STUDIES ON THE CONFORMATION OF AMINO ACIDS

Benzoyl Valine Quasiracemates: Pairing CF3 Quasienantiomers with H to t-Butyl

Understanding the interplay of structural features responsible for molecular assembly is essential for molecular crystal engineering. When assembling molecules with encoded motifs, first choice supramolecular strategies almost always include robust directional nonbonded contacts. Quasiracemic materials, considered near racemates since cocrystallization occurs with chemically unique components, lack a molecular framework or functional group restrictions, highlighting the importance of molecular shape to molecular assembly. Recently, our group reported quasiracemates derived from benzoyl leucine/phenylalanine derivatives with two points of chemical difference. In this study, we modified the chemical framework with valine and increased the scope of the work by imposing a larger variance in the side chain substituents. Pairing a CF3 component with quasienantiomers that differ iteratively from hydrogen to t-butyl offers an important view into the supramolecular landscape of these materials. Single-crystal X-ray crystallography and lattice energy assessments, coupled with conformational and crystal structure similarity searches, show an elevated degree of isomorphism for many of the targeted 17 racemates and quasiracemates. These benzoyl amino acid molecular architectures create extended hydrogen-bond patterns in the crystal that provide enhanced opportunities to study the shape space and molecular recognition profiles for a diverse family of quasienantiomeric components.

Data-Efficient Generation of Protein Conformational Ensembles with Backbone-to-Side-Chain Transformers

Excitement at the prospect of using data-driven generative models to sample configurational ensembles of biomolecular systems stems from the extraordinary success of these models on a diverse set of high-dimensional sampling tasks. Unlike image generation or even the closely related problem of protein structure prediction, there are currently no data sources with sufficient breadth to parametrize generative models for conformational ensembles. To enable discovery, a fundamentally different approach to building generative models is required: models should be able to propose rare, albeit physical, conformations that may not arise in even the largest data sets. Here we introduce a modular strategy to generate conformations based on "backmapping" from a fixed protein backbone that (1) maintains conformational diversity of the side chains and (2) couples the side-chain fluctuations using global information about the protein conformation. Our model combines simple statistical models of side-chain conformations based on rotamer libraries with the now ubiquitous transformer architecture to sample with atomistic accuracy. Together, these ingredients provide a strategy for rapid data acquisition and hence a crucial ingredient for scalable physical simulation with generative neural networks.

Exploiting Sequence-Dependent Rotamer Information in Global Optimization of Proteins

Rotamers, namely amino acid side chain conformations common to many different peptides, can be compiled into libraries. These rotamer libraries are used in protein modeling, where the limited conformational space occupied by amino acid side chains is exploited. Here, we construct a sequence-dependent rotamer library from simulations of all possible tripeptides, which provides rotameric states dependent on adjacent amino acids. We observe significant sensitivity of rotamer populations to sequence and find that the library is successful in locating side chain conformations present in crystal structures. The library is designed for applications with basin-hopping global optimization, where we use it to propose moves in conformational space. The addition of rotamer moves significantly increases the efficiency of protein structure prediction within this framework, and we determine parameters to optimize efficiency.

Protein design via deep learning

Proteins with desired functions and properties are important in fields like nanotechnology and biomedicine. De novo protein design enables the production of previously unseen proteins from the ground up and is believed as a key point for handling real social challenges. Recent introduction of deep learning into design methods exhibits a transformative influence and is expected to represent a promising and exciting future direction. In this review, we retrospect the major aspects of current advances in deep-learning-based design procedures and illustrate their novelty in comparison with conventional knowledge-based approaches through noticeable cases. We not only describe deep learning developments in structure-based protein design and direct sequence design, but also highlight recent applications of deep reinforcement learning in protein design. The future perspectives on design goals, challenges and opportunities are also comprehensively discussed.

Toward a Computational NMR Procedure for Modeling Dipeptide Side-Chain Conformation

Theoretical relationships between the vicinal spin–spin coupling constants (SSCCs) and the χ₁ torsion angles have been studied to predict the conformations of protein side chains. An efficient computational procedure is developed to obtain the conformation of dipeptides through theoretical and experimental SSCCs, Karplus equations, and quantum chemistry methods, and it is applied to three aliphatic hydrophobic residues (Val, Leu, and Ile). Three models are proposed: unimodal-static, trimodal-static-stepped, and trimodal-static-trigonal, where the most important factors are incorporated (coupled nuclei, nature and orientation of the substituents, and local geometric properties). Our results are validated by comparison with NMR and X-ray empirical data described in the literature, obtaining successful results on the 29 residues considered. Using out trimodal residue treatment, it is possible to detect and resolve residues with a simple conformation and those with two or three staggered conformers. In four residues, a deeper analysis explains that they do not have a unique conformation and that the population of each conformation plays an important role.

Recent advances in de novo protein design: Principles, methods, and applications

The computational de novo protein design is increasingly applied to address a number of key challenges in biomedicine and biological engineering. Successes in expanding applications are driven by advances in design principles and methods over several decades. Here, we review recent innovations in major aspects of the de novo protein design and include how these advances were informed by principles of protein architecture and interactions derived from the wealth of structures in the Protein Data Bank. We describe developments in de novo generation of designable backbone structures, optimization of sequences, design scoring functions, and the design of the function. The advances not only highlight design goals reachable now but also point to the challenges and opportunities for the future of the field.

New Dynamic Rotamer Libraries: Data-Driven Analysis of Side-Chain Conformational Propensities

Most rotamer libraries are generated from subsets of the PDB and do not fully represent the conformational scope of protein side chains. Previous attempts to rectify this sparse coverage of conformational space have involved application of weighting and smoothing functions. We resolve these limitations by using physics-based molecular dynamics simulations to determine more accurate frequencies of rotameric states. This work forms part of our Dynameomics initiative and uses a set of 807 proteins selected to represent 97% of known autonomous protein folds, thereby eliminating the bias toward common topologies found within the PDB. Our Dynameomics derived rotamer libraries encompass 4.8 × 10(9) rotamers, sampled from at least 51,000 occurrences of each of 93,642 residues. Here, we provide a backbone-dependent rotamer library, based on secondary structure ϕ/ψ regions, and an update to our 2011 backbone-independent library that addresses the doubling of our dataset since its original publication.

SDRL: a sequence-dependent protein side-chain rotamer library

Since the introduction of the first protein side-chain rotamer library (RL) almost half a century ago, RLs have been components of many programs and algorithms in structural bioinformatics. Based on the dependence of side-chain dihedral angles on the local backbone, three types of RLs have been identified: backbone-independent, secondary-structure-dependent and backbone-dependent. In all previous studies, the effect of sequence specificity on side-chain conformational preferences was neglected. In the effort to develop a new class of RLs, we considered that the side-chain conformation of the central residue in each triplet on a protein backbone depends on the sequence of the triplet; therefore, we developed a sequence-dependent rotamer library (SDRL). To accomplish this, 400 possible triplet sequences for 18 natural amino acids as the central residue, which corresponds to 7200 triplet sequences in total, were considered. Searching the set of 11 546 selected PDB entries for the 7200 triplet sequences resulted in 2 364 541 instances occurring for 18 amino acids. Our results show that Leu and Val experience minimal impact from the adjacent residues in adopting side-chain conformations. Cys, Ile, Trp, His, Asp, Met, Glu, Gln, Arg and Lys, on the other hand, adopt their side-chain conformations mostly based on the adjacent residues on the backbone. The remaining residue types were moderately dependent on the adjacent residues. Using the new library, side-chain repacking algorithms can find preferred conformations of each residue more easily than with other backbone-independent RLs.

A three dimensional visualisation approach to protein heavy-atom structure reconstruction

Background

A commonly recurring problem in structural protein studies, is the determination of all heavy atom positions from the knowledge of the central α-carbon coordinates.

Results

We employ advances in virtual reality to address the problem. The outcome is a 3D visualisation based technique where all the heavy backbone and side chain atoms are treated on equal footing, in terms of the C_α coordinates. Each heavy atom is visualised on the surfaces of a different two-sphere, that is centered at another heavy backbone and side chain atoms. In particular, the rotamers are visible as clusters, that display a clear and strong dependence on the underlying backbone secondary structure.

Conclusions

We demonstrate that there is a clear interdependence between rotameric states and secondary structure. Our method easily detects those atoms in a crystallographic protein structure which are either outliers or have been likely misplaced, possibly due to radiation damage. Our approach forms a basis for the development of a new generation, visualization based side chain construction, validation and refinement tools. The heavy atom positions are identified in a manner which accounts for the secondary structure environment, leading to improved accuracy.

Electronic supplementary material

The online version of this article (doi:10.1186/s12900-014-0027-8) contains supplementary material, which is available to authorized users.

Design of a rotamer library for coarse-grained models in protein-folding simulations

Rotamer libraries usually contain geometric information to trace an amino acid side chain, atom by atom, onto a protein backbone. These libraries have been widely used in protein design, structure refinement and prediction, homology modeling, and X-ray and NMR structure validation. However, they usually present too much information and are not always fully compatible with the coarse-grained models of the protein geometry that are frequently used to tackle the protein-folding problem through molecular simulation. In this work, we introduce a new backbone-dependent rotamer library for side chains compatible with low-resolution models in polypeptide chains. We have dispensed with an atomic description of proteins, representing each amino acid side chain by its geometric center (or centroid). The resulting rotamers have been estimated from a statistical analysis of a large structural database consisting of high-resolution X-ray protein structures. As additional information, each rotamer includes the frequency with which it has been found during the statistical analysis. More importantly, the library has been designed with a careful control to ensure that the vast majority of side chains in protein structures (at least 95% of residues) are properly represented. We have tested our library using an independent set of proteins, and our results support a good correlation between the reconstructed centroids from our rotamer library and those in the experimental structures. This new library can serve to improve the definition of side chain centroids in coarse-grained models, avoiding at the same time an excessive additional complexity in a geometric model for the polypeptide chain.

Correlation analysis of the side-chains conformational distribution in bound and unbound proteins

BACKGROUND

Protein interactions play a key role in life processes. Characterization of conformational properties of protein-protein interactions is important for understanding the mechanisms of protein association. The rapidly increasing amount of experimentally determined structures of proteins and protein-protein complexes provides foundation for research on protein interactions and complex formation. The knowledge of the conformations of the surface side chains is essential for modeling of protein complexes. The purpose of this study was to analyze and compare dihedral angle distribution functions of the side chains at the interface and non-interface areas in bound and unbound proteins.

RESULTS

To calculate the dihedral angle distribution functions, the configuration space was divided into grid cells. Statistical analysis showed that the similarity between bound and unbound interface and non-interface surface depends on the amino acid type and the grid resolution. The correlation coefficients between the distribution functions increased with the grid spacing increase for all amino acid types. The Manhattan distance showing the degree of dissimilarity between the distribution functions decreased accordingly. Short residues with one or two dihedral angles had higher correlations and smaller Manhattan distances than the longer residues. Met and Arg had the slowest growth of the correlation coefficient with the grid spacing increase. The correlations between the interface and non-interface distribution functions had a similar dependence on the grid resolution in both bound and unbound states. The interface and non-interface differences between bound and unbound distribution functions, caused by biological protein-protein interactions or crystal contacts, disappeared at the 70° grid spacing for interfaces and 30° for non-interface surface, which agrees with an average span of the side-chain rotamers.

CONCLUSIONS

The two-fold difference in the critical grid spacing indicates larger conformational changes upon binding at the interface than at the rest of the surface. At the same time, transitions between rotamers induced by interactions across the interface or the crystal packing are rare, with most side chains having local readjustments that do not change the rotameric state. The analysis is important for better understanding of protein interactions and development of flexible docking approaches.

Rotamer libraries and probabilities of transition between rotamers for the side chains in protein-protein binding

Conformational changes in the side chains are essential for protein-protein binding. Rotameric states and unbound- to-bound conformational changes in the surface residues were systematically studied on a representative set of protein complexes. The side-chain conformations were mapped onto dihedral angles space. The variable threshold algorithm was developed to cluster the dihedral angle distributions and to derive rotamers, defined as the most probable conformation in a cluster. Six rotamer libraries were generated: full surface, surface noninterface, and surface interface-each for bound and unbound states. The libraries were used to calculate the probabilities of the rotamer transitions upon binding. The stability of amino acids was quantified based on the transition maps. The noninterface residues' stability was higher than that of the interface. Long side chains with three or four dihedral angles were less stable than the shorter ones. The transitions between the rotamers at the interface occurred more frequently than on the noninterface surface. Most side chains changed conformation within the same rotamer or moved to an adjacent rotamer. The highest percentage of the transitions was observed primarily between the two most occupied rotamers. The probability of the transition between rotamers increased with the decrease of the rotamer stability. The analysis revealed characteristics of the surface side-chain conformational transitions that can be utilized in flexible docking protocols.

Discrete RNA libraries from pseudo-torsional space

The discovery that RNA molecules can fold into complex structures and carry out diverse cellular roles has led to interest in developing tools for modeling RNA tertiary structure. While significant progress has been made in establishing that the RNA backbone is rotameric, few libraries of discrete conformations specifically for use in RNA modeling have been validated. Here, we present six libraries of discrete RNA conformations based on a simplified pseudo-torsional notation of the RNA backbone, comparable to phi and psi in the protein backbone. We evaluate the ability of each library to represent single nucleotide backbone conformations, and we show how individual library fragments can be assembled into dinucleotides that are consistent with established RNA backbone descriptors spanning from sugar to sugar. We then use each library to build all-atom models of 20 test folds, and we show how the composition of a fragment library can limit model quality. Despite the limitations inherent in using discretized libraries, we find that several hundred discrete fragments can rebuild RNA folds up to 174 nucleotides in length with atomic-level accuracy (<1.5 Å RMSD). We anticipate that the libraries presented here could easily be incorporated into RNA structural modeling, analysis, or refinement tools.

The Dynameomics rotamer library: amino acid side chain conformations and dynamics from comprehensive molecular dynamics simulations in water

We have recently completed systematic molecular dynamics simulations of 807 different proteins representing 95% of the known autonomous protein folds in an effort we refer to as Dynameomics. Here we focus on the analysis of side chain conformations and dynamics to create a dynamic rotamer library. Overall this library is derived from 31,000 occurrences of each of 86,217 different residues, or 2.7 × 10(9) rotamers. This dynamic library has 74% overlap of rotamer distributions with rotamer libraries derived from static high-resolution crystal structures. Seventy-five percent of the residues had an assignable primary conformation, and 68% of the residues had at least one significant alternate conformation. The average correlation time for switching between rotamers ranged from 22 ps for Met to over 8 ns for Cys; this time decreased 20-fold on the surface of the protein and modestly for dihedral angles further from the main chain. Side chain S(2) axis order parameters were calculated and they correlated well with those derived from NMR relaxation experiments (R = 0.9). Relationships relating the S(2) axis order parameters to rotamer occupancy were derived. Overall the Dynameomics rotamer library offers a comprehensive depiction of side chain rotamer preferences and dynamics in solution, and more realistic distributions for dynamic proteins in solution at ambient temperature than libraries derived from crystal structures, in particular charged surface residues are better represented. Details of the rotamer library are presented here and the library itself can be downloaded at http://www.dynameomics.org.

From isotropic to anisotropic side chain representations: comparison of three models for residue contact estimation

The criterion to determine residue contact is a fundamental problem in deriving knowledge-based mean-force potential energy calculations for protein structures. A frequently used criterion is to require the side chain center-to-center distance or the -to- atom distance to be within a pre-determined cutoff distance. However, the spatially anisotropic nature of the side chain determines that it is challenging to identify the contact pairs. This study compares three side chain contact models: the Atom Distance criteria (ADC) model, the Isotropic Sphere Side chain (ISS) model and the Anisotropic Ellipsoid Side chain (AES) model using 424 high resolution protein structures in the Protein Data Bank. The results indicate that the ADC model is the most accurate and ISS is the worst. The AES model eliminates about 95% of the incorrectly counted contact-pairs in the ISS model. Algorithm analysis shows that AES model is the most computational intensive while ADC model has moderate computational cost. We derived a dataset of the mis-estimated contact pairs by AES model. The most misjudged pairs are Arg-Glu, Arg-Asp and Arg-Tyr. Such a dataset can be useful for developing the improved AES model by incorporating the pair-specific information for the cutoff distance.

Fine grained sampling of residue characteristics using molecular dynamics simulation

In a fine-grained computational analysis of protein structure, we investigated the relationships between a residue's backbone conformations and its side-chain packing as well as conformations. To produce continuous distributions in high resolution, we ran molecular dynamics simulations over a set of protein folds (dynameome). In effect, the dynameome dataset samples not only the states well represented in the PDB but also the known states that are not well represented in the structural database. In our analysis, we characterized the mutual influence among the backbone phi,psi angles with the first side-chain torsion angles (chi(1)) and the volumes occupied by the side-chains. The dependencies of these relationships on side-chain environment and amino acids are further explored. We found that residue volumes exhibit dependency on backbone 2 degrees structure conformation: side-chains pack more densely in extended beta-sheet than in alpha-helical structures. As expected, residue volumes on the protein surface were larger than those in the interior. The first side-chain torsion angles are found to be dependent on the backbone conformations in agreement with previous studies, but the dynameome dataset provides higher resolution of rotamer preferences based on the backbone conformation. All three gauche(-), gauche(+), and trans rotamers show different patterns of phi,psi dependency, and variations in chi(1) value are skewed from their canonical values to relieve the steric strains. By demonstrating the utility of dynameomic modeling on the native state ensemble, this study reveals details of the interplay among backbone conformations, residue volumes and side-chain conformations.

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.

Results

In this work we present BASILISK: a generative, probabilistic model of the conformational space of side chains that makes it possible to sample in continuous space. In addition, sampling can be conditional upon the protein's detailed backbone conformation, again in continuous space - without involving discretization.

Conclusions

A careful analysis of the model and a comparison with various rotamer libraries indicates that the model forms an excellent, fully continuous model of side chain conformational space. We also illustrate how the model can be used for rigorous, unbiased sampling with a physical force field, and how it improves side chain prediction when used as a pseudo-energy term. In conclusion, BASILISK is an important step forward on the way to a rigorous probabilistic description of protein structure in continuous space and in atomic detail.

A historical perspective of template-based protein structure prediction

This chapter presents a broad and a historical overview of the problem of protein structure prediction. Different structure prediction methods, including homology modeling, fold recognition (FR)/protein threading, ab initio/de novo approaches, and hybrid techniques involving multiple types of approaches, are introduced in a historical context. The progress of the field as a whole, especially in the threading/FR area, as reflected by the CASP/CAFASP contests, is reviewed. At the end of the chapter, we discuss the challenging issues ahead in the field of protein structure prediction.

Computing van der Waals energies in the context of the rotamer approximation

The rotamer approximation states that protein side-chain conformations can be described well using a finite set of rotational isomers. This approximation is often applied in the context of computational protein design and structure prediction to reduce the complexity of structural sampling. It is an effective way of reducing the structure space to the most relevant conformations. However, the appropriateness of rotamers for sampling structure space does not imply that a rotamer-based energy landscape preserves any of the properties of the true continuous energy landscape. Specifically, because the energy of a van der Waals interaction can be very sensitive to small changes in atomic separation, meaningful van der Waals energies are particularly difficult to calculate from rotamer-based structures. This presents a problem for computational protein design, where the total energy of a given structure is often represented as a sum of precalculated rigid rotamer self and pair contributions. A common way of addressing this issue is to modify the van der Waals function to reduce its sensitivity to atomic position, but excessive modification may result in a strongly nonphysical potential. Although many different van der Waals modifications have been used in protein design, little is known about which performs best, and why. In this paper, we study 10 ways of computing van der Waals energies under the rotamer approximation, representing four general classes, and compare their performance using a variety of metrics relevant to protein design and native-sequence repacking calculations. Scaling van der Waals radii by anywhere from 85 to 95% gives the best performance. Linearizing and capping the repulsive portion of the potential can give additional improvement, which comes primarily from getting rid of unrealistically large clash energies. On the other hand, continuously minimizing individual rotamer pairs prior to evaluating their interaction works acceptably in native-sequence repacking, but fails in protein design. Additionally, we show that the problem of predicting relevant van der Waals energies from rotamer-based structures is strongly nonpairwise decomposable and hence further modifications of the potential are unlikely to give significant improvement.

Design of peptides with branched beta-carbon dehydro-residues: syntheses, crystal structures and molecular conformations of two peptides, (I) N-Carbobenzoxy-DeltaVal-Ala-Leu-OCH3 and (II) N-Carbobenzoxy-DeltaIle-Ala-Leu-OCH3

Highly specific structures can be designed by inserting dehydro-residues into peptide sequences. The conformational preferences of branched beta-carbon residues are known to be different from other residues. As an implication it was expected that the branched beta-carbon dehydro-residues would also induce different conformations when substituted in peptides. So far, the design of peptides with branched beta-carbon dehydro-residues at (i + 1) position has not been reported. It may be recalled that the nonbranched beta-carbon residues induced beta-turn II conformation when placed at (i + 2) position while branched beta-carbon residues induced beta-turn III conformation. However, the conformation of a peptide with a nonbranched beta-carbon residue when placed at (i + 1) position was not found to be unique as it depended on the stereochemical nature of its neighbouring residues. Therefore, in order to induce predictably unique structures with dehydro-residues at (i + 1) position, we have introduced branched beta-carbon dehydro-residues instead of nonbranched beta-carbon residues and synthesized two peptides: (I) N-Carbobenzoxy-DeltaVal-Ala-Leu-OCH3 and (II) N-Carbobenzoxy-DeltaIle-Ala-Leu-OCH3 with DeltaVal and DeltaIle, respectively. The crystal structures of peptides (I) and (II) have been determined and refined to R-factors of 0.065 and 0.063, respectively. The structures of both peptides were essentially similar. Both peptides adopted type II beta-turn conformations with torsion angles; (I): phi1 = -38.7 (4) degrees, psi1 = 126.0 (3) degrees; phi2 = 91.6 (3) degrees, psi2 = -9.5 (4) degrees and (II): phi1 = -37.0 (6) degrees, psi1 = 123.6 (4) degrees, phi2 = 93.4 (4), psi2 = -11.0(4) degrees respectively. Both peptide structures were stabilized by intramolecular 4-->1 hydrogen bonds. The molecular packing in both crystal structures were stabilized in each by two identical hydrogen bonds N1...O1' (-x, y + 1/2, -z) and N2...O2' (-x + 1, y + 1/2, -z) and van der Waals interactions.

Rotamer libraries in the 21st century

Rotamer libraries are widely used in protein structure prediction, protein design, and structure refinement. As the size of the structure data base has increased rapidly in recent years, it has become possible to derive well-refined rotamer libraries using strict criteria for data inclusion and for studying dependence of rotamer populations and dihedral angles on local structural features.

A stochastic algorithm for global optimization and for best populations: a test case of side chains in proteins

The problem of global optimization is pivotal in a variety of scientific fields. Here, we present a robust stochastic search method that is able to find the global minimum for a given cost function, as well as, in most cases, any number of best solutions for very large combinatorial "explosive" systems. The algorithm iteratively eliminates variable values that contribute consistently to the highest end of a cost function's spectrum of values for the full system. Values that have not been eliminated are retained for a full, exhaustive search, allowing the creation of an ordered population of best solutions, which includes the global minimum. We demonstrate the ability of the algorithm to explore the conformational space of side chains in eight proteins, with 54 to 263 residues, to reproduce a population of their low energy conformations. The 1,000 lowest energy solutions are identical in the stochastic (with two different seed numbers) and full, exhaustive searches for six of eight proteins. The others retain the lowest 141 and 213 (of 1,000) conformations, depending on the seed number, and the maximal difference between stochastic and exhaustive is only about 0.15 Kcal/mol. The energy gap between the lowest and highest of the 1,000 low-energy conformers in eight proteins is between 0.55 and 3.64 Kcal/mol. This algorithm offers real opportunities for solving problems of high complexity in structural biology and in other fields of science and technology.

Accurate reconstruction of all-atom protein representations from side-chain-based low-resolution models

A procedure for the reconstruction of all-atom protein structures from side-chain center-based low-resolution models is introduced and applied to a set of test proteins with high-resolution X-ray structures. The accuracy of the rebuilt all-atom models is measured by root mean square deviations to the corresponding X-ray structures and percentages of correct chi(1) and chi(2) side-chain dihedrals. The benefit of including C(alpha) positions in the low-resolution model is examined, and the effect of lattice-based models on the reconstruction accuracy is discussed. Programs and scripts implementing the reconstruction procedure are made available through the NIH research resource for Multiscale Modeling Tools in Structural Biology (http://mmtsb.scripps.edu).

Visualizing and quantifying molecular goodness-of-fit: small-probe contact dots with explicit hydrogen atoms

The technique of small-probe contact dot surfaces is described as a method for calculating and displaying the detailed atomic contacts inside or between molecules. It allows one both to measure and to visualize directly the goodness-of-fit of packing interactions. It requires both highly accurate structures and also the explicit inclusion of all hydrogen atoms and their van der Waals interactions. A reference dataset of 100 protein structures was chosen on the basis of resolution (1.7 A or better), crystallographic R-value, non-homology, and the absence of any unusual problems. Hydrogen atoms were added in standard geometry and, where needed, with rotational optimization of OH, SH, and NH+3 positions. Side-chain amide orientations were corrected where required by NH van der Waals clashes, as described in the accompanying paper. It was determined that, in general, methyl groups pack well in the default staggered conformation, except for the terminal methyl groups of methionine residues, which required rotational optimization. The distribution of serious clashes (i.e. non-H-bond overlap of >/=0.4 A) was studied as a function of resolution, alternate conformations, and temperature factor (B), leading to the decision that packing and other structural features would not be analyzed for residues in 'b' alternate conformations or with B-factors of 40 or above. At the level of the fine details analyzed here, structural accuracy improves quite significantly over the range from 1.7 to 1.0 A resolution. These high-resolution structures show impressively well-fitted packing interactions, with some regions thoroughly interdigitated and other regions somewhat sparser. Lower-resolution structures or model structures could undoubtedly be improved in accuracy by the incorporation of this additional information: for example, nucleic acid structures in non-canonical conformations are often very accurate for the bases and much less reliable for the backbone, whose conformation could be specified better by including explicit H atom geometry and contacts. The contact dots are an extremely sensitive method of finding problem areas, and often they can suggest how to make improvements. They can also provide explanations for structural features that have been described only as empirical regularities, which is illustrated by showing that the commonest rotamer of methionine (a left-handed spiral, with all chi values near -60 degrees) is preferred because it provides up to five good H atom van der Waals contacts. This methodology is thus applicable in two different ways: (1) for finding and correcting errors in structure models (either experimental or theoretical); and (2) for analyzing interaction patterns in the molecules themselves.

Asparagine and glutamine rotamers: B-factor cutoff and correction of amide flips yield distinct clustering

Previous rotamer libraries showed little significant clustering for asparagine chi2 or glutamine chi3 values, but none of those studies corrected amide orientations or omitted disordered side chains. The current survey used 240 proteins at /=0.4 A). All H atoms were added and optimized, and amide orientation was flipped by 180 degrees if required by H bonding or atomic clashes. A side chain was included only if its amide orientation was clearly determined and if no atom had a B factor >/=40, alternate conformation, or severe clash; that selection process yielded 1,490 Asn and 863 Gln side chains. Clear clustering was observed for Asn chi2 and Gln chi3 (except when Gln chi2 is trans). For Gln, five major and four minor rotamers cover 87% of examples. For Asn, there are seven backbone-independent rotamers covering 94% of examples plus rotamers specified for strictly alpha-helical, beta, and left-handed (+phi) Asn. Although the strongest influence on chi angles is avoidance of atomic clashes (especially with the NH2 hydrogens), some Asn or Gln rotamers are influenced by favorable van der Waals contacts and others by specific local H-bond patterns.

Ideal architecture of residue packing and its observation in protein structures

A simple model of sphere packing has been investigated as an ideal model for long-range interactions for the packing of non-bonded residues in protein structures. By superposing all residues, the geometry of packing around a central residue is investigated. It is found that all residues conform almost perfectly to this lattice model for sphere packing when a radius of 6.5 A is used to define non-bonded (virtual) interacting residues. Side-chain positions with respect to sequential backbone segments are relatively regular as well. This lattice can readily be used in conformation simulations to reduce the conformational space.

Bayesian statistical analysis of protein side-chain rotamer preferences

We present a Bayesian statistical analysis of the conformations of side chains in proteins from the Protein Data Bank. This is an extension of the backbone-dependent rotamer library, and includes rotamer populations and average chi angles for a full range of phi, psi values. The Bayesian analysis used here provides a rigorous statistical method for taking account of varying amounts of data. Bayesian statistics requires the assumption of a prior distribution for parameters over their range of possible values. This prior distribution can be derived from previous data or from pooling some of the present data. The prior distribution is combined with the data to form the posterior distribution, which is a compromise between the prior distribution and the data. For the chi 2, chi 3, and chi 4 rotamer prior distributions, we assume that the probability of each rotamer type is dependent only on the previous chi rotamer in the chain. For the backbone-dependence of the chi 1 rotamers, we derive prior distributions from the product of the phi-dependent and psi-dependent probabilities. Molecular mechanics calculations with the CHARMM22 potential show a strong similarity with the experimental distributions, indicating that proteins attain their lowest energy rotamers with respect to local backbone-side-chain interactions. The new library is suitable for use in homology modeling, protein folding simulations, and the refinement of X-ray and NMR structures.

Prediction of protein side-chain rotamers from a backbone-dependent rotamer library: a new homology modeling tool

Modeling by homology is the most accurate computational method for translating an amino acid sequence into a protein structure. Homology modeling can be divided into two sub-problems, placing the polypeptide backbone and adding side-chains. We present a method for rapidly predicting the conformations of protein side-chains, starting from main-chain coordinates alone. The method involves using fewer than ten rotamers per residue from a backbone-dependent rotamer library and a search to remove steric conflicts. The method is initially tested on 299 high resolution crystal structures by rebuilding side-chains onto the experimentally determined backbone structures. A total of 77% of chi1 and 66% of chi(1 + 2) dihedral angles are predicted within 40 degrees of their crystal structure values. We then tested the method on the entire database of known structures in the Protein Data Bank. The predictive accuracy of the algorithm was strongly correlated with the resolution of the structures. In an effort to simulate a realistic homology modeling problem, 9424 homology models were created using three different modeling strategies. For prediction purposes, pairs of structures were identified which shared between 30% and 90% sequence identity. One strategy results in 82% of chi1 and 72% chi(1 + 2) dihedral angles predicted within 40 degrees of the target crystal structure values, suggesting that movements of the backbone associated with this degree of sequence identity are not large enough to disrupt the predictive ability of our method for non-native backbones. These results compared favorably with existing methods over a comprehensive data set.

Conformational analysis of the backbone-dependent rotamer preferences of protein sidechains

Amino acids have sidechain rotamer preferences dependent on the backbone dihedral angles phi and psi. These preferences provide a method for rapid structure prediction which is a significant improvement over backbone-independent rotamer libraries. We demonstrate here that simple arguments based on conformational analysis can account for many of the features of the observed backbone dependence of the sidechain rotamers. Steric repulsions corresponding to the 'butane' and 'syn-pentane' effects make certain conformers rare, as has been observed experimentally.

Intrahelical hydrogen bonding of serine, threonine and cysteine residues within alpha-helices and its relevance to membrane-bound proteins

A survey of known protein structures reveals that approximately 70% of serine residues and at least 85% (potentially 100%) of threonine residues in helices make hydrogen bonds to carbonyl oxygen atoms in the preceding turn of the helix. The high frequency of intrahelical hydrogen bonding is of particular significance for intrinsic membrane-bound proteins that form transmembrane helices. Hydrogen bonding within a helix provides a way for serine, threonine and cysteine residues to satisfy their hydrogen-bonding potential permitting such residues to occur in helices buried within a hydrophobic milieu.

Statistical and energetic analysis of side-chain conformations in oligopeptides

The distributions of side-chain conformations in 258 crystal structures of oligopeptides have been analyzed. The sample contains 321 residues having side chains that extend beyond the C beta atom. Statistically observed preferences of side-chain dihedral angles are summarized and correlated with stereochemical and energetic constraints. The distributions are compared with observed distributions in proteins of known X-ray structures and with computed minimum-energy conformations of amino acid derivatives. The distributions are similar in all three sets of data, and they appear to be governed primarily by intraresidue interactions. In side chains with no beta-branching, the most important interactions that determine chi 1 are those between the C gamma H2 group and atoms of the neighboring peptide groups. As a result, the g- conformation (chi 1 congruent to -60 degrees) occurs most frequently for rotation around the C alpha-C beta bond in oligopeptides, followed by the t conformation (chi 1 congruent to 180 degrees), while the g+ conformation (chi 1 congruent to 60 degrees) is least favored. In residues with beta-branching, steric repulsions between the C gamma H2 or C gamma H3 groups and backbone atoms govern the distribution of chi 1. The extended (t) conformation is highly favored for rotation around the C beta-C gamma and C gamma-C delta bonds in unbranched side chains, because the t conformer has a lower energy than the g+ and g- conformers in hydrocarbon chains. This study of the observed side-chain conformations has led to a refinement of one of the energy parameters used in empirical conformational energy computations.

CD and 1H-n.m.r. studies on the side-chain conformation of tyrosine derivatives and tyrosine residues in di- and tripeptides

Tyrosine, tyrosine peptides and derivatives, in total 11 species, were selected as models for the study of optical properties (1Lb band of phenolic group) and side-chain arrangement (rotamers around C alpha-C beta bond) of tyrosine as a function of chemical structure and pH effects. Circular dichroism spectra between 240 and 320 nm and n.m.r. spectra were recorded for the different ionization states. Results are discussed in terms of charge effects from N- and C-terminal groups and local conformation influence on 1Lb band of the phenolic chromophore and on distribution of rotamer populations in side-chain of tyrosine. Fractions of rotamer populations were estimated from alpha-beta proton-proton coupling constants and, in the cases of tyrosine and N-acetyl-tyrosine, from 15N-beta nitrogen-proton coupling constants, which allow the stereospecific assignment of the beta and beta' protons. The rotamer populations of tyrosine, averaged from all the data of the samples In solution, were then compared with their statistical distribution in th solid state. Interestingly, agreement is excellent when we refer to crystal of tyrosine, tyrosine derivatives or small peptides (31 samples) and poor in the case of proteins. This leads to a discussion on both the validity of using statistical distributions of rotamers in proteins as reference for rotamer preferences inside small peptides in solution and the choice of the appropriate Jg and Jt values in Pachler's approach. The possible existence of a correlation between ellipticity and rotamer populations for such samples is examined.

Nuclear magnetic resonance conformational studies on the chemotactic tripeptide formyl-L-methionyl-L-leucyl-L-phenylalanine. A small beta sheet

Previous work by several groups has shown that the combination of spin--spin coupling constants and spectral density components (derived from spin--lattice relaxation and/or nuclear Overhauser measurements) may aid in the task of conformational determination of peptides in solution. Using the peptide formyl-L-methionyl-L-leucyl-L-phenylalanine, which is a potent specific chemotactic agent for leucocytes, we show the following: (a) that 3JNHCH coupling constants are consistent with a high degree of rigidity in the peptide backbone in solution, (b) that 3H isotopic substitution in combination with relaxation data taken at different Larmor frequencies enables spectral density, and thence conformational, information to be obtained, (c) that side-chain conformations for this molecule mirror, in some aspects, those found in the solid state for other peptides containing the same residues, and (d) that temperature dependence of amide chemical shifts does not have direct implication concerning the existence of intramolecular hydrogen bonds in peptides. We are able to propose a family of conformations which appear to interchange rapidly on the NMR time scale and are characterized by a distribution of side-chain rotamers. The basic backbone conformation is, or closely approximates, a small beta antiparallel pleated sheet and as such suggests a possible mode of receptor--chemotactic peptide interaction.

Side-chain torsional potentials: effect of dipeptide, protein, and solvent environment

Side-chain torsional potentials in the bovine pancreatic trypsin inhibitor are calculated from empirical energy functions by use of the known X-ray structure of the protein and the rigid-geometry mapping technique. The potentials are analyzed to determine the roles and relative importance of contributions from the dipeptide backbone, the protein, and the crystalline environment of solvent and other protein molecules. The structural characteristics of the side chains determine two major patterns of energy surfaces, E(X1,X2): a gamma-branched pattern and a pattern for longer, straight side chains (Arg, Lys, Glu, and Met). Most of the dipeptide potential curves and surfaces have a local minimum corresponding to the side-chain torsional angles in the X-ray structure. Addition of the protein forces sharpens and/or selects from these minima, providing very good agreement with the experimental conformation for most side chains at the surface or in the core of the protein. Inclusion of the crystalline environment produces still better results, especially for the side chains extending away from the protein. The results are discussed in terms of the details of the interactions due to the surrounding, calculated solvent-accessibility figures and the temperature factors derived from the crystallographic refinement of the pancreatic trypsin inhibitor.

An analysis of side-chain conformation in proteins

The crystal structures of a number of globular proteins are currently available. An analysis of the distribution of side-chains among different allowed conformations in these proteins has been carried out. The observed conformations of individual residues are discussed on the basis of well-known stereochemical criteria. The population distribution of side-chains in different allowed regions in conformational space can be explained largely on the basis of simple steric considerations. In addition to examining the conformational behaviour of individual residues, some population distributions of conformational angles of general interest involving groups of residues have also been analyzed.