Artificial beta-sheets: chemical models of beta-sheets

Chemical models provide tools with which to simplify and study complicated biological systems. Forces and chemical processes that govern the structure, function, and interactions of a biomacromolecule can be explored with a simple, easy-to-study synthetic molecule. Chemical models of beta-sheet structures have helped to elucidate the factors influencing protein structures and functions. Chemical models that mimic beta-sheet quaternary structure and interactions are emerging as valuable tools with which to better understand and control protein recognition and protein aggregation.     

Singular points of protein beta-sheets.

Protein beta-sheets can be regarded as surfaces. Two surfaces can be connected along a common edge to form a larger surface, or two edges of a surface can coalesce to form a closed sheet such as a beta-barrel. Singular points are locations where these connections are not perfect. In protein beta-sheets, a singular point is characterized by a residue separating two beta-ladders. In this paper, we study the singular points of protein beta-sheets from the surface topologic viewpoint, summarize our search results from the protein structural data in the Protein Data Bank, and present examples where singular points are near the active sites and may contribute to forming the proper relative positions of catalytic residues.     

A new catalog of protein beta-sheets

Systematic protein folding studies depend on protein three-dimensional structure annotation, the assignment of amino acid structural types from atomic coordinates. Significant stabilizing factors between adjacent beta-sheet peptide chains have recently been characterized and were not considered during the development of previously published annotation methods. To produce an accurate beta-sheet domain catalog and to encompass the full beta-sheet spectacle, we developed a method, beta-Spider, which evaluates a packing energy between adjacent peptide chains in accordance with the newly discovered stabilizing factors. While considering important energetic factors, our approach also minimizes the use of subjective criteria, such as (phi,psi) boundaries and sets of H-bonding motifs that are used in other existing methods. As a result of the application of beta-Spider to a set of available high-resolution X-ray crystal structures, we present here a new beta-sheet catalog that differs considerably from the one produced by the most acclaimed DSSP method. The catalog includes new H-bonding motifs that were never reported.     

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.     

Model systems for beta-hairpins and beta-sheets

beta-Sheets and alpha-helices are the two principal secondary structures in proteins. However, our understanding of beta-sheet structure lags behind that of alpha-helices, largely because, until recently, there was no model system to study the beta-sheet secondary structure in isolation. With the development of well-folded beta-hairpins, this is changing rapidly. Recent advances include: increased understanding of the relative contributions of turn, strand and sidechain interactions to beta-hairpin and beta-sheet stability, with the role of aromatic residues as a common subtheme; experimental and theoretical kinetic and thermodynamic studies of beta-hairpin and beta-sheet folding; de novo protein design, including all-beta structures, mixed alpha/beta motifs and switchable systems; and the creation of functional beta-hairpins.     

Infrared dichroism of isotope-edited alpha-helices and beta-sheets

Isotope editing of amide infrared bands not only localises secondary structural elements within the protein but also yields conformational information that is not available from the linear dichroism of aligned samples without isotope editing. The additional information that can be derived on the orientational distribution of alpha-helices in membranes by the combined use of different amide bands and several positions of labelling is presented here. Also, the relationship between the azimuthal orientation of the transition moment and the protein structure is treated explicitly. A comprehensive analysis of the infrared dichroism for beta-sheets and beta-barrels is given here, for the first time. The orientation of the individual transition moments in a beta-sheet that is essential for this analysis is derived for the different amide bands.     

Bending undulations and elasticity of the erythrocyte membrane: effects of cell shape and membrane organization

The undulatory excitations (flickering) of human and camel erythrocytes were evaluated by employing the previously used flicker spectroscopy and by local measurements of the autocorrelation function K (t) of the cell thickness fluctuations using a dynamic image processing technique. By fitting theoretical and experimental flicker spectra relative values of the bending elastic modulus K _c of the membrane and of the cytoplasmic viscosity were obtained. The effects of shape changes were monitored by simultaneous measurement of the average light intensity I ₀ passing the cells and by phase contrast microscopic observation of the cells. Evaluation of the cellular excitations in terms of the quasi-spherical model yielded values of K _c /R _inf0 ^sup3 and · R ₀ (R ₀=equivalent sphere radius) and allowed us to account (1) for volume changes, (2) for effects of surface tension and spontaneous curvature and (3) for the non-exponential decay of K (t). From the long time decay of K (t) we obtained an upper limit of the bending elastic modulus of normal cells of K _c = 2–3 · 10^–19 Nm which is an order of magnitude larger than the value found by reflection interference contrast microscopy (RICT, K _c , = 3.4 · 10^–20 Nm, Zilker et al. 1987) but considerably lower than expected for a bilayer containing 50% cholesterol (K _c = 5 · 10^–19 Nm, Duwe et al. 1989). The major part of the paper deals with long time measurements (order of hours) of variations of the apparent K _c and values of single cells (and their reversibility) caused (1) by osmotic volume changes, (2) by discocytestomatocyte transitions induced by albumin and triflouperazine, (3) by discocyte-echinocyte transitions induced by expansion of the lipid/protein bilayer (by incubation with lipid vesicles) and by ATP-depletion in physiological NaCI solution, (4), by coupling or decoupling of bilayer and cytoskeleton using wheat germ agglutinin or erythrocytes with elliptocytosis and (5) by cross-linking the cytoskeleton using diamide. These experiments showed: (1) K _c and are minimal at physiological osmolarity and temperature and well controlled over a large range of these parameters. (2) Echinocyte formation does not markedly alter the apparent membrane bending stiffness. (3) During swelling the cell may undergo a transient discocyte-stomatocyte transition. (4) Strong increases of the apparent K _c and after cup-formation or strong swelling and deflation are due to the effect of shear elasticity and surface tension. Our major conclusions are: (1) The erythrocyte membrane exhibits a shear free deformation regime which requires ATP for its maintenance. (2) Shape transitions may be caused by relative area changes either of the two monolayers of the lipid/protein bilayer (corresponding to the bilayer coupling hypothesis) or of the bilayer and the cytoskeleton where the latter mechanism appears to be more frequent. (3) The low bending stiffness and the shear free deformation regime are explained in terms of a slight excess area of the lipid bilayer leading to a pre-undulated surface profile. Freeze fracture electron microscopy studies provide direct evidence for a pre-undulated bilayer with an undulation wavelength of approximately 100 nm. Offprint requests to: E. Sackmann     

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.     

Reversible unfolding of beta-sheets in membranes: a calorimetric study

The hexapeptide acetyl-Trp-Leu(5) (AcWL(5)) has the remarkable ability to assemble reversibly and spontaneously into beta-sheets on lipid membranes as a result of monomer partitioning followed by cooperative assembly. This system provides a unique opportunity to study the thermodynamics of protein folding in membranes, which we have done using isothermal titration calorimetry (ITC) and differential scanning calorimetry (DSC). The results, which may represent the first example of reversible thermal unfolding of peptides in membranes, help to define the contribution of hydrogen bonding to the extreme thermal stability of membrane proteins. ITC revealed that the enthalpy change for partitioning of monomeric, unstructured AcWL(5) from water into membranes was zero within experimental error over the temperature range of 5 degrees C to 75 degrees C. DSC showed that the beta-sheet aggregates underwent a reversible, endothermic, and very asymmetric thermal transition with a concentration-dependent transition temperature (T(m)) in the range of 60 degrees C to 80 degrees C. A numerical model of nucleation and growth-dependent assembly of oligomeric beta-sheets, proposed earlier to describe beta-sheet formation in membranes, recreated remarkably well the unusual shape and concentration-dependence of the transition peaks. The enthalpy for thermal unfolding of AcWL(5) beta-sheets in the membrane was found to be about 8(+/-1)kcal mol(-1), or about 1.3(+/-0.2)kcal mol(-1) per residue.     

Determinants of strand register in antiparallel beta-sheets of proteins.

Antiparallel beta-sheets present two distinct environments to inter-strand residue pairs: beta(A,HB) sites have two backbone hydrogen bonds; whereas at beta(A,NHB) positions backbone hydrogen bonding is precluded. We used statistical methods to compare the frequencies of amino acid pairs at each site. Only approximately 10% of the 210 possible pairs showed occupancies that differed significantly between the two sites. Trends were clear in the preferred pairs, and these could be explained using stereochemical arguments. Cys-Cys, Aromatic-Pro, Thr-Thr, and Val-Val pairs all preferred the beta(A,NHB) site. In each case, the residues usually adopted sterically favored chi1 conformations, which facilitated intra-pair interactions: Cys-Cys pairs formed disulfide bonds; Thr-Thr pairs made hydrogen bonds; Aromatic-Pro and Val-Val pairs formed close van der Waals contacts. In contrast, to make intimate interactions at a beta(A,HB) site, one or both residues had to adopt less favored chi1 geometries. Nonetheless, pairs containing glycine and/or aromatic residues were favored at this site. Where glycine and aromatic side chains combined, the aromatic residue usually adopted the gauche conformation, which promoted novel aromatic ring-peptide interactions. This work provides rules that link protein sequence and tertiary structure, which will be useful in protein modeling, redesign, and de novo design. Our findings are discussed in light of previous analyses and experimental studies.     

Flexibility of beta-sheets: principal component analysis of database protein structures

Protein folds are built primarily from the packing together of two types of structures: alpha-helices and beta-sheets. Neither structure is rigid, and the flexibility of helices and sheets is often important in determining the final fold (e.g., coiled coils and beta-barrels). Recent work has quantified the flexibility of alpha-helices using a principal component analysis (PCA) of database helical structures (J. Mol. Bio. 2003, 327, pp. 229-237). Here, we extend the analysis to beta-sheet flexibility using PCA on a database of beta-sheet structures. For sheets of varying dimension and geometry, we find two dominant modes of flexibility: twist and bend. The distributions of amplitudes for these modes are found to be Gaussian and independent, suggesting that the PCA twist and bend modes can be identified as the soft elastic normal modes of sheets. We consider the scaling of mode eigenvalues with sheet size and find that parallel beta-sheets are more rigid than antiparallel sheets over the entire range studied. Finally, we discuss the application of our PCA results to modeling and design of beta-sheet proteins.     

Amino acid pairing preferences in parallel beta-sheets in proteins

Statistical approaches have been applied to examine amino acid pairing preferences within parallel beta-sheets. The main chain hydrogen bonding pattern in parallel beta-sheets means that, for each residue pair, only one of the residues is involved in main chain hydrogen bonding with the strand containing the partner residue. We call this the hydrogen bonded (HB) residue and the partner residue the non-hydrogen bonded (nHB) residue, and differentiate between the favorability of a pair and that of its reverse pair, e.g. Asn(HB)-Thr(nHB)versus Thr(HB)-Asn(nHB). Significantly (p < or = 0.000001) favoured pairings were rationalised using stereochemical arguments. For instance, Asn(HB)-Thr(nHB) and Arg(HB)-Thr(nHB) were favoured pairs, where the residues adopted favoured chi1 rotamer positions that allowed side-chain interactions to occur. In contrast, Thr(HB)-Asn(nHB) and Thr(HB)-Arg(nHB) were not significantly favoured, and could only form side-chain interactions if the residues involved adopted less favourable chi1 conformations. The favourability of hydrophobic pairs e.g. Ile(HB)-Ile(nHB), Val(HB)-Val(nHB) and Leu(HB)-Ile(nHB) was explained by the residues adopting their most preferred chi1 and chi2 conformations, which enabled them to form nested arrangements. Cysteine-cysteine pairs are significantly favoured, although these do not form intrasheet disulphide bridges. Interactions between positively and negatively charged residues were asymmetrically preferred: those with the negatively charged residue at the HB position were more favoured. This trend was accounted for by the presence of general electrostatic interactions, which, based on analysis of distances between charged atoms, were likely to be stronger when the negatively charged residue is the HB partner. The Arg(HB)-Asp(nHB) interaction was an exception to this trend and its favorability was rationalised by the formation of specific side-chain interactions. This research provides rules that could be applied to protein structure prediction, comparative modelling and protein engineering and design. The methods used to analyse the pairing preferences are automated and detailed results are available (http://www.rubic.rdg.ac.uk/betapairprefsparallel/).     

Context-dependence of amino acid residue pairing in antiparallel beta-sheets.

In an effort to understand the driving forces behind antiparallel beta-sheet assembly, we have investigated the mutational tolerance of four pairs of residues in CspA, the major cold shock protein of E. coli. Two buried pairs and two exposed pairs of neighboring amino acids were separately randomized and the corresponding effects on protein stability were assessed using a protein expression screen. The thermal denaturation of a subset of the recovered proteins was measured by circular dichroism spectroscopy in order to determine the range of stabilities sampled by the expressed mutants. As anticipated, buried sites are substantially less tolerant of substitutions than exposed sites with more than half of the exposed residue combinations giving rise to stably folded proteins. The two exposed residue pairs, however, display different degrees of tolerance to substitution and accept different residue pair combinations. Except for the prohibition of proline from interior strand positions, no obvious correlations of mutant stability with any single parameter such as beta-sheet propensity or hydrophobicity can be detected. Mutant combinations recovered in both orientations (e.g. XY and YX) at a given exposed pair site often show markedly different stabilities, indicating that the local environment plays a substantial role in modulating the pairing preferences of residues in beta-sheets.     

Analysis and prediction of inter-strand packing distances between beta-sheets of globular proteins

Any two beta-strands belonging to two different beta-sheets in a protein structure are considered to pack interactively if each beta-strand has at least one residue that undergoes a loss of one tenth or more of its solvent contact surface area upon packing. A data set of protein 3-D structures (determined at 2.5 A resolution or better), corresponding to 428 protein chains, contains 1986 non-identical pairs of beta-strands involved in interactive packing. The inter-axial distance between these is significantly correlated to the weighted sum of the volumes of the interacting residues at the packing interface. This correlation can be used to predict the changes in the inter-sheet distances in equivalent beta-sheets in homologous proteins and, therefore, is of value in comparative modelling of proteins.     

Theoretical determination of the CD of proteins containing closely packed antiparallel beta-sheets

Proteins containing two closely packed β-sheets comprise an important class of biopolymers. Rotational and dipole strengths have been determined by the excition coupling model for interacting pairs of two idealized flat β-sheets and for the double β-sheets of seven globular proteins: plastocyanin, human prealbumin, immunoglobulin V_REI, concanavalin A, Cu,Zn superoxide dismutase, staphylococcal nuclease, and elastase. The effects of various geometrical factors on the CD spectra were investigated. Results for the idealized sheets indicate that two sheets display through-space interactions that are large at distances of 5–7 Å and remain significant even at distances typical of the intersheet separations in globular proteins (12–15 Å). The CD spectra are sensitive to the angle (Ω) between the strand directions of the two sheets, with maximum intersheet contributions at Ω = ±45°. Both the intrastrand and interstrand twisting were determined in the seven proteins, and their effects on the calculated CD are discussed. This work represents the first theoretical CD study on the interactions of two regular protein secondary structures, including rotational strength calculations on large sections (up to 135 residues) of globular proteins.     

3D domain-swapped human cystatin C with amyloidlike intermolecular beta-sheets

Oligomerization of human cystatin C (HCC) leads to amyloid deposits in brain arteries, and this process is greatly accelerated with a naturally occurring L68Q variant. The crystal structures of N-truncated and full-length HCC (cubic form) showed dimer formation via three-dimensional (3D) domain swapping, and this observation has led to the suggestion that an analogous domain-swapping mechanism, but propagated in an open-ended fashion, could be the basis of HCC fibril formation. Here we report that full-length HCC, when crystallized in a new, tetragonal form, dimerizes by swapping the same secondary structure elements but with a very different overall structure generated by the flexibility of the hinge linking the moveable elements. The beta-strands of the beta-cores of the two folding units of the present dimer are roughly parallel, while they formed an angle of about 100 degrees in the previous two structures. The dimers pack around a crystallographic dyad by extending their molecular beta-sheets in an intermolecular context. At the other edge of the molecular beta-sheet, side-chain-side-chain hydrogen bonds propagate the beta-structure in the same direction. In consequence, a supramolecular crystal structure is generated, with all the beta-strands of the domain-swapped dimers being perpendicular to one crystallographic direction. This observation is relevant to amyloid aggregation of HCC, as X-ray diffraction studies of amyloid fibrils show them to have ordered, repeating structure, consistent with the so-called cross-beta structure, in which extended polypeptide chains are perpendicular to the fiber axis and form infinite beta-sheets that are parallel to this axis.     

Natural polypeptide scaffolds: beta-sheets, beta-turns, and beta-hairpins

This paper provides an introduction to fundamental conformational states of polypeptides in the beta-region of phi,psi space, in which the backbone is extended near to its maximal length, and to more complex architectures in which extended segments are linked by turns and loops. There are several variants on these conformations, and they comprise versatile scaffolds for presentation of side chains and backbone amides for molecular recognition and designed catalysts. In addition, the geometry of these fundamental folds can be readily mimicked in peptidomimetics.