Comparison of the chemical and thermal denaturation of proteins by a two-state transition model.

The conformational stabilities of eight proteins in terms of the free energy differences between the native "folded" state of the protein and its "unfolded" state were determined at 298 K by two methods: chemical denaturation at 298 K and extrapolation to 298 K of the thermal denaturation results at high temperature. The proteins were expressed in Escherichia coli from the Haemophilus influenzae and E. coli genes at different levels of expression, covered a molecular mass range from 13 to 37 kg mol(-1) per monomeric unit (some exhibiting unique structural features), and were oligomeric up to four subunits. The free energy differences were determined by application of a two-state transition model to the chemical and thermal denaturation results, ranged from 9.4 to 148 kJ mol(-1) at 298 K, and were found to be within the experimental uncertainties of both methods for all of the proteins. Any contributions from intermediate states detectable from chemical and thermal denaturation differences in the unfolding free energy differences in these proteins are within the experimental uncertainties of both methods.

Completeness in structural genomics.

Structural genomics has the goal of obtaining useful, three-dimensional models of all proteins by a combination of experimental structure determination and comparative model building. We evaluate different strategies for optimizing information return on effort. The strategy that maximizes structural coverage requires about seven times fewer structure determinations compared with the strategy in which targets are selected at random. With a choice of reasonable model quality and the goal of 90% coverage, we extrapolate the estimate of the total effort of structural genomics. It would take approximately 16,000 carefully selected structure determinations to construct useful atomic models for the vast majority of all proteins. In practice, unless there is global coordination of target selection, the total effort will likely increase by a factor of three. The task can be accomplished within a decade provided that selection of targets is highly coordinated and significant funding is available.

SNPs, protein structure, and disease.

Inherited disease susceptibility in humans is most commonly associated with single nucleotide polymorphisms (SNPs). The mechanisms by which this occurs are still poorly understood. We have analyzed the effect of a set of disease-causing missense mutations arising from SNPs, and a set of newly determined SNPs from the general population. Results of in vitro mutagenesis studies, together with the protein structural context of each mutation, are used to develop a model for assigning a mechanism of action of each mutation at the protein level. Ninety percent of the known disease-causing missense mutations examined fit this model, with the vast majority affecting protein stability, through a variety of energy related factors. In sharp contrast, over 70% of the population set are found to be neutral. The remaining 30% are potentially involved in polygenic disease.

Processing and evaluation of predictions in CASP4.

The Livermore Prediction Center conducted the target collection and prediction submission processes for Critical Assessment of Protein Structure Prediction (CASP4) and Critical Assessment of Fully Automated Structure Prediction Methods (CAFASP2). We have also evaluated all the submitted predictions using criteria and methods developed during the course of three previous CASP experiments and preparation for CASP4. We present an overview of the implemented system. Particular attention is paid to newly developed evaluation techniques and data presentation schemes. With the rapid increase in CASP participation and in the number of submitted predictions, special emphasis is placed on methods allowing reliable pre-classification of submissions and on techniques useful in automated evaluation of predictions. We also present an overview of our website, including target structures, predictions, and their evaluations ( http://predictioncenter.llnl.gov).

Comparison of performance in successive CASP experiments.

As the number of completed CASP (Critical Assessment of Protein Structure Prediction) experiments grows, so does the need for stable, standard methods for comparing performance in successive experiments. It is critical to develop methods for determining the areas in which there is progress and in which areas are static. We have added an analysis of the CASP4 results to that previously published for CASPs 1, 2, and 3. We again use a unified difficulty scale to permit comparison of performance as a function of target difficulty in the different CASPs. The scale is used to compare performance in aligning target sequences to a structural template. There was a clear improvement in alignment quality between CASP1 (1994) and CASP2 (1996). No change is apparent between CASP2 and CASP3 (1998). There is a small barely detectable improvement between CASP3 and the latest experiment (CASP4, 2000). Alignment remains the major source of error in all models based on less than about 30% sequence identity. Comparison of performance in the new fold modeling regime is complicated by issues in devising an objective target difficulty scale. We have found limited numerical support for significant progress between CASP3 and CASP4 in this area. More subjectively, most observers are convinced that there has been substantial progress. Progress is dominated by a single group.

From fold to function.

A number of recent advances have been made in deriving function information from protein structure. A fold relationship to an already characterized protein will often allow general information about function to be deduced. More detailed information can be obtained using sequence relationships to already studied proteins. Methods of deducing function directly from structure, without the use of evolutionary relationships, are developing rapidly. All such methods may be used with models of protein structure, rather than with experimentally determined ones, but model accuracy imposes limitations. The rapid expansion of the structural genomics field has created a new urgency for improved methods of structure-based annotation of function.

Biological function made crystal clear - annotation of hypothetical proteins via structural genomics.

Many of the gene products of completely sequenced organisms are 'hypothetical' - they cannot be related to any previously characterized proteins - and so are of completely unknown function. Structural studies provide one means of obtaining functional information in these cases. A 'structural genomics' project has been initiated aimed at determining the structures of 50 hypothetical proteins from Haemophilus influenzae to gain an understanding of their function. Each stage of the project - target selection, protein production, crystallization, structure determination, and structure analysis - makes use of recent advances to streamline procedures. Early results from this and similar projects are encouraging in that some level of functional understanding can be deduced from experimentally solved structures.

Predicting protein three-dimensional structure.

The current state of the art in modeling protein structure has been assessed, based on the results of the CASP (Critical Assessment of protein Structure Prediction) experiments. In comparative modeling, improvements have been made in sequence alignment, sidechain orientation and loop building. Refinement of the models remains a serious challenge. Improved sequence profile methods have had a large impact in fold recognition. Although there has been some progress in alignment quality, this factor still limits model usefulness. In ab initio structure prediction, there has been notable progress in building approximately correct structures of 40-60 residue-long protein fragments. There is still a long way to go before the general ab initio prediction problem is solved. Overall, the field is maturing into a practical technology, able to deliver useful models for a large number of sequences.

Processing and analysis of CASP3 protein structure predictions.

Livermore Prediction Center provides basic infrastructure for the CASP (Critical Assessment of Structure Prediction) experiments, including prediction processing and verification servers, a system of prediction evaluation tools, and interactive numerical and graphical displays. Here we outline the essentials of our approach, with discussion of the superposition procedures, definitions of basic measures, and descriptions of new methods developed to analyze predictions. Our primary focus is on the evaluation of three-dimensional models and secondary structure predictions. To put the results of the three prediction experiments held to date on the same footing, the latest CASP3 evaluation criteria were retrospectively applied to both CASP1 and CASP2 predictions. Finally, we give an overview of our website (http:/(/)PredictionCenter.llnl.gov), which makes the target structures, predictions, and the evaluation system accessible to the community.

Some measures of comparative performance in the three CASPs.

Performance in the three Critical Assessment of protein Structure Prediction (CASP) experiments has been compared in the areas of alignment accuracy for models based on homology and three-dimensional accuracy for models produced by using ab initio prediction methods. The homologous models span the comparative modeling and fold-recognition regimes. Each CASP target is assigned a relative difficulty based on the extent of sequence identity and the degree of structural overlap with the best available template. There is a clear improvement in alignment accuracy between CASP1 and CASPs 2 and 3 over much of the difficulty scale but no apparent improvement between CASP2 and CASP3. Encouragingly, the best ab initio models of small targets are clearly more accurate in CASP3 than in CASPs 1 and 2.

Local electrostatic optimization in proteins.

A simple electrostatic model has been used to investigate the extent to which the structure of protein molecules is organized to optimize the internal electrostatic interactions. We find that the model provides a favorable total intra-protein electrostatic energy for almost all polar and charged groups of atoms, suggesting a high degree of structural optimization. By contrast, a significant fraction of individual group-group interactions are found to be unfavorable. An analysis as a function of the range of interactions included shows the electrostatic organization is generally relatively short range (up to 6 or 7 A between group centers). Although the model is very simple, it is useful for assessing the overall quality of protein experimental structures, for pin-pointing some types of errors and as a guide to improving protein design.

A graph-theoretic algorithm for comparative modeling of protein structure.

The interconnected nature of interactions in protein structures appears to be the major hurdle in preventing the construction of accurate comparative models. We present an algorithm that uses graph theory to handle this problem. Each possible conformation of a residue in an amino acid sequence is represented using the notion of a node in a graph. Each node is given a weight based on the degree of the interaction between its side-chain atoms and the local main-chain atoms. Edges are then drawn between pairs of residue conformations/nodes that are consistent with each other (i.e. clash-free and satisfying geometrical constraints). The edges are weighted based on the interactions between the atoms of the two nodes. Once the entire graph is constructed, all the maximal sets of completely connected nodes (cliques) are found using a clique-finding algorithm. The cliques with the best weights represent the optimal combinations of the various main-chain and side-chain possibilities, taking the respective environments into account. The algorithm is used in a comparative modeling scenario to build side-chains, regions of main chain, and mix and match between different homologs in a context-sensitive manner. The predictive power of this method is assessed by applying it to cases where the experimental structure is not known in advance.

Conformation of the sebacyl beta1Lys82-beta2Lys82 crosslink in T-state human hemoglobin.

The crystal structure of human T state hemoglobin crosslinked with bis(3,5-dibromo-salicyl) sebacate has been determined at 1.9 A resolution. The final crystallographic R factor is 0.168 with root-mean-square deviations (RMSD) from ideal bond distance of 0.018 A. The 10-carbon sebacyl residue found in the beta cleft covalently links the two betaLys82 residues. The sebacyl residue assumes a zigzag conformation with cis amide bonds formed by the NZ atoms of betaLys82's and the sebacyl carbonyl oxygens. The atoms of the crosslink have an occupancy factor of 1.0 with an average temperature factor for all atoms of 34 A2. An RMSD of 0.27 for all CA's of the tetramer is observed when the crosslinked deoxyhemoglobin is compared with deoxyhemoglobin refined by using a similar protocol, 2HHD [Fronticelli et al. J. Biol. Chem. 269: 23965-23969, 1994]. Thus, no significant perturbations in the tertiary or quaternary structure are introduced by the presence of the sebacyl residue. However, the sebacyl residue does displace seven water molecules in the beta cleft and the conformations of the beta1Lys82 and beta2Lys82 are altered because of the crosslinking. The carbonyl oxygen that is part of the amide bond formed with the NZ of beta2Lys82 forms a hydrogen bond with side chain of beta2Asn139 that is in turn hydrogen-bonded to the side chain of beta2Arg104. A comparison of the observed conformation with that modeled [Bucci et al. Biochemistry 35:3418-3425, 1996] shows significant differences. The differences in the structures can be rationalized in terms of compensating changes in the estimated free-energy balance, based on differences in exposed surface areas and the observed shift in the side-chain hydrogen-bonding pattern involving beta2Arg104, beta2Asn139, and the associated sebacyl carbonyl group.

An all-atom distance-dependent conditional probability discriminatory function for protein structure prediction.

We present a formalism to compute the probability of an amino acid sequence conformation being native-like, given a set of pairwise atom-atom distances. The formalism is used to derive three discriminatory functions with different types of representations for the atom-atom contacts observed in a database of protein structures. These functions include two virtual atom representations and one all-heavy atom representation. When applied to six different decoy sets containing a range of correct and incorrect conformations of amino acid sequences, the all-atom distance-dependent discriminatory function is able to identify correct from incorrect more often than the discriminatory functions using approximate representations. We illustrate the importance of using a detailed atomic description for obtaining the most accurate discrimination, and the necessity for testing discriminatory functions against a wide variety of decoys. The discriminatory function is also shown to be capable of capturing the fine details of atom-atom preferences. These results suggest that the all-atom distance-dependent discriminatory function will be useful for protein structure prediction and model refinement.

Determinants of side chain conformational preferences in protein structures.

A discriminatory function based on a statistical analysis of atomic contacts in protein structures is used for selecting side chain rotamers given a peptide main chain. The function allows us to rank different possible side chain conformations on the basis of contacts between side chain atoms and atoms in the environment. We compare the differences in constructing side chain conformations using contacts with only the local main chain, using the entire main chain, and by building pairs of side chains simultaneously with local main chain information. Using only the local main chain allows us to construct side chains with approximately 75% of the chi1 angles within 30 degrees of the experimental value, and an average side chain atom r.m.s.d. of 1.72 A in a set of 10 proteins. The results of constructing side chains for the 10 proteins are compared with the results of other side chain building methods previously published. The comparison shows similar accuracies. An advantage of the present method is that it can be used to select a small number of likely side chain conformations for each residue, thus permitting limited combinatorial searches for building multiple protein side chains simultaneously.

Chaos in protein dynamics.

MD simulations, currently the most detailed description of the dynamic evolution of proteins, are based on the repeated solution of a set of differential equations implementing Newton's second law. Many such systems are known to exhibit chaotic behavior, i.e., very small changes in initial conditions are amplified exponentially and lead to vastly different, inherently unpredictable behavior. We have investigated the response of a protein fragment in an explicit solvent environment to very small perturbations of the atomic positions (10(-3)-10(-9) A). Independent of the starting conformation (native-like, compact, extended), perturbed dynamics trajectories deviated rapidly, leading to conformations that differ by approximately 1 A RMSD within 1-2 ps. Furthermore, introducing the perturbation more than 1-2 ps before a significant conformational transition leads to a loss of the transition in the perturbed trajectories. We present evidence that the observed chaotic behavior reflects physical properties of the system rather than numerical instabilities of the calculation and discuss the implications for models of protein folding and the use of MD as a tool to analyze protein folding pathways.

Protein folding simulations with genetic algorithms and a detailed molecular description.

We have explored the application of genetic algorithms (GA) to the determination of protein structure from sequence, using a full atom representation. A free energy function with point charge electrostatics and an area based solvation model is used. The method is found to be superior to previously investigated Monte Carlo algorithms. For selected fragments, up to 14 residues long, the lowest free energy structures produced by the GA are similar in conformation to the corresponding experimental structures in most cases. There are three main conclusions from these results. First, the genetic algorithm is an effective method for searching amongst the compact conformations of a polypeptide chain. Second, the free energy function is generally able to select native-like conformations. However, some deficiencies are identified, and further development is proposed. Third, the selection of native-like conformations for some protein fragments establishes that in these cases the conformation observed in the full protein structure is largely context independent. The implications for the nature of protein folding pathways are discussed.