Nonaxiality in infrared dichroic ratios of polytopic transmembrane proteins.

In polytopic alpha-helical transmembrane proteins, the distribution of amide vibrational transition moments can be nonaxial, if the helix axes are tilted relative to the symmetry axis of the helix bundle. The infrared dichroic ratios from oriented samples then contain nonaxial terms and, in the most general case, require a second-order parameter for the axis of the helix bundle. The extent of nonaxiality depends on the summation over the individual amide transition moments along the helix. Because this is strongly oscillatory, with a 3.6-residue periodicity, complete axial symmetry is not achieved rapidly on progressive summation. Expressions for the contributions of residual nonaxiality to the dichroic ratios are derived. A similar situation arises for oligomers of transmembrane beta-barrel proteins, e.g., the porin trimer. In this case, the extent of nonaxiality depends not only on the number of residues in the beta-barrel, but also on the tilt of the beta-strands relative to the barrel axis and the characteristic dimensions of a beta-sheet, which together determine the axial periodicity. The nonaxial contributions to the dichroic ratios of beta-barrel oligomers are also derived. Estimates are given of the likely size of the nonaxial contributions for the different alpha-helical and beta-sheet systems.     

Symmetry, homology, and phrasing in the recognition of helical regulatory sequences in DNA.

Regulatory regions in DNA which have been sequenced have generally been found to contain one or more axes of two-fold rotational symmetry. If this symmetry is to be maintained in the helical sequence, the axis of rotation must be aligned with one of the two dyad axes of the helix. This is equivalent to saying that the rotational symmetry of the sequence can only be seen from certain viewing points in a circuit about the helix. More surprising is the fact that new symmetrical sequence arrangements can be seen at +/- 36 degrees, +/- 72 degrees, +/- 108 degrees, and +/- 144 degrees relative to the point at which the rotational symmetry is seen. This "amplification" of symmetry suggests a three-dimensional approach to sequence analysis. A specific reading frame, suggested by the geometry of the helix, is examined with regard to its elucidation of intra- and inter-sequence homologies. Two sequences are thus identified as being recurrent in a number of different regulatory sequences.     

Infrared dichroism of polynucleotides of repeated sequence. I. Poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)]

Infrared dichroism measurements of oriented films of poly(dA)·poly(dT) and poly[d(A-T)]·poly[d(A-T)] have been made under the conditions of low salts content and high humidity for which the geometry is known. The angles which the transition moments make with the helix axis are compared with the orientations of the corresponding bonds. Except for the in-plane base model of poly[(A-T)]·poly[d(A-T)], there is no agreement. This may imply either that a model which assumes bonds and transition moments to be colinear is not acceptable or that x-ray data are inaccurate. These possibilities are discussed especially with respect to phosphate group orientation. An appendix gives the derivations of dichroic-ratio expressions for helical molecules of different symmetry types.     

The cell envelope of Thermoproteus tenax: three-dimensional structure of the surface layer and its role in shape maintenance

The sulphur-dependent archaebacterium Thermoproteus tenax has a cylindrical cell shape variable in length, but constant in diameter. Its whole surface is covered by a regular protein layer (S-layer). The lattice has p6 symmetry and a lattice constant of 32.8 nm. The three-dimensional reconstruction from a tilt series of isolated and negatively stained S-layer shows a complex mass distribution of the protein: a prominent, pillar-shaped protrusion is located at the 6-fold crystallographic axis with radiating arms connecting neighbouring hexamers in the vicinity of the 3-fold axis. The base vectors of the S-layer lattice have a preferred orientation with respect to the longitudinal axis of the cell. The layer can be seen as a helical structure consisting of a right-handed, two-stranded helix, with the individual chains running parallel. Supposing that new S-layer protein is inserted at lattice faults (wedge disclinations) near the poles, growing of the layer would then proceed by moving a disclination at the end of the helix. The constant shape of the cell, as well as the particular structure of the layer, strongly suggest that this S-layer has a shape-maintaining function.     

Helical structures in complex plasma I: Noncollective interaction

The conditions for the formation and stability of helical quasi-crystals in a complex plasma containing dust grains of equal size are investigated. A study is made of both the confinement of such helical structures in a direction transverse to the cylinder axis by means of an external parabolic potential well and the possibility of their self-confinement. Computer simulations of the helical dust structures were carried for two cases: for a structure of infinite length along the symmetry axis (or a closed structure in toroidal geometry) and for a structure of finite length. The dust grains were assumed to interact through a potential that is a superposition of the non-Debye nonlinear screened potential and the nonscreened noncollective attractive potential (the Lesage effect). Molecular dynamics simulations showed that, in the presence of dissipation, any initial random distribution of the dust grains interacting through such a potential in cylindrical geometry evolves to an equilibrium helical structure. When the external control parameter was varied smoothly, the pitch angle of the helix was observed to bifurcate (i.e., to undergo sharp jumps). The structure of the helix was also observed to bifurcate when the external parameter was varied: a helix changed into two interwoven helices, which then changed into three interwoven helices, etc. The smaller the confinement parameter (and, accordingly, the larger the radius of the helical structures) and the stronger the attractive forces between the grains, the larger the number of bifurcations. The results of analytical calculations of the parameters of the equilibrium structures and of their energies are in complete agreement with numerical results. It is also shown that noncollective attraction between dust grains makes it probable that helical structures will exists when the external confinement parameter is zero or even when it is negative. Bifurcations in such systems may provide the possibility of creating new types of memory elements.     

Simulation studies on bacteriorhodopsin bundle of transmembrane α segments

Bacteriorhodopsin (BR) is a membrane protein which pumps protons through the plasma membrane. Seven transmembrane BR helical segments are subjected to simulation studies in order to investigate the packing process of transmembrane helices. A Monte Carlo simulated annealing protocol is employed to optimize the helix bundle system. Helix packing is optimized according to a semi-empirical potential mainly composed of six components: a bilayer potential, a crossing angle potential, a helix dipole potential, a helix-helix distance potential, a helix orientation potential and a helix-helix distance restraint potential (a loop potential). Necessary parameters are derived from theoretical studies and statistical analysis of experimentally determined protein structures. The structures from the simulations are compared with the experimentally determined structures in terms of geometry. The structures generated show similar shapes to the experimentally suggested structure even without the helix-helix distance restraint potential. However, the relative locations of individual helices were reproduced only when the helix-helix distance restraint potential was used with restraint conditions. Our results suggest that transmembrane helix bundles resembling those observed experimentally may be generated by simulations using simple potentials. Received: 19 April 1999 / Revised version: 6 September 1999 / Accepted: 17 September 1999     

Geometrical principles of homomeric β‐barrels and β‐helices: Application to modeling amyloid protofilaments

Examples of homomeric β‐helices and β‐barrels have recently emerged. Here we generalize the theory for the shear number in β‐barrels to encompass β‐helices and homomeric structures. We introduce the concept of the “β‐strip,” the set of parallel or antiparallel neighboring strands, from which the whole helix can be generated giving it n‐fold rotational symmetry. In this context, the shear number is interpreted as the sum around the helix of the fixed register shift between neighboring identical β‐strips. Using this approach, we have derived relationships between helical width, pitch, angle between strand direction and helical axis, mass per length, register shift, and number of strands. The validity and unifying power of the method is demonstrated with known structures including α‐hemolysin, T4 phage spike, cylindrin, and the HET‐s(218‐289) prion. From reported dimensions measured by X‐ray fiber diffraction on amyloid fibrils, the relationships can be used to predict the register shift and the number of strands within amyloid protofilaments. This was used to construct models of transthyretin and Alzheimer β(40) amyloid protofilaments that comprise a single strip of in‐register β‐strands folded into a “β‐strip helix.” Results suggest both stabilization of an individual β‐strip helix and growth by addition of further β‐strip helices can involve the same pair of sequence segments associating with β‐sheet hydrogen bonding at the same register shift. This process would be aided by a repeat sequence. Hence, understanding how the register shift (as the distance between repeat sequences) relates to helical dimensions will be useful for nanotube design.     

Protein folding: evaluation of some simple rules for the assembly of helices into tertiary structures with myoglobin as an example

A computer program designed to fold a peptide chain consisting solely of helical segments and connecting links of known length is described and evaluated. This study is a detailed extension of certain aspects of the earlier work of Ptitsyn &; Rashin (1975). Possible interaction sites on the helices are sequence dependent and are calculated as described by Richmond &; Richards (1978) using probable changes in solvent contact area as a guide. The helices are then paired according to the list of potential sites, with each helix being paired at least once. The lists of pairings are then examined geometrically, each site having a defined dihedral helix axis angle, a specified inter-helix axis distance, and defined rotations, when required, about each helix axis. Two simplified filters are used: (1) lengths of connecting links must be equal to or greater than the end-to-end distances of the helices; and (2) non-paired helices must not collide. With myoglobin as a test example and only six of the eight helices being considered, a conformation space consisting of more than 3 × 10⁸ structures was surveyed. The two filters reduced the acceptable structure list to 121. Slight readjustment of the parameters in the filters would have reduced this to 20 structures. Of these 20, one closely resembles the actual distribution of helices in myoglobin. The possible utility and pitfalls of this approach as part of an overall protein folding program are discussed.     

Caulobacter crescentus bacteriophage phiCbK: structure and in vitro self-assembly of the tail

Electron micrographs of negatively stained and platinum-shadowed bacteriophage φCbK have been analyzed by optical diffraction and computer Fourier transformation. The results show that the phage tail is a helical “stacked disc” structure with an annular repeat of about 38 Å and with 3-fold rotational symmetry about the helix axis. Phage tails exhibited lateral and rotational flexibility and were found to possess variable helical parameters. The smaller angle of rotation about the helix axis between equivalent asymmetric units on adjacent discs measured from a number of tail images was found to have an average value of 41.5±0.9 °. Cross-sectional views of short tail fragments were obtained after sonication at 0 °C. These views confirmed the 3-fold symmetry of the 38 Å annular unit, which most probably consists of three identical subunits of the major tail protein. Formation of extended tail polymers, both linear and circular, was found to take place spontaneously in vitro after sonication. On the basis of these results, a low-resolution model for the tail helix is presented. The questions of head-tail symmetry mismatch in the phage and of tail length regulation are discussed.     

A non-perturbation method for the optical properties of helical polymers

The optical absorption and circular dichroism (CD) of poly-L -alanine in an α-helical conformation are computed in terms of monomer properties by use of Bogoliubov exciton theory (a non-perturbation method). It was shown earlier that a proper formulation of the theory of CD for large molecular systems permits the use of periodic boundary conditions, a feature which greatly simplifies calculations as well as conceptual understanding. If is found that the shape of the observed CD spectrum can be explained in terms of the two rotational strength components and an electric dipole strength component referred to as the helix term. Comparisons of the results of perturbation theory and Bogoliubov exciton theory show that perturbation theory is valid for absorption but is inadequate for CD if the coupling among monomers is sufficiently large lo predict the observed hypochromism.     

General method for calculating helical parameters of polymer chains from bond lengths,bond angles,and internal-rotation angles

Helical conformations of infinite polymer chains may be described by the helical parameters, d and θ (the translation along the helix axis and the angle of rotation about the axis per repeat unit), _pi (the distance of the ith atom from the axis), d_ij, and d_ij (the translation along the axis and the angle of rotation, respectively, on passing from the ith atom to the jth). A general method has been worked out for calculating all those helical parameters from the bond lengths, bond angles, and internal-rotation angles. The positions of the main chain and side chain atoms with respect to the axis may also be calculated. All the equations are applicable to any helical polymer chain and are readily programmed for electronic computers. A method is also presented for calculating the partial derivatives of helical parameters with respect to molecular parameters.     

Backbone cyclic helix mimetic of chemokine (C–C motif) receptor 2: A rational approach for inhibiting dimerization of G protein-coupled receptors

The transmembrane helical bundle of G protein-coupled receptors (GPCRs) dimerize through helix–helix interactions in response to inflammatory stimulation. A strategy was developed to target the helical dimerization site of GPCRs by peptidomimetics with drug like properties. The concept was demonstrated by selecting a potent backbone cyclic helix mimetic from a library that derived from the dimerization region of chemokine (C–C motif) receptor 2 (CCR2) that is a key player in Multiple Sclerosis. We showed that CCR2 based backbone cyclic peptide having a stable helix structure inhibits specific CCR2-mediated chemotactic migration     

Transformations in flagellar structure of Rhodobacter sphaeroides and possible relationship to changes in swimming speed

Rhodobacter sphaeroides is a photosynthetic bacterium which swims by rotating a single flagellum in one direction, periodically stopping, and reorienting during these stops. Free-swimming R. sphaeroides was examined by both differential interference contrast (DIC) microscopy, which allows the flagella of swimming cells to be seen in vivo, and tracking microscopy, which tracks swimming patterns in three dimensions. DIC microscopy showed that when rotation stopped, the helical flagellum relaxed into a high-amplitude, short-wavelength coiled form, confirming previous observations. However, DIC microscopy also revealed that the coiled filament could rotate slowly, reorienting the cell before a transition back to the functional helix. The time taken to reform a functional helix depended on the rate of rotation of the helix and the length of the filament. In addition to these coiled and helical forms, a third conformation was observed: a rapidly rotating, apparently straight form. This form took shape from the cell body out and was seen to form directly from flagella that were initially in either the coiled or the helical conformation. This form was always significantly longer than the coiled or helical form from which it was derived. The resolution of DIC microscopy made it impossible to identify whether this form was genuinely in a straight conformation or was a low-amplitude, long-wavelength helix. Examination of the three-dimensional swimming pattern showed that R. sphaeroides changed speed while swimming, sometimes doubling the swimming speed between stops. The rate of acceleration out of stops was also variable. The transformations in waveform are assumed to be torsionally driven and may be related to the changes in speed measured in free-swimming cells. The roles of and mechanisms that may be involved in the transformations of filament conformations and changes in swimming speed are discussed.     

Structural analysis of F18 fimbriae expressed by porcine toxigenic Escherichia coli

The F18 fimbriae expressed by porcine toxigenic Escherichia coli strains are 1- to 2-mm-long filaments that mediate the adhesion of the bacteria to enterocytes. The backbone of these fimbriae is built from a major structural 15.1-kDa protein, FedA. The structure of isolated negatively stained F18 fimbriae imaged by dark-field scanning transmission electron microscopy (STEM) was resolved to approximately 2 nm. Analyzing their helical symmetry showed the axially repeating units to alternate in a "zigzag" manner around the helical axis with an axial rise of 2.2 nm. Two repeating units give rise to the observed 4.3-nm helical repeat, which is practically identical to the pitch of the one-start helix formed. Additionally, an axially repeating pattern with a 27-nm spacing was found on rotary-shadowed fimbriae. Mass-per-length determination of unstained F18 fimbriae by STEM revealed the axially repeating unit to have a molecular mass of 25.4 kDa, indicating that it is a FedA monomer, with the difference in mass arising from the minor subunits, FedE and FedF. The presence of the latter two proteins might cause the observed 27-nm axial pattern.     

A structural model for the polyadenylic acid single helix.

In the crystal, the poly(A) fragment ApApA assumes a conformation with the 5′-terminal and middle adenosines in a single helical arrangement. From the atomic co-ordinates of these two nucleotides the structure of the poly(A) single helix was derived mathematically. The helix has a pitch height of 25.4 Å, nine nucleotides per turn and the normals to the adenine bases form an angle of 66 ° with the helix axis.     

Solution conformation of a heptadecapeptide comprising the DNA binding helix F of the cyclic AMP receptor protein of Escherichia coli. Combined use of 1H nuclear magnetic resonance and restrained molecular dynamics

A nuclear magnetic resonance study on a heptadecamer (17-mer) peptide comprising the DNA binding helix F of the cyclic AMP receptor protein of Escherichia coli is presented under solution conditions (viz. 40% (v/v) trifluorethanol) where it adopts an ordered helical structure as judged by circular dichroism. Using a combination of two-dimensional nuclear magnetic resonance techniques, complete resonance assignments are obtained in a sequential manner. From the two-dimensional nuclear Overhauser enhancement spectra, a set of 87 approximate distance restraints is derived and used as the basis for three-dimensional structure determination with a restrained molecular dynamics algorithm in which the interproton distances are incorporated into the total energy function of the system in the form of an additional effective potential term. The convergence properties of this approach are tested by starting from three different initial structures, namely an alpha-helix, a beta-strand and a 3-10 helix. In all three cases, convergence to an alpha-helical structure is achieved with a root mean square difference of less than 3 A for all atoms and less than 2 A for the backbone atoms.     

Pseudo 2-fold symmetry in the copper-binding domain of arthropodan haemocyanins. Possible implications for the evolution of oxygen transport proteins

Investigation of the copper-binding centre of Panulirus interruptus haemocyanin led to the discovery of a pseudo 2-fold axis relating two helical pairs surrounding and co-ordinating the two copper ions. The pseudo 2-fold symmetry relating one helical pair, co-ordinating Cu-A, to the second helical pair co-ordinating Cu-B is quite precise with 31 equivalent C alpha atoms having a root-mean-square deviation of only 1.47 A. The 2-fold consists of a rotation of 174.6 degrees and a translation parallel to the rotation axis of 0.7 A. After superposition of the helical pairs, the two copper ions are within 1.1 A and the three C alpha atoms of the histidine ligands of Cu-A are within a root-mean-square deviation of 1.0 A from the C alpha atoms of the histidine residues co-ordinating Cu-B. Of the superimposed residues, 26% are identical in sequence. These data suggest that the current oxygen-binding centre of arthropodan haemocyanins is the result of dimerization, gene duplication and gene fusion of an ancestral mono-copper-binding helical pair. This suggestion is supported by the recent discovery that in the sequence of functional domains of molluscan haemocyanins only amino acid sequence homology with the arthropodan Cu-B helical pair has been found and no evidence for similarity with a Cu-A binding helical pair was observed. This provides strong evidence that a mono-copper-binding helical pair has been the ancestor of both the arthropodan and molluscan haemocyanins. Turning to the Fe-binding helical pairs in haemerythrins, it appears that they are less similar to each other than the two Cu-binding helical pairs in arthropodan haemocyanins. Nevertheless, the Fe-B haemerythrin helical pair superimposes well onto the Cu-A helical pair of Panulirus haemocyanin. A root-mean-square deviation of 1.9 A for 24 equivalent C alpha carbon atoms is obtained, while Fe-B deviates 1.4 A from Cu-A after superposition of the helices. Moreover, the three histidine ligands of the Cu-A helical pair are equivalent with three histidine ligands of the Fe-B pair. The structural similarity and correspondence in metal-binding ligands suggests that both haemocyanins and haemerythrins have originated from an ancestral mono-metal-binding helical pair having two ligands provided by the first helix and one ligand by the second helix.(ABSTRACT TRUNCATED AT 400 WORDS)     

Structural Analysis of F18 Fimbriae Expressed by Porcine Toxigenic Escherichia coli

The F18 fimbriae expressed by porcine toxigenic Escherichia coli strains are 1- to 2-mm-long filaments that mediate the adhesion of the bacteria to enterocytes. The backbone of these fimbriae is built from a major structural 15.1-kDa protein, FedA. The structure of isolated negatively stained F18 fimbriae imaged by dark-field scanning transmission electron microscopy (STEM) was resolved to approximately 2 nm. Analyzing their helical symmetry showed the axially repeating units to alternate in a “zigzag” manner around the helical axis with an axial rise of 2.2 nm. Two repeating units give rise to the observed 4.3-nm helical repeat, which is practically identical to the pitch of the one-start helix formed. Additionally, an axially repeating pattern with a 27-nm spacing was found on rotary-shadowed fimbriae. Mass-per-length determination of unstained F18 fimbriae by STEM revealed the axially repeating unit to have a molecular mass of 25.4 kDa, indicating that it is a FedA monomer, with the difference in mass arising from the minor subunits, FedE and FedF. The presence of the latter two proteins might cause the observed 27-nm axial pattern.