RosettaHoles: Rapid assessment of protein core packing for structure prediction,refinement, design,and validation

We present a novel method called RosettaHoles for visual and quantitative assessment of underpacking in the protein core. RosettaHoles generates a set of spherical cavity balls that fill the empty volume between atoms in the protein interior. For visualization, the cavity balls are aggregated into contiguous overlapping clusters and small cavities are discarded, leaving an uncluttered representation of the unfilled regions of space in a structure. For quantitative analysis, the cavity ball data are used to estimate the probability of observing a given cavity in a high‐resolution crystal structure. RosettaHoles provides excellent discrimination between real and computationally generated structures, is predictive of incorrect regions in models, identifies problematic structures in the Protein Data Bank, and promises to be a useful validation tool for newly solved experimental structures.     

Atomic contacts in protein structures. A detailed analysis of atomic radii, packing, and overlaps

A rigorous quantitative assessment of atomic contacts and packing in native protein structures is presented. The analysis is based on optimized atomic radii derived from a set of high-resolution protein structures and reveals that the distribution of atomic contacts and overlaps is a structural constraint in proteins, irrespective of structural or functional classification and size. Furthermore, a newly developed method for calculating packing properties is introduced and applied to sets of protein structures at different levels of resolution. The results show that limited resolution yields decreasing packing quality, which underscores the relevance of packing considerations for structure prediction, design, dynamics, and docking.     

PackHelix: a tool for helix-sheet packing during protein structure prediction

The three‐dimensional structure of a protein is organized around the packing of its secondary structure elements. Predicting the topology and constructing the geometry of structural motifs involving α‐helices and/or β‐strands are therefore key steps for accurate prediction of protein structure. While many efforts have focused on how to pack helices and on how to sample exhaustively the topologies and geometries of multiple strands forming a β‐sheet in a protein, there has been little progress on generating native‐like packings of helices on sheets. We describe a method that can generate the packing of multiple helices on a given β‐sheet for αβα sandwich type protein folds. This method mines the results of a statistical analysis of the conformations of αβ₂ motifs in protein structures to provide input values for the geometric attributes of the packing of a helix on a sheet. It then proceeds with a geometric builder that generates multiple arrangements of the helices on the sheet of interest by sampling through these values and performing consistency checks that guarantee proper loop geometry between the helices and the strands, minimal number of collisions between the helices, and proper formation of a hydrophobic core. The method is implemented as a module of ProteinShop. Our results show that it produces structures that are within 4–6 Å RMSD of the native one, regardless of the number of helices that need to be packed, though this number may increase if the protein has several helices between two consecutive strands in the sequence that pack on the sheet formed by these two strands. Proteins 2011; Published 2011 Wiley‐Liss, Inc.     

Analysis of the structure and stability of omega loop A replacements in yeast iso-1-cytochrome c.

Omega (omega)-loop A, residues 18-32 in wild-type yeast iso-1-cytochrome c, has been deleted and replaced with loop sequences from three other cytochromes c and one from esterase. Yeast expressing a partial loop deletion do not contain perceptible amounts of holoprotein as measured by low-temperature spectroscopy and cannot grow on nonfermentable media. Strains expressing loop replacement mutations accumulate holoprotein in vivo, but the protein function varies depending on the sequence and length of the replacement loop; in vivo expression levels do not correlate with their thermal denaturation temperatures. In vitro spectroscopic studies of the loop replacement proteins indicate that all fold into a native-like cytochrome c conformation, but are less stable than the wild-type protein. Decreases in thermal stability are caused by perturbation of loop C backbone in one case and a slight reorganization of the protein hydrophobic core in another case, rather than rearrangement of the loop A backbone. A single-site mutation in one of the replacement mutants designed to relieve inefficient hydrophobic core packing caused by the new loop recovers some, but not all, of the lost stability.     

Side chain burial and hydrophobic core packing in protein folding transition states

A critical step in the folding pathway of globular proteins is the formation of a tightly packed hydrophobic core. Several mutational studies have addressed the question of whether tight packing interactions are present during the rate-limiting step of folding. In some of these investigations, substituted side chains have been assumed to form native-like interactions in the transition state when the folding rates of mutant proteins correlate with their native-state stabilities. Alternatively, it has been argued that side chains participate in nonspecific hydrophobic collapse when the folding rates of mutant proteins correlate with side-chain hydrophobicity. In a reanalysis of published data, we have found that folding rates often correlate similarly well, or poorly, with both native-state stability and side-chain hydrophobicity, and it is therefore not possible to select an appropriate transition state model based on these one-parameter correlations. We show that this ambiguity can be resolved using a two-parameter model in which side chain burial and the formation of all other native-like interactions can occur asynchronously. Notably, the model agrees well with experimental data, even for positions where the one-parameter correlations are poor. We find that many side chains experience a previously unrecognized type of transition state environment in which specific, native-like interactions are formed, but hydrophobic burial dominates. Implications of these results to the design and analysis of protein folding studies are discussed.     

Shorter side chains optimize helix-helix packing

A systematic study of helix-helix packing in a comprehensive database of protein structures revealed that the side chains inside helix-helix interfaces on average are shorter than those in the noninterface parts of the helices. The study follows our earlier study of this effect in transmembrane helices. The results obtained on the entire database of protein structures are consistent with those obtained on the transmembrane helices. The difference in the length of interface and noninterface side chains is small but statistically significant. It indicates that helices, if viewed along their main axis, statistically are not circular, but have a flattened interface. This effect brings the helices closer to each other and creates a tighter structural packing. The results provide an interesting insight into the aspects of protein structure and folding.     

Mechanics and dynamics of B1 domain of protein G: role of packing and surface hydrophobic residues

The structural organization of the B1 domain of streptococcal protein G (PGA) has been probed using molecular dynamics simulations, with a particular emphasis on the role of the solvent exposed Ile6 residue. In addition to the native protein (WT-PGA), three single-mutants (I6G-PGA, I6F-PGA, and I6T-PGA), one double-mutant (I6T,T53G-PGA), and three isolated peptide fragments (corresponding to the helix and the two beta-hairpins) were studied in the presence of explicit water molecules. Comparative analysis of the various systems showed that the level of perturbation was directly related to the hydrophobicity and the size of the side chain of residue 6, the internal rigidity of the proteins decreasing in the order I6T-PGA > I6G-PGA > WT-PGA > I6F-PGA. The results emphasized the importance of residue 6 in controlling both the integrity of the sheet's surface and the orientation of the helix in relation to the sheet by modulation of surface/core interactions. The effects of mutations were delocalized across the structure, and glycine residues, in particular, absorbed most of the introduced strain. A qualitative structural decomposition of the native fold into elementary building-blocks was achieved using principal component analysis and mechanical response matrices. Within this framework, internal motions of the protein were described as coordinated articulations of these structural units, mutations affecting mostly the amplitude of the motions rather than the structure/location of the building-blocks. Analysis of the isolated peptidic fragments suggested that packing did not play a determinant role in defining the elementary building-blocks, but that chain topology was mostly responsible.     

Physical principles of protein structure and protein folding

Physical principles determining the protein structure and protein folding are reviewed: (i) the molecular theory of protein secondary structure and the method of its prediction based on this theory; (ii) the existence of a limited set of thermodynamically favourable folding patterns of α- and β-regions in a compact globule which does not depend on the details of the amino acid sequence; (iii) the moderns approaches to the prediction of the folding patterns of α- and β-regions in concrete proteins; (iv) experimental approaches to the mechanism of protein folding. The review reflects theoretical and experimental works of the author and his collaborators as well as those of other groups.     

A database of protein structure families with common folding motifs.

The availability of fast and robust algorithms for protein structure comparison provides an opportunity to produce a database of three-dimensional comparisons, called families of structurally similar proteins (FSSP). The database currently contains an extended structural family for each of 154 representative (below 30% sequence identity) protein chains. Each data set contains: the search structure; all its relatives with 70-30% sequence identity, aligned structurally; and all other proteins from the representative set that contain substructures significantly similar to the search structure. Very close relatives (above 70% sequence identity) rarely have significant structural differences and are excluded. The alignments of remote relatives are the result of pairwise all-against-all structural comparisons in the set of 154 representative protein chains. The comparisons were carried out with each of three novel automatic algorithms that cover different aspects of protein structure similarity. The user of the database has the choice between strict rigid-body comparisons and comparisons that take into account interdomain motion or geometrical distortions; and, between comparisons that require strictly sequential ordering of segments and comparisons, which allow altered topology of loop connections or chain reversals. The data sets report the structurally equivalent residues in the form of a multiple alignment and as a list of matching fragments to facilitate inspection by three-dimensional graphics. If substructures are ignored, the result is a database of structure alignments of full-length proteins, including those in the twilight zone of sequence similarity.(ABSTRACT TRUNCATED AT 250 WORDS)     

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.     

Solution structure of switch Arc,a mutant with 3(10) helices replacing a wild-type beta-ribbon

Adjacent N11L and L12N mutations in the antiparallel beta-ribbon of Arc repressor result in dramatic changes in local structure in which each beta-strand is replaced by a right-handed helix. The full solution structure of this "switch" Arc mutant shows that irregular 3(10) helices compose the new secondary structure. This structural metamorphosis conserves the number of main-chain and side-chain to main-chain hydrogen bonds and the number of fully buried core residues. Apart from a slight widening of the interhelical angle between alpha-helices A and B and changes in side-chain conformation of a few core residues in Arc, no large-scale structural adjustments in the remainder of the protein are necessary to accommodate the ribbon-to-helix change. Nevertheless, some changes in hydrogen-exchange rates are observed, even in regions that have very similar structures in the two proteins. The surface of switch Arc is packed poorly compared to wild-type, leading to approximately 1000A(2) of additional solvent-accessible surface area, and the N termini of the 3(10) helices make unfavorable head-to-head electrostatic interactions. These structural features account for the positive m value and salt dependence of the ribbon-to-helix transition in Arc-N11L, a variant that can adopt either the mutant or wild-type structures. The tertiary fold is capped in different ways in switch and wild-type Arc, showing how stepwise evolutionary transformations can arise through small changes in amino acid sequence.     

Using physical features of protein core packing to distinguish real proteins from decoys

The ability to consistently distinguish real protein structures from computationally generated model decoys is not yet a solved problem. One route to distinguish real protein structures from decoys is to delineate the important physical features that specify a real protein. For example, it has long been appreciated that the hydrophobic cores of proteins contribute significantly to their stability. We used two sources to obtain datasets of decoys to compare with real protein structures: submissions to the biennial Critical Assessment of protein Structure Prediction competition, in which researchers attempt to predict the structure of a protein only knowing its amino acid sequence, and also decoys generated by 3DRobot, which have user‐specified global root‐mean‐squared deviations from experimentally determined structures. Our analysis revealed that both sets of decoys possess cores that do not recapitulate the key features that define real protein cores. In particular, the model structures appear more densely packed (because of energetically unfavorable atomic overlaps), contain too few residues in the core, and have improper distributions of hydrophobic residues throughout the structure. Based on these observations, we developed a feed‐forward neural network, which incorporates key physical features of protein cores, to predict how well a computational model recapitulates the real protein structure without knowledge of the structure of the target sequence. By identifying the important features of protein structure, our method is able to rank decoy structures with similar accuracy to that obtained by state‐of‐the‐art methods that incorporate many additional features. The small number of physical features makes our model interpretable, emphasizing the importance of protein packing and hydrophobicity in protein structure prediction.     

An amino acid code for irregular and mixed protein packing

To advance our understanding of protein tertiary structure, the development of the knob‐socket model is completed in an analysis of the packing in irregular coil and turn secondary structure packing as well as between mixed secondary structure. The knob‐socket model simplifies packing based on repeated patterns of two motifs: a three‐residue socket for packing within secondary (2°) structure and a four‐residue knob‐socket for tertiary (3°) packing. For coil and turn secondary structure, knob‐sockets allow identification of a correlation between amino acid composition and tertiary arrangements in space. Coil contributes almost as much as α‐helices to tertiary packing. In irregular sockets, Gly, Pro, Asp, and Ser are favored, while in irregular knobs, the preference order is Arg, Asp, Pro, Asn, Thr, Leu, and Gly. Cys, His,Met, and Trp are not favored in either. In mixed packing, the knob amino acid preferences are a function of the socket that they are packing into, whereas the amino acid composition of the sockets does not depend on the secondary structure of the knob. A unique motif of a coil knob with an XYZ β‐sheet socket may potentially function to inhibit β‐sheet extension. In addition, analysis of the preferred crossing angles for strands within a β‐sheet and mixed α‐helice/β‐sheet identifies canonical packing patterns useful in protein design. Lastly, the knob‐socket model abstracts the complexity of protein tertiary structure into an intuitive packing surface topology map. Proteins 2015; 83:2147–2161. © 2015 Wiley Periodicals, Inc.     

Benchmarking of structure refinement methods for protein complex models

Protein structure docking is the process in which the quaternary structure of a protein complex is predicted from individual tertiary structures of the protein subunits. Protein docking is typically performed in two main steps. The subunits are first docked while keeping them rigid to form the complex, which is then followed by structure refinement. Structure refinement is crucial for a practical use of computational protein docking models, as it is aimed for correcting conformations of interacting residues and atoms at the interface. Here, we benchmarked the performance of eight existing protein structure refinement methods in refinement of protein complex models. We show that the fraction of native contacts between subunits is by far the most straightforward metric to improve. However, backbone dependent metrics, based on the Root Mean Square Deviation proved more difficult to improve via refinement.     

Occluded molecular surface: Analysis of protein packing

We describe a novel method to calculate the packing interactions in protein structural models. The method calculates the interatomic occluded surface areas for each atom in the protein model. The identification of, and degree of interaction with, neighboring atoms is accomplished by extending surface normal from a dot surface of each atom to the point of intersection with neighboring atoms. The combined occluded and non-occluded surface areas may be normalized for the amino acid composition of the protein providing a single parameter, the normalized protein surface ratio, which is diagnostic for native-like Structures. Individual residues in the model which are in infrequent occluded surface environments may be identified. The method provides a means to explicitly describe packing densities and packing environments of individual atoms in a protein model. Finally, the method allows estimation of the complementarity between any interacting molecules, for example a ligand binding to a receptor.     

Non-randomness in side-chain packing: the distribution of interplanar angles

We analyze the distributions of interplanar angles between interacting side chains with well-defined planar regions, to see whether these distributions correspond to random packing or alternatively show orientational preferences. We use a non-homologous set of 79 high-resolution protein chain structures to show that the observed distributions are significantly different from the sinusoidal one expected for random packing. Overall, we see a relative excess of small angles and a paucity of large interplanar angles; the difference between the expected and observed distributions can be described as a shift of 5% of the interplanar angles from large (≥60°) to small (<30°) values. By grouping the residue pairs into categories based on chemical similarity, we find that some categories have very non-sinusoidal interplanar angle distributions, whereas other categories have distributions that are close to sinusoidal. For a few categories, observed deviations from a sinusoidal distribution can be explained by the electrostatic anisotropy of the isolated pair potential energy. In other cases, the observed distributions reflect the longer range effects of different possible interaction geometries. In particular, geometries that disrupt external hydrogen bonding are disfavored. Proteins 29:370–380, 1997. © 1997 Wiley-Liss, Inc.     

The 0.83 A resolution crystal structure of alpha-lytic protease reveals the detailed structure of the active site and identifies a source of conformational strain

The crystal structure of the extracellular bacterial serine protease α-lytic protease (αLP) has been solved at 0.83 Å resolution at pH 8. This ultra-high resolution structure allows accurate analysis of structural elements not possible with previous structures. Hydrogen atoms are visible, and confirm active-site hydrogen-bonding interactions expected for the apo enzyme. In particular, His57 N^δ1 participates in a normal hydrogen bond with Asp102 in the catalytic triad, with a hydrogen atom visible 0.83(±0.06) Å from the His N^δ1. The catalytic Ser195 occupies two conformations, one corresponding to a population of His57 that is doubly protonated, the other to the singly protonated His57. Based on the occupancy of these conformations, the pK_a of His57 is calculated to be ∼8.8 when a sulfate ion occupies the active site. This 0.83 Å structure has allowed critical analysis of geometric distortions within the structure. Interestingly, Phe228 is significantly distorted from planarity. The distortion of Phe228, buried in the core of the C-terminal domain, occurs at an estimated energetic cost of 4.1 kcal/mol. The conformational space for Phe228 is severely limited by the presence of Trp199, which prevents Phe228 from adopting the rotamer observed in many other chymotrypsin family members. In αLP, the only allowed rotamer leads to the deformation of Phe228 due to steric interactions with Thr181. We hypothesize that tight packing of co-evolved residues in this region, and the subsequent deformation of Phe228, contributes to the high cooperativity and large energetic barriers for folding and unfolding of αLP. The kinetic stability imparted by the large, cooperative unfolding barrier plays a critical role in extending the lifetime of the protease in its harsh environment.     

Partial unfolding and refolding for structure refinement: A unified approach of geometric simulations and molecular dynamics

The most successful protein structure prediction methods to date have been template‐based modeling (TBM) or homology modeling, which predicts protein structure based on experimental structures. These high accuracy predictions sometimes retain structural errors due to incorrect templates or a lack of accurate templates in the case of low sequence similarity, making these structures inadequate in drug‐design studies or molecular dynamics simulations. We have developed a new physics based approach to the protein refinement problem by mimicking the mechanism of chaperons that rehabilitate misfolded proteins. The template structure is unfolded by selectively (targeted) pulling on different portions of the protein using the geometric based technique FRODA, and then refolded using hierarchically restrained replica exchange molecular dynamics simulations (hr‐REMD). FRODA unfolding is used to create a diverse set of topologies for surveying near native‐like structures from a template and to provide a set of persistent contacts to be employed during re‐folding. We have tested our approach on 13 previous CASP targets and observed that this method of folding an ensemble of partially unfolded structures, through the hierarchical addition of contact restraints (that is, first local and then nonlocal interactions), leads to a refolding of the structure along with refinement in most cases (12/13). Although this approach yields refined models through advancement in sampling, the task of blind selection of the best refined models still needs to be solved. Overall, the method can be useful for improved sampling for low resolution models where certain of the portions of the structure are incorrectly modeled. Proteins 2015; 83:2279–2292. © 2015 Wiley Periodicals, Inc.     

Crystal packing effects on protein loops

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

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.