Ramachandran maps for side chains in globular proteins

The Ramachandran plot for backbone ϕ,ψ-angles in a blocked monopeptide has played a central role in understanding protein structure. Curiously, a similar analysis for side chain χ-angles has been comparatively neglected. Instead, efforts have focused on compiling various types of side chain libraries extracted from proteins of known structure. Departing from this trend, the following analysis presents backbone-based maps of side chains in blocked monopeptides. As in the original ϕ,ψ-plot, these maps are derived solely from hard-sphere steric repulsion. Remarkably, the side chain biases exhibit marked similarities to corresponding biases seen in high-resolution protein structures. Consequently, some of the entropic cost for side chain localization in proteins is prepaid prior to the onset of folding events because conformational bias is built into the chain at the covalent level. Furthermore, side chain conformations are seen to experience fewer steric restrictions for backbone conformations in either the α or β basins, those map regions where repetitive ϕ,ψ-angles result in α-helices or strands of β-sheet, respectively. Here, these α and β basins are entropically favored for steric reasons alone; a blocked monopeptide is too short to accommodate the peptide hydrogen bonds that stabilize repetitive secondary structure. Thus, despite differing energetics, α/β-basins are favored for both monopeptides and repetitive secondary structure, underpinning an energetically unfrustrated compatibility between these two levels of protein structure.     

Comparison of protein secondary structures based on backbone dihedral angles

In this article, we propose a relatively similar measure to compare protein secondary structures. We first transform a protein secondary structure into a special sequence representation (angle sequence) based on a partition of the backbone φ,ψ-space. Then, pairwise sequence distance is evaluated on the basis of a symbolic sequence complexity. To illustrate our approach, we construct the similarity tree of 24 proteins from PDB.     

Transformation of the ϕ-ψ plot for proteins to a new representation with local helicity and peptide torsional angles as variables

A new representation of protein structure is obtained by the angular coordinate transformations η_i = (?_i+1?ψ_i)/2 and ξ_i = ?_i+1+ψ_i with careful mathematical attention to the cyclical boundary conditions of all of the variables involved. From published ?-ψ data it is possible to obtain a new η-ξ plot. As the angle ξ_i is varied from – 180° through 0° to + 180° in this plot, the local helicity of the polypeptide chain changes continuously and contiguously without sudden reversals in handedness. The variable, η_i, gives the torsional position of the ith peptide group. Some peptide groups in proteins, such as the second peptide residue in a type II β-turn, are nonhydrogen-bonded and can undergo considerable torsional oscillation. In such cases the η angle should be represented by a line whose length reflects the allowed dynamical variations in the peptide torsional position. Certain peptide residues in proteins may be able to undergo a complete torsional rotation of 360°. Such residues would be represented on the η-ξ plot as a straight line across the plot parallel to the abscissa. Other examples of the possible usefulness of this plot are also given.     

Protein backbone and sidechain torsion angles predicted from NMR chemical shifts using artificial neural networks

A new program, TALOS-N, is introduced for predicting protein backbone torsion angles from NMR chemical shifts. The program relies far more extensively on the use of trained artificial neural networks than its predecessor, TALOS+. Validation on an independent set of proteins indicates that backbone torsion angles can be predicted for a larger, ≥90 % fraction of the residues, with an error rate smaller than ca 3.5 %, using an acceptance criterion that is nearly two-fold tighter than that used previously, and a root mean square difference between predicted and crystallographically observed (?, ψ) torsion angles of ca 12º. TALOS-N also reports sidechain χ¹ rotameric states for about 50 % of the residues, and a consistency with reference structures of 89 %. The program includes a neural network trained to identify secondary structure from residue sequence and chemical shifts.     

(φ,ψ)₂ motifs: a purely conformation-based fine-grained enumeration of protein parts at the two-residue level

A deep understanding of protein structure benefits from the use of a variety of classification strategies that enhance our ability to effectively describe local patterns of conformation. Here, we use a clustering algorithm to analyze 76,533 all-trans segments from protein structures solved at 1.2 Å resolution or better to create a purely φ,ψ-based comprehensive empirical categorization of common conformations adopted by two adjacent φ,ψ pairs (i.e., (φ,ψ)₂ motifs). The clustering algorithm works in an origin-shifted four-dimensional space based on the two φ,ψ pairs to yield a parameter-dependent list of (φ,ψ)₂ motifs, in order of their prominence. The results are remarkably distinct from and complementary to the standard hydrogen-bond-centered view of secondary structure. New insights include an unprecedented level of precision in describing the φ,ψ angles of both previously known and novel motifs, ordering of these motifs by their population density, a data-driven recommendation that the standard C^α_i…C^α_i + 3 < 7 Å criteria for defining turns be changed to 6.5 Å, identification of β-strand and turn capping motifs, and identification of conformational capping by residues in polypeptide II conformation. We further document that the conformational preferences of a residue are substantially influenced by the conformation of its neighbors, and we suggest that accounting for these dependencies will improve protein modeling accuracy. Although the CUEVAS-4D(r₁₀?₁₄) ‘parts list’ presented here is only an initial exploration of the complex (φ,ψ)₂ landscape of proteins, it shows that there is value to be had from this approach, and it opens the door to more in-depth characterizations at the (φ,ψ)₂ level and at higher dimensions.     

New Insights into the Interdependence between Amino Acid Stereochemistry and Protein Structure

To successfully design new proteins and understand the effects of mutations in natural proteins, we must understand the geometric and physicochemical principles underlying protein structure. The side chains of amino acids in peptides and proteins adopt specific dihedral angle combinations; however, we still do not have a fundamental quantitative understanding of why some side-chain dihedral angle combinations are highly populated and others are not. Here we employ a hard-sphere plus stereochemical constraint model of dipeptide mimetics to enumerate the side-chain dihedral angles of leucine (Leu) and isoleucine (Ile), and identify those conformations that are sterically allowed versus those that are not as a function of the backbone dihedral angles ? and ψ. We compare our results with the observed distributions of side-chain dihedral angles in proteins of known structure. With the hard-sphere plus stereochemical constraint model, we obtain agreement between the model predictions and the observed side-chain dihedral angle distributions for Leu and Ile. These results quantify the extent to which local, geometrical constraints determine protein side-chain conformations.     

Statistical torsion angle potential energy functions for protein structure modeling: A bicubic interpolation approach

A set of grid type knowledge‐based energy functions is introduced for ?–χ₁, ψ–χ₁, ?–ψ, and χ₁–χ₂ torsion angle combinations. Boltzmann distribution is assumed for the torsion angle populations from protein X‐ray structures, and the functions are named as statistical torsion angle potential energy functions. The grid points around periodic boundaries are duplicated to force periodicity, and the remedy relieves the derivative discontinuity problem. The devised functions rapidly improve the quality of model structures. The potential bias in the functions and the usefulness of additional secondary structure information are also investigated. The proposed guiding functions are expected to facilitate protein structure modeling, such as protein structure prediction, protein design, and structure refinement. Proteins 2013. Proteins 2013; 81:1156–1165. © 2013 Wiley Periodicals, Inc.     

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model

Conformational entropy is expected to contribute significantly to the thermodynamics of structural transitions in intrinsically disordered proteins or regions in response to protein/ligand binding, posttranslational modifications, and environmental changes. We calculated the backbone (dihedral) conformational entropy of oligoglycine $\left({\text{Gly}}_N\right)$, a protein backbone mimic and model intrinsically disordered region, as a function of chain length ($N=3$, 4, 5, 10, and 15) from simulations using three different approaches. The backbone conformational entropy scales linearly with chain length with a slope consistent with the entropy of folding of well-structured proteins. The entropic contributions of second-order dihedral correlations are predominantly through intraresidue ?-ψ pairs, suggesting that oligoglycine may be thermodynamically modeled as a system of independent glycine residues. We find the backbone conformational entropy to be largely independent of global structural parameters, like the end-to-end distance and radius of gyration. We introduce a framework referred to herein as “ensemble confinement” to estimate the loss (gain) of conformational free energy and its entropic component when individual residues are constrained to (released from) particular regions of the ?-ψ map. Quantitatively, we show that our protein backbone model resists ordering/folding with a significant, unfavorable ensemble confinement free energy because of the loss of a substantial portion of the absolute backbone entropy. Proteins can couple this free-energy reservoir to distal binding events as a regulatory mechanism to promote or suppress binding.     

Tensile Mechanics of Alanine-Based Helical Polypeptide: Force Spectroscopy versus Computer Simulations

In nature, an α-helix is commonly used to build thermodynamically stable and mechanically rigid protein conformations. In view of growing interest in the mechanical rigidity of proteins, we measured the tensile profile of an alanine-based α-helical polypeptide on an atomic-force microscope to investigate the basic mechanics of helix extension with minimal interference from side-chain interactions. The peptide was extended to its maximum contour length with much less force than in reported cases of poly-L-Glu or poly-L-Lys, indicating that chain stiffness strongly depended on the physicochemical properties of side chains, such as their bulkiness. The low tensile-force extension originated presumably in locally unfolded parts because of spontaneous structural fluctuations. In 50% trifluoroethanol, the well-known helix-promoting agent, the rigidity of the sample polypeptide was markedly increased. Computer simulations of the peptide-stretching process showed that a majority of constituent residues underwent a transition from an α-helical to an extended conformation by overcoming an energy barrier around ψ ∼0° on the Ramachandran plot. The observed lability of an isolated helix signified the biological importance of the lateral bundling of helices to maintain a rigid protein structure.     

Analysis of dihedral angle preferences for alanine and glycine residues in alpha and beta transmembrane regions

For the past 50?years, the Ramachandran map has been used effectively to study the protein structure and folding. However, though extensive analysis has been done on dihedral angle preferences of residues in globular proteins, related studies and reports of membrane proteins are limited. It is of interest to explore the conformational preferences of residues in transmembrane regions of membrane proteins which are involved in several important and diverse biological processes. Hence, in the present work, a systematic comparative computational analysis has been made on dihedral angle preferences of alanine and glycine in alpha and beta transmembrane regions (the two major classes of transmembrane proteins) with the aid of the Ramachandran map. Further, the conformational preferences of residues in transmembrane regions were compared with the non-transmembrane regions. We have extracted cation-pi interacting residues present in transmembrane regions and explored the dihedral angle preferences. From our observations, we reveal the higher percentage of occurrences of glycine in alpha and beta transmembrane regions than other hydrophobic residues. Further, we noted a clear shift in ψ-angle preferences of glycine residues from negative bins in alpha transmembrane regions to positive bins in beta transmembrane regions. Also, cation-pi interacting residues in beta transmembrane regions avoid preferring ψ-angles in the range of ?59° to ?30°. In this article, we insist that the studies on preferences of dihedral angles in transmembrane regions, thorough understanding of structure and folding of transmembrane proteins, can lead to modeling of novel transmembrane regions towards designing membrane proteins.     

Contribution of villus and intervillus epithelium to intestinal transmural potential difference and response to theophylline and sugar

A chamber design is described which permits isolation of villus or intervillus epithelium from proximal segments of Amphiuma intestine and measurement of the transepithelial potential difference (ψ_ms) and short-circuit current (I_sc) produced by each. In media containing Cl^? and 10 mequiv./l HCO₃^? the villus generated a basal ψ_ms of 0.8 mV (serosa negative) and I_sc of 12 μA/cm² while the intervillus ψ_ms and I_sc were not different from zero. Acetazolamide altered the villus ψ_ms by 1.2 mV; the intervillus ψ_ms by only 0.3 mV. Transepithelial gradients of HCO₃^? appeared to generate diffusion potentials across the intervillus but not the villus epithelium. The actively transported sugar galactose elevated ψ_ms by 0.6 ± 0.1 mV in the intervillus epithelium and by 1.5 ± 0.2 mV in the villus epithelium for a response ratio $\text{(}\text{0.6}\text{1.5}\text{) = 0.4}$. The response ratio for valine was 0.3. In contrast, the response ratios for theophylline (0.7) and cyclic AMP (0.7) were significantly higher. These observations indicate that the entire epithelium is responsive to theophylline and cyclic AMP while Na⁺-dependent solute transport and the basal electrogenic ion transport processes are primarily functions of the cells lining the intestinal villus.     

Structural effects of the binding of GTP to the wild-type and oncogenic forms of theras-gene-encoded p21 proteins

Molecular dynamics calculations have been performed to determine the average structures ofras-gene-encoded p21 proteins bound to GTP, i.e., the normal (wild-type) protein and two oncogenic forms of this protein, the Val 12- and Leu 61-p21 proteins. We find that the average structures for all of these proteins exhibit low coordinate fluctuations (which are highest for the normal protein), indicating convergence to specific structures. From previous dynamics calculations of the average structures of these proteins bound to GDP, major regional differences were found among these proteins (Monacoet al. (1995),J. Protein Chem., in press). We now find that the average structures of the oncogenic proteins are more similar to one another when the proteins are bound to GTP than when they are bound to GDP (Monacoet al. (1995),J. Protein Chem., in press). However, they still differ in structureat specific amino acid residues rather than in whole regions, in contradistinction to the results found for the p21-GDP complexes. Two exceptions are the regions 25–32, in anα-helical region, and 97–110. The two oncogenic (Val 12- and Leu 61-) proteins have similar structures which differ significantly in the region of residues 97–110. This region has recently been identified as being critical in the interaction of p21 with kinase target proteins. The differences in structure between the oncogenic proteins suggest the existence of more than one oncogenic form of the p21 protein that can activate different signaling pathways.     

Conformational similarity among amino acid residues: 1. Analysis of protein crystal structure data

The probability distribution in the (?,ψ)-plane obtained for each amino acid residue from cyrstal structure data of globular proteins is compared. This has shown amino acid residues. Pro and Gly to be conformationally unique. Conformational similarity in the (?,ψ)-plane of amino acid reced does not necessarily mean that they will have the same chemical or biochemical properties or similar secondary structures. A set of amino acid residues are given which can adopt the conformations of other amino acid residues without much difficulty either in the whole (?,ψ)-plane or in regions, where the observed conformations are maximum.     

Benchmarks for flexible and rigid transcription factor-DNA docking

Background

Although structural domains in proteins (SDs) are important, half of the regions in the human proteome are currently left with no SD assignments. These unassigned regions consist not only of novel SDs, but also of intrinsically disordered (ID) regions since proteins, especially those in eukaryotes, generally contain a significant fraction of ID regions. As ID regions can be inferred from amino acid sequences, a method that combines SD and ID region assignments can determine the fractions of SDs and ID regions in any proteome.

Results

In contrast to other available ID prediction programs that merely identify likely ID regions, the DICHOT system we previously developed classifies the entire protein sequence into SDs and ID regions. Application of DICHOT to the human proteome revealed that residue-wise ID regions constitute 35%, SDs with similarity to PDB structures comprise 52%, while SDs with no similarity to PDB structures account for the remaining 13%. The last group consists of novel structural domains, termed cryptic domains, which serve as good targets of structural genomics. The DICHOT method applied to the proteomes of other model organisms indicated that eukaryotes generally have high ID contents, while prokaryotes do not. In human proteins, ID contents differ among subcellular localizations: nuclear proteins had the highest residue-wise ID fraction (47%), while mitochondrial proteins exhibited the lowest (13%). Phosphorylation and O-linked glycosylation sites were found to be located preferentially in ID regions. As O-linked glycans are attached to residues in the extracellular regions of proteins, the modification is likely to protect the ID regions from proteolytic cleavage in the extracellular environment. Alternative splicing events tend to occur more frequently in ID regions. We interpret this as evidence that natural selection is operating at the protein level in alternative splicing.

Conclusions

We classified entire regions of proteins into the two categories, SDs and ID regions and thereby obtained various kinds of complete genome-wide statistics. The results of the present study are important basic information for understanding protein structural architectures and have been made publicly available at http://spock.genes.nig.ac.jp/~genome/DICHOT.     

Dihedral angle and secondary structure database of short amino acid fragments

Dihedral angles of amino acids are of considerable importance in protein tertiary structure prediction as they define the backbone of a protein and hence almost define the protein's entire conformation. Most ab initio protein structure prediction methods predict the secondary structure of a protein before predicting the tertiary structure because three-dimensional fold consists of repeating units of secondary structures. Hence, both dihedral angles and secondary structures are important in tertiary structure prediction of proteins. Here we describe a database called DASSD (Dihedral Angle and Secondary Structure Database of Short Amino acid Fragments) that contains dihedral angle values and secondary structure details of short amino acid fragments of lengths 1, 3 and 5. Information stored in this database was extracted from a set of 5,227 non-redundant high resolution (less than 2-angstroms) protein structures. In total, DASSD stores details for about 733,000 fragments. This database finds application in the development of ab initio protein structure prediction methods using fragment libraries and fragment assembly techniques. It is also useful in protein secondary structure prediction.

Availability     

The Effect of Loops on the Structural Organization of α-Helical Membrane Proteins

Loops connecting the transmembrane (TM) α-helices in membrane proteins are expected to affect the structural organization of the thereby connected helices and the helical bundles as a whole. This effect, which has been largely ignored previously, is studied here by analyzing the x-ray structures of 41 α-helical membrane proteins. First we define the loop flexibility ratio, R, and find that 53% of the loops are stretched, where a stretched loop constrains the distance between the two connected helices. The significance of this constraining effect is supported by experiments carried out with bacteriorhodopsin and rhodopsin, in which cutting or eliminating their (predominately stretched) loops has led to a decrease in protein stability, and for rhodopsin, in most cases, also to the destruction of the structure. We show that for nonstretched loops in the extramembranous regions, the fraction of hydrophobic residues is comparable to that for soluble proteins; furthermore (as is also the case for soluble proteins), the hydrophobic residues in these regions are preferentially buried. This is expected to lead to the compact structural organization of the loops, which is transferred to the TM helices, causing them to assemble. We argue that a soluble protein complexed with a membrane protein similarly promotes compactness; other properties of such complexes are also studied. We calculate complementary attractive interactions between helices, including hydrogen bonds and van der Waals interactions of sequential motifs, such as GXXXG. The relative and combined effects of all these factors on the association of the TM helices are discussed and protein structures with only a few of these factors are analyzed. Our study emphasizes the need for classifying membrane proteins into groups according to structural organization. This classification should be considered when procedures for structural analysis or prediction are developed and applied. Detailed analysis of each structure is provided at http://flan.blm.cs.cmu.edu/memloop/     

Ramachandran analysis of conserved glycyl residues in homologous proteins of known structure

High conservation of glycyl residues in homologous proteins is fairly frequent. It is commonly understood that glycine tends to be highly conserved either because of its unique Ramachandran angles or to avoid steric clash that would arise with a larger side chain. Using a database of aligned 3D structures of homologous proteins we identified conserved Gly in 288 alignment positions from 85 families. Ninety‐six of these alignment positions correspond to conserved Gly residue with (φ, ψ) values allowed for non‐glycyl residues. Reasons for this observation were investigated by in‐silico mutation of these glycyl residues to Ala. We found in 94% of the cases a short contact exists between the C^β atom of the introduced Ala with the atoms which are often distant in the primary structure. This suggests the lack of space even for a short side chain thereby explaining high conservation of glycyl residues even when they adopt (φ, ψ) values allowed for Ala. In 189 alignment positions, the conserved glycyl residues adopt (φ, ψ) values which are disallowed for Ala. In‐silico mutation of these Gly residues to Ala almost always results in steric hindrance involving C^β atom of Ala as one would expect by comparing Ramachandran maps for Ala and Gly. Rare occurrence of the disallowed glycyl conformations even in ultrahigh resolution protein structures are accompanied by short contacts in the crystal structures and such disallowed conformations are not conserved in the homologues. These observations raise the doubt on the accuracy of such glycyl conformations in proteins.     

Structural mapping of the ClpB ATPases of Plasmodium falciparum: Targeting protein folding and secretion for antimalarial drug design

Caseinolytic chaperones and proteases (Clp) belong to the AAA+ protein superfamily and are part of the protein quality control machinery in cells. The eukaryotic parasite Plasmodium falciparum, the causative agent of malaria, has evolved an elaborate network of Clp proteins including two distinct ClpB ATPases. ClpB1 and ClpB2 are involved in different aspects of parasitic proteostasis. ClpB1 is present in the apicoplast, a parasite-specific and plastid-like organelle hosting various metabolic pathways necessary for parasite growth. ClpB2 localizes to the parasitophorous vacuole membrane where it drives protein export as core subunit of a parasite-derived protein secretion complex, the Plasmodium Translocon of Exported proteins (PTEX); this process is central to parasite virulence and survival in the human host. The functional associations of these two chaperones with parasite-specific metabolism and protein secretion make them prime drug targets. ClpB proteins function as unfoldases and disaggregases and share a common architecture consisting of four domains—a variable N-terminal domain that binds different protein substrates, followed by two highly conserved catalytic ATPase domains, and a C-terminal domain. Here, we report and compare the first crystal structures of the N terminal domains of ClpB1 and ClpB2 from Plasmodium and analyze their molecular surfaces. Solution scattering analysis of the N domain of ClpB2 shows that the average solution conformation is similar to the crystalline structure. These structures represent the first step towards the characterization of these two malarial chaperones and the reconstitution of the entire PTEX to aid structure-based design of novel anti-malarial drugs.     

Characterizing the effects of the protein environment on the reduction potentials of metalloproteins

The reduction potentials of electron transfer proteins are critically determined by the degree of burial of the redox site within the protein and the degree of permanent polarization of the polypeptide around the redox site. Although continuum electrostatics calculations of protein structures can predict the net effect of these factors, quantifying each individual contribution is a difficult task. Here, the burial of the redox site is characterized by a dielectric radius R _p (a Born-type radius for the protein), the polarization of the polypeptide is characterized by an electret potential ? _p (the average electrostatic potential at the metal atoms), and an electret-dielectric spheres (EDS) model of the entire protein is then defined in terms of R _p and ? _p. The EDS model shows that for a protein with a redox site of charge Q, the dielectric response free energy is a function of Q ², while the electret energy is a function of Q. In addition, R _p and ? _p are shown to be characteristics of the fold of a protein and are predictive of the most likely redox couple for redox sites that undergo different redox couples.