Distributions of beta sheets in proteins with application to structure prediction

We recently developed the Rosetta algorithm for ab initio protein structure prediction, which generates protein structures from fragment libraries using simulated annealing. The scoring function in this algorithm favors the assembly of strands into sheets. However, it does not discriminate between different sheet motifs. After generating many structures using Rosetta, we found that the folding algorithm predominantly generates very local structures. We surveyed the distribution of beta-sheet motifs with two edge strands (open sheets) in a large set of non-homologous proteins. We investigated how much of that distribution can be accounted for by rules previously published in the literature, and developed a filter and a scoring method that enables us to improve protein structure prediction for beta-sheet proteins. Proteins 2002;48:85-97.     

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.     

Interaction cutoff effect on ruggedness of protein-protein energy landscape

The concept of the energy landscape is important for better understanding of protein-protein interactions and for designing adequate docking procedures. The intermolecular landscape has a rugged terrain that impedes search procedures. Its inherent ruggedness is related to the conformational characteristics of the molecules and to the form of the potential function--more rugged for short-range potentials and less rugged for "soft," typically long-range potentials. Our study determined that the landscape ruggedness is further substantially exacerbated by truncation of the potentials. This additional ruggedness appears below certain critical interaction ranges that depend on the form of the potential. The theoretical model describing the cutoff effect on the landscape ruggedness is confirmed by the energy calculation on a dataset of protein-protein complexes. The negative effect of the potentials cutoff is well known. However, revealing its physical basis in terms of the energy landscape is important for better understanding of intermolecular interactions.     

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.     

Large-scale characteristics of the energy landscape in protein-protein interactions

Characterization of intermolecular energy landscapes in protein-protein interactions is important for understanding the mechanisms of these interactions as well as for designing better protein docking methods. A simplified representation of the landscape was used for a systematic study of its large-scale characteristics in a large nonredundant dataset of protein complexes. The focus of the study is on the basic features of the low-resolution energy basins and their distribution on the landscape. The results clearly show that, in general, the number of such basins is small, these basins are well formed, correlated with actual binding modes, and the pattern of basins distribution depends on the type of the complex. For docking studies, the results suggest that adequate starting points for the structural refinement are detectable by low-resolution procedures and the number of such starting points is relatively small.     

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.     

Improved beta-protein structure prediction by multilevel optimization of nonlocal strand pairings and local backbone conformation

Proteins with complex, nonlocal beta-sheets are challenging for de novo structure prediction, due in part to the difficulty of efficiently sampling long-range strand pairings. We present a new, multilevel approach to beta-sheet structure prediction that circumvents this difficulty by reformulating structure generation in terms of a folding tree. Nonlocal connections in this tree allow us to explicitly sample alternative beta-strand pairings while simultaneously exploring local conformational space using backbone torsion-space moves. An iterative, energy-biased resampling strategy is used to explore the space of beta-strand pairings; we expect that such a strategy will be generally useful for searching large conformational spaces with a high degree of combinatorial complexity.     

Relaxation of backbone bond geometry improves protein energy landscape modeling

A key issue in macromolecular structure modeling is the granularity of the molecular representation. A fine‐grained representation can approximate the actual structure more accurately, but may require many more degrees of freedom than a coarse‐grained representation and hence make conformational search more challenging. We investigate this tradeoff between the accuracy and the size of protein conformational search space for two frequently used representations: one with fixed bond angles and lengths and one that has full flexibility. We performed large‐scale explorations of the energy landscapes of 82 protein domains under each model, and find that the introduction of bond angle flexibility significantly increases the average energy gap between native and non‐native structures. We also find that incorporating bonded geometry flexibility improves low resolution X‐ray crystallographic refinement. These results suggest that backbone bond angle relaxation makes an important contribution to native structure energetics, that current energy functions are sufficiently accurate to capture the energetic gain associated with subtle deformations from chain ideality, and more speculatively, that backbone geometry distortions occur late in protein folding to optimize packing in the native state.     

Probing the high energy states in proteins by proteolysis

Unless the native conformation has an unstructured region, proteases cannot effectively digest a protein under native conditions. Digestion must occur from a higher energy form, when at least some part of the protein is exposed to solvent and becomes accessible by proteases. Monitoring the kinetics and denaturant dependence of proteolysis under native conditions yields insight into the mechanism of proteolysis as well as these high-energy conformations. We propose here a generalized approach to exploit proteolysis as a tool to probe high-energy states in proteins. This "native state proteolysis" experiment was carried out on Escherichia coli ribonuclease HI. Mass spectrometry and N-terminal sequencing showed that thermolysin cleaves the peptide bond between Thr92 and Ala93 in an extended loop region of the protein. By comparing the proteolysis rate of the folded protein and a peptidic substrate mimicking the sequence at the cleavage site, the energy required to reach the susceptible state (Delta G(proteolysis)) was determined. From the denaturant dependence of Delta G(proteolysis), we determined that thermolysin digests this protein through a local fluctuation, i.e. localized unfolding with minimal change in solvent assessable surface area. Proteolytic susceptibilities of proteins are discussed based on the finding of this local fluctuation mechanism for proteolysis under native conditions.     

Exploring alternate states and oligomerization preferences of coiled‐coils by de novo structure modeling

Homomeric coiled‐coils can self‐assemble into a wide range of structural states with different helix topologies and oligomeric states. In this study, we have combined de novo structure modeling with stability calculations to simultaneously predict structure and oligomeric states of homomeric coiled‐coils. For dimers an asymmetric modeling protocol was developed. Modeling without symmetry constraints showed that backbone asymmetry is important for the formation of parallel dimeric coiled‐coils. Collectively, our results demonstrate that high‐resolution structure of coiled‐coils, as well as parallel and antiparallel orientations of dimers and tetramers, can be accurately predicted from sequence. De novo modeling was also used to generate models of competing oligomeric states, which were used to compare stabilities and thus predict the native stoichiometry from sequence. In a benchmark set of 33 coiled‐coil sequences, forming dimers to pentamers, up to 70% of the oligomeric states could be correctly predicted. The calculations demonstrated that the free energy of helix folding could be an important factor for determining stability and oligomeric state of homomeric coiled‐coils. The computational methods developed here should be broadly applicable to studies of sequence‐structure relationships in coiled‐coils and the design of higher order assemblies with improved oligomerization specificity. Proteins 2015; 83:235–247. © 2014 Wiley Periodicals, Inc.     

Probing the energy landscape of protein folding/unfolding transition states

Previous molecular dynamics (MD) simulations of the thermal denaturation of chymotrypsin inhibitor 2 (CI2) have provided atomic-resolution models of the transition state ensemble that is well supported by experimental studies. Here, we use simulations to further investigate the energy landscape around the transition state region. Nine structures within approximately 35 ps and 3 A C(alpha) RMSD of the transition state ensemble identified in a previous 498 K thermal denaturation simulation were quenched under the quasi-native conditions of 335 K and neutral pH. All of the structures underwent hydrophobically driven collapse in response to the drop in temperature. Structures less denatured than the transition state became structurally more native-like, while structures that were more denatured than the transition state tended to show additional loss of native structure. The structures in the immediate region of the transition state fluctuated between becoming more and less native-like. All of the starting structures had the same native-like topology and were quite similar (within 3.5 A C(alpha) RMSD). That the structures all shared native-like topology, yet diverged into either more or less native-like structures depending on which side of the transition state they occupied on the unfolding trajectory, indicates that topology alone does not dictate protein folding. Instead, our results suggest that a detailed interplay of packing interactions and interactions with water determine whether a partially denatured protein will become more native-like under refolding conditions.     

De novo structure generation using chemical shifts for proteins with high‐sequence identity but different folds

Proteins with high‐sequence identity but very different folds present a special challenge to sequence‐based protein structure prediction methods. In particular, a 56‐residue three‐helical bundle protein (GA⁹⁵) and an α/β‐fold protein (GB⁹⁵), which share 95% sequence identity, were targets in the CASP‐8 structure prediction contest. With only 12 out of 300 submitted server‐CASP8 models for GA⁹⁵ exhibiting the correct fold, this protein proved particularly challenging despite its small size. Here, we demonstrate that the information contained in NMR chemical shifts can readily be exploited by the CS‐Rosetta structure prediction program and yields adequate convergence, even when input chemical shifts are limited to just amide ¹H^N and ¹⁵N or ¹H^N and ¹H^α values.     

Sampling Bottlenecks in De novo Protein Structure Prediction

The primary obstacle to de novo protein structure prediction is conformational sampling: the native state generally has lower free energy than nonnative structures but is exceedingly difficult to locate. Structure predictions with atomic level accuracy have been made for small proteins using the Rosetta structure prediction method, but for larger and more complex proteins, the native state is virtually never sampled, and it has been unclear how much of an increase in computing power would be required to successfully predict the structures of such proteins. In this paper, we develop an approach to determining how much computer power is required to accurately predict the structure of a protein, based on a reformulation of the conformational search problem as a combinatorial sampling problem in a discrete feature space. We find that conformational sampling for many proteins is limited by critical “linchpin” features, often the backbone torsion angles of individual residues, which are sampled very rarely in unbiased trajectories and, when constrained, dramatically increase the sampling of the native state. These critical features frequently occur in less regular and likely strained regions of proteins that contribute to protein function. In a number of proteins, the linchpin features are in regions found experimentally to form late in folding, suggesting a correspondence between folding in silico and in reality.     

Comparison of NMR and crystal structures of membrane proteins and computational refinement to improve model quality

Membrane proteins are challenging to study and restraints for structure determination are typically sparse or of low resolution because the membrane environment that surrounds them leads to a variety of experimental challenges. When membrane protein structures are determined by different techniques in different environments, a natural question is “which structure is most biologically relevant?” Towards answering this question, we compiled a dataset of membrane proteins with known structures determined by both solution NMR and X‐ray crystallography. By investigating differences between the structures, we found that RMSDs between crystal and NMR structures are below 5 Å in the membrane region, NMR ensembles have a higher convergence in the membrane region, crystal structures typically have a straighter transmembrane region, have higher stereo‐chemical correctness, and are more tightly packed. After quantifying these differences, we used high‐resolution refinement of the NMR structures to mitigate them, which paves the way for identifying and improving the structural quality of membrane proteins.     

Conserved residue clustering and protein structure prediction

Protein residues that are critical for structure and function are expected to be conserved throughout evolution. Here, we investigate the extent to which these conserved residues are clustered in three-dimensional protein structures. In 92% of the proteins in a data set of 79 proteins, the most conserved positions in multiple sequence alignments are significantly more clustered than randomly selected sets of positions. The comparison to random subsets is not necessarily appropriate, however, because the signal could be the result of differences in the amino acid composition of sets of conserved residues compared to random subsets (hydrophobic residues tend to be close together in the protein core), or differences in sequence separation of the residues in the different sets. In order to overcome these limits, we compare the degree of clustering of the conserved positions on the native structure and on alternative conformations generated by the de novo structure prediction method Rosetta. For 65% of the 79 proteins, the conserved residues are significantly more clustered in the native structure than in the alternative conformations, indicating that the clustering of conserved residues in protein structures goes beyond that expected purely from sequence locality and composition effects. The differences in the spatial distribution of conserved residues can be utilized in de novo protein structure prediction: We find that for 79% of the proteins, selection of the Rosetta generated conformations with the greatest clustering of the conserved residues significantly enriches the fraction of close-to-native structures.     

Challenges in structure prediction of oligomeric proteins at the united-residue level: searching the multiple-chain energy landscape with CSA and CFMC

A revised version of the Conformational Space Annealing (CSA) global optimization method is developed, with three separate measures of structural similarity, in order to overcome the inability of a single distance measure to evaluate multiple-chain protein structures adequately. A second search method, Conformational Family Monte Carlo (CFMC), involving genetic-type moves, Monte Carlo-with-minimization perturbations, and explicit clustering of the population into conformational families, is adapted to treat multiple-chain proteins. These two methods are applied to two oligomeric proteins, the retro-GCN4 leucine zipper and the synthetic domain-swapped dimer. CFMC proves superior to CSA in its search for low-energy representatives of its conformational families, but both methods encounter difficulty in finding the native packing arrangements in the absence of native-like symmetry constraints, even when native monomers are present in the population.     

Progress and challenges in high-resolution refinement of protein structure models

Achieving atomic level accuracy in de novo structure prediction presents a formidable challenge even in the context of protein models with correct topologies. High-resolution refinement is a fundamental test of force field accuracy and sampling methodology, and its limited success in both comparative modeling and de novo prediction contexts highlights the limitations of current approaches. We constructed four tests to identify bottlenecks in our current approach and to guide progress in this challenging area. The first three tests showed that idealized native structures are stable under our refinement simulation conditions and that the refinement protocol can significantly decrease the root mean square deviation (RMSD) of perturbed native structures. In the fourth test we applied the refinement protocol to de novo models and showed that accurate models could be identified based on their energies, and in several cases many of the buried side chains adopted native-like conformations. We also showed that the differences in backbone and side-chain conformations between the refined de novo models and the native structures are largely localized to loop regions and regions where the native structure has unusual features such as rare rotamers or atypical hydrogen bonding between beta-strands. The refined de novo models typically have higher energies than refined idealized native structures, indicating that sampling of local backbone conformations and side-chain packing arrangements in a condensed state is a primary obstacle.     

Systematic evaluation of CS‐Rosetta for membrane protein structure prediction with sparse NOE restraints

We critically test and validate the CS‐Rosetta methodology for de novo structure prediction of ‐helical membrane proteins (MPs) from NMR data, such as chemical shifts and NOE distance restraints. By systematically reducing the number and types of NOE restraints, we focus on determining the regime in which MP structures can be reliably predicted and pinpoint the boundaries of the approach. Five MPs of known structure were used as test systems, phototaxis sensory rhodopsin II (pSRII), a subdomain of pSRII, disulfide binding protein B (DsbB), microsomal prostaglandin E2 synthase‐1 (mPGES‐1), and translocator protein (TSPO). For pSRII and DsbB, where NMR and X‐ray structures are available, resolution‐adapted structural recombination (RASREC) CS‐Rosetta yields structures that are as close to the X‐ray structure as the published NMR structures if all available NMR data are used to guide structure prediction. For mPGES‐1 and Bacillus cereus TSPO, where only X‐ray crystal structures are available, highly accurate structures are obtained using simulated NMR data. One main advantage of RASREC CS‐Rosetta is its robustness with respect to even a drastic reduction of the number of NOEs. Close‐to‐native structures were obtained with one randomly picked long‐range NOEs for every 14, 31, 38, and 8 residues for full‐length pSRII, the pSRII subdomain, TSPO, and DsbB, respectively, in addition to using chemical shifts. For mPGES‐1, atomically accurate structures could be predicted even from chemical shifts alone. Our results show that atomic level accuracy for helical membrane proteins is achievable with CS‐Rosetta using very sparse NOE restraint sets to guide structure prediction. Proteins 2017; 85:812–826. © 2016 Wiley Periodicals, Inc.