Infrared dichroism of twisted beta-sheet barrels. The structure of E. coli outer membrane proteins

The infrared dichroic ratios of the amide bands from oriented beta-barrels yield an experimental value for the mean orientation, beta, of the beta-strands, relative to the barrel axis. For a barrel of n strands, this then gives the shear number, S, that characterizes the stagger of the beta-sheet. Combining values of beta and n specifies the barrel geometry by using the optimized model of Murzin, Lesk & Chothia for regular barrels. Application to published infrared data on the Escherichia coli outer membrane protein, OmpA yields S=9-10 (n=8), a barrel radius of 0.81(+/-0.01) nm, and an internal free volume of 0.031 nm(3) per residue, where the average twist of the beta-sheets is theta approximately 28 degrees, and their coiling angle is epsilon approximately 1 degrees. Hydrophobic matching of the 2.6 nm transmembrane stretch partly determines the shear number of the OmpA beta-barrel.     

Conformational and geometrical properties of idealized beta-barrels in proteins

An equation for calculating the distances between the atoms involved in forming an idealized hydrogen bond in a parallel or antiparallel beta-barrel has been derived by adjusting the corresponding data given by Pauling and Corey for a beta-sheet. Based on these distances, a geometrical optimization method was developed, by which one can generate various idealized beta-barrels: parallel or antiparallel, tilted or non-tilted, right-tilted or left-tilted. For each type of idealized beta-barrel thus obtained, the corresponding conformation and characteristic geometric parameters as well as their relationship are analyzed and discussed. Since the strand in a tilted beta-barrel traces a curve rather than a straight line on a cylinder-like surface, a regular chain in which the dihedral angles of each residue are the same cannot form a tilted beta-barrel but only a non-tilted beta-barrel. As observed, the strands of a right-tilted beta-barrel possess a very strong right-handed twist. The radii of the idealized tilted parallel and antiparallel beta-barrels are greater than those of the corresponding non-tilted ones by approximately 1 A and approximately 1.5 A, respectively. Consequently, there is relatively more room for a tilted beta-barrel to accommodate the internal side-chains, suggesting that a conformational change from a non-tilted beta-barrel to a tilted one would ease the repulsion among the crowded internal side-chains so as to make the structure more stable. The values of root-mean-square fits indicate that the idealized right-tilted beta-barrels coincide quite well with the observed beta-barrels in both parallel and antiparallel cases.     

Energetics of the structure and chain tilting of antiparallel beta-barrels in proteins

The preferred structural pattern of antiparallel beta-barrels in proteins, described as the right-handed tilting of the peptide strands with respect to the axis of the barrel, is accounted for in terms of intra- and interchain interaction energies. It is related to the preference of beta-sheets for right-handed twisting. Conformational energy computations have been carried out on three eight-stranded antiparallel beta-barrels composed of six-residue strands, in which L-Val and Gly alternate, and having a right-handed, a left-handed, or no tilt. After energy minimization, the relative energies of these structures were 0.0, 8.6, and 46.1 kcal/mol, respectively; i.e., the right-tilted beta-barrel is favored energetically, in agreement with anti-parallel beta-barrels observed in proteins. Tilting of the barrel is favored, relative to the nontilted structure, by both intra- and interstrand interactions, because tilting allows better packing of the bulky side chains. On the other hand, the energy difference between the left- and right-tilted barrels arises essentially from intrachain interactions. This is a consequence of the preference of beta-sheets for a right-handed twist. Space limitations inside the barrel are satisfied if there is an alternation of bulky residues and residues with small or no side chain (preferably Gly) in neighboring positions on adjacent strands. Such a pattern is seen frequently in antiparallel beta-barrels of globular proteins. The computations indicate that a structure with Val...Gly pairs can be accommodated in a beta-barrel with no distortion.     

Transbilayer pores formed by beta-barrels: molecular modeling of pore structures and properties.

Transmembrane beta-barrels, first observed in bacterial porins, are possible models for a number of membrane channels. Restrained molecular dynamics simulations based on idealized C alpha beta templates have been used to generate models of such beta-barrels. Model beta-barrels have been analyzed in terms of their conformational, energetic, and pore properties. Model beta-barrels formed by N = 4, 8, 12 and 16 anti-parallel Ala10 strands have been developed. For each N, beta-barrels with shear numbers S = N to 2N have been modeled. In all beta-barrel models the constituent beta-strands adopt a pronounced right-handed twist. Interstrand interactions are of approximately equal stability for all models with N > or = 8, whereas such interactions are weaker for the N = 4 beta-barrels. In N = 4 beta-barrels the pore is too narrow (minimum radius approximately 0.6 A) to allow ion permeation. For N > or = 8, the pore radius depends on both N and S; for a given value of N an increase in S from N to 2N is predicted to result in an approximately threefold increase in pore conductance. Calculated maximal conductances for the beta-barrel models are compared with experimental values for porins and for K+ channels.     

Gene duplication of the eight-stranded beta-barrel OmpX produces a functional pore: a scenario for the evolution of transmembrane beta-barrels

The repeating unit of outer membrane beta-barrels from Gram-negative bacteria is the beta-hairpin, and representatives of this protein family always have an even strand number between eight and 22. Two dominant structural forms have eight and 16 strands, respectively, suggesting gene duplication as a possible mechanism for their evolution. We duplicated the sequence of OmpX, an eight-stranded beta-barrel protein of known structure, and obtained a beta-barrel, designated Omp2X, which can fold in vitro and in vivo. Using single-channel conductance measurements and PEG exclusion assays, we found that Omp2X has a pore size similar to that of OmpC, a natural 16-stranded barrel. Fusions of the homologous proteins OmpX, OmpA and OmpW were able to fold in vitro in all combinations tested, revealing that the general propensity to form a beta-barrel is sufficient to evolve larger barrels by simple genetic events.     

Estimating the twist of beta-strands embedded within a regular parallel beta-barrel structure

The parallel beta-barrel is a recurrent structural motif found in a large variety of different enzymes belonging to the family of alpha/beta-proteins. It has been shown previously that the hyperboloid can be considered as a scaffold describing the parallel beta-barrel structure. To assess restraints on beta-strand twist imposed by a given scaffold geometry, the notion of scaffold twist, Ts, is introduced. From Ts, the beta-strand twist (Tw beta) expected for a given scaffold geometry can be derived and it is verified that this computed twist can be used to identify beta-barrels characterized by good hydrogen bonding. It is noted that Tw beta is only slightly affected for beta-barrels differing in the number (N) of beta-strands, suggesting that restraints on main-chain conformation of beta-strands are not likely to account for the N = 8 invariability observed in natural parallel beta-barrels thereby strengthening previous work rationalizing this constancy.     

Folding kinetics of the outer membrane proteins OmpA and FomA into phospholipid bilayers

The folding mechanism of outer membrane proteins (OMPs) of Gram-negative bacteria into lipid bilayers has been studied using OmpA of E. coli and FomA of F. nucleatum as examples. Both, OmpA and FomA are soluble in unfolded form in urea and insert and fold into phospholipid bilayers upon strong dilution of the denaturant urea. OmpA is a structural protein and forms a small ion channel, composed of an 8-stranded transmembrane beta-barrel domain. FomA is a voltage-dependent porin, predicted to form a 14 stranded beta-barrel. Both OMPs fold into a range of model membranes of very different phospholipid compositions. Three membrane-bound folding intermediates of OmpA were discovered in folding studies with dioleoylphosphatidylcholine bilayers that demonstrated a highly synchronized mechanism of secondary and tertiary structure formation of beta-barrel membrane proteins. A study on FomA folding into lipid bilayers indicated the presence of parallel folding pathways for OMPs with larger transmembrane beta-barrels.     

Topological diversity of artificial beta-barrels in water

Rigid-rod beta-barrels are composed of interdigitating, short, amphiphilic peptide strands flanked by stabilizing rigid-rod "staves". We here report studies on the topological diversity of these recently devised artificial beta-barrels with regard to their length. For this purpose, homologous p-octiphenyl, p-sexiphenyl, and p-quarterphenyl rods were equipped with complementary tripeptide strands based on the sequences Lys-Leu-Lys and Glu-Leu-Glu. The stability of rigid-rod beta-barrels of different length was determined by denaturation with guanidinium chloride. Free energies of delta GH2O = -5.2 kcalmol-1, delta GH2O = -2.9 kcalmol-1, and delta GH2O < -0.3 kcalmol-1 found for homologous p-octiphenyl, p-sexiphenyl, and p-quarterphenyl beta-barrels demonstrated strong dependence of beta-barrel stability on beta-barrel length. These results revealed a very qualitative minimal (approximately 23 A) and an "ideal" beta-barrel length (approximately 34 A), synergistic formation (alpha = 1.4) and remarkable stability for "ideal" p-octiphenyl beta-barrels exceeding that of several proteins and most synthetic models. Rigid-rod beta-barrels with p-oligophenyl "staves" longer than approximately 34 A will be very difficult to make and study because of rapidly decreasing rod solubilities. However, a strategy to bypass this apparent upper limitation of beta-barrel length is introduced: supramolecular matching of mismatched rods yielded elongated beta-barrels (61 A) of acceptable stability (delta GH2O = 2.2 - 3.1 kcalmol-1).     

Toward genomic identification of β-barrel membrane proteins: Composition and architecture of known structures

The amino acid composition and architecture of all beta-barrel membrane proteins of known three-dimensional structure have been examined to generate information that will be useful in identifying beta-barrels in genome databases. The database consists of 15 nonredundant structures, including several novel, recent structures. Known structures include monomeric, dimeric, and trimeric beta-barrels with between 8 and 22 membrane-spanning beta-strands each. For this analysis the membrane-interacting surfaces of the beta-barrels were identified with an experimentally derived, whole-residue hydrophobicity scale, and then the barrels were aligned normal to the bilayer and the position of the bilayer midplane was determined for each protein from the hydrophobicity profile. The abundance of each amino acid, relative to the genomic abundance, was calculated for the barrel exterior and interior. The architecture and diversity of known beta-barrels was also examined. For example, the distribution of rise-per-residue values perpendicular to the bilayer plane was found to be 2.7 +/- 0.25 A per residue, or about 10 +/- 1 residues across the membrane. Also, as noted by other authors, nearly every known membrane-spanning beta-barrel strand was found to have a short loop of seven residues or less connecting it to at least one adjacent strand. Using this information we have begun to generate rapid screening algorithms for the identification of beta-barrel membrane proteins in genomic databases. Application of one algorithm to the genomes of Escherichia coli and Pseudomonas aeruginosa confirms its ability to identify beta-barrels, and reveals dozens of unidentified open reading frames that potentially code for beta-barrel outer membrane proteins.     

Orientation of beta-barrel proteins OmpA and FhuA in lipid membranes. Chain length dependence from infrared dichroism

The outer-membrane proteins OmpA and FhuA of Escherichia coli are monomeric beta-barrels of widely differing size. Polarized attenuated total reflection infrared spectroscopy has been used to determine the orientation of the beta-barrels in phosphatidylcholine host matrices of different lipid chain lengths. The linear dichroism of the amide I band from OmpA and FhuA in hydrated membranes generally increases with increasing chain length from diC(12:0) to diC(17:0) phosphatidylcholine, in both the fluid and gel phases. Measurements of the amide I and amide II dichroism from dry samples are used to deduce the strand tilt (beta = 46 degrees for OmpA and beta = 44.5 degrees for FhuA). These values are then used to deduce the order parameters, P(2)(cos alpha), of the beta-barrels from the amide I dichroic ratios of the hydrated membranes. The orientational ordering of the beta-barrels and their assembly in the membrane are discussed in terms of hydrophobic matching with the lipid chains.     

Comparison of the hemocyanin beta-barrel with other Greek key beta-barrels: possible importance of the "beta-zipper" in protein structure and folding.

The Greek key beta-barrel topology is a folding motif observed in many proteins of widespread evolutionary origin. The arthropodan hemocyanins also have such a Greek key beta-barrel, which forms the core of the third domain of this protein. The hemocyanin beta-barrel was found to be structurally very similar to the beta-barrels of the immunoglobulin domains, Cu,Zn-superoxide dismutase and the chromophore carrying antitumor proteins. The structural similarity within this group of protein families is not accompanied by an evolutionary or functional relationship. It is therefore possible to study structure-sequence relations without bias from nonstructural constraints. The present study reports a conserved pattern of features in these Greek key beta-barrels that is strongly suggestive of a folding nucleation site. This proposed nucleation site, which we call a "beta-zipper," shows a pattern of well-conserved, large hydrophobic residues on two sequential beta-strands joined by a short loop. Each beta-zipper strand is near the center of one of the beta-sheets, so that the two strands face each other from opposite sides of the barrel and interact through their hydrophobic side chains, rather than forming a hydrogen-bonded beta-hairpin. Other protein families with Greek key beta-barrels that do not as strongly resemble the immunoglobulin fold--such as the azurins, plastocyanins, crystallins, and prealbumins--also contain the beta-zipper pattern, which might therefore be a universal feature of Greek key beta-barrel proteins.     

The structure of bacterial outer membrane proteins

Integral membrane proteins come in two types, alpha-helical and beta-barrel proteins. In both types, all hydrogen bonding donors and acceptors of the polypeptide backbone are completely compensated and buried while nonpolar side chains point to the membrane. The alpha-helical type is more abundant and occurs in cytoplasmic (or inner) membranes, whereas the beta-barrels are known from outer membranes of bacteria. The beta-barrel construction is described by the number of strands and the shear number, which is a measure for the inclination angle of the beta-strands against the barrel axis. The common right-handed beta-twist requires shear numbers slightly larger than the number of strands. Membrane protein beta-barrels contain between 8 and 22 beta-strands and have a simple topology that is probably enforced by the folding process. The smallest barrels form inverse micelles and work as enzymes or they bind to other macromolecules. The medium-range barrels form more or less specific pores for nutrient uptake, whereas the largest barrels occur in active Fe(2+) transporters. The beta-barrels are suitable objects for channel engineering, because the structures are simple and because many of these proteins can be produced into inclusion bodies and recovered therefrom in the exact native conformation.     

A multidomain outer membrane protein from Pasteurella multocida: modelling and simulation studies of PmOmpA

PmOmpA is a two-domain outer membrane protein from Pasteurella multocida. The N-terminal domain of PmOmpA is a homologue of the transmembrane beta-barrel domain of OmpA from Escherichia coli, whilst the C-terminal domain of PmOmpA is a homologue of the extra-membrane Neisseria meningitidis RmpM C-terminal domain. This enables a model of a complete two domain PmOmpA to be constructed and its conformational dynamics explored via MD simulations of the protein embedded within two different phospholipid bilayers (DMPC and DMPE). The conformational stability of the transmembrane beta-barrel is similar to that of a homology model of OprF from Pseudomonas aeruginosa in bilayer simulations. There is a degree of water penetration into the interior of the beta-barrel, suggestive of a possible transmembrane pore. Although the PmOmpA model is stable over 20 ns simulations, retaining its secondary structure and fold integrity throughout, substantial flexibility is observed in a short linker region between the N- and the C-terminal domains. At low ionic strength, the C-terminal domain moves to interact electrostatically with the lipid bilayer headgroups. This study demonstrates that computational approaches may be applied to more complex, multi-domain outer membrane proteins, rather than just to transmembrane beta-barrels, opening the possibility of in silico proteomics approaches to such proteins.     

Analysis of the stability of hemoglobin S double strands.

The deoxyhemoglobin S (deoxy-HbS) double strand is the fundamental building block of both the crystals of deoxy-HbS and the physiologically relevant fibers present within sickle cells. To use the atomic-resolution detail of the hemoglobin-hemoglobin interaction known from the crystallography of HbS as a basis for understanding the interactions in the fibers, it is necessary to define precisely the relationship between the straight double strands in the crystal and the twisted, helical double strands in the fibers. The intermolecular contact conferring the stability of the double strand in both crystal and fiber is between the beta6 valine on one HbS molecule and residues near the EF corner of an adjacent molecule. Models for the helical double strands were constructed by a geometric transformation from crystal to fiber that preserves this critical interaction, minimizes distortion, and makes the transformation as smooth as possible. From these models, the energy of association was calculated over the range of all possible helical twists of the double strands and all possible distances of the double strands from the fiber axis. The calculated association energies reflect the fact that the axial interactions decrease as the distance between the double strand and the fiber axis increases, because of the increased length of the helical path taken by the double strand. The lateral interactions between HbS molecules in a double strand change relatively little between the crystal and possible helical double strands. If the twist of the fiber or the distance between the double strand and the fiber axis is too great, the lateral interaction is broken by intermolecular contacts in the region around the beta6 valine. Consequently, the geometry of the beta6 valine interaction and the residues surrounding it severely restricts the possible helical twist, radius, and handedness of helical aggregates constructed from the double strands. The limitations defined by this analysis establish the structural basis for the right-handed twist observed in HbS fibers and demonstrates that for a subunit twist of 8 degrees, the fiber diameter cannot be more than approximately 300 A, consistent with electron microscope observations. The energy of interaction among HbS molecules in a double strand is very slowly varying with helical pitch, explaining the variable pitch observed in HbS fibers. The analysis results in a model for the HbS double strand, for use in the analysis of interactions between double strands and for refinement of models of the HbS fibers against x-ray diffraction data.     

Local sequence of protein β‐strands influences twist and bend angles

β‐Sheet twisting is thought to be mainly determined by interstrand hydrogen bonds with little contribution from side chains, but some proteins have large, flat β‐sheets, suggesting that side chains influence β‐structures. We therefore investigated the relationship between amino acid composition and twists or bends of β‐strands. We calculated and statistically analyzed the twist and bend angles of short frames of β‐strands in known protein structures. The most frequent twist angles were strongly negatively correlated with the proportion of hydrophilic amino acid residues. The majority of hydrophilic residues (except serine and threonine) were found in the edge regions of β‐strands, suggesting that the side chains of these residues likely do not affect β‐strand structure. In contrast, the majority of serine, threonine, and asparagine side‐chains in β‐strands made contacts with a nitrogen atom of the main chain, suggesting that these residues suppress β‐strand twisting. Proteins 2014; 82:1484–1493. © 2014 Wiley Periodicals, Inc.     

Analysis of the Intermolecular Contacts within Sickle Hemoglobin Fibers: Effect of Site-Specific Substitutions, Fiber Pitch, and Double-Strand Disorder

An atomic model of the sickle hemoglobin (HbS) fiber was synthesized by combining the molecular coordinates of the fiber (obtained from electron microscopy) with atomic coordinates of the sickle hemoglobin double strand (obtained from X-ray crystallography). The model is stereochemically acceptable. The majority of polymerization-sensitive HbS mutants are located at fiber contact sites and the majority of the mutants that do not affect polymerization are not located at contact sites. The residues at intermolecular contacts in the fiber model are reported. We have searched the coordinate space in the vicinity of the EM reconstructions to find models with alternative sets of coordinates that satisfy the mutant data, contain 5-Å contacts between double strands, and are stereochemically acceptable. This involved a systematic examination over 297 different models. The alternative fiber models were generated with a range of fiber pitch, double-strand positions, and double-strand polarity. Models which had unacceptably close contacts between atoms, failed to satisfy the mutant data, or did not have 5-Å contacts between double strands were considered unacceptable. None of the acceptable alternative fiber models improved the agreement between the polymerization behavior of HbS mutants and their contact site location. However, several models could account for the polymerization data equally well. Residue locations for single-site HbS mutations that could discriminate between alternative fiber models are proposed. The twist of HbS fibers varies in an apparent random manner with an average rotation of 7.8 ± 2.5° per molecule and a maximum rotation of 16° per molecule. The number of interdouble-strand contacts as a function of fiber twist shows a broad maximum around 9° and may account for the observed range of fiber pitch. This study shows that the upper limit on the fiber twist could result from a loss of axial contacts and repulsive van der Waals interactions between residues involved in interstrand contacts. The loss of axial contacts limits the radial growth of the fiber. In the appendix we analyze the methodology used by I. Cretegny and S. J. Edelstein [(1993) J. Mol. Biol. 230, 733-738] to build a model of the fiber. Our examination reveals shortcomings in the methodology of Cretegny and Edelstein. One result of these shortcomings is that the model synthesized by Cretegny and Edelstein is not stereochemically acceptable because it gives rise to a large number of excessively close (less than 1.4 Å) atom-atom contacts, suggesting interpenetration of the molecular envelopes.     

Computer simulations of the OmpF porin from the outer membrane of Escherichia coli.

Molecular dynamics simulations were used to study the structure and dynamics of the Escherichia coli OmpF porin, which is composed of three identical 16-stranded beta-barrels. Simulations of the full trimer in the absence of water and the membrane led to significant contraction of the channel in the interior of each beta-barrel. With very weak harmonic constraints (0.005 kcal/mol A2/atom) applied to the main-chain C alpha atoms of the beta-barrel, the structure was stabilized without alteration of the average fluctuations. The resulting distribution of the fluctuations (small for beta-strands, large for loops and turns) is in good agreement with the x-ray B factors. Dynamic cross-correlation functions showed the importance of coupling between the loop motions and barrel flexibility. This was confirmed by the application of constraints corresponding to the observed temperature factors to the barrel C alpha atoms. With these constraints, the beta-barrel fluctuations were much smaller than the experimental values because of the intrinsic restrictions on the atomic motions, and the loop motions were reduced significantly. This result indicates that considerable care is required in introducing constraints to keep proteins close to the experimental structure during simulations, as has been done in several recent studies. Loop 3, which is thought to be important in gating the pore, undergoes a displacement that shifts it away from the x-ray structure. Analysis shows that this arises from the breakdown of a hydrogen bond network, which appears to result more from the absence of solvent that from the use of standard ionization states for the side chains of certain beta-barrel residues.     

The DNA Phosphate orientation. Infrared data and energetically favorable structures

The conformation of nucleic acids can be probed reliably by the geometrical arrangement of the PO₂- groups in the backbone. The phosphate arrangement is described by two angles, θ_OO and θ_OPO, which can be determined by several methods. In the present paper, the two angles obtained for the A, B, and C forms of DNA, experimentally by ir linear dichroism (LD) of oriented films as well as theoretically from energy-minimized structures. The methodology of the phosphate angle determination from the ir dichroism spectra is presented in detail, elucidating the potentialities and limitations of this method. Advantageously, tilt and twist angles of the DNA bases, found by theoretical calculations, were used in the ir data processing. The phosphate angles were compared with the corresponding x-ray and nmr results from the literature. Regarding the rather high flexibility of the double helix, as well as the sequence-dependent variation of the conformational angles, a fairly good agreement between our results and the majority of all discussed data can be established. Thus ir LD provides reliable data on the orientation of phosphate groups in DNA. Reasons for discrepancies with some literature data from x-ray fiber-diffraction analysis, published several years ago, will be discussed.