Modeling of loops in protein structures

Comparative protein structure prediction is limited mostly by the errors in alignment and loop modeling. We describe here a new automated modeling technique that significantly improves the accuracy of loop predictions in protein structures. The positions of all nonhydrogen atoms of the loop are optimized in a fixed environment with respect to a pseudo energy function. The energy is a sum of many spatial restraints that include the bond length, bond angle, and improper dihedral angle terms from the CHARMM-22 force field, statistical preferences for the main-chain and side-chain dihedral angles, and statistical preferences for nonbonded atomic contacts that depend on the two atom types, their distance through space, and separation in sequence. The energy function is optimized with the method of conjugate gradients combined with molecular dynamics and simulated annealing. Typically, the predicted loop conformation corresponds to the lowest energy conformation among 500 independent optimizations. Predictions were made for 40 loops of known structure at each length from 1 to 14 residues. The accuracy of loop predictions is evaluated as a function of thoroughness of conformational sampling, loop length, and structural properties of native loops. When accuracy is measured by local superposition of the model on the native loop, 100, 90, and 30% of 4-, 8-, and 12-residue loop predictions, respectively, had <2 A RMSD error for the mainchain N, C(alpha), C, and O atoms; the average accuracies were 0.59 +/- 0.05, 1.16 +/- 0.10, and 2.61 +/- 0.16 A, respectively. To simulate real comparative modeling problems, the method was also evaluated by predicting loops of known structure in only approximately correct environments with errors typical of comparative modeling without misalignment. When the RMSD distortion of the main-chain stem atoms is 2.5 A, the average loop prediction error increased by 180, 25, and 3% for 4-, 8-, and 12-residue loops, respectively. The accuracy of the lowest energy prediction for a given loop can be estimated from the structural variability among a number of low energy predictions. The relative value of the present method is gauged by (1) comparing it with one of the most successful previously described methods, and (2) describing its accuracy in recent blind predictions of protein structure. Finally, it is shown that the average accuracy of prediction is limited primarily by the accuracy of the energy function rather than by the extent of conformational sampling.     

A pH-dependent variation in alpha-helix structure of the S-peptide of ribonuclease A studied by Monte Carlo simulated annealing.

Low-energy conformations of the S-peptide fragment (20 amino acid residues long) of ribonuclease A were studied by Monte Carlo simulated annealing. The obtained lowest-energy structures have alpha-helices with different size and location, depending distinctively on the ionizing states of acidic amino acid residues. The simulation started from completely random initial conformation and was performed without any bias toward a particular structure. The most conspicuous alpha-helices arose from the simulation when both Glu 9 and Asp 14 were assumed to be electrically neutral, whereas the resulting conformations became much less helical when Asp 14 rather than Glu 9 was allowed to have a negative charge. Together with experimental evidence that the alpha-helix in the S-peptide is most stable at pH 3.8, we consider the helix formation need the carboxyl group of Asp 14 to be electrically neutral in this weakly acidic condition. In contrast, a negative charge at Asp 14 appears to function in support of a view that this residue is crucial to helix termination owing to its possibility to form a salt bridge with His 12. These results indicate that the conformation of the S-peptide depends considerably on the ionizing state of Asp 14.     

A multibody, whole-residue potential for protein structures, with testing by Monte Carlo simulated annealing

A new multibody, whole-residue potential for protein tertiary structure is described. The potential is based on the local environment surrounding each main-chain alpha carbon (CA), defined as the set of all residues whose CA coordinates lie within a spherical volume of set radius in 3-dimensional (3D) space surrounding that position. It is shown that the relative positions of the CAs in these local environments belong to a set of preferred templates. The templates are derived by cluster analysis of the presently available database of over 3000 protein chains (750,000 residues) having not more than 30% sequence similarity. For each template is derived also a set of residue propensities for each topological position in the template. Using lookup tables of these derived templates, it is then possible to calculate an energy for any conformation of a given protein sequence. The application of the potential to ab initio protein tertiary structure prediction is evaluated by performing Monte Carlo simulated annealing on test protein sequences.     

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 noncon-served 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. © 1995 Wiley-Liss, Inc.     

Modeling large regions in proteins: applications to loops, termini, and folding

Template-based methods for predicting protein structure provide models for a significant portion of the protein but often contain insertions or chain ends (InsEnds) of indeterminate conformation. The local structure prediction "problem" entails modeling the InsEnds onto the rest of the protein. A well-known limit involves predicting loops of ≤12 residues in crystal structures. However, InsEnds may contain as many as ~50 amino acids, and the template-based model of the protein itself may be imperfect. To address these challenges, we present a free modeling method for predicting the local structure of loops and large InsEnds in both crystal structures and template-based models. The approach uses single amino acid torsional angle "pivot" moves of the protein backbone with a C(β) level representation. Nevertheless, our accuracy for loops is comparable to existing methods. We also apply a more stringent test, the blind structure prediction and refinement categories of the CASP9 tournament, where we improve the quality of several homology based models by modeling InsEnds as long as 45 amino acids, sizes generally inaccessible to existing loop prediction methods. Our approach ranks as one of the best in the CASP9 refinement category that involves improving template-based models so that they can function as molecular replacement models to solve the phase problem for crystallographic structure determination.     

A computer model to dynamically simulate protein folding: studies with crambin

The current work describes a simplified representation of protein structure with uses in the simulation of protein folding. The model assumes that a protein can be represented by a freely rotating rigid chain with a single atom approximating the effect of each side chain. Potentials describing the attraction or repulsion between different types of amino acids are determined directly from the distribution of amino acids in the database of known protein structures. The optimization technique of simulated annealing has been used to dynamically sample the conformations available to this simple model, allowing the protein to evolve from an extended, random coil into a compact globular structure. Many characteristics expected of true proteins, such as the sequence-dependent formation of secondary structure, the partitioning of hydrophobic residues, and specific disulfide pairing, are reproduced by the simulation, suggesting the model may accurately simulate the folding process.     

Automated docking of substrates to proteins by simulated annealing

The Metropolis technique of conformation searching is combined with rapid energy evaluation using molecular affinity potentials to give an efficient procedure for docking substrates to macromolecules of known structure. The procedure works well on a number of crystallographic test systems, functionally reproducing the observed binding modes of several substrates.     

Crystal packing effects on protein loops

The effects of crystal packing on protein loop structures are examined by (1) a comparison of loops in proteins that have been crystallized in alternate packing arrangements, and (2) theoretical prediction of loops both with and without the inclusion of the crystal environment. Results show that in a minority of cases, loop geometries are dependent on crystal packing effects. Explicit representation of the crystal environment in a loop prediction algorithm can be used to model these effects and to reconstruct the structures, and relative energies, of a loop in alternative packing environments. By comparing prediction results with and without the inclusion of the crystal environment, the loop prediction algorithm can further be used to identify cases in which a crystal structure does not represent the most stable state of a loop in solution. We anticipate that this capability has implications for structural biology.     

De novo protein structure prediction by dynamic fragment assembly and conformational space annealing

Ab initio protein structure prediction is a challenging problem that requires both an accurate energetic representation of a protein structure and an efficient conformational sampling method for successful protein modeling. In this article, we present an ab initio structure prediction method which combines a recently suggested novel way of fragment assembly, dynamic fragment assembly (DFA) and conformational space annealing (CSA) algorithm. In DFA, model structures are scored by continuous functions constructed based on short- and long-range structural restraint information from a fragment library. Here, DFA is represented by the full-atom model by CHARMM with the addition of the empirical potential of DFIRE. The relative contributions between various energy terms are optimized using linear programming. The conformational sampling was carried out with CSA algorithm, which can find low energy conformations more efficiently than simulated annealing used in the existing DFA study. The newly introduced DFA energy function and CSA sampling algorithm are implemented into CHARMM. Test results on 30 small single-domain proteins and 13 template-free modeling targets of the 8th Critical Assessment of protein Structure Prediction show that the current method provides comparable and complementary prediction results to existing top methods.     

Modeling of peptides and proteins in a membrane environment: I. A solvation model mimicking a lipid bilayer

A theoretical solvation model of peptides and proteins that mimics the heterogeneous membrane-water system was proposed. Our approach is based on the combined use of atomic parameters of solvation for water and hydrocarbons, which approximates the hydrated polar groups and acyl chains of lipids, respectively. This model was tested in simulations of several peptides: a nonpolar 20-mer polyleucine, a hydrophobic peptide with terminal polar groups, and a strongly amphiphilic peptide. The conformational space of the peptides in the presence of the membrane was studied by the Monte Carlo method. Unlike a polar solvent and vacuum, the membrane-like environment was shown to stabilize the α-helical conformation: low-energy structures have a helicity index of 100% in all cases. At the same time, the energetically most favorable orientations of the peptides relative to the membrane depend on their hydrophobic properties: nonpolar polyleucine is entirely immersed in the bilayer and the hydrophobic peptide with polar groups at the termini adopts a transbilayer orientation, whereas the amphiphilic peptide lies at the interface parallel to the membrane plane. The results of the simulations agree well with the available experimental data for these systems. In the following communications of this series, we plan to describe applications of the solvation model to membrane-bound proteins and peptides with biologically important functional activities.     

Refinement of protein termini in template-based modeling using conformational space annealing

The rapid increase in the number of experimentally determined protein structures in recent years enables us to obtain more reliable protein tertiary structure models than ever by template-based modeling. However, refinement of template-based models beyond the limit available from the best templates is still needed for understanding protein function in atomic detail. In this work, we develop a new method for protein terminus modeling that can be applied to refinement of models with unreliable terminus structures. The energy function for terminus modeling consists of both physics-based and knowledge-based potential terms with carefully optimized relative weights. Effective sampling of both the framework and terminus is performed using the conformational space annealing technique. This method has been tested on a set of termini derived from a nonredundant structure database and two sets of termini from the CASP8 targets. The performance of the terminus modeling method is significantly improved over our previous method that does not employ terminus refinement. It is also comparable or superior to the best server methods tested in CASP8. The success of the current approach suggests that similar strategy may be applied to other types of refinement problems such as loop modeling or secondary structure rearrangement.     

Conformational analysis and clustering of short and medium size loops connecting regular secondary structures: a database for modeling and prediction.

Loops are regions of nonrepetitive conformation connecting regular secondary structures. We identified 2,024 loops of one to eight residues in length, with acceptable main-chain bond lengths and peptide bond angles, from a database of 223 protein and protein-domain structures. Each loop is characterized by its sequence, main-chain conformation, and relative disposition of its bounding secondary structures as described by the separation between the tips of their axes and the angle between them. Loops, grouped according to their length and type of their bounding secondary structures, were superposed and clustered into 161 conformational classes, corresponding to 63% of all loops. Of these, 109 (51% of the loops) were populated by at least four nonhomologous loops or four loops sharing a low sequence identity. Another 52 classes, including 12% of the loops, were populated by at least three loops of low sequence similarity from three or fewer nonhomologous groups. Loop class suprafamilies resulting from variations in the termini of secondary structures are discussed in this article. Most previously described loop conformations were found among the classes. New classes included a 2:4 type IV hairpin, a helix-capping loop, and a loop that mediates dinucleotide-binding. The relative disposition of bounding secondary structures varies among loop classes, with some classes such as beta-hairpins being very restrictive. For each class, sequence preferences as key residues were identified; those most frequently at these conserved positions than in proteins were Gly, Asp, Pro, Phe, and Cys. Most of these residues are involved in stabilizing loop conformation, often through a positive phi conformation or secondary structure capping. Identification of helix-capping residues and beta-breakers among the highly conserved positions supported our decision to group loops according to their bounding secondary structures. Several of the identified loop classes were associated with specific functions, and all of the member loops had the same function; key residues were conserved for this purpose, as is the case for the parvalbumin-like calcium-binding loops. A significant number, but not all, of the member loops of other loop classes had the same function, as is the case for the helix-turn-helix DNA-binding loops. This article provides a systematic and coherent conformational classification of loops, covering a broad range of lengths and all four combinations of bounding secondary structure types, and supplies a useful basis for modelling of loop conformations where the bounding secondary structures are known or reliably predicted.     

Modeling protein conformational ensembles: from missing loops to equilibrium fluctuations

Characterizing protein flexibility is an important goal for understanding the physical-chemical principles governing biological function. This paper presents a Fragment Ensemble Method to capture the mobility of a protein fragment such as a missing loop and its extension into a Protein Ensemble Method to characterize the mobility of an entire protein at equilibrium. The underlying approach in both methods is to combine a geometric exploration of conformational space with a statistical mechanics formulation to generate an ensemble of physical conformations on which thermodynamic quantities can be measured as ensemble averages. The Fragment Ensemble Method is validated by applying it to characterize loop mobility in both instances of strongly stable and disordered loop fragments. In each instance, fluctuations measured over generated ensembles are consistent with data from experiment and simulation. The Protein Ensemble Method captures the mobility of an entire protein by generating and combining ensembles of conformations for consecutive overlapping fragments defined over the protein sequence. This method is validated by applying it to characterize flexibility in ubiquitin and protein G. Thermodynamic quantities measured over the ensembles generated for both proteins are fully consistent with available experimental data. On these proteins, the method recovers nontrivial data such as order parameters, residual dipolar couplings, and scalar couplings. Results presented in this work suggest that the proposed methods can provide insight into the interplay between protein flexibility and function.     

Modeling protein loops using a phi i + 1, psi i dimer database.

We present an automated method for modeling backbones of protein loops. The method samples a database of phi i + 1 and psi i angles constructed from a nonredundant version of the Protein Data Bank (PDB). The dihedral angles phi i + 1 and psi i completely define the backbone conformation of a dimer when standard bond lengths, bond angles, and a trans planar peptide configuration are used. For the 400 possible dimers resulting from 20 natural amino acids, a list of allowed phi i + 1, psi i pairs for each dimer is created by pooling all such pairs from the loop segments of each protein in the nonredundant version of the PDB. Starting from the N-terminus of the loop sequence, conformations are generated by assigning randomly selected pairs of phi i + 1, psi i for each dimer from the respective pool using standard bond lengths, bond angles, and a trans peptide configuration. We use this database to simulate protein loops of lengths varying from 5 to 11 amino acids in five proteins of known three-dimensional structures. Typically, 10,000-50,000 models are simulated for each protein loop and are evaluated for stereochemical consistency. Depending on the length and sequence of a given loop, 50-80% of the models generated have no stereochemical strain in the backbone atoms. We demonstrate that, when simulated loops are extended to include flanking residues from homologous segments, only very few loops from an ensemble of sterically allowed conformations orient the flanking segments consistent with the protein topology. The presence of near-native backbone conformations for loops from five different proteins suggests the completeness of the dimeric database for use in modeling loops of homologous proteins. Here, we take advantage of this observation to design a method that filters near-native loop conformations from an ensemble of sterically allowed conformations. We demonstrate that our method eliminates the need for a loop-closure algorithm and hence allows for the use of topological constraints of the homologous proteins or disulfide constraints to filter near-native loop conformations.     

Analysis of fragments induced by simulated lattice protein folding

The folding process of a set of 42 proteins, representative of the various folds, has been simulated by means of a Monte Carlo method on a discrete lattice, using two different potentials of mean force. Multiple compact fragments of contiguous residues are formed in the simulation, stable in composition, but not in geometry. During time, the number of fragments decreases until one final compact globular state is reached. We focused on the early steps of the folding in order to evidence the maximum number of fragments, provided they are sufficiently stable in sequence. A correlation has been established between these proto fragments and regular secondary-structure elements, whatever their nature, alpha helices or beta strands. Quantitatively, this is revealed by an overall mean one-residue quality factor of nearly 60%, which is better for proteins mainly composed of alpha helices. The correspondence between the number of fragments and the number of secondary-structure elements is of 77% and the regions separating successive fragments are mainly located in loops. Besides, hydrophobic clusters deduced from HCA correspond to fragments with an equivalent accuracy. These results suggest that folding pathways do not contain structurally static intermediate. However, since the beginning of folding, most residues that will later form one given secondary structure are kept close in space by being involved in the same fragment. This aggregation may be a way to accelerate the formation of the native state and enforces the key role played by hydrophobic residues in the formation of the fragments, thus in the folding process itself.     

Application of statistical potentials to protein structure refinement from low resolution ab initio models

Recently ab initio protein structure prediction methods have advanced sufficiently so that they often assemble the correct low resolution structure of the protein. To enhance the speed of conformational search, many ab initio prediction programs adopt a reduced protein representation. However, for drug design purposes, better quality structures are probably needed. To achieve this refinement, it is natural to use a more detailed heavy atom representation. Here, as opposed to costly implicit or explicit solvent molecular dynamics simulations, knowledge-based heavy atom pair potentials were employed. By way of illustration, we tried to improve the quality of the predicted structures obtained from the ab initio prediction program TOUCHSTONE by three methods: local constraint refinement, reduced predicted tertiary contact refinement, and statistical pair potential guided molecular dynamics. Sixty-seven predicted structures from 30 small proteins (less than 150 residues in length) representing different structural classes (alpha, beta, alpha;/beta) were examined. In 33 cases, the root mean square deviation (RMSD) from native structures improved by more than 0.3 A; in 19 cases, the improvement was more than 0.5 A, and sometimes as large as 1 A. In only seven (four) cases did the refinement procedure increase the RMSD by more than 0.3 (0.5) A. For the remaining structures, the refinement procedures changed the structures by less than 0.3 A. While modest, the performance of the current refinement methods is better than the published refinement results obtained using standard molecular dynamics.     

Ab initio protein structure assembly using continuous structure fragments and optimized knowledge-based force field

Ab initio protein folding is one of the major unsolved problems in computational biology owing to the difficulties in force field design and conformational search. We developed a novel program, QUARK, for template-free protein structure prediction. Query sequences are first broken into fragments of 1-20 residues where multiple fragment structures are retrieved at each position from unrelated experimental structures. Full-length structure models are then assembled from fragments using replica-exchange Monte Carlo simulations, which are guided by a composite knowledge-based force field. A number of novel energy terms and Monte Carlo movements are introduced and the particular contributions to enhancing the efficiency of both force field and search engine are analyzed in detail. QUARK prediction procedure is depicted and tested on the structure modeling of 145 nonhomologous proteins. Although no global templates are used and all fragments from experimental structures with template modeling score >0.5 are excluded, QUARK can successfully construct 3D models of correct folds in one-third cases of short proteins up to 100 residues. In the ninth community-wide Critical Assessment of protein Structure Prediction experiment, QUARK server outperformed the second and third best servers by 18 and 47% based on the cumulative Z-score of global distance test-total scores in the FM category. Although ab initio protein folding remains a significant challenge, these data demonstrate new progress toward the solution of the most important problem in the field.     

Prediction of the conformation and geometry of loops in globular proteins: testing ArchDB, a structural classification of loops

In protein structure prediction, a central problem is defining the structure of a loop connecting 2 secondary structures. This problem frequently occurs in homology modeling, fold recognition, and in several strategies in ab initio structure prediction. In our previous work, we developed a classification database of structural motifs, ArchDB. The database contains 12,665 clustered loops in 451 structural classes with information about phi-psi angles in the loops and 1492 structural subclasses with the relative locations of the bracing secondary structures. Here we evaluate the extent to which sequence information in the loop database can be used to predict loop structure. Two sequence profiles were used, a HMM profile and a PSSM derived from PSI-BLAST. A jack-knife test was made removing homologous loops using SCOP superfamily definition and predicting afterwards against recalculated profiles that only take into account the sequence information. Two scenarios were considered: (1) prediction of structural class with application in comparative modeling and (2) prediction of structural subclass with application in fold recognition and ab initio. For the first scenario, structural class prediction was made directly over loops with X-ray secondary structure assignment, and if we consider the top 20 classes out of 451 possible classes, the best accuracy of prediction is 78.5%. In the second scenario, structural subclass prediction was made over loops using PSI-PRED (Jones, J Mol Biol 1999;292:195-202) secondary structure prediction to define loop boundaries, and if we take into account the top 20 subclasses out of 1492, the best accuracy is 46.7%. Accuracy of loop prediction was also evaluated by means of RMSD calculations.     

Assembly of protein tertiary structures from secondary structures using optimized potentials

We present a simulated annealing-based method for the prediction of the tertiary structures of proteins given knowledge of the secondary structure associated with each amino acid in the sequence. The backbone is represented in a detailed fashion whereas the sidechains and pairwise interactions are modeled in a simplified way, following the LINUS model of Srinivasan and Rose. A perceptron-based technique is used to optimize the interaction potentials for a training set of three proteins. For these proteins, the procedure is able to reproduce the tertiary structures to below 3 A in root mean square deviation (rmsd) from the PDB targets. We present the results of tests on twelve other proteins. For half of these, the lowest energy decoy has a rmsd from the native state below 6 A and, in 9 out of 12 cases, we obtain decoys whose rmsd from the native states are also well below 5 A.