Bayesian models and algorithms for protein β-sheet prediction

Prediction of the 3D structure greatly benefits from the information related to secondary structure, solvent accessibility, and nonlocal contacts that stabilize a protein's structure. We address the problem of \beta-sheet prediction defined as the prediction of \beta--strand pairings, interaction types (parallel or antiparallel), and \beta-residue interactions (or contact maps). We introduce a Bayesian approach for proteins with six or less \beta-strands in which we model the conformational features in a probabilistic framework by combining the amino acid pairing potentials with a priori knowledge of \beta-strand organizations. To select the optimum \beta-sheet architecture, we significantly reduce the search space by heuristics that enforce the amino acid pairs with strong interaction potentials. In addition, we find the optimum pairwise alignment between \beta-strands using dynamic programming in which we allow any number of gaps in an alignment to model \beta-bulges more effectively. For proteins with more than six \beta-strands, we first compute \beta-strand pairings using the BetaPro method. Then, we compute gapped alignments of the paired \beta-strands and choose the interaction types and \beta--residue pairings with maximum alignment scores. We performed a 10-fold cross-validation experiment on the BetaSheet916 set and obtained significant improvements in the prediction accuracy.     

Feature space resampling for protein conformational search

De novo protein structure prediction requires location of the lowest energy state of the polypeptide chain among a vast set of possible conformations. Powerful approaches include conformational space annealing, in which search progressively focuses on the most promising regions of conformational space, and genetic algorithms, in which features of the best conformations thus far identified are recombined. We describe a new approach that combines the strengths of these two approaches. Protein conformations are projected onto a discrete feature space which includes backbone torsion angles, secondary structure, and beta pairings. For each of these there is one “native” value: the one found in the native structure. We begin with a large number of conformations generated in independent Monte Carlo structure prediction trajectories from Rosetta. Native values for each feature are predicted from the frequencies of feature value occurrences and the energy distribution in conformations containing them. A second round of structure prediction trajectories are then guided by the predicted native feature distributions. We show that native features can be predicted at much higher than background rates, and that using the predicted feature distributions improves structure prediction in a benchmark of 28 proteins. The advantages of our approach are that features from many different input structures can be combined simultaneously without producing atomic clashes or otherwise physically inviable models, and that the features being recombined have a relatively high chance of being correct. Proteins 2010. © 2009 Wiley‐Liss, Inc.     

Retrospective analysis of a secondary structure prediction: the catalytic domain of matrix metalloproteinases.

Secondary structure prediction of the catalytic domain of matrix metalloproteinases is evaluated in the light of recently published experimentally determined structures. The prediction was made by combining conformational propensity, surface probability, and residue conservation calculated for an alignment of 19 sequences. The position of each observed secondary structure element was correctly predicted with a high degree of accuracy, with a single beta-strand falsely predicted. The domain fold was also anticipated from the prediction by analogy with the structural elements found in the distantly related metalloproteinases thermolysin, astacin, and adamalysin.     

Side-chain entropy effects on protein secondary structure formation

Loss of conformational entropy is one of the primary factors opposing protein folding. Both the backbone and side-chain of each residue in a protein will have their freedom of motion restricted in the final folded structure. The type of secondary structure of which a residue is part will have a significant impact on how much side-chain entropy is lost. Side-chain conformational entropies have previously been determined for folded proteins, simple models of unfolded proteins, alpha-helices, and a dipeptide model for beta-strands, but not for polyproline II (PII) helices. In this work, we present side-chain conformational estimates for the three regular secondary structure types: alpha-helices, beta-strands, and PII helices. Entropies are estimated from Monte Carlo computer simulations. Beta-strands are modeled as two structures, parallel and antiparallel beta-strands. Our data indicate that restraining a residue to the PII helix or antiparallel beta-strand conformations results in side-chain entropies equal to or higher than those obtained by restraining residues to the parallel beta-strand conformation. Side-chains in the alpha-helix conformation have the lowest side-chain entropies. The observation that extended structures retain the most side-chain entropy suggests that such structures would be entropically favored in unfolded proteins under folding conditions. Our data indicate that the PII helix conformation would be somewhat favored over beta-strand conformations, with antiparallel beta-strand favored over parallel. Notably, our data imply that, under some circumstances, residues may gain side-chain entropy upon folding. Implications of our findings for protein folding and unfolded states are discussed.     

Secondary structure prediction for the spectrin 106-amino acid segment, and a proposed model for tertiary structure

A collective secondary structure prediction for the human erythrocyte spectrin 106-residue repeat segment is developed, based on the sequences of nine segments that have been reported in the literature, utilizing a consensus of several secondary structure prediction methods for locating turn regions. The analysis predicts a five-fold structure, with three alpha-helices and two beta-strand regions, and differs from previous models on the lengths of the helices and the existence of beta-strand structure. We also demonstrate that this structural motif can be folded into tertiary structures that satisfy the experimental spectrin data and several general principles of protein organization.     

Sampling realistic protein conformations using local structural bias

The prediction of protein structure from sequence remains a major unsolved problem in biology. The most successful protein structure prediction methods make use of a divide-and-conquer strategy to attack the problem: a conformational sampling method generates plausible candidate structures, which are subsequently accepted or rejected using an energy function. Conceptually, this often corresponds to separating local structural bias from the long-range interactions that stabilize the compact, native state. However, sampling protein conformations that are compatible with the local structural bias encoded in a given protein sequence is a long-standing open problem, especially in continuous space. We describe an elegant and mathematically rigorous method to do this, and show that it readily generates native-like protein conformations simply by enforcing compactness. Our results have far-reaching implications for protein structure prediction, determination, simulation, and design.     

Distributions in protein conformation space: implications for structure prediction and entropy

By considering how polymer structures are distributed in conformation space, we show that it is possible to quantify the difficulty of structural prediction and to provide a measure of progress for prediction calculations. The critical issue is the probability that a conformation is found within a specified distance of another conformer. We address this question by constructing a cumulative distribution function (CDF) for the average probability from observations about its limiting behavior at small displacements and numerical simulations of polyalanine chains. We can use the CDF to estimate the likelihood that a structure prediction is better than random chance. For example, the chance of randomly predicting the native backbone structure of a 150-amino-acid protein to low resolution, say within 6 A, is 10(-14). A high-resolution structural prediction, say to 2 A, is immensely more difficult (10(-57)). With additional assumptions, the CDF yields the conformational entropy of protein folding from native-state coordinate variance. Or, using values of the conformational entropy change on folding, we can estimate the native state's conformational span. For example, for a 150-mer protein, equilibrium alpha-carbon displacements in the native ensemble would be 0.3-0.5 A based on T Delta S of 1.42 kcal/(mol residue).     

Interstrand pairing patterns in beta-barrel membrane proteins: the positive-outside rule, aromatic rescue, and strand registration prediction

beta-Barrel membrane proteins are found in the outer membrane of Gram-negative bacteria, mitochondria, and chloroplasts. Little is known about how residues in membrane beta-barrels interact preferentially with other residues on adjacent strands. We have developed probabilistic models to quantify propensities of residues for different spatial locations and for interstrand pairwise contact interactions involving strong H-bonds, side-chain interactions, and weak H-bonds. Using the reference state of exhaustive permutation of residues within the same beta-strand, the propensity values and p-values measuring statistical significance are calculated exactly by analytical formulae we have developed. Our findings show that there are characteristic preferences of residues for different membrane locations. Contrary to the "positive-inside" rule for helical membrane proteins, beta-barrel membrane proteins follow a significant albeit weaker "positive-outside" rule, in that the basic residues Arg and Lys are disproportionately favored in the extracellular cap region and disfavored in the periplasmic cap region. We find that different residue pairs prefer strong backbone H-bonded interstrand pairings (e.g. Gly-aromatic) or non-H-bonded pairings (e.g. aromatic-aromatic). In addition, we find that Tyr and Phe participate in aromatic rescue by shielding Gly from polar environments. We also show that these propensities can be used to predict the registration of strand pairs, an important task for the structure prediction of beta-barrel membrane proteins. Our accuracy of 44% is considerably better than random (7%). It also significantly outperforms a comparable registration prediction for soluble beta-sheets under similar conditions. Our results imply several experiments that can help to elucidate the mechanisms of in vitro and in vivo folding of beta-barrel membrane proteins. The propensity scales developed in this study will also be useful for computational structure prediction and for folding simulations.     

BuildBeta—A system for automatically constructing beta sheets

We describe a method that can thoroughly sample a protein conformational space given the protein primary sequence of amino acids and secondary structure predictions. Specifically, we target proteins with β‐sheets because they are particularly challenging for ab initio protein structure prediction because of the complexity of sampling long‐range strand pairings. Using some basic packing principles, inverse kinematics (IK), and β‐pairing scores, this method creates all possible β‐sheet arrangements including those that have the correct packing of β‐strands. It uses the IK algorithms of ProteinShop to move α‐helices and β‐strands as rigid bodies by rotating the dihedral angles in the coil regions. Our results show that our approach produces structures that are within 4–6 Å RMSD of the native one regardless of the protein size and β‐sheet topology although this number may increase if the protein has long loops or complex α‐helical regions. Proteins 2010. © Published 2009 Wiley‐Liss, Inc.     

Evolution of structurally disordered proteins promotes neostructuralization

Protein structure is generally more conserved than sequence, but for regions that can adopt different structures in different environments, does this hold true? Understanding how structurally disordered regions evolve altered secondary structure element propensities as well as conformational flexibility among paralogs are fundamental questions for our understanding of protein structural evolution. We have investigated the evolutionary dynamics of structural disorder in protein families containing both orthologs and paralogs using phylogenetic tree reconstruction, protein structure disorder prediction, and secondary structure prediction in order to shed light upon these questions. Our results indicate that the extent and location of structurally disordered regions are not universally conserved. As structurally disordered regions often have high conformational flexibility, this is likely to have an effect on how protein structure evolves as spatially altered conformational flexibility can also change the secondary structure propensities for homologous regions in a protein family.     

Improving the prediction of secondary structure of 'TIM-barrel' enzymes.

The information contained in aligned sets of homologous protein sequences should improve the score of secondary structure prediction. Seven different enzymes having the (beta/alpha)8 or TIM-barrel fold were used to optimize the prediction with regard to this class of enzymes. The alpha-helix, beta-strand and loop propensities of the Garnier-Osguthorpe-Robson method were averaged at aligned residue positions, leading to a significant improvement over the average score obtained from single sequences. The increased accuracy correlates with the average sequence variability of the aligned set. Further improvements were obtained by using the following averaged properties as weights for the averaged state propensities: amphipathic moment and alpha-helix; hydropathy and beta-strand; chain flexibility and loop. The clustering of conserved residues at the C-terminal ends of the beta-strands was used as an additional positive weight for beta-strand propensity and increased the prediction of otherwise unpredicted beta-strands decisively. The automatic weighted prediction method identifies greater than 95% of the secondary structure elements of the set of seven TIM-barrel enzymes.     

A graphic approach to evaluate algorithms of secondary structure prediction

Algorithms of secondary structure prediction have undergone the developments of nearly 30 years. However, the problem of how to appropriately evaluate and compare algorithms has not yet completely solved. A graphic method to evaluate algorithms of secondary structure prediction has been proposed here. Traditionally, the performance of an algorithm is evaluated by a number, i.e., accuracy of various definitions. Instead of a number, we use a graph to completely evaluate an algorithm, in which the mapping points are distributed in a three-dimensional space. Each point represents the predictive result of the secondary structure of a protein. Because the distribution of mapping points in the 3D space generally contains more information than a number or a set of numbers, it is expected that algorithms may be evaluated and compared by the proposed graphic method more objectively. Based on the point distribution, six evaluation parameters are proposed, which describe the overall performance of the algorithm evaluated. Furthermore, the graphic method is simple and intuitive. As an example of application, two advanced algorithms, i.e., the PHD and NNpredict methods, are evaluated and compared. It is shown that there is still much room for further improvement for both algorithms. It is pointed out that the accuracy for predicting either the alpha-helix or beta-strand in proteins with higher alpha-helix or beta-strand content, respectively, should be greatly improved for both algorithms.     

Substrate-induced conformational changes of the periplasmic N-terminus of an outer-membrane transporter by site-directed spin labeling

The structure and dynamics of the N-terminal and core regions of BtuB, an outer membrane vitamin B(12) transporter from Escherichia coli, were investigated by site-directed spin labeling. Cysteine mutants were generated by site-directed mutagenesis to place spin labels in the N-terminal region (residues 1-17), the core region (residues 25-30), and double labels into the Ton box (residues 6-12). BtuB mutants were expressed, spin labeled, purified, and reconstituted into phosphatidylcholine. In the presence of substrate (vitamin B(12)), EPR spectroscopy demonstrates that there is a conformational change in the Ton box similar to that seen previously for BtuB in intact outer membranes. The Ton box is positioned within the beta-barrel of BtuB in the absence of substrate (docked configuration) but becomes unfolded and increases its aqueous exposure upon substrate binding (undocked configuration). This conformational change and the similarity in the EPR spectra between reconstituted and native membranes indicate that BtuB is correctly folded and functional in the reconstituted system. The protein segment on the N-terminal side of the Ton box is highly mobile, and it becomes more mobile in the presence of substrate. Side chains in the region C-terminal to the Ton box also show increases in mobility with substrate addition, but position 16 appears to define a hinge point for this conformation change. EPR line shapes and relaxation data indicate that residues 25-30 form a beta-strand structure, which is analogous to the first beta-strand in the cores of the homologous iron transporters. When substrate binds to BtuB, this first beta-strand remains folded. The EPR spectra of double-nitroxide labels within the Ton box are broadened because of dipolar and collisional exchange interactions. The broadening pattern indicates that the Ton box is not helical but is in an extended or beta-strand structure.     

Highly fluctuating protein structures revealed by variable-pressure nuclear magnetic resonance

Although our knowledge of basic folded structures of proteins has dramatically improved, the extent of our corresponding knowledge of higher-energy conformers remains extremely slim. The latter information is crucial for advancing our understanding of mechanisms of protein function, folding, and conformational diseases. Direct spectroscopic detection and analysis of structures of higher-energy conformers are limited, particularly under physiological conditions, either because their equilibrium populations are small or because they exist only transiently in the folding process. A new experimental strategy using pressure perturbation in conjunction with multidimensional NMR spectroscopy is being used to overcome this difficulty. A number of rare conformers are detected under pressure for a variety of proteins such as the Ras-binding domain of RalGDS, beta-lactoglobulin, dihydrofolate reductase, ubiquitin, apomyoglobin, p13(MTCP1), and prion, which disclose a rich world of protein structure between basically folded and globally unfolded states. Specific structures suggest that these conformers are designed for function and are closely identical to kinetic intermediates. Detailed structural determination of higher-energy conformers with variable-pressure NMR will extend our knowledge of protein structure and conformational fluctuation over most of the biologically relevant conformational space.     

距离约束的HMC采样算法在蛋白质结构预测中的运用

蛋白质结构预测中,采样是指在构象空间中生成具有最小自由能的状态。传统的采样方法是对自由度直接赋值。这种方法在处理较少的残基时能取得好的效果。但是对于包含100个残基以上的蛋白质结构,由于构象空间的急剧增长,难以得到理想的结构。本文引入深度学习中的HMC(Hybrid Monte Carlo)采样方法,以概率分布为依据对蛋白质的自由度进行采样,能够对包含100、200甚至更多个残基的蛋白质结构进行采样。并且,在采样的过程中加入残基间的距离约束,使得一个结构中,相对于Rosetta的ab initio最多有75%(平均40%)的残基对得到优化,满足距离约束。     

Stochastic search strategy for estimation of maximum likelihood phylogenetic trees

The maximum likelihood (ML) method of phylogenetic tree construction is not as widely used as other tree construction methods (e.g., parsimony, neighbor-joining) because of the prohibitive amount of time required to find the ML tree when the number of sequences under consideration is large. To overcome this difficulty, we propose a stochastic search strategy for estimation of the ML tree that is based on a simulated annealing algorithm. The algorithm works by moving through tree space by way of a "local rearrangement" strategy so that topologies that improve the likelihood are always accepted, whereas those that decrease the likelihood are accepted with a probability that is related to the proportionate decrease in likelihood. Besides greatly reducing the time required to estimate the ML tree, the stochastic search strategy is less likely to become trapped in local optima than are existing algorithms for ML tree estimation. We demonstrate the success of the modified simulated annealing algorithm by comparing it with two existing algorithms (Swofford's PAUP* and Felsenstein's DNAMLK) for several theoretical and real data examples.     

Beyond rotamers: a generative,probabilistic model of side chains in proteins

Background  

Accurately covering the conformational space of amino acid side chains is essential for important applications such as protein design, docking and high resolution structure prediction. Today, the most common way to capture this conformational space is through rotamer libraries - discrete collections of side chain conformations derived from experimentally determined protein structures. The discretization can be exploited to efficiently search the conformational space. However, discretizing this naturally continuous space comes at the cost of losing detailed information that is crucial for certain applications. For example, rigorously combining rotamers with physical force fields is associated with numerous problems.     

Fourier transform infrared spectroscopy for the characterization of a model peptide-DNA interaction

To better understand the structural basis of protein-DNA interactions, the conformational changes that accompany these interactions need to be described. In order to develop a methodological approach to this problem, Fourier transform infrared spectroscopy (FTIR) with derivative resolution enhancement has been used to identify conformational changes that occur when a 29-residue synthetic peptide binds nonspecifically to heterogeneous cellular DNA in aqueous solution. The peptide sequence was chosen de novo, in order to rationally design a peptide model that would allow the relationship between DNA binding and the stability of protein secondary structure to be studied. Peptide at a concentration of 100-200 microM produces 50% saturation of heterogeneous phage DNA sequences as well as of short synthetic oligonucleotides. FTIR spectra reveal significant changes in peptide and DNA upon binding. Second-derivative spectra resolve the amide I band of native peptide into components located at 1627 (beta-strand), 1658 (alpha-helix), and 1681 (turn or beta-strand) cm-1, with a distinct shoulder at 1647 cm-1 (disordered structure). Assignment of the 1681 cm-1 vibration to a turn conformation is supported by uv CD studies, which indicate significant amounts of turn structure in unbound peptide. Ultraviolet CD also confirms the existence of disordered and beta-strand regions in the free peptide. Upon interacting with DNA the band at 1681 cm-1 (turn) is no longer seen; a new band appears at 1675 cm-1; the 1627 cm-1 band (beta-strand) is considerably reduced in intensity; the position of the alpha-helical (1658 cm-1) component remains unchanged; the shoulder at 1647 cm-1 (disorder) disappears. The new vibration at 1675 cm-1 is characteristic of beta-strand structures. The asymmetric stretch (vAS) of the DNA phosphates shifts from 1223 (unbound) to 1229 cm-1 (bound); the relative intensities of vAS and the PO2- symmetric stretch (vS) are altered upon peptide binding.(ABSTRACT TRUNCATED AT 400 WORDS)     

Role of the beta-strand insert in the central domain of the fibrinogen gamma-module

The crystal structure of the fibrinogen gamma-module (residues gamma143-411) [Yee, V. C., et al. (1997) Structure 5, 125-138] revealed an unusual feature. Namely, residues gamma381-390 in the functionally important COOH-terminal region form a beta-strand that is inserted into an antiparallel beta-sheet of the central domain (gamma192-286), while the rest (gamma393-411) seems to be flexible. To clarify the structural and functional importance of this beta-strand insert, we analyzed the folding status of the plasmin-derived fibrinogen fragment D(3) and several truncated variants of the gamma-module expressed in Escherichia coli. It was found that D(3), in which most of the COOH-terminal domain of the gamma-module (gamma287-379) is removed proteolytically, retains a gamma374-405 peptide that seems to be associated noncovalently with the bulk of the molecule via its beta-strand insert region. A study of the denaturation-renaturation process of D(3) suggested that without this peptide its truncated gamma-module remains folded but is destabilized. This was confirmed directly with the truncated recombinant variants of the gamma-module, including residues gamma148-392, gamma148-373, and gamma148-286. They all were folded, but those devoid of the beta-strand insert were destabilized. The results indicate that although the beta-strand insert contributes to the stabilization of the gamma-module, it can be removed without destroying the compact structure of the latter. On the basis of this finding and some other observations, we propose a mechanism for the function-related conformational changes in the fibrin(ogen) gamma-modules.     

On the Relation Between the Predicted Secondary Structure and the Protein Size

Accurately predicted protein secondary structure provides useful information for target selection, to analyze protein function and to predict higher dimensional structure. Existing research shows that more data + refined search = better prediction. We analyze relation between the prediction accuracy and another crucial factor, the protein size. Empirical tests performed with two secondary structure predictors on a large set of high-resolution, non-redundant proteins show that the average accuracies for small proteins (<100 residues) equal 73% and 54% for alpha-helices and beta-strands, respectively. The alpha-helix/beta-strand accuracies for very large proteins (>300 residues) equal 77%/68%, respectively. Similarly, the tests with three secondary structure content predictors show that the prediction errors for the small/very large proteins equal 0.13/0.09 and 0.09/0.06 for alpha-helix and beta-strand content, respectively. Our tests confirm that the secondary structure/content predictions for the very large proteins are characterized statistically significantly better quality than prediction for the small proteins. This is in contrast with the tertiary structure predictions in which higher accuracy is obtained for smaller proteins.