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

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

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

Generation of full protein coordinates from limited information, e.g., the Cα coordinates, is an important step in protein homology modeling and structure determination, and molecular dynamics (MD) simulations may prove to be important in this task. We describe a new method, in which the protein backbone is built quickly in a rather crude way and then refined by minimization techniques. Subsequently, the side chains are positioned using extensive MD calculations. The method is tested on two proteins, and results compared to proteins constructed using two other MD-based methods. In the first method, we supplemented an existing backbone building method with a new procedure to add side chains. The second one largely consists of available methodology. The constructed proteins are compared to the corresponding X-ray structures, which became available during this study, and they are in good agreement (backbone RMS values of 0.5–0.7 Å, and all-atom RMS values of 1.5–1.9 Å). This comparative study indicates that extensive MD simulations are able, to some extent, to generate details of the native protein structure, and may contribute to the development of a standardized methodology to predict reliably (parts of) protein structures when only partial coordinate data are available. © 1994 John Wiley & Sons, Inc.     

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

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

Recurrent alpha beta loop structures in TIM barrel motifs show a distinct pattern of conserved structural features.

A systematic survey of seven parallel alpha/beta barrel protein domains, based on exhaustive structural comparisons, reveals that a sizable proportion of the alpha beta loops in these proteins--20 out of a total of 49--belong to either one of two loop types previously described by Thornton and co-workers. Six loops are of the alpha beta 1 type, with one residue between the alpha-helix and beta-strand, and 13 are of the alpha beta 3 type, with three residues between the helix and the strand. Protein fragments embedding the identified loops, and termed alpha beta connections since they contain parts of the flanking helix and strand, have been analyzed in detail revealing that each type of connection has a distinct set of conserved structural features. The orientation of the beta-strand relative to the helix and loop portions is different owing to a very localized difference in backbone conformation. In alpha beta 1 connections, the chain enters the beta-strand via a residue adopting an extended conformation, while in alpha beta 3 it does so via a residue in a near alpha-helical conformation. Other conserved structural features include distinct patterns of side chain orientation relative to the beta-sheet surface and of main chain H-bonds in the loop and the beta-strand moieties. Significant differences also occur in packing interactions of conserved hydrophobic residues situated in the last turn of the helix. Yet the alpha-helix surface of both types of connections adopts similar orientations relative to the barrel sheet surface. Our results suggest furthermore that conserved hydrophobic residues along the sequence of the connections, may be correlated more with specific patterns of interactions made with neighboring helices and sheet strands than with helix/strand packing within the connection itself. A number of intriguing observations are also made on the distribution of the identified alpha beta 1 and alpha beta 3 loops within the alpha/beta-barrel motifs. They often occur adjacent to each other; alpha beta 3 loops invariably involve even numbered beta-strands, while alpha beta 1 loops involve preferentially odd beta-strands; all the analyzed proteins contain at least one alpha beta 3 loop in the first half of the eightfold alpha/beta barrel. Possible origins of all these observations, and their relevance to the stability and folding of parallel alpha/beta barrel motifs are discussed.     

Stereochemical quality of protein structure coordinates.

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

Designed molecules that fold to mimic protein secondary structures

Molecules that fold to mimic protein secondary structures have emerged as important targets of bioorganic chemistry. Recently, a variety of compounds that mimic helices, turns, and sheets have been developed, with notable advances in the design of beta-peptides that mimic each of these structures. These compounds hold promise as a step toward synthetic molecules with protein-like properties and as drugs that block protein-protein interactions.     

Determination of protein fold class from Raman or Raman optical activity spectra using random forests

Knowledge of the fold class of a protein is valuable because fold class gives an indication of protein function and evolution. Fold class can be accurately determined from a crystal structure or NMR structure, though these methods are expensive, time-consuming, and inapplicable to all proteins. In contrast, vibrational spectra [infra-red, Raman, or Raman optical activity (ROA)] are rapidly obtained for proteins under wide range of biological molecules under diverse experimental and physiological conditions. Here, we show that the fold class of a protein can be determined from Raman or ROA spectra by converting a spectrum into data of 10 cm⁻¹ bin widths and applying the random forest machine learning algorithm. Spectral data from 605 and 1785 cm⁻¹ were analyzed, as well as the amide I, II, and III regions in isolation and in combination. ROA amide II and III data gave the best performance, with 33 of 44 proteins assigned to one of the correct four top-level structural classification of proteins (SCOP) fold class (all α, all β, α and β, and disordered). The method also shows which spectral regions are most valuable in assigning fold class.     

Three-dimensional model and quaternary structure of the human eye lens protein gamma S-crystallin based on beta- and gamma-crystallin X-ray coordinates and ultracentrifugation.

A 3-dimensional model of the human eye lens protein gamma S-crystallin has been constructed using comparative modeling approaches encoded in the program COMPOSER on the basis of the 3-dimensional structure of gamma-crystallin and beta-crystallin. The model is biased toward the monomeric gamma B-crystallin, which is more similar in sequence. Bovine gamma S-crystallin was shown to be monomeric by analytical ultracentrifugation without any tendency to form assemblies up to concentrations in the millimolar range. The connecting peptide between domains was therefore built assuming an intramolecular association as in the monomeric gamma-crystallins. Because the linker has 1 extra residue compared with gamma B and beta B2, the conformation of the connecting peptide was constructed by using a fragment from a protein database. gamma S-crystallin differs from gamma B-crystallin mainly in the interface region between domains. The charged residues are generally paired, although in a different way from both beta- and gamma-crystallins, and may contribute to the different roles of these proteins in the lens.     

The importance of surface loops for stabilizing an eightfold beta alpha barrel protein.

An important step in understanding how a protein folds is to determine those regions of the sequence that are critical to both its stability and its folding pathway. We chose phosphoribosyl anthranilate isomerase from Escherichia coli, which is a monomeric representative of the (beta alpha)8 barrel family of proteins, to construct a variant that carries an internal tandem duplication of the fifth beta alpha module. This (beta alpha)9 variant was enzymically active and therefore must have a wild-type (beta alpha)8 core. It had a choice a priori to fold to three different folding frames, which are distinguished by carrying the duplicated segment as an insert into one out of three different loops. Steady-state kinetic constants, the fluorescence properties of a crucial tryptophan residue, and limited proteolysis showed that the stable (beta alpha)9 variant carries the insertion between beta-strand 5 and alpha-helix 5. This preference can be explained by the important role of loops between alpha helices and beta strands in stabilizing the structure of the enzyme.     

An optimization approach to predicting protein structural class from amino acid composition.

Proteins are generally classified into four structural classes: all-alpha proteins, all-beta proteins, alpha + beta proteins, and alpha/beta proteins. In this article, a protein is expressed as a vector of 20-dimensional space, in which its 20 components are defined by the composition of its 20 amino acids. Based on this, a new method, the so-called maximum component coefficient method, is proposed for predicting the structural class of a protein according to its amino acid composition. In comparison with the existing methods, the new method yields a higher general accuracy of prediction. Especially for the all-alpha proteins, the rate of correct prediction obtained by the new method is much higher than that by any of the existing methods. For instance, for the 19 all-alpha proteins investigated previously by P.Y. Chou, the rate of correct prediction by means of his method was 84.2%, but the correct rate when predicted with the new method would be 100%! Furthermore, the new method is characterized by an explicable physical picture. This is reflected by the process in which the vector representing a protein to be predicted is decomposed into four component vectors, each of which corresponds to one of the norms of the four protein structural classes.     

Prediction of protein secondary structures from conformational biases

We use LINUS (the "Local Independently Nucleated Units of Structure"), a procedure developed by Srinivasan and Rose, to provide a physical interpretation of and predict the secondary structures of proteins. The secondary structure type at a given site is identified by the largest conformational bias during short simulations. We examine the rate of successful prediction as a function of temperature and the interaction window. At high temperatures, there is a large propensity for the establishment of beta-strands whereas alpha-helices appear only when the temperature is lower than a certain threshold value. It is found that there exists an optimal temperature at which the correct secondary structures are predicted most accurately. We find that this temperature is close to the peak temperature of the specific heat. Changing the interaction window or carrying out longer simulations approaching equilibrium lead to little change in the optimal success rate. Our findings are in accord with the observation by Srinivasan and Rose that the secondary structures are mainly determined by local interactions and appear in the early stage of folding.     

Analysis of interactive packing of secondary structural elements in alpha/beta units in proteins

An alpha-helix and a beta-strand are said to be interactively packed if at least one residue in each of the secondary structural elements loses 10% of its solvent accessible contact area on association with the other secondary structural element. An analysis of all such 5,975 nonidentical alpha/beta units in protein structures, defined at < or = 2.5 A resolution, shows that the interaxial distance between the alpha-helix and the beta-strand is linearly correlated with the residue-dependent function, log[(V/nda)/n-int], where V is the volume of amino acid residues in the packing interface, nda is the normalized difference in solvent accessible contact area of the residues in packed and unpacked secondary structural elements, and n-int is the number of residues in the packing interface. The beta-sheet unit (beta u), defined as a pair of adjacent parallel or antiparallel hydrogen-bonded beta-strands, packing with an alpha-helix shows a better correlation between the interaxial distance and log(V/nda) for the residues in the packing interface. This packing relationship is shown to be useful in the prediction of interaxial distances in alpha/beta units using the interacting residue information of equivalent alpha/beta units of homologous proteins. It is, therefore, of value in comparative modeling of protein structures.     

Thermal folding and mechanical unfolding pathways of protein secondary structures

Mechanical stretching of secondary structures is studied through molecular dynamics simulations of a Go-like model. Force versus displacement curves are studied as a function of the stiffness and velocity of the pulling device. The succession of stretching events, as measured by the order in which contacts are ruptured, is compared to the sequencing of events during thermal folding and unfolding. Opposite cross-correlations are found for an alpha-helix and a beta-hairpin structure. In a tandem of two alpha-helices, the two constituent helices unravel nearly simultaneously. A simple condition for simultaneous versus sequential unraveling of repeat units is presented.     

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

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

Elucidating protein secondary structures using alpha-carbon recurrence quantifications.

Secondary structures of proteins were studied by recurrence quantification analysis (RQA). High-resolution, 3-dimensional coordinates of alpha-carbon atoms comprising a set of 68 proteins were downloaded from the Protein Data Bank. By fine-tuning four recurrence parameters (radius, line, residue, separation), it was possible to establish excellent agreement between percent contribution of alpha-helix and beta-sheet structures determined independently by RQA and that of the DSSP algorithm (Define Secondary Structure of Proteins). These results indicate that there is an equivalency between these two techniques, which are based upon totally different pattern recognition strategies. RQA enhances qualitative contact maps by quantifying the arrangements of recurrent points of alpha carbons close in 3-dimensional space. For example, the radius was systematically increased, moving the analysis beyond local alpha-carbon neighborhoods in order to capture super-secondary and tertiary structures. However, differences between proteins could only be detected within distances up to about 6-11 A, but not higher. This result underscores the complexity of alpha-carbon spacing when super-secondary structures appear at larger distances. Finally, RQA-defined secondary structures were found to be robust against random displacement of alpha carbons upwards of 1 A. This finding has potential import for the dynamic functions of proteins in motion.     

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.     

Representing an ensemble of NMR-derived protein structures by a single structure.

The usefulness of representing an ensemble of NMR-derived protein structures by a single structure has been investigated. Two stereochemical properties have been used to assess how a single structure relates to the ensemble from which it was derived, namely the distribution of phi psi torsion angles and the distribution of chi 1 torsion angles. The results show that the minimized average structure derived from the ensemble (a total of 11 ensembles from the Brookhaven Protein Data Bank were analyzed) does not always correspond well with this ensemble, particularly for those ensembles generated with a smaller number of experimentally derived restraints per residue. An alternative method that selects the member of the ensemble which is closest to the "average" of the ensemble has been investigated (a total of 23 ensembles from the Brookhaven Protein Data Bank were analyzed). Although this method selected a structure that on the whole corresponded more closely to the ensemble than did the minimized average structure, this is still not a totally reliable means of selecting a single structure to represent the ensemble. This suggests that it is advisable to study the ensemble as a whole. A study has also been made of the practice of selecting the "best" rather than the most representative member of the ensemble. This too suggests that the ensemble should be studied as a whole. A study of the conformational space occupied by the ensemble also suggests the need to consider the ensemble as a whole, particularly for those ensembles generated with a smaller number of experimentally derived restraints per residue.     

Structure of the human glycogen-associated protein phosphatase 1 regulatory subunit hGM: homology modeling revealed an (alpha/beta)8-barrel-like fold in the multidomain protein

Protein phosphatase 1 (PP1) is widely distributed among tissues and species and acts as a regulator of many important cellular processes. By targeting the catalytic part of PP1 (PP1C) toward particular loci and substrates, regulatory subunits constitute key elements conferring specificity to the holoenzyme. Here, we report the identification of an (alpha/beta)8-barrel-like structure within the N-ter stretch of the human PP1 regulatory subunit hGM, which is part of the family of diverse proteins associated with glycogen metabolism. Protein homology modeling gave rise to a three-dimensional (3D) model for the 381 N-ter residue stretch of hGM, based on sequence similarity with Streptomyces olivochromogenes xylose isomerase, identified by using FASTA. The alignment was subsequently extended by using hydrophobic cluster analysis. The homology-derived model includes the putative glycogen binding area located within the 142-230 domain of hGM as well as a structural characterization of the PP1C interacting domain (segment 51-67). Refinement of the latter by molecular dynamics afforded a topology that is in agreement with previous X-ray studies (Egloff et al., 1997). Finite difference Poisson-Boltzmann calculations performed on the interacting domains of PP1C and hGM confirm the complementarity of the local electrostatic potentials of the two partners. This work highlights the presence of a conserved fold among distant species (mammalian, Caenorhabditis elegans, yeast) and, thus, emphasizes the involvement of PP1 in crucial basic cellular functions.