Flexibility of alpha-helices: results of a statistical analysis of database protein structures

Alpha-helices stand out as common and relatively invariant secondary structural elements of proteins. However, alpha-helices are not rigid bodies and their deformations can be significant in protein function (e.g. coiled coils). To quantify the flexibility of alpha-helices we have performed a structural principal-component analysis of helices of different lengths from a representative set of protein folds in the Protein Data Bank. We find three dominant modes of flexibility: two degenerate bend modes and one twist mode. The data are consistent with independent Gaussian distributions for each mode. The mode eigenvalues, which measure flexibility, follow simple scaling forms as a function of helix length. The dominant bend and twist modes and their harmonics are reproduced by a simple spring model, which incorporates hydrogen-bonding and excluded volume. As an application, we examine the amount of bend and twist in helices making up all coiled-coil proteins in SCOP. Incorporation of alpha-helix flexibility into structure refinement and design is discussed.     

Minimal surface as a model of beta-sheets

The purpose of this article is to present arguments based on experimental data that the beta-sheet structures in proteins are the result of the tendency to minimize surface areas. Thus, we propose the model that all beta-sheet structures are almost minimal surfaces, namely, their mean curvatures are nearly zero. To support this model, we chose 1740 disjoint beta-sheets with less than 10 strands from the all beta-protein class in a nonredundant 40% Structural Classification of Proteins (SCOP) database and applied the least-squares method to fit the minimal surface catenoid (and in some rare cases, the plane) to the beta-sheet structures. The fitting errors were extremely small: The error of 1729 beta-sheets with catenoid minimal surface is 0.90 +/- 0.55 A and the error of the remaining 11 flat sheets with the plane is 0.64 +/- 0.46 A. The fact that the commonly used models for some beta-sheet surfaces (i.e., the hyperboloid and strophoid) have very small mean curvatures (< 0.05) supports our model. Moreover, we showed that this model also includes the isotropically stressed configuration model proposed by Salemme, in which the intrastrand tendency of the individual chains to twist or coil is in equilibrium with the tendency of the interstrand hydrogen bonding to resist twisting of the sheet as a whole. As an application we used our model to quantify the two principal independent modes in the flexibility of beta-sheets, that is, the bending parameter of beta-sheets and the inclined angle of beta-strands in a sheet.     

Beta-sheet capping: signals that initiate and terminate beta-sheet formation

In the present work, we address the question of whether different amino acids have different beta-sheet initiating and terminating characteristics. Using a large scale analysis of parallel and antiparallel beta-sheets in a non-redundant dataset of proteins, we observed that most of the amino acids show significant under- or over-representation in at least one of the positions at the two ends of beta-sheets, which are denoted as N-cap and C-cap. In addition, based on statistical data and structural comparison, we found that certain amino acids, especially Asp, Asn, Gly and Pro have strong tendencies to block beta-sheet continuation. Hence, we can consider these residues as beta-sheet terminators. It was also proposed that the dipole moments in parallel beta-sheets, whose direction is from C-terminal (partially negative) to N-terminal (partially positive), are much stronger than has previously been suggested. In fact, enhancement of dipole moments in parallel beta-sheets is a result of the positioning of positively charged residues at N-cap and negatively charged residues at C-cap. This enhancement in dipole moment magnitude leads to strengthened dipolar interactions between parallel beta-sheets dipoles and other partners especially alpha-helices dipoles. The results provide an explanation for the antiparallel alignment of parallel beta-sheets with alpha-helices.     

A new protein folding algorithm based on hydrophobic compactness: Rigid Unconnected Secondary Structure Iterative Assembly (RUSSIA). II: Applications

The RUSSIA procedure (Rigid Unconnected Secondary Structure Iterative Assembly) produces structural models of cores of small- and medium-sized proteins. Loops are omitted from this treatment and regular secondary structures are reduced to points, the centers of their hydrophobic faces. This methodology relies on the maximum compactness of the hydrophobic residues, as described in detail in Part I. Starting data are the sequence and the predicted limits and natures of regular secondary structures (alpha or beta). Helices are treated as rigid cylinders, whereas beta-strands are collectively taken into account within beta-sheets modeled by helicoid surfaces. Strands are allowed to shift along their mean axis to allow some flexibility and the alpha-helices can be placed on either side of beta-sheets. Numerous initial conformations are produced by discrete rotations of the helices and sheets around the direction going from the center of their hydrophobic face to the global center of the protein. Selection of proposed models is based upon a criterion lying on the minimization of distances separating hydrophobic residues belonging to different regular secondary structures. The procedure is rapid and appears to be robust relative to the quality of starting data (nature and length of regular secondary structures). This dependence of the quality of the model on secondary structure prediction and in particular the beta-sheet topology, is one of the limits of the present algorithm. We present here some results for a set of 12 proteins (alpha, beta and alpha/beta classes) of lengths 40-166 amino acids. The r.m.s. deviations for core models with respect to the native proteins are in the range 1.4-3.7 A.     

New aspects of the alpha-helix to beta-sheet transition in stretched hard alpha-keratin fibers

The putative transformation of alpha-helices into beta-sheets has been studied for more than 50 years in the case of hard alpha-keratin. In a previous study of stretched keratin fibers, we specified the conditions for beta-sheet appearance within horsehair: the formation of beta-sheets requires at least 30% relative humidity. However, this phenomenon was observed in the whole tissue. Then there was no clear chemical identification of the beta-sheets (keratin or matrix proteins) and the exact location of the beta-sheets across the fiber could not be specified. In this study, using wide-angle x-ray scattering and high spatial resolution infrared microspectroscopy, we could determine and characterize the structural elements across hair sections stretched in water, which provides new information about the aforementioned transition. Our results show that the process can be split into three steps: 1), unraveling of the alpha-helical coiled-coil domains, which starts at roughly 5% macroscopic strain; 2), further transformation of the unraveled coiled-coils into beta-sheet structures, which occurs above roughly 20% macroscopic strain; and 3), spatial expanding of the beta-structured zones from the sample center to its periphery.     

Fourier transform infrared analysis of bacteriorhodopsin secondary structure.

Fourier transform infrared spectroscopy at a resolution of 1 cm-1 has been used to study the conformation of dark-adapted bacteriorhodopsin in the native purple membrane, in H2O and D2O suspensions. A detailed analysis of the amide I bands was made using derivative and deconvolution techniques. Curve-fitting results of four independent experiments indicate, after estimation of the methodological errors, that native bacteriorhodopsin contains 52-73% alpha-helices, 13-19% reverse turns, 11-16% beta-sheets, and 3-7% unordered segments. Our analysis has enabled the identification of several components corresponding to alpha-helices, beta-sheets, and reverse turns. Besides the alpha I- and alpha II-helices (peaking at 1658 and 1665 cm-1), we propose that two more infrared bands arise from alpha-helical structures: one at 1650 cm-1 from alpha I and another one at 1642 cm-1 in H2O suspension, which could originate from type III beta-turns (i.e., one turn of 3(10)-helix). The relatively high content of reverse turns suggests the presence of one reverse turn per loop, plus another one in the C-terminal segment. On the other hand, several reasons argue that the calculated mean beta-sheet content of around 14% should be decreased somewhat. These beta-sheets could be located in the noncytoplasmatic links of the bacteriorhodopsin molecule.     

NMR characterization of structure, backbone dynamics, and glutathione binding of the human macrophage migration inhibitory factor (MIF).

Human macrophage migration inhibitory factor is a 114 amino acid protein that belongs to the family of immunologic cytokines. Assignments of 1H, 15N, and 13C resonances have enabled the determination of the secondary structure of the protein, which consists of two alpha-helices (residues 18-31 and 89-72) and a central four-stranded beta-sheet. In the beta-sheet, two parallel beta-sheets are connected in an antiparallel sense. From the total of three cysteines present in the primary structure of MIF, none was found to form disulfide bridges. 1H-15N heteronuclear T1, T2, and steady-state NOE measurements indicate that the backbone of MIF exists in a rigid structure of limited conformational flexibility (on the nanosecond to picosecond time scale). Several residues located in the loop regions and at the N termini of two helices exhibit internal motions on the 1-3 ns time scale. The capacity to bind glutathione was investigated by titration of a uniform 15N-labeled sample and led us to conclude that MIF has, at best, very low affinity for glutathione.     

Dependence of alpha-helical and beta-sheet amino acid propensities on the overall protein fold type

ABSTRACT: BACKGROUND: A large number of studies have been carried out to obtain amino acid propensities for alpha- helices and beta-sheets. The obtained propensities for alpha-helices are consistent with each other, and the pair-wise correlation coefficient is frequently high. On the other hand, the beta-sheet propensities obtained by several studies differed significantly, indicating that the context significantly affects beta-sheet propensity. RESULTS: We calculated amino acid propensities for alpha-helices and beta-sheets for 39 and 24 protein folds, respectively, and addressed whether they correlate with the fold. The propensities were also calculated for exposed and buried sites, respectively. Results showed that alpha-helix propensities do not differ significantly by fold, but beta-sheet propensities are diverse and depend on the fold. The propensities calculated for exposed sites and buried sites are similar for alpha-helix, but such is not the case for the beta-sheet propensities. We also found some fold dependence on amino acid frequency in beta-strands. Folds with a high Ser, Thr and Asn content at exposed sites in beta-strands tend to have a low Leu, Ile, Glu, Lys and Arg content (correlation coefficient = 0.90) and to have flat beta-sheets. At buried sites in beta-strands, the content of Tyr, Trp, Gln and Ser correlates negatively with the content of Val, Ile and Leu (correlation coefficient = 0.93). "All-beta" proteins tend to have a higher content of Tyr, Trp, Gln and Ser, whereas alpha/beta proteins tend to have a higher content of Val, Ile and Leu. CONCLUSIONS: The alpha-helix propensities are similar for all folds and for exposed and buried residues. However, beta-sheet propensities calculated for exposed residues differ from those for buried residues, indicating that the exposed-residue fraction is one of the major factors governing amino acid composition in beta-strands. Furthermore, the correlations we detected suggest that amino acid composition is related to folding properties such as the twist of a beta-strand or association between two beta sheets.     

Normal mode analysis suggests a quaternary twist model for the nicotinic receptor gating mechanism

We present a three-dimensional model of the homopentameric alpha7 nicotinic acetylcholine receptor (nAChR), that includes the extracellular and membrane domains, developed by comparative modeling on the basis of: 1), the x-ray crystal structure of the snail acetylcholine binding protein, an homolog of the extracellular domain of nAChRs; and 2), cryo-electron microscopy data of the membrane domain collected on Torpedo marmorata nAChRs. We performed normal mode analysis on the complete three-dimensional model to explore protein flexibility. Among the first 10 lowest frequency modes, only the first mode produces a structural reorganization compatible with channel gating: a wide opening of the channel pore caused by a concerted symmetrical quaternary twist motion of the protein with opposing rotations of the upper (extracellular) and lower (transmembrane) domains. Still, significant reorganizations are observed within each subunit, that involve their bending at the domain interface, an increase of angle between the two beta-sheets composing the extracellular domain, the internal beta-sheet being significantly correlated to the movement of the M2 alpha-helical segment. This global symmetrical twist motion of the pentameric protein complex, which resembles the opening transition of other multimeric ion channels, reasonably accounts for the available experimental data and thus likely describes the nAChR gating process.     

Structural composition of betaI- and betaII-proteins

Circular dichroism spectra of proteins are sensitive to protein secondary structure. The CD spectra of alpha-rich proteins are similar to those of model alpha-helices, but beta-rich proteins exhibit CD spectra that are reminiscent of CD spectra of either model beta-sheets or unordered polypeptides. The existence of these two types of CD spectra for beta-rich proteins form the basis for their classification as betaI- and betaII-proteins. Although the conformation of beta-sheets is largely responsible for the CD spectra of betaI-proteins, the source of betaII-protein CD, which resembles that of unordered polypeptides, is not completely understood. The CD spectra of unordered polypeptides are similar to that of the poly(Pro)II helix, and the poly(Pro)II-type (P2) structure forms a significant fraction of the unordered conformation in globular proteins. We have compared the beta-sheet and P2 structure contents in beta-rich proteins to understand the origin of betaII-protein CD. We find that betaII-proteins have a ratio of P2 to beta-sheet content greater than 0.4, whereas for betaI-proteins this ratio is less than 0.4. The beta-sheet content in betaI-proteins is generally higher than that in betaII-proteins. The origin of two classes of CD spectra for beta-rich proteins appears to lie in their relative beta-sheet and P2 structure contents.     

Twist and shear in beta-sheets and beta-ribbons

The structures of the beta-sheets and the beta-ribbons have been analysed using high-resolution protein structure data. Systematic asymmetries measured in both parallel and antiparallel beta-structures include the sheet twist and the strand shear. In order to determine the origin of these asymmetries, numerous interactions and correlations were examined. The strongest correlations are observed for residues in antiparallel beta-sheets and beta-ribbons that form non-H-bonded pairs. For these residues, the sheet twist is correlated to the backbone phi angle but not to the psi angle. Our analysis supports the existence of an inter-strand C(alpha)H(alpha)...O weak H-bond, which, together with the CO...HN H-bond, constitutes a bifurcated H-bond that links neighbouring beta-strands. Residues of beta-sheets and beta-ribbons in high-resolution protein structures form a distinct region of the Ramachandran plot, which is determined by the formation of the bifurcated H-bond, the formation of an intra-strand O...H(alpha) non-bonded polar interaction, and an intra-strand O...C(beta) steric clash. Using beta-strands parameterised by phi-psi values from the allowed beta-sheet region of the Ramachandran plot, the shear and the right-hand twist can be reproduced in a simple model of the antiparallel and parallel beta-ribbon that models the bifurcated H-bonds specifically. The conformations of interior residues of beta-sheets are shown to be subsets of the conformations of residues of beta-ribbons.     

Local propensities and statistical potentials of backbone dihedral angles in proteins

The following three issues concerning the backbone dihedral angles of protein structures are presented. (1) How do the dihedral angles of the 20 amino acids depend on the identity and conformation of their nearest residues? (2) To what extent are the native dihedral angles determined by local (dihedral) potentials? (3) How to build a knowledge-based potential for a residue's dihedral angles, considering the identity and conformation of its nearest residues? We find that the dihedral angle distribution for a residue can significantly depend on the identity and conformation of its adjacent residues. These correlations are in sharp contrast to the Flory isolated-pair hypothesis. Statistical potentials are built for all combinations of residue triplets and depend on the dihedral angles between consecutive residues. First, a low-resolution potential is obtained, which only differentiates between the main populated basins in the dihedral angle density plots. Minimization of the dihedral potential for 125 test proteins reveals that most native alpha-helical residues (89%) and a large fraction of native beta-sheet residues (47%) adopt conformations close to their native one. For native loop residues, the percentage is 48%. It is also found that this fraction is higher for residues away from the ends of alpha or beta secondary structure elements. In addition, a higher resolution potential is built as a function of dihedral angles by a smoothing procedure and continuous functions interpolations. Monte Carlo energy minimization with this potential results in a lower fraction for native beta-sheet residues. Nevertheless, because of the higher flexibility and entropy of beta structures, they could be preferred under the influence of non-local interactions. In general, most alpha-helices and many beta-sheets are strongly determined by the local potential, while the conformations in loops and near the end of beta-sheets are more influenced by non-local interactions.     

On the significance of alternating patterns of polar and non-polar residues in beta-strands

A common assumption about protein sequences in beta-strands is that they have alternating patterns of polar and non-polar residues. It is thought that such patterns reflect the interior/exterior geometry of amino acid residue side-chains on a beta-sheet. Here we study the prevalence of simple hydrophobicity patterns in parallel and antiparallel beta-sheets in proteins of known structure and in the sequences of amyloidogenic proteins. The occurrence of 32 possible pentapeptide binary patterns (polar (P)/non-polar (N)) is computed in 1911 non-homologous protein structures. Despite their tendency to aggregate in experimentally designed proteins, the purely alternating hydrophobic/polar patterns (PNPNP and NPNPN) are most frequent in beta-sheets, typically occurring in antiparallel strands. The overall distribution of the pentapeptide binary patterns is significantly different in strands within parallel and antiparallel sheets. In both types of sheets, complementary patterns (where the hydrophobic and polar residues pair with one another) associate preferentially. We do not find alternating patterns to be common in amyloidogenic proteins or in short fragments involved directly in amyloid formation. However, we do note some similarities between patterns present in amyloidogenic sequences and those in parallel strands.     

Molecular chemical structure of barley proteins revealed by ultra-spatially resolved synchrotron light sourced FTIR microspectroscopy: comparison of barley varieties

Barley protein structure affects the barley quality, fermentation, and degradation behavior in both humans and animals among other factors such as protein matrix. Publications show various biological differences among barley varieties such as Valier and Harrington, which have significantly different degradation behaviors. The objectives of this study were to reveal the molecular structure of barley protein, comparing various varieties (Dolly, Valier, Harrington, LP955, AC Metcalfe, and Sisler), and quantify protein structure profiles using Gaussian and Lorentzian methods of multi-component peak modeling by using the ultra-spatially resolved synchrotron light sourced Fourier transform infrared microspectroscopy (SFTIRM). The items of the protein molecular structure revealed included protein structure alpha-helices, beta-sheets, and others such as beta-turns and random coils. The experiment was performed at the National Synchrotron Light Source in Brookhaven National Laboratory (BNL, US Department of Energy, NY). The results showed that with the SFTIRM, the molecular structure of barley protein could be revealed. Barley protein structures exhibited significant differences among the varieties in terms of proportion and ratio of model-fitted alpha-helices, beta-sheets, and others. By using multi-component peaks modeling at protein amide I region of 1710-1576 cm-1, the results show that barley protein consisted of approximately 18-34% of alpha-helices, 14-25% of beta-sheets, and 44-69% others. AC Metcalfe, Sisler, and LP955 consisted of higher (P<0.05) proportions of alpha-helices (30-34%) than Dolly and Valier (alpha-helices 18-23%). Harrington was in between which was 25%. For protein beta-sheets, AC Metcalfe, and LP955 consisted of higher proportions (22-25%) than Dolly and Valier (13-17%). Different barley varieties contained different alpha-helix to beta-sheet ratios, ranging from 1.4 to 2.0, although the difference were insignificant (P>0.05). The ratio of alpha-helices to others (0.3 to 1.0, P<0.05) and that of beta-sheets to others (0.2 to 0.8, P<0.05) were different among the barley varieties. It needs to be pointed out that using a multi-peak modeling for protein structure analysis is only for making relative estimates and not exact determinations and only for the comparison purpose between varieties. The principal component analysis showed that protein amide I Fourier self-deconvolution spectra were different among the barley varieties, indicating that protein internal molecular structure differed. The above results demonstrate the potential of the SFTIRM to localize relatively pure protein areas in barley tissues and reveal protein molecular structure. The results indicated relative differences in protein structures among the barley varieties, which may partly explain the biological differences among the barley varieties. Further study is needed to understand the relationship between barley molecular chemical structure and biological features in terms of nutrient availability and digestive behavior.     

Discovering structural correlations in alpha-helices.

We have developed a new representation for structural and functional motifs in protein sequences based on correlations between pairs of amino acids and applied it to alpha-helical and beta-sheet sequences. Existing probabilistic methods for representing and analyzing protein sequences have traditionally assumed conditional independence of evidence. In other words, amino acids are assumed to have no effect on each other. However, analyses of protein structures have repeatedly demonstrated the importance of interactions between amino acids in conferring both structure and function. Using Bayesian networks, we are able to model the relationships between amino acids at distinct positions in a protein sequence in addition to the amino acid distributions at each position. We have also developed an automated program for discovering sequence correlations using standard statistical tests and validation techniques. In this paper, we test this program on sequences from secondary structure motifs, namely alpha-helices and beta-sheets. In each case, the correlations our program discovers correspond well with known physical and chemical interactions between amino acids in structures. Furthermore, we show that, using different chemical alphabets for the amino acids, we discover structural relationships based on the same chemical principle used in constructing the alphabet. This new representation of 3-dimensional features in protein motifs, such as those arising from structural or functional constraints on the sequence, can be used to improve sequence analysis tools including pattern analysis and database search.     

Role of interchain interactions in the stabilization of the right-handed twist of beta-sheets

Conformational energy computations have been carried out for parallel and antiparallel beta-sheets composed of poly-L-Val and poly-L-Ile peptide chains, each consisting of four and of six residues, respectively, with CH3CO- and-NHCH3 end groups. The beta-sheets considered contained three and five equivalent chains, respectively. All computed minimum-energy beta-sheets were found to have a large right-handed twist of a magnitude that corresponds to the mean twist of beta-sheets observed in globular proteins. The twist has the same sign but is much larger than in beta-sheets of poly-L-Ala, because of intra- and interchain interactions between the bulky beta-branched side-chains. While the right-handed twist is a result of intrachain interactions between side-chains in the case of poly-L-Val, these interactions would favor a left-handed twist in poly-L-Ile, and the right-handed twist in the latter is a result of interchain interactions. Parallel beta-sheets are more stable than antiparallel sheets for both poly-L-Val and poly-L-Ile, in contrast to poly-L-Ala. This result agrees with observations on the preferred orientation of the chains in oligopeptides that form beta-structures. It also explains the observed high relative frequencies of occurrence of Val and Ile residues in parallel beta-sheets, as compared with antiparallel sheets, in globular proteins.     

Molecular modeling and characterization of the B. thuringiensis and B. thuringiensis LDC-9 cytolytic proteins

The Cyt toxins are able to lyse a wide range of cell types in vitro, unlike the Cry delta-endotoxins. It exerts its activity by the formation of pores within target cell membranes. The structural information available for Cyt2Aa (PDB id: 1CBY) consists of a single domain in which two outer layers of alpha-helix wrap around a mixed beta-sheet. Beta-barrel was suggested as a possible structure of the pores. Hence, this study seeks to investigate the structural properties of other Cytolytic proteins by predicting the three-dimensional (3D) model using Cyt2Aa as template. The predicted models are expected to be significantly more accurate as all the Cyt proteins showed significant similarity with the template (PDB id: 1CBY). The refined homology models revealed similar secondary structures (alpha-helices and beta-sheets) and tertiary features as Cyt2Aa. The variation in the loop regions of the tertiary structure accounts for the differential toxicity.