopeptide sequences found in different conformations in unrelated proteins. VNTFV, for example, adopts a beta-strand in ribonuclease but it is found in an alpha-helical conformation in erythrocruorin. In the case of VNTFV the ensemble obtained consists of a single cluster of beta-strand conformations, indicating that this may be the preferred conformation for the pentapeptide. When the flanking residues are included in the calculation the hepapeptide P-VNTFV-H (ribonuclease) again yields an ensemble of beta-strands. However, in the ensemble of D-VNTFV-A (erythrocruorin) the major cluster is of alpha-helical type. In the present study we concentrate on the local aspects of protein conformations. However, the theory presented is quite general and not restricted to oligopeptides. We indicate extensions of the approach to the calculation of global conformations of proteins as well as conceivable applications to a number of molecular systems.

Structure-derived hydrophobic potential. Hydrophobic potential derived from X-ray structures of globular proteins is able to identify native folds.

We present a model for the hydrophobic interaction in globular proteins that is based entirely on an analysis of known X-ray structures. This structure-derived hydrophobic force is identified as the strongest among the non-covalent interactions that stabilize native folds. The functional form of the hydrophobic interaction is found to be linear, corresponding to a constant force along the observable distance range (5 to 70 A). The parameters of the hydrophobic amino acid pair potentials yield a structure-derived hydrophobicity scale that correlates strongly with scales derived by a variety of complementary approaches. We demonstrate that the structure-derived hydrophobic interaction alone is able to distinguish a substantial number of native conformations from a large pool of misfolded structures.

Characterization of novel proteins based on known protein structures.

The genome sciences face the challenge to characterize structure and function of a vast number of novel genes. Sequence search techniques are used to infer functional and structural information from similarities to experimentally characterized genes or proteins. The persistent goal is to refine these techniques and to develop alternative and complementary methods to increase the range of reliable inference.Here, we focus on the structural and functional assignments that can be inferred from the known three-dimensional structures of proteins. The study uses all structures in the Protein Data Bank that were known by the end of 1997. The protein structures released in 1998 were then characterized in terms of functional and structural similarity to the previously known structures, yielding an estimate of the maximum amount of information on novel protein sequences that can be obtained from inference techniques. The 147 globular proteins corresponding to 196 domains released in 1998 have no clear sequence similarity to previously known structures. However, 75 % of the domains have extensive structure similarity to previously known folds, and most importantly, in two out of three cases similarity in structure coincides with related function. In view of this analysis, full utilization of existing structure data bases would provide information for many new targets even if the relationship is not accessible from sequence information alone. Currently, the most sophisticated techniques detect of the order of one-third of these relationships.

Structure-based evaluation of sequence comparison and fold recognition alignment accuracy.

The biological role, biochemical function, and structure of uncharacterized protein sequences is often inferred from their similarity to known proteins. A constant goal is to increase the reliability, sensitivity, and accuracy of alignment techniques to enable the detection of increasingly distant relationships. Development, tuning, and testing of these methods benefit from appropriate benchmarks for the assessment of alignment accuracy.Here, we describe a benchmark protocol to estimate sequence-to-sequence and sequence-to-structure alignment accuracy. The protocol consists of structurally related pairs of proteins and procedures to evaluate alignment accuracy over the whole set. The set of protein pairs covers all the currently known fold types. The benchmark is challenging in the sense that it consists of proteins lacking clear sequence similarity. Correct target alignments are derived from the three-dimensional structures of these pairs by rigid body superposition. An evaluation engine computes the accuracy of alignments obtained from a particular algorithm in terms of alignment shifts with respect to the structure derived alignments. Using this benchmark we estimate that the best results can be obtained from a combination of amino acid residue substitution matrices and knowledge-based potentials.

Identification of native protein folds amongst a large number of incorrect models. The calculation of low energy conformations from potentials of mean force.

We present an approach that is able to detect native folds amongst a large number of non-native conformations. The method is based on the compilation of potentials of mean force of the interactions of the C beta atoms of all amino acid pairs from a database of known three-dimensional protein structures. These potentials are used to calculate the conformational energy of amino acid sequences in a number of different folds. For a substantial number of proteins we find that the conformational energy of the native state is lowest amongst the alternatives. Exceptions are proteins containing large prosthetic groups, Fe-S clusters or polypeptide chains that do not adopt globular folds. We discuss briefly potential applications in various fields of protein structural research.

Assembly of polypeptide and protein backbone conformations from low energy ensembles of short fragments: development of strategies and construction of models for myoglobin, lysozyme, and thymosin beta 4.

Recently we developed methods for the construction of knowledge-based mean fields from a data base of known protein structures. As shown previously, this approach can be used to calculate ensembles of probable conformations for short fragments of polypeptide chains. Here we develop procedures for the assembly of short fragments to complete three-dimensional models of polypeptide chains. The amino acid sequence of a given protein is decomposed into all possible overlapping fragments of a given length, and an ensemble of probable conformations is calculated for each fragment. The fragments are assembled to a complete model by choosing appropriate conformations from the individual ensembles and by averaging over equivalent angles. Finally a consistent model is obtained by rebuilding the conformation from the average angles. From the average angles the local variability of the structure can be calculated, which is a useful criterion for the reliability of the model. The procedure is applied to the calculation of the local backbone conformations of myoglobin and lysozyme whose structures have been solved by X-ray analysis and thymosin beta 4, a polypeptide of 43 amino acid residues whose structure was recently investigated by NMR spectroscopy. We demonstrate that substantial fractions of the calculated local backbone conformations are similar to the experimentally determined structures.

The role of protein structure in genomics.

The genome projects produce an enormous amount of sequence data that needs to be annotated in terms of molecular structure and biological function. These tasks have triggered additional initiatives like structural genomics. The intention is to determine as many protein structures as possible, in the most efficient way, and to exploit the solved structures for the assignment of biological function to hypothetical proteins. We discuss the impact of these developments on protein classification, gene function prediction, and protein structure prediction.

Molecular basis of lipoprotein lipase deficiency in two Austrian families with type I hyperlipoproteinemia.

To determine the molecular basis for type I hyperlipoproteinemia in two Austrian families, the lipoprotein lipase (LPL) gene of two patients exhibiting LPL deficiency was analyzed by Southern blotting and by direct genomic sequencing of DNA amplified by polymerase chain reaction (PCR). All exons of the LPL gene except part of the noncoding region of exon 10, all splice donor and acceptor sites, as well as 430 basepairs of the 5'-region including the promotor were sequenced. A homozygous substitution of adenine for guanine in the fifth exon at cDNA position 818 of the LPL gene was found in both patients. Our sequencing strategy largely ruled out a linkage disequilibrium of the identified nucleotide change with another defect potentially causing the clinical phenotype. The base change described abolishes a normally present AvaII restriction site allowing the identification of carriers of the mutant allele by AvaII digestion of PCR fragments of exon 5; three members of the two families were homozygous for this mutation and ten members were heterozygous. The activity of LPL in postheparin plasma was almost completely absent in homozygotes and about half normal in heterozygotes. The loss of activity was related to LPL protein structure. This mutation alters the amino acid sequence at residue 188 from Gly to Glu. The conformational preferences of the protein chain around position 188 were calculated with the use of a knowledge-based computerized method. The most probable conformation is a beta-turn formed by residues 189-192. The mutation seems to destabilize the beta-turn and/or a yet larger domain critical for substrate alignment.

Boltzmann's principle, knowledge-based mean fields and protein folding. An approach to the computational determination of protein structures.

The data base of known protein structures contains a tremendous amount of information on protein-solvent systems. Boltzmann's principle enables the extraction of this information in the form of potentials of mean force. The resulting force field constitutes an energetic model for protein-solvent systems. We outline the basic physical principles of this approach to protein folding and summarize several techniques which are useful in the development of knowledge-based force fields. Among the applications presented are the validation of experimentally determined protein structures, data base searches which aim at the identification of native-like sequence structure pairs, sequence structure alignments and the calculation of protein conformations from amino acid sequences.

Recognition of errors in three-dimensional structures of proteins.

A major problem in the determination of the three-dimensional structure of proteins concerns the quality of the structural models obtained from the interpretation of experimental data. New developments in X-ray crystallography and nuclear magnetic resonance spectroscopy have accelerated the process of structure determination and the biological community is confronted with a steadily increasing number of experimentally determined protein folds. However, in the recent past several experimentally determined protein structures have been proven to contain major errors, indicating that in some cases the interpretation of experimental data is difficult and may yield incorrect models. Such problems can be avoided when computational methods are employed which complement experimental structure determinations. A prerequisite of such computational tools is that they are independent of the parameters obtained from a particular experiment. In addition such techniques are able to support and accelerate experimental structure determinations. Here we present techniques based on knowledge based mean fields which can be used to judge the quality of protein folds. The methods can be used to identify misfolded structures as well as faulty parts of structural models. The techniques are even applicable in cases where only the C alpha trace of a protein conformation is available. The capabilities of the technique are demonstrated using correct and incorrect protein folds.

Detection of native-like models for amino acid sequences of unknown three-dimensional structure in a data base of known protein conformations.

We present an approach which can be used to identify native-like folds in a data base of protein conformations in the absence of any sequence homology to proteins in the data base. The method is based on a knowledge-based force field derived from a set of known protein conformations. A given sequence is mounted on all conformations in the data base and the associated energies are calculated. Using several conformations and sequences from the globin family we show that the native conformation is identified correctly. In fact the resolution of the force field is high enough to discriminate between a native fold and several closely related conformations. We then apply the procedure to several globins of known sequence but unknown three dimensional structure. The homology of these sequences to globins of known structures in the data base ranges from 49 to 17%. With one exception we find that for all globin sequences one of the known globin folds is identified as the most favorable conformation. These results are obtained using a force field derived from a data base devoid of globins of known structure. We briefly discuss useful applications in protein structural research and future development of our approach.

Optimum superimposition of protein structures: ambiguities and implications.

BACKGROUND: Techniques for comparison and optimum superimposition of protein structures are indispensable tools, providing the basis for statistical analysis, modeling, prediction and classification of protein folds. Observed similarity of structures is frequently interpreted as an indication of evolutionary relatedness. A variety of advanced techniques are available, but so far the important issue of uniqueness of structural superimposition has been largely neglected. We set out to investigate this issue by implementing an efficient algorithm for structure superimposition enabling routine searches for alternative alignments. RESULTS: The algorithm is based on optimum superimposition of structures and dynamic programming. The implementation is tested and validated using published results. In particular, an automatic classification of all protein folds in a recent release of the protein data bank is performed. The results obtained are closely related to published data. Surprisingly, for many protein pairs alternative alignments are obtained. These alignments are indistinguishable in terms of number of equivalent residues and root mean square error of superimposition, but the respective sets of equivalent residue pairs are completely distinct. Alternative alignments are observed for all protein architectures, including mixed alpha/beta folds. CONCLUSIONS: Superimposition of protein folds is frequently ambiguous. This has several implications on the interpretation of structural similarity with respect to evolutionary relatedness and it restricts the range of applicability of superimposed structures in statistical analysis. In particular, studies based on the implicit assumption that optimum superimposition of structures is unique are bound to be misleading.

Cayley-Menger coordinates.

A major obstacle in applying distance geometry techniques is the analytical complexity of the Cayley-Menger determinants that are used to characterize euclidian spaces in terms of distances between points. In this paper we show that, with the aid of a theorem of Jacobi, the complex Cayley-Menger determinants can be replaced by simpler determinants, and we derive the concept of Cayley-Menger coordinates, a coordinate system in terms of which each point of En is characterized by n + 1 distances to n + 1 points of a reference. We also show that this coordinate system provides a natural norm for the incomplete embedding problem. This paper provides the tools to treat the problem of filling out an incomplete distance matrix so that our previous procedure can then be used to embed the corresponding structure in a three-dimensional space.

Solution of the embedding problem and decomposition of symmetric matrices.

A solution of the problem of calculating cartesian coordinates from a matrix of interpoint distances (the embedding problem) is reported. An efficient and numerically stable algorithm for the transformation of distances to coordinates is then obtained. It is shown that the embedding problem is intimately related to the theory of symmetric matrices, since every symmetric matrix is related to a general distance matrix by a one-to-one transformation. Embedding of a distance matrix yields a decomposition of the associated symmetric matrix in the form of a sum over outer products of a linear independent system of coordinate vectors. It is shown that such a decomposition exists for every symmetric matrix and that it is numerically stable. From this decomposition, the rank and the numbers of positive, negative, and zero eigenvalues of the symmetric matrix are obtained directly.

Knowledge-based potentials--back to the roots.

Applications of knowledge-based quantities in protein structure theory are well established but their theoretical foundation, physical interpretation, and range of applicability seems unclear or even controversial. Moreover, the current literature contains terms like "pseudo-energy", "energy-like quantity", or "true energy" which are vague and unclear and terms like "mean-force potential" corresponding to well defined concepts. Seemingly contradictory results are often caused by inconsistent terminology. Often such problems are resolved when the physical nature of the involved quantities is properly defined. We summarize the fundamental principles of mean-force potentials and radial distribution functions as defined in statistical mechanics and put these into perspective with the term "knowledge-based potential".