Using networks to identify fine structural differences between functionally distinct protein states

The vast increase in available data from the "-omics" revolution has enabled the fields of structural proteomics and structure prediction to make great progress in assigning realistic three-dimensional structures to each protein molecule. The challenge now lies in determining the fine structural details that endow unique functions to sequences that assume a common fold. Similar problems are encountered in understanding how distinct conformations contribute to different phases of a single protein's dynamic function. However, efforts are hampered by the complexity of these large, three-dimensional molecules. To overcome this limitation, structural data have been recast as two-dimensional networks. This analysis greatly reduces visual complexity but retains information about individual residues. Such diagrams are very useful for comparing multiple structures, including (1) homologous proteins, (2) time points throughout a dynamics simulation, and (3) functionally different conformations of a given protein. Enhanced structural examination results in new functional hypotheses to test experimentally. Here, network representations were key to discerning a difference between unliganded and inducer-bound lactose repressor protein (LacI), which were previously presumed to be identical structures. Further, the interface of unliganded LacI was surprisingly similar to that of the K84L variant and various structures generated by molecular dynamics simulations. Apo-LacI appears to be poised to adopt the conformation of either the DNA- or inducer-bound structures, and the K84L mutation appears to freeze the structure partway through the conformational transition. Additional examination of the effector binding pocket results in specific hypotheses about how inducer, anti-inducer, and neutral sugars exert their effects on repressor function.     

Can local energy minimization refine the PDB structures of different resolution universally?

Local energy minimization was statistically tested as the refinement strategy for PDB structure pairs of different resolution. The 13 pairs of structures with the only difference being the resolution were extracted from PDB and represented structures of 11 identical proteins obtained with different x-ray diffraction techniques. The rmsd distribution was calculated for these pairs before and after local energy minimization of each structure. MMFF94 was used for energy calculations and the quasi-Newtonian method was used for local energy minimization. By comparison of these two rmsd distributions, the local energy minimization was proved to statistically increase the structural differences in pairs, so it cannot be used for refinement purposes. To explore the prospects of complex refinement strategies based on energy minimization, randomized structures were obtained by moving the initial PDB structures as far as the minimized structures had been moved in the multidimensional space of atomic coordinates. For these randomized structures the rmsd distribution was calculated and compared with the one for minimized structures. The significant differences in their mean values proved the energy surface of the protein to have only few minima near the conformations of different resolution obtained by x-ray analysis for PDB. Some other results we obtained exploring the energy surface near these conformations are also presented. These results are expected to be useful for the development of new protein refinement strategies based on energy minimization.     

Spatial structure of the rp142 peptide containing the immunodominant epitope of the HIV-1 gp120 protein. A theoretical study]

A model of spatial structure of the synthetic peptide rp142 (24 amino acid residues) containing the immunodominant epitope of the HIV-1 protein gp120 in the region Gly-10-Phe-15 was constructed by the method of "constrained" molecular mechanics, which uses the algorithms of theoretical conformational analysis, based on NMR spectroscopy data. A comparative analysis of calculated conformations revealed that the spatial structure of rp142 in solution can be described by a family of conformations to which nine different structural clusters involving the sets of topologically close conformers correspond. It is shown that the main chain of the peptide forms irregular but "structured" conformations in which the main portion of amino acid residues is incorporated into beta-turns and helix-like fragments, while Pro-11 and Gly-12 form in some structures inverse gamma-turns, which rarely occur in protein-peptide molecules. It was found that the spatial packing of the Gly-10-Phe-15 hexapeptide in different clusters is realized at different internal rotation angles, to which topologically close structures correspond. It is assumed that this invariant structural element describes the "conformation of complex formation" that is complementary to the antigen-binding center of antibodies and is responsible for their binding to the peptide.     

Adaptability in protein structures: structural dynamics and implications in ligand design

The basic framework of understanding the mechanisms of protein functions is achieved from the knowledge of their structures which can model the molecular recognition. Recent advancement in the structural biology has revealed that in spite of the availability of the structural data, it is nontrivial to predict the mechanism of the molecular recognition which progresses via situation-dependent structural adaptation. The mutual selectivity of protein–protein and protein–ligand interactions often depends on the modulations of conformations empowered by their inherent flexibility, which in turn regulates the function. The mechanism of a protein’s function, which used to be explained by the ideas of ‘lock and key’ has evolved today as the concept of ‘induced fit’ as well as the ‘population shift’ models. It is felt that the ‘dynamics’ is an essential feature to take into account for understanding the mechanism of protein’s function. The design principles of therapeutic molecules suffer from the problems of plasticity of the receptors whose binding conformations are accurately not predictable from the prior knowledge of a template structure. On the other hand, flexibility of the receptors provides the opportunity to improve the binding affinity of a ligand by suitable substitution that will maximize the binding by modulating the receptors surface. In this paper, we discuss with example how the protein’s flexibility is correlated with its functions in various systems, revealing the importance of its understanding and for making applications. We also highlight the methodological challenges to investigate it computationally and to account for the flexible nature of the molecules in drug design.     

Rigid domains in proteins: An algorithmic approach to their identification

A rigid domain, defined here as a tertiary structure common to two or more different protein conformations, can be identified numerically from atomic coordinates by finding sets of residues, one in each conformation, such that the distance between any two residues within the set belonging to one conformation is the same as the distance between the two structurally equivalent residues within the set belonging to any other conformation. The distance between two residues is taken to be the distance between their respective α carbon atoms. With the methods of this paper we have found in the deoxy and oxy conformations of the human hemoglobin α₁β₁ dimer a rigid domain closely related to that previously identified by Baldwin and Chothia (J. Mol. Biol. 129:175–220,1979). We provide two algorithms, both using the difference-distance matrix, with which to search for rigid domains directly from atomic coordinates. The first finds all rigid domains in a protein but has storage and processing demands that become prohibitively large with increasing protein size. The second, although not necessarily finding every rigid domain, is computationally tractable for proteins of any size. Because of its efficiency we are able to search protein conformations recursively for groups of non-intersecting domains. Different protein conformations, when aligned by superimposing their respective domain structures; can be examined for structural differences in regions complementing a rigid domain. © 1995 Wiley-Liss, Inc.     

Exhaustive enumeration of protein conformations using experimental restraints.

We present an efficient new algorithm that enumerates all possible conformations of a protein that satisfy a given set of distance restraints. Rapid growth of all possible self-avoiding conformations on the diamond lattice provides construction of alpha-carbon representations of a protein fold. We investigated the dependence of the number of conformations on pairwise distance restraints for the proteins crambin, pancreatic trypsin inhibitor, and ubiquitin. Knowledge of between one and two contacts per monomer is shown to be sufficient to restrict the number of candidate structures to approximately 1,000 conformations. Pairwise RMS deviations of atomic position comparisons between pairs of these 1,000 structures revealed that these conformations can be grouped into about 25 families of structures. These results suggest a new approach to assessing alternative protein folds given a very limited number of distance restraints. Such restraints are available from several experimental techniques such as NMR, NOESY, energy transfer fluorescence spectroscopy, and crosslinking experiments. This work focuses on exhaustive enumeration of protein structures with emphasis on the possible use of NOESY-determined distance restraints.     

Close correspondence between the motions from principal component analysis of multiple HIV-1 protease structures and elastic network modes

The large number of available HIV-1 protease structures provides a remarkable sampling of conformations of the different conformational states, which can be viewed as direct structural information about the dynamics of the HIV-1 protease. After structure matching, we apply principal component analysis (PCA) to obtain the important apparent motions for both bound and unbound structures. There are significant similarities between the first few key motions and the first few low-frequency normal modes calculated from a static representative structure with an elastic network model (ENM), strongly suggesting that the variations among the observed structures and the corresponding conformational changes are facilitated by the low-frequency, global motions intrinsic to the structure. Similarities are also found when the approach is applied to an NMR ensemble, as well as to molecular dynamics (MD) trajectories. Thus, a sufficiently large number of experimental structures can directly provide important information about protein dynamics, but ENM can also provide similar sampling of conformations.     

Visualization of conformational distribution of short to medium size segments in globular proteins and identification of local structural motifs

Analysis of the conformational distribution of polypeptide segments in a conformational space is the first step for understanding a principle of structural diversity of proteins. Here, we present a statistical analysis of protein local structures based on interatomic C(alpha) distances. Using principal component analysis (PCA) on the intrasegment C(alpha)-C(alpha) atomic distances, the conformational space of protein segments, which we call the protein segment universe, has been visualized, and three essential coordinate axes, suitable for describing the universe, have been identified. Three essential axes specified radius of gyration, structural symmetry, and separation of hairpin structures from other structures. Among the segments of arbitrary length, 6-22 residues long, the conservation of those axes was uncovered. Further application of PCA to the two largest clusters in the universe revealed local structural motifs. Although some of motifs have already been reported, we identified a possibly novel strand motif. We also showed that a capping box, which is one of the helix capping motifs, was separated into independent subclusters based on the C(alpha) geometry. Implications of the strand motif, which may play a role for protein-protein interaction, are discussed. The currently proposed method is useful for not only mapping the immense universe of protein structures but also identification of structural motifs.     

Structure collisions between interacting proteins

Protein-protein interactions take place at defined binding interfaces. One protein may bind two or more proteins at different interfaces at the same time. So far it has been commonly accepted that non-overlapping interfaces allow a given protein to bind other proteins simultaneously while no collisions occur between the binding protein structures. To test this assumption, we performed a comprehensive analysis of structural protein interactions to detect potential collisions. Our results did not indicate cases of biologically relevant collisions in the Protein Data Bank of protein structures. However, we discovered a number of collisions that originate from alternative protein conformations or quaternary structures due to different experimental conditions.     

Evidence for ligandable sites in structured RNA throughout the Protein Data Bank

RNA has attracted considerable attention as a target for small molecules. However, methods to identify, study, and characterize suitable RNA targets have lagged behind strategies for protein targets. One approach that has received considerable attention for protein targets has been to utilize computational analysis to investigate ligandable “pockets” on proteins that are amenable to small molecule binding. These studies have shown that selected physical properties of pockets are important parameters that govern the ability of a structure to bind to small molecules. This work describes a similar analysis to study pockets on all RNAs in the Protein Data Bank (PDB). Using parameters such as buriedness, hydrophobicity, volume, and other properties, the set of all RNAs is analyzed and compared to all proteins. Considerable overlap is observed between the properties of pockets on RNAs and proteins. Thus, many RNAs are capable of populating conformations with pockets that are likely suitable for small molecule binding. Further, principal moment of inertia (PMI) calculations reveal that liganded RNAs exist in diverse structural space, much of which overlaps with protein structural space. Taken together, these results suggest that complex folded RNAs adopt unique structures with pockets that may represent viable opportunities for small molecule targeting.     

Monoclonal antibody higher order structure analysis by high throughput protein conformational array

The elucidation of antibody higher order structure (HOS) is critical in therapeutic antibody development. Since HOS determines the protein bioactivity and chemo-physical properties, this knowledge can help to ensure that the safety and efficacy attributes are not compromised. Protein conformational array (PCA) is a novel method for determining the HOS of monoclonal antibodies. Previously, we successfully utilized an enzyme-linked immunosorbent assay (ELISA)-based PCA along with other bioanalytical tools to elucidate the structures of antibody aggregates. In this study, applying a new multiplex-based PCA with 48-fold higher throughput than the ELISA-based one we revealed structural differences between different antibody molecules and antibody structure changes affected by various processing conditions. The PCA analysis of antibody molecules clearly demonstrated significant differences between IgG1 and IgG4 subclasses in epitope exposure and folding status. Furthermore, we applied small angle X-ray scattering to decipher mechanistic insights of PCA technology and validate structural information obtained using PCA. These findings enhance our fundamental understanding of mAbs' HOS in general. The PCA analysis of antibody samples from various processing conditions also revealed that antibody aggregation caused significantly higher exposure of antibody epitopes, which potentially led to a “foreign” molecule that could cause immunogenicity. The PCA data correlated well with protein stability results from traditional methods such as size-exclusion chromatography and protein thermal shift assay. Our study demonstrated that high throughput PCA is a suitable method for HOS analysis in the discovery and development of therapeutic antibodies.     

Characterizing and predicting the functional and conformational diversity of seven-transmembrane proteins

The activation of seven-transmembrane receptors (7TMRs) allows cells to sense their environment and convert extracellular signals (like hormone binding) into intracellular signals (through G protein-coupled and/or β arrestin-coupled pathways). A single 7TMR is capable of transducing a wide spectrum of physiological responses inside a cell by coupling to these pathways. This intracellular pleiotropic action is enabled by multiple conformations exhibited by these receptors. Developments in membrane protein structure determination technologies have led to a rapid increase in crystal structures for many 7TMRs. Majority of these receptors have been crystallized in their inactive conformation and, for some, one of the many active conformations has also been crystallized. Given the topological constraints of a lipid bilayer that results in a single fold of seven almost parallel TM helices connected by mostly unstructured loops, these structures exhibit a diversity of conformations not only across the receptors but also across the different functional forms for receptors with structures for one of the functionally active conformations. Here we present a method to characterize this conformational diversity in terms of transmembrane helix topology (TMHTOP) parameters and how to use these helix orientation parameters to predict functionally-distinct multiple conformations for these receptors. The TMHTOP parameters enable a quantification of the structural changes that underlie 7TMR activation and also sheds a unique mechanistic light on the pleiotropic nature of these receptors. It provides a common language to describe the 7TMR activation mechanisms as well as differences across many receptors in terms of visually intuitive structural parameters. Protein structure prediction methods can use these parameters to describe 7TMR conformational ensembles, which coupled to experimental data can be used to develop testable hypotheses for the structural basis of 7TMR functions.     

Solvent accessibility in native and isolated domain environments: general features and implications to interface predictability

A non-redundant database of 4536 structural domains, comprising more than 790,000 residues, has been used for the calculation of their solvent accessibility in the native protein environment and then in the isolated domain environment. Nearly 140,000 (18%) residues showed a change in accessible surface area in the above two conditions. General features of this change under these two circumstances have been pointed out. Propensities of these interfacing amino acid residues have been calculated and their variation for different secondary structure types has been analyzed. Actual amount of surface area lost by different secondary structures is higher in the case of helix and strands compared to coil and other conformations. Overall change in surface area in hydrophobic and uncharged residues is higher than that in charged residues. An attempt has been made to know the predictability of interface residues from sequence environments. This analysis and prediction results have significant implications towards determining interacting residues in proteins and for the prediction of protein-protein, protein-ligand, protein-DNA and similar interactions.     

The limit of accuracy of protein modeling: influence of crystal packing on protein structure

The size of the protein database (PDB) makes it now feasible to arrive at statistical conclusions regarding structural effects of crystal packing. These effects are relevant for setting upper practical limits of accuracy on protein modeling. Proteins whose crystals have more than one molecule in the asymmetric unit or whose structures were determined at least twice by X-ray crystallography were paired and their differences analyzed. We demonstrate a clear influence of crystal environment on protein structure, including backbone conformations, hinge-like motions and side-chain conformations. The positions of surface water molecules tend to be variable in different crystal environments while those of ligands are not. Structures determined by independent groups vary more than structures determined by the same authors. The use of different refinement methods is a major source for this effect. Our pair-wise analysis derives a practical limit to the accuracy of protein modeling. For different crystal forms, the limit of accuracy (C(alpha), root-mean-square deviation (RMSD)) is approximately 0.8A for the entire protein, which includes approximately 0.3A due to crystal packing. For organized secondary elements, the upper limit of C(alpha) RMSD is 0.5-0.6A while for loops or protein surface it reaches 1.0A. Twenty percent of exposed side- chains exhibit different chi(1+2) conformations with approximately half of the effect also resulting from crystal packing. A web based tool for analysis and graphic presentation of surface areas of crystal contacts is available (http://ligin.weizmann.ac.il/cryco).     

Structural insights into the conformational variability of FtsZ

FtsZ is a prokaryotic homologue of the eukaryotic cytoskeletal protein tubulin and plays a central role in prokaryotic cell division. Both FtsZ and tubulin are known to pass through cycles of polymerization and depolymerization, but the structural mechanisms underlying this cycle remain to be determined. Comparison of tubulin structures obtained in different states has led to a model in which the tubulin monomer undergoes a conformational switch between a "straight" form found in the walls of microtubules and a "curved" form associated with depolymerization, and it was proposed recently that this model may apply also to FtsZ. Here, we present new structures of FtsZ from47 Aquifex aeolicus,47 Bacillus subtilis, Methanococcus jannaschii and Pseudomonas aeruginosa that provide strong constraints on any proposed role for a conformational switch in the FtsZ monomer. By comparing the full range of FtsZ structures determined in different crystal forms and nucleotide states, and in the presence or in the absence of regulatory proteins, we find no evidence of a conformational change involving domain movement. Our new structural data make it clear that the previously proposed straight and curved conformations of FtsZ were related to inter-species differences in domain orientation rather than two interconvertible conformations. We propose a new model in which lateral interactions help determine the curvature of protofilaments.     

Monte Carlo sampling of near-native structures of proteins with applications

Since a protein's dynamic fluctuation inside cells affects the protein's biological properties, we present a novel method to study the ensemble of near-native structures (NNS) of proteins, namely, the conformations that are very similar to the experimentally determined native structure. We show that this method enables us to (i) quantify the difficulty of predicting a protein's structure, (ii) choose appropriate simplified representations of protein structures, and (iii) assess the effectiveness of knowledge-based potential functions. We found that well-designed simple representations of protein structures are likely as accurate as those more complex ones for certain potential functions. We also found that the widely used contact potential functions stabilize NNS poorly, whereas potential functions incorporating local structure information significantly increase the stability of NNS.     

Structural diversity of sequentially identical subsequences of proteins: Identical octapeptides can have different conformations

One of the most important questions in the protein folding problem is whether secondary structures are formed entirely by local interactions. One way to answer this question is to compare identical subsequences of proteins to see if they have identical structures. Such an exercise would also reveal a lower limit on the number of amino acids needed to form unique secondary structures. In this context, we have searched the April 1996 release of the Protein Data Bank for sequentially identical subsequences of proteins and compared their structures. We find that identical octamers can have different conformations. In addition, there are several examples of identical heptamers with different conformations, and the number of identical hexamers with different conformations has increased since the previous PDB releases. These observations imply that secondary structure can be formed entirely by non-local interactions and that an identical match of up to eight amino acids may not imply structural similarity. In addition to the larger context of the protein folding problem, these observations have implications for protein structure prediction methods. Proteins 30:228–231, 1998. © 1998 Wiley-Liss, Inc.     

Failures of inverse folding and threading with gapped alignment

To calculate the tertiary structure of a protein from its amino acid sequence, the thermodynamic approach requires a potential function of sequence and conformation that has its global minimum at the native conformation for many different proteins. Here we study the behavior of such functions for the simplest model system that still has some of the features of the protein folding problem, namely two-dimensional square lattice chain configurations involving two residue types. First we show that even the given contact potential, which by definition is used to identify the folding sequences and their unique native conformations, cannot always correctly select which sequences will fold to a given structure. Second, we demonstrate that the given contact potential is not always able to favor the native alignment of a native sequence on its own native conformation over other gapped alignments of different folding sequences onto that same conformation. Because of these shortcomings, even in this simple model system in which all conformations and all native sequences are known and determined directly by the given potential, we must reexamine our expectations for empirical potentials used for inverse folding and gapped alignment on more realistic representations of proteins. © 1996 Wiley-Liss, Inc.     

Reduced representation model of protein structure prediction: statistical potential and genetic algorithms.

A reduced representation model, which has been described in previous reports, was used to predict the folded structures of proteins from their primary sequences and random starting conformations. The molecular structure of each protein has been reduced to its backbone atoms (with ideal fixed bond lengths and valence angles) and each side chain approximated by a single virtual united-atom. The coordinate variables were the backbone dihedral angles phi and psi. A statistical potential function, which included local and nonlocal interactions and was computed from known protein structures, was used in the structure minimization. A novel approach, employing the concepts of genetic algorithms, has been developed to simultaneously optimize a population of conformations. With the information of primary sequence and the radius of gyration of the crystal structure only, and starting from randomly generated initial conformations, I have been able to fold melittin, a protein of 26 residues, with high computational convergence. The computed structures have a root mean square error of 1.66 A (distance matrix error = 0.99 A) on average to the crystal structure. Similar results for avian pancreatic polypeptide inhibitor, a protein of 36 residues, are obtained. Application of the method to apamin, an 18-residue polypeptide with two disulfide bonds, shows that it folds apamin to native-like conformations with the correct disulfide bonds formed.