Improving fragment quality for de novo structure prediction

De novo structure prediction can be defined as a search in conformational space under the guidance of an energy function. The most successful de novo structure prediction methods, such as Rosetta, assemble the fragments from known structures to reduce the search space. Therefore, the fragment quality is an important factor in structure prediction. In our study, a method is proposed to generate a new set of fragments from the lowest energy de novo models. These fragments were subsequently used to predict the next‐round of models. In a benchmark of 30 proteins, the new set of fragments showed better performance when used to predict de novo structures. The lowest energy model predicted using our method was closer to native structure than Rosetta for 22 proteins. Following a similar trend, the best model among top five lowest energy models predicted using our method was closer to native structure than Rosetta for 20 proteins. In addition, our experiment showed that the C‐alpha root mean square deviation was improved from 5.99 to 5.03 Å on average compared to Rosetta when the lowest energy models were picked as the best predicted models. Proteins 2014; 82:2240–2252. © 2014 Wiley Periodicals, Inc.     

Fragment-based local statistical potentials derived by combining an alphabet of protein local structures with secondary structures and solvent accessibilities

General and transferable statistical potentials to quantify the compatibility between local structures and local sequences of peptide fragments in proteins were derived. In the derivation, structure clusters of fragments are obtained by clustering five-residue fragments in native proteins based on their conformations represented by a local structure alphabet (de Brevern et al., Proteins 2000;41:271-287), secondary structure states, and solvent accessibilities. On the basis of the native sequences of the structurally clustered fragments, the probabilities of different amino acid sequences were estimated for each structure cluster. From the sequence probabilities, statistical energies as a function of sequence for a given structure were directly derived. The same sequence probabilities were employed in a database-matching approach to derive statistical energies as a function of local structure for a given sequence. Compared with prior models of local statistical potentials, we provided an integrated approach in which local conformations and local environments are treated jointly, structures are treated in units of fragments instead of individual residues so that coupling between the conformations of adjacent residues is included, and strong interdependences between the conformations of overlapping or neighboring fragment units are also considered. In tests including fragment threading, pseudosequence design, and local structure predictions, the potentials performed at least comparably and, in most cases, better than a number of existing models applicable to the same contexts indicating the advantages of such an integrated approach for deriving local potentials and suggesting applicability of the statistical potentials derived here in sequence designs and structure predictions.     

Energy minimization method using automata network for sequence and side-chain conformation prediction from given backbone geometry

Globular proteins have high packing densities as a result of residue side chains in the core achieving a tight, complementary packing. The internal packing is considered the main determinant of native protein structure. From that point of view, we present here a method of energy minimization using an automata network to predict a set of amino acid sequences and their side-chain conformations from a desired backbone geometry for de novo design of proteins. Using discrete side-chain conformations, that is, rotamers, the sequence generation problem from a given backbone geometry becomes one of combinatorial problems. We focused on the residues composing the interior core region and predicted a set of amino acid Sequences and their side-chain conformations only from a given backbone geometry. The kinds of residues were restricted to six hydrophobic amino acids (Ala, Ile, Met, Leu, Phe, and Val) because the core regions are almost always composed of hydrophobic residues. The obtained sequences were well packed as was the native sequence. The method can be used for automated sequence generation in the de novo design of proteins. © 1994 Wiley-Liss, Inc.     

A computational method for the design of nested proteins by loop‐directed domain insertion

The computational design of novel nested proteins—in which the primary structure of one protein domain (insert) is flanked by the primary structure segments of another (parent)—would enable the generation of multifunctional proteins. Here we present a new algorithm, called Loop‐Directed Domain Insertion (LooDo), implemented within the Rosetta software suite, for the purpose of designing nested protein domain combinations connected by flexible linker regions. Conformational space for the insert domain is sampled using large libraries of linker fragments for linker‐to‐parent domain superimposition followed by insert‐to‐linker superimposition. The relative positioning of the two domains (treated as rigid bodies) is sampled efficiently by a grid‐based, mutual placement compatibility search. The conformations of the loop residues, and the identities of loop as well as interface residues, are simultaneously optimized using a generalized kinematic loop closure algorithm and Rosetta EnzymeDesign, respectively, to minimize interface energy. The algorithm was found to consistently sample near‐native conformations and interface sequences for a benchmark set of structurally similar but functionally divergent domain‐inserted enzymes from the α/β hydrolase superfamily, and discriminates well between native and nonnative conformations and sequences, although loop conformations tended to deviate from the native conformations. Furthermore, in cross‐domain placement tests, native insert‐parent domain combinations were ranked as the best‐scoring structures compared to nonnative domain combinations. This algorithm should be broadly applicable to the design of multi‐domain protein complexes with any combination of inserted or tandem domain connections.     

Enhanced sampling near the native conformation using statistical potentials for local side-chain and backbone interactions

In the preceding article in this issue of Proteins, an empirical energy function consisting of 4 statistical potentials that quantify local side-chain-backbone and side-chain-side-chain interactions has been demonstrated to successfully identify the native conformations of short sequence fragments and the native structure within large sets of high-quality decoys. Because this energy function consists entirely of interactions between residues separated by fewer than 5 positions, it can be used at the earliest stage of ab initio structure prediction to enhance the efficiency of conformational search. In this article, protein fragments are generated de novo by recombining very short segments of protein structures (2, 4, or 6 residues), either selected at random or optimized with respect this local energy function. When local energy is optimized in selected fragments, more efficient sampling of conformational space near the native conformation is consistently observed for 450 randomly selected single turn fragments, with turn lengths varying from 3 to 12 residues and all 4 combinations of flanking secondary structure. These results further demonstrate the energetic significance of local interactions in protein conformations. When used in combination with longer range energy functions, application of these potentials should lead to more accurate prediction of protein structure.     

An improved protein decoy set for testing energy functions for protein structure prediction

We have improved the original Rosetta centroid/backbone decoy set by increasing the number of proteins and frequency of near native models and by building on sidechains and minimizing clashes. The new set consists of 1,400 model structures for 78 different and diverse protein targets and provides a challenging set for the testing and evaluation of scoring functions. We evaluated the extent to which a variety of all-atom energy functions could identify the native and close-to-native structures in the new decoy sets. Of various implicit solvent models, we found that a solvent-accessible surface area-based solvation provided the best enrichment and discrimination of close-to-native decoys. The combination of this solvation treatment with Lennard Jones terms and the original Rosetta energy provided better enrichment and discrimination than any of the individual terms. The results also highlight the differences in accuracy of NMR and X-ray crystal structures: a large energy gap was observed between native and non-native conformations for X-ray structures but not for NMR structures.     

Prediction of structures of zinc‐binding proteins through explicit modeling of metal coordination geometry

Metal ions play an essential role in stabilizing protein structures and contributing to protein function. Ions such as zinc have well‐defined coordination geometries, but it has not been easy to take advantage of this knowledge in protein structure prediction efforts. Here, we present a computational method to predict structures of zinc‐binding proteins given knowledge of the positions of zinc‐coordinating residues in the amino acid sequence. The method takes advantage of the “atom‐tree” representation of molecular systems and modular architecture of the Rosetta3 software suite to incorporate explicit metal ion coordination geometry into previously developed de novo prediction and loop modeling protocols. Zinc cofactors are tethered to their interacting residues based on coordination geometries observed in natural zinc‐binding proteins. The incorporation of explicit zinc atoms and their coordination geometry in both de novo structure prediction and loop modeling significantly improves sampling near the native conformation. The method can be readily extended to predict protein structures bound to other metal and/or small chemical cofactors with well‐defined coordination or ligation geometry.     

Modeling structurally variable regions in homologous proteins with rosetta

A major limitation of current comparative modeling methods is the accuracy with which regions that are structurally divergent from homologues of known structure can be modeled. Because structural differences between homologous proteins are responsible for variations in protein function and specificity, the ability to model these differences has important functional consequences. Although existing methods can provide reasonably accurate models of short loop regions, modeling longer structurally divergent regions is an unsolved problem. Here we describe a method based on the de novo structure prediction algorithm, Rosetta, for predicting conformations of structurally divergent regions in comparative models. Initial conformations for short segments are selected from the protein structure database, whereas longer segments are built up by using three- and nine-residue fragments drawn from the database and combined by using the Rosetta algorithm. A gap closure term in the potential in combination with modified Newton's method for gradient descent minimization is used to ensure continuity of the peptide backbone. Conformations of variable regions are refined in the context of a fixed template structure using Monte Carlo minimization together with rapid repacking of side-chains to iteratively optimize backbone torsion angles and side-chain rotamers. For short loops, mean accuracies of 0.69, 1.45, and 3.62 A are obtained for 4, 8, and 12 residue loops, respectively. In addition, the method can provide reasonable models of conformations of longer protein segments: predicted conformations of 3A root-mean-square deviation or better were obtained for 5 of 10 examples of segments ranging from 13 to 34 residues. In combination with a sequence alignment algorithm, this method generates complete, ungapped models of protein structures, including regions both similar to and divergent from a homologous structure. This combined method was used to make predictions for 28 protein domains in the Critical Assessment of Protein Structure 4 (CASP 4) and 59 domains in CASP 5, where the method ranked highly among comparative modeling and fold recognition methods. Model accuracy in these blind predictions is dominated by alignment quality, but in the context of accurate alignments, long protein segments can be accurately modeled. Notably, the method correctly predicted the local structure of a 39-residue insertion into a TIM barrel in CASP 5 target T0186.     

Algorithm for selection of optimized EPR distance restraints for de novo protein structure determination

A hybrid protein structure determination approach combining sparse Electron Paramagnetic Resonance (EPR) distance restraints and Rosetta de novo protein folding has been previously demonstrated to yield high quality models (Alexander et al. (2008)). However, widespread application of this methodology to proteins of unknown structures is hindered by the lack of a general strategy to place spin label pairs in the primary sequence. In this work, we report the development of an algorithm that optimally selects spin labeling positions for the purpose of distance measurements by EPR. For the α-helical subdomain of T4 lysozyme (T4L), simulated restraints that maximize sequence separation between the two spin labels while simultaneously ensuring pairwise connectivity of secondary structure elements yielded vastly improved models by Rosetta folding. 54% of all these models have the correct fold compared to only 21% and 8% correctly folded models when randomly placed restraints or no restraints are used, respectively. Moreover, the improvements in model quality require a limited number of optimized restraints, which is determined by the pairwise connectivities of T4L α-helices. The predicted improvement in Rosetta model quality was verified by experimental determination of distances between spin labels pairs selected by the algorithm. Overall, our results reinforce the rationale for the combined use of sparse EPR distance restraints and de novo folding. By alleviating the experimental bottleneck associated with restraint selection, this algorithm sets the stage for extending computational structure determination to larger, traditionally elusive protein topologies of critical structural and biochemical importance.     

Native fold and docking pose discrimination by the same residue‐based scoring function

Structure prediction and quality assessment are crucial steps in modeling native protein conformations. Statistical potentials are widely used in related algorithms, with different parametrizations typically developed for different contexts such as folding protein monomers or docking protein complexes. Here, we describe BACH‐SixthSense, a single residue‐based statistical potential that can be successfully employed in both contexts. BACH‐SixthSense shares the same approach as BACH, a knowledge‐based potential originally developed to score monomeric protein structures. A term that penalizes steric clashes as well as the distinction between polar and apolar sidechain‐sidechain contacts are crucial novel features of BACH‐SixthSense. The performance of BACH‐SixthSense in discriminating correctly the native structure among a competing set of decoys is significantly higher than other state‐of‐the‐art scoring functions, that were specifically trained for a single context, for both monomeric proteins (QMEAN, Rosetta, RF_CB_SRS_OD, benchmarked on CASP targets) and protein dimers (IRAD, Rosetta, PIE*PISA, HADDOCK, FireDock, benchmarked on 14 CAPRI targets). The performance of BACH‐SixthSense in recognizing near‐native docking poses within CAPRI decoy sets is good as well. Proteins 2015; 83:621–630. © 2015 Wiley Periodicals, Inc.     

Contact order and ab initio protein structure prediction

Although much of the motivation for experimental studies of protein folding is to obtain insights for improving protein structure prediction, there has been relatively little connection between experimental protein folding studies and computational structural prediction work in recent years. In the present study, we show that the relationship between protein folding rates and the contact order (CO) of the native structure has implications for ab initio protein structure prediction. Rosetta ab initio folding simulations produce a dearth of high CO structures and an excess of low CO structures, as expected if the computer simulations mimic to some extent the actual folding process. Consistent with this, the majority of failures in ab initio prediction in the CASP4 (critical assessment of structure prediction) experiment involved high CO structures likely to fold much more slowly than the lower CO structures for which reasonable predictions were made. This bias against high CO structures can be partially alleviated by performing large numbers of additional simulations, selecting out the higher CO structures, and eliminating the very low CO structures; this leads to a modest improvement in prediction quality. More significant improvements in predictions for proteins with complex topologies may be possible following significant increases in high-performance computing power, which will be required for thoroughly sampling high CO conformations (high CO proteins can take six orders of magnitude longer to fold than low CO proteins). Importantly for such a strategy, simulations performed for high CO structures converge much less strongly than those for low CO structures, and hence, lack of simulation convergence can indicate the need for improved sampling of high CO conformations. The parallels between Rosetta simulations and folding in vivo may extend to misfolding: The very low CO structures that accumulate in Rosetta simulations consist primarily of local up-down beta-sheets that may resemble precursors to amyloid formation.     

Analysis of anisotropic side-chain packing in proteins and application to high-resolution structure prediction

pi-pi, Cation-pi, and hydrophobic packing interactions contribute specificity to protein folding and stability to the native state. As a step towards developing improved models of these interactions in proteins, we compare the side-chain packing arrangements in native proteins to those found in compact decoys produced by the Rosetta de novo structure prediction method. We find enrichments in the native distributions for T-shaped and parallel offset arrangements of aromatic residue pairs, in parallel stacked arrangements of cation-aromatic pairs, in parallel stacked pairs involving proline residues, and in parallel offset arrangements for aliphatic residue pairs. We then investigate the extent to which the distinctive features of native packing can be explained using Lennard-Jones and electrostatics models. Finally, we derive orientation-dependent pi-pi, cation-pi and hydrophobic interaction potentials based on the differences between the native and compact decoy distributions and investigate their efficacy for high-resolution protein structure prediction. Surprisingly, the orientation-dependent potential derived from the packing arrangements of aliphatic side-chain pairs distinguishes the native structure from compact decoys better than the orientation-dependent potentials describing pi-pi and cation-pi interactions.     

Modeling disordered regions in proteins using Rosetta

Protein structure prediction methods such as Rosetta search for the lowest energy conformation of the polypeptide chain. However, the experimentally observed native state is at a minimum of the free energy, rather than the energy. The neglect of the missing configurational entropy contribution to the free energy can be partially justified by the assumption that the entropies of alternative folded states, while very much less than unfolded states, are not too different from one another, and hence can be to a first approximation neglected when searching for the lowest free energy state. The shortcomings of current structure prediction methods may be due in part to the breakdown of this assumption. Particularly problematic are proteins with significant disordered regions which do not populate single low energy conformations even in the native state. We describe two approaches within the Rosetta structure modeling methodology for treating such regions. The first does not require advance knowledge of the regions likely to be disordered; instead these are identified by minimizing a simple free energy function used previously to model protein folding landscapes and transition states. In this model, residues can be either completely ordered or completely disordered; they are considered disordered if the gain in entropy outweighs the loss of favorable energetic interactions with the rest of the protein chain. The second approach requires identification in advance of the disordered regions either from sequence alone using for example the DISOPRED server or from experimental data such as NMR chemical shifts. During Rosetta structure prediction calculations the disordered regions make only unfavorable repulsive contributions to the total energy. We find that the second approach has greater practical utility and illustrate this with examples from de novo structure prediction, NMR structure calculation, and comparative modeling.     

Recognizing protein folds by cluster distance geometry

Cluster distance geometry is a recent generalization of distance geometry whereby protein structures can be described at even lower levels of detail than one point per residue. With improvements in the clustering technique, protein conformations can be summarized in terms of alternative contact patterns between clusters, where each cluster contains four sequentially adjacent amino acid residues. A very simple potential function involving 210 adjustable parameters can be determined that favors the native contacts of 31 small, monomeric proteins over their respective sets of nonnative contacts. This potential then favors the native contacts for 174 small, monomeric proteins that have low sequence identity with any of the training set. A broader search finds 698 small protein chains from the Protein Data Bank where the native contacts are preferred over all alternatives, even though they have low sequence identity with the training set. This amounts to a highly predictive method for ab initio protein folding at low spatial resolution.     

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.     

Benchmarking a computational design method for the incorporation of metal ion‐binding sites at symmetric protein interfaces

The design of novel metal‐ion binding sites along symmetric axes in protein oligomers could provide new avenues for metalloenzyme design, construction of protein‐based nanomaterials and novel ion transport systems. Here, we describe a computational design method, symmetric protein recursive ion‐cofactor sampling (SyPRIS), for locating constellations of backbone positions within oligomeric protein structures that are capable of supporting desired symmetrically coordinated metal ion(s) chelated by sidechains (chelant model). Using SyPRIS on a curated benchmark set of protein structures with symmetric metal binding sites, we found high recovery of native metal coordinating rotamers: in 65 of the 67 (97.0%) cases, native rotamers featured in the best scoring model while in the remaining cases native rotamers were found within the top three scoring models. In a second test, chelant models were crossmatched against protein structures with identical cyclic symmetry. In addition to recovering all native placements, 10.4% (8939/86013) of the non‐native placements, had acceptable geometric compatibility scores. Discrimination between native and non‐native metal site placements was further enhanced upon constrained energy minimization using the Rosetta energy function. Upon sequence design of the surrounding first‐shell residues, we found further stabilization of native placements and a small but significant (1.7%) number of non‐native placement‐based sites with favorable Rosetta energies, indicating their designability in existing protein interfaces. The generality of the SyPRIS approach allows design of novel symmetric metal sites including with non‐natural amino acid sidechains, and should enable the predictive incorporation of a variety of metal‐containing cofactors at symmetric protein interfaces.     

Structure motif discovery and mining the PDB

MOTIVATION: Many of the most interesting functional and evolutionary relationships among proteins are so ancient that they cannot be reliably detected through sequence analysis and are apparent only through a comparison of the tertiary structures. The conserved features can often be described as structural motifs consisting of a few single residues or Secondary Structure (SS) elements. Confidence in such motifs is greatly boosted when they are found in more than a pair of proteins. RESULTS: We describe an algorithm for the automatic discovery of recurring patterns in protein structures. The patterns consist of individual residues having a defined order along the protein's backbone that come close together in the structure and whose spatial conformations are similar. The residues in a pattern need not be close in the protein's sequence. The work described in this paper builds on an earlier reported algorithm for motif discovery. This paper describes a significant improvement of the algorithm which makes it very efficient. The improved efficiency allows us to use it for doing unsupervised learning of patterns occurring in small subsets in a large set of structures, a non-redundant subset of the Protein Data Bank (PDB) database of all known protein structures.     

Three topologically equivalent core residues affect the transition state ensemble in a protein folding reaction

The single domain protein, interleukin-1beta, is representative of a distinct class of proteins characterized by their beta-trefoil topology. Each subdomain of this structural class is composed of a beta beta beta loop beta (betabetabetaLbeta) motif comprised of approximately 50 residues and gives the protein a pseudo- 3-fold axis of symmetry. A common feature of proteins in this topological family appears to be that they are slow folders, which reach the native state on the order of tens to 100s of seconds. Sequence analysis of interleukin-1beta indicates that three phenylalanine residues located at positions 42, 101, and 146 are well conserved, separated by approximately 50 residues in the primary sequence, located in similar positions in the pseudo-symmetric units of the trefoil, and are juxtaposed to one another in conformational space. These residues surround the hydrophobic cavity and "pin" the hairpin triplet cap to the core beta-barrel. To determine if cap-barrel interactions are involved in maintaining the structural stability and cooperativity or in controlling the slow formation of the native state, we performed a series of mutational studies. The results indicate that interleukin-1beta tolerates large increases in side-chain volume at these three topologically conserved sites with little effect on stability, while the kinetics show significant differences in both the unfolding and refolding rates. Taken together, our results indicate that these conserved core residues are essential contacts in the transition-state ensemble for folding.     

SimFold energy function for de novo protein structure prediction: consensus with Rosetta

Predicting protein tertiary structures by in silico folding is still very difficult for proteins that have new folds. Here, we developed a coarse-grained energy function, SimFold, for de novo structure prediction, performed a benchmark test of prediction with fragment assembly simulations for 38 test proteins, and proposed consensus prediction with Rosetta. The SimFold energy consists of many terms that take into account solvent-induced effects on the basis of physicochemical consideration. In the benchmark test, SimFold succeeded in predicting native structures within 6.5 A for 12 of 38 proteins; this success rate was the same as that by the publicly available version of Rosetta (ab initio version 1.2) run with default parameters. We investigated which energy terms in SimFold contribute to structure prediction performance, finding that the hydrophobic interaction is the most crucial for the prediction, whereas other sequence-specific terms have weak but positive roles. In the benchmark, well-predicted proteins by SimFold and by Rosetta were not the same for 5 of 12 proteins, which led us to introduce consensus prediction. With combined decoys, we succeeded in prediction for 16 proteins, four more than SimFold or Rosetta separately. For each of 38 proteins, structural ensembles generated by SimFold and by Rosetta were qualitatively compared by mapping sampled structural space onto two dimensions. For proteins of which one of the two methods succeeded and the other failed in prediction, the former had a less scattered ensemble located around the native. For proteins of which both methods succeeded in prediction, often two ensembles were mixed up.