Windex: a toolset for indexing helices

We describe here a set of procedures and algorithms that may be used as an aid in determining the indexing rule of a helical specimen. Crystallizing macromolecules into helical arrays has the potential to speed up and simplify the process of three-dimensional reconstruction of the macromolecular structure. The process of helical reconstruction has been largely automated except for the critical first step of indexing the helical diffraction pattern. This is quite often the rate-limiting step in the overall process, particularly in the case of large helical tubes, which have complicated helical diffraction patterns that may vary from tube to tube. We have developed a set of procedures, supported by a graphical user interface, that provide a straightforward and semi-automated approach to indexing a helical structure. The new procedures have been tested using a number of helical specimens, including TMV, acto-myosin, decorated microtubules, and a variety of helical tubes of a bacterial membrane protein.     

Studies of synthetic helical peptides using circular dichroism and nuclear magnetic resonance

We have designed a set of 17-residue synthetic peptides to be monomeric helices in aqueous solution. Circular dichrosim experiments indicate the presence of helical structure in aqueous solution at low temperature and low pH. The two-dimensional nuclear magnetic resonance results for one of the peptides show a segment of ten residues which clearly meets all of the criteria for the existence of helical structure at both 5 degrees C and 15 degrees C. The first four residues of the peptide are in a largely extended conformation. Calculations suggest that residues 5 through 14 are significantly helical at 5 degrees C. When the temperature is increased, circular dichroism spectra indicate that the helical content decreases. At 15 degrees C, the 3JN alpha coupling constants increase in the helical region, indicating an increase in motion or conformational averaging in the helical segment. None of the peptides has pH titration behavior consistent with salt bridge stabilization of helical conformation. Our data lend themselves to interpretation with the helix dipole model and specific side-chain interactions. When the N and C termini charges are removed the helical content of the peptides increases. The amount of helicity increases as the pH is lowered, due to the ionization of His16. Much of the helical stabilization appears to be due to a specific side-chain interaction between His16 and Tyr12.     

Change of plasmid DNA structure, hypermethylation, and Lon-proteolysis as steps in a replicative cascade.

I have defined conditions under which RepFIC plasmid DNA can be maintained in a state of lowered helical density. In exponentially growing cultures, the DNA of lowered helical density is present in small amounts but never totally absent, suggesting that it is a normal variant of plasmid maintenance. It is fully methylated at frequent sites by dam-methyltransferase, some not previously recognized, further suggesting that the variant is a precursor of replication. The low-helical density plasmid is present in dam hosts, indicating that methylation is not essential for the change in helical density. The lowered helical density is stabilized in lon hosts, suggesting that Lon-protease may remove both the protein(s) that lower the helical density and the dam-methyltransferase after each round of replication.     

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)     

The 12 A structure of trypsin-treated measles virus N-RNA

Recombinant measles virus nucleoprotein (N) was produced in insect cells where it bound to cellular RNA to form helical N-RNA structures. These structures were observed by electron microscopy but were too flexible for high-resolution image analysis. Removal of the C-terminal tail of N by trypsin treatment resulted in structures that were much more rigid and seemed more regular. Several methods of image analysis were employed in order to make a helical reconstruction of the digested N-RNA. During this analysis, it became clear that the apparently regular coils of digested N-RNA consisted of a series of closely related helical states. The iterative helical real space reconstruction method allowed the identification of two helical states for which a reconstruction could be calculated. The model with the highest resolution shows N monomers that consist of three domains and that are connected to their neighbours by two narrow connections, one close to the helical axis and another toward the middle of the monomers. There are no connections between N molecules in subsequent helical turns. After labelling the RNA in the structure with cis-platinum, the connection closest to the helical axis increased in density, suggesting the position of the RNA. The shapes of the monomers of the nucleoproteins of influenza virus, rabies virus (both determined before) and that of measles virus (determined here) are all similar, whereas the overall shapes of their respective N-RNAs (nucleocapsids) is very different. This is probably due to the position and number of the connections between the N subunits in the N-RNA, one for influenza virus allowing much flexibility, two for rabies virus at either end of the N molecules leading to ribbons and two for measles virus leading to the typical paramyxovirus helical nucleocapsid.     

Mechanistic insight into the physiological relevance of helical blood flow in the human aorta: an in vivo study

The hemodynamics within the aorta of five healthy humans were investigated to gain insight into the complex helical flow patterns that arise from the existence of asymmetries in the aortic region. The adopted approach is aimed at (1) overcoming the relative paucity of quantitative data regarding helical blood flow dynamics in the human aorta and (2) identifying common characteristics in physiological aortic flow topology, in terms of its helical content. Four-dimensional phase-contrast magnetic resonance imaging (4D PC MRI) was combined with algorithms for the calculation of advanced fluid dynamics in this study. These algorithms allowed us to obtain a 4D representation of intra-aortic flow fields and to quantify the aortic helical flow. For our purposes, helicity was used as a measure of the alignment of the velocity and the vorticity. There were two key findings of our study: (1) intra-individual analysis revealed a statistically significant difference in the helical content at different phases of systole and (2) group analysis suggested that aortic helical blood flow dynamics is an emerging behavior that is common to normal individuals. Our results also suggest that helical flow might be caused by natural optimization of fluid transport processes in the cardiovascular system, aimed at obtaining efficient perfusion. The approach here applied to assess in vivo helical blood flow could be the starting point to elucidate the role played by helicity in the generation and decay of rotating flows in the thoracic aorta.     

Study of hydrodynamic characteristics in tubular photobioreactors

In this work, the hydrodynamic characteristics in tubular photobioreactors with a series of helical static mixers built-in were numerically investigated using computational fluid dynamics (CFD). The influences of height and screw pitch of the helical static mixer and fluid inlet velocity on the cell trajectories, swirl numbers and energy consumption were examined. In order to verify the actual results for cultivation of microalgae, cultivation experiments of freshwater Chlorella sp. were carried out in photobioreactor with and without helical static mixer built-in at the same time. It was shown that with built-in helical static mixer, the mixing of fluid could be intensified, and the light/dark cycle could also be achieved which is of benefit for the growth of microalgae. The biomass productivity of Chlorella sp. in tubular photobioreactor with helical static mixer built-in was 37.26 % higher than that in the photobioreactor without helical static mixer.     

Structure of HIV-1 Capsid Assemblies by Cryo-electron Microscopy and Iterative Helical Real-space Reconstruction

Cryo-electron microscopy (cryo-EM), combined with image processing, is an increasingly powerful tool for structure determination of macromolecular protein complexes and assemblies. In fact, single particle electron microscopy¹ and two-dimensional (2D) electron crystallography² have become relatively routine methodologies and a large number of structures have been solved using these methods. At the same time, image processing and three-dimensional (3D) reconstruction of helical objects has rapidly developed, especially, the iterative helical real-space reconstruction (IHRSR) method³, which uses single particle analysis tools in conjunction with helical symmetry. Many biological entities function in filamentous or helical forms, including actin filaments⁴, microtubules⁵, amyloid fibers⁶, tobacco mosaic viruses⁷, and bacteria flagella⁸, and, because a 3D density map of a helical entity can be attained from a single projection image, compared to the many images required for 3D reconstruction of a non-helical object, with the IHRSR method, structural analysis of such flexible and disordered helical assemblies is now attainable.In this video article, we provide detailed protocols for obtaining a 3D density map of a helical protein assembly (HIV-1 capsid⁹ is our example), including protocols for cryo-EM specimen preparation, low dose data collection by cryo-EM, indexing of helical diffraction patterns, and image processing and 3D reconstruction using IHRSR. Compared to other techniques, cryo-EM offers optimal specimen preservation under near native conditions. Samples are embedded in a thin layer of vitreous ice, by rapid freezing, and imaged in electron microscopes at liquid nitrogen temperature, under low dose conditions to minimize the radiation damage. Sample images are obtained under near native conditions at the expense of low signal and low contrast in the recorded micrographs. Fortunately, the process of helical reconstruction has largely been automated, with the exception of indexing the helical diffraction pattern. Here, we describe an approach to index helical structure and determine helical symmetries (helical parameters) from digitized micrographs, an essential step for 3D helical reconstruction. Briefly, we obtain an initial 3D density map by applying the IHRSR method. This initial map is then iteratively refined by introducing constraints for the alignment parameters of each segment, thus controlling their degrees of freedom. Further improvement is achieved by correcting for the contrast transfer function (CTF) of the electron microscope (amplitude and phase correction) and by optimizing the helical symmetry of the assembly.     

Helical swimming can provide robust upwards transport for gravitactic single-cell algae; a mechanistic model

In still fluid, many phytoplankton swim in helical paths with an average upwards motion. A new mechanistic model for gravitactic algae subject to an intrinsic torque is developed here, based on Heterosigma akashiwo, which results in upwards helical trajectories in still fluid. The resultant upwards swimming speed is calculated as a function of the gravitactic and intrinsic torques. Helical swimmers have a reduced upwards speed in still fluid compared to cells which swim straight upwards. However a novel result is obtained when the effect of fluid shear is considered. For intermediate values of shear and intrinsic torque, a new stable equilibrium solution for swimming direction is obtained for helical swimmers. This results in positive upwards transport in vertical shear flow, in contrast to the stable equilibrium solution for straight swimmers which results in downwards transport in vertical shear flow. Furthermore, for strong intrinsic torque, when there is no longer a stable orientation equilibrium, we show that the average downwards transport of helical swimmers in vertical shear flow is greatly suppressed compared to straight swimmers. We hypothesise that helical swimming provides robustness for upwards transport in the presence of fluid shearing motions.     

Intrinsic helical propensities and stable secondary structure in a membrane-bound fragment (S4) of the shaker potassium channel.

The location and stability of helical secondary structure in a fragment comprising an extended sequence of the S4 transmembrane segment of the Shaker potassium channel was determined in methanol, and when bound to vesicles composed of egg phosphatidylcholine: egg phosphatidylglycerol (4:1; mol:mol) in water. The N-acetylated, C-amidated peptide corresponds to the sequence comprising residues A355-I384 in the Shaker potassium channel. Although NOEs characteristic of helical structure encompass essentially the full peptide sequence in methanol, analysis of amide and CH(alpha) chemical shifts, and amide exchange protection factors establish that stable helical structure comprises only around the first 22 amino acids of the 30 residue peptide. This sequence corresponds to that predicted to have the highest helical stability in water, indicating that while helical structure is considerably stabilised in methanol, the relative helical propensities of amino acids in methanol may be similar to those in water.In the presence of vesicles containing negatively charged lipids, helical structure corresponding to a maximum of around 40 % of the extended S4 peptide is induced; no helical structure is induced in the presence of vesicles composed only of neutral lipids. The location of stable helical structure in the membrane-bound peptide was determined by amide hydrogen-deuterium exchange trapping, and was shown to encompass the sequence between residues near M2 and I18. This sequence is similar to that having high helix propensity in water and methanol, supporting the idea that intrinsic helical propensities are important in defining the location of stable helical structure in polypeptides bound in the interfacial region of lipid bilayers. The study defines an approach to determining the location of, and contributions to, the stability of helical secondary structure in membrane-reconstituted polypeptides.     

Collagens as multidomain proteins

The number of proteins known to contain collagen-like triple helical domains is rapidly increasing. The functions of these domains are to provide molecular rods that separate spatially non-triple helical domains with varied properties and structures and to permit lateral interactions between molecules. Two-thirds of the amino acids of the triple helical domains have their side-chains at the surface of the protein. The triple helix is also a structure that is easily predictable from the primary structure. The structure of several recently discovered collagens are discussed in terms of domains and functions. The triple helical domains have sizes varying from 33 to over 1,000 amino acid residues. The longest uninterrupted triple helices are involved in the formation of the classical quarter-staggered fibrils. Other triple helical domains permit varied molecular aggregates. A very broad spectrum of non-triple helical or globular domains are interspersed by triple helices. Only those located at the extremities of the molecules are large in size, sometimes several hundred kDa, while the domains separating 2 triple helices are small (less than 50 amino acids) and provide the molecules with hinges, proteolytic cleavage sites or other specialized functions like a glycosaminoglycan attachment site. If the assembly of the 3 chains required for the triple helix formation can be controlled in vitro, collagen-like molecules offer an as yet unexploited potential for protein engineering.     

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.     

On the mysterious propulsion of Synechococcus

We propose a model for the self-propulsion of the marine bacterium Synechococcus utilizing a continuous looped helical track analogous to that found in Myxobacteria [1]. In our model cargo-carrying protein motors, driven by proton-motive force, move along a continuous looped helical track. The movement of the cargo creates surface distortions in the form of small amplitude traveling ridges along the S-layer above the helical track. The resulting fluid motion adjacent to the helical ribbon provides the propulsive thrust. A variation on the helical rotor model of [1] allows the motors to be anchored to the peptidoglycan layer, where they drive rotation of the track creating traveling helical waves along the S-layer. We derive expressions relating the swimming speed to the amplitude, wavelength, and velocity of the surface waves induced by the helical rotor, and show that they fall in reasonable ranges to explain the velocity and rotation rate of swimming Synechococcus.     

Helical flow as fluid dynamic signature for atherogenesis risk in aortocoronary bypass. A numeric study

The main purpose of the study was to verify if helical flow, widely observed in several vessels, might be a signature of the blood dynamics of vein graft anastomosis. We investigated the existence of a relationship between helical flow structures and vascular wall indexes of atherogenesis in aortocoronary bypass models with different geometric features. In particular, we checked for the existence of a relationship between the degree of helical motion and the magnitude of oscillating shear stress in conventional hand-sewn proximal anastomosis. The study is based on the numerical evaluation of four bypass geometries that are attached to a simplified computer representation of the ascending aorta with different angulations relative to aortic outflow. The finite volume technique was used to simulate realistic graft fluid dynamics, including aortic compliance and proper aortic and graft flow rates. A quantitative method was applied to evaluate the level of helicity in the flow field associated with the four bypass models under investigation. A linear inverse relationship (R = -0.97) was found between the oscillating shear index and the helical flow index for the models under investigation. The results obtained support the hypothesis that an arrangement of the flow field in helical patterns may elicit damping in wall shear stress temporal gradients at the proximal graft. Accordingly, helical flow might play a significant role in preventing plaque deposition or in tuning the mechanotransduction pathways of cells. Therefore, results confirm that helical flow constitutes an important flow signature in vessels, and its strength as a fluid dynamic index (for instance in combination with magnetic resonance imaging flow visualization techniques) for risk stratification, in the activation of both mechanical and biological pathways leading to fibrointimal hyperplasia.     

Thermodynamic parameters of the helix-coil transition in polypeptide chains. III. Random copolymers of L-leucine and L-glutamic acid.

Conformational transitions induced by pH changes in random copolymers of leucine and glutamic acid have been studied. Significant differences were observed in the potentiometric titration curves of copolymers with small (up to 4%) and large leucine contents. The helical stability of copolymers with small leucine content, determined from titration curves by the Zimm and Rice method, decreases slightly with an increase in the leucine content, whereas the helical stability of copolymers with large leucine content increases sharply with an increase of the leucine content. It is shown that copolymers with large leucine content aggregate in the region of transition into the helical state, but the increase of their helical state stability is not connected with intermolecular aggregation, as it was also observed for a nonaggregating fraction isolated from one of the copolymers by gel chromatography. A conclusion is made that the helix–coil equilibrium constant s for leucine does not itself exceed the s constant for uncharged polyglutamic acid. The stabilization of the helical state in copolymers with large leucine content is due to intramolecular aggregation of helices in these copolymers. The analysis of the leucine residue distribution between helical and nonhelical regions in globular proteins also gives no real arguments to ascribe special helix-forming properties to leucine.     

Water permeation through gramicidin A: desformylation and the double helix: a molecular dynamics study

Multinanosecond molecular dynamics simulations of gramicidin A embedded in a dimyristoylphosphatidylcholine bilayer show a remarkable structural stability for both experimentally determined conformations: the head-to-head helical dimer and the double helix. Water permeability was found to be much higher in the double helical conformation, which is explained by lower hydrogen bond-mediated enthalpic barriers at the channel entrance and its larger pore size. Free-energy perturbation calculations show that the double helical structure is stabilized by the positive charges at the N termini introduced by the desformylation, whereas the helical dimer is destabilized. Together with the recent experimental observation that desformyl gramicidin conducts water hundredfold better than gramicidin, this suggests that desformyl gramicidin A predominantly occurs in the double helical conformation.     

Protein structural models for nucleic acid interactions

It is proposed that particular segments of some ribosomal, histone and plant viral capsid proteins adopt a helical structural mode for interaction with nucleic acid. The amino acid regions were determined by three probes applied to 26 protein sequences: searches for helical wheels displaying asymmetric basic charge distributions, secondary structural predictions, and searches for primary structural homologies. In 11 of the protein sequences examined, homologous heptapeptides were found in the residue spans delineated by the three probes. A helical wheel analysis of the oligopeptide amino acids showed a distinct positive charge clustering. It is suggested that the basic amino acid side chains on the hydrophilic helical side interact with nucleic acid negative phosphate groups while the somewhat hydrophobic side is available for interaction within the protein or possibly with the major groove of double-stranded nucleic acid.     

High-resolution electron microscopy of helical specimens: a fresh look at tobacco mosaic virus

The treatment of helical objects as a string of single particles has become an established technique to resolve their three-dimensional (3D) structure using electron cryo-microscopy. It can be applied to a wide range of helical particles such as viruses, microtubules and helical filaments. We have made improvements to this approach using Tobacco Mosaic Virus (TMV) as a test specimen and obtained a map from 210,000 asymmetric units at a resolution better than 5 A. This was made possible by performing a full correction of the contrast transfer function of the microscope. Alignment of helical segments was helped by constraints derived from the helical symmetry of the virus. Furthermore, symmetrization was implemented by multiple inclusions of symmetry-related views in the 3D reconstruction. We used the density map to build an atomic model of TMV. The model was refined using a real-space refinement strategy that accommodates multiple conformers. The atomic model shows significant deviations from the deposited model for the helical form of TMV at the lower-radius region (residues 88 to 109). This region appears more ordered with well-defined secondary structure, compared with the earlier helical structure. The RNA phosphate backbone is sandwiched between two arginine side-chains, stabilizing the interaction between RNA and coat protein. A cluster of two or three carboxylates is buried in a hydrophobic environment isolating it from neighboring subunits. These carboxylates may represent the so-called Caspar carboxylates that form a metastable switch for viral disassembly. Overall, the observed differences suggest that the new model represents a different, more stable state of the virus, compared with the earlier published model.     

Disruption Mechanism in the Helix of SPF Peptide by Interchanging E5 and K10 Residues: Inference from Molecular Dynamics Study

Abstract

Seminalplasmin (SPLN) is a 47-residue peptide (SDEKASPDKHHRFSLSRYAKLANR LANPKLLETFLSKWIGDRGNRSV) from bovine seminal plasma. It has broad spectrum antimicrobial activity, without any hemolytic activity. The 28–40 segment of SPLN with the sequence PKLLETFLSKWIG, designated as SPF, is the most hydrophobic stretch of SPLN and primarily responsible for the membrane-perturbing activity of SPLN. It was reported that SPF has a helical structure and the interchange of E5 and K10 residues disrupted the helical structure. The present paper reports a possible mechanism of disruption of the helical structure of SPF peptide during the interchange of E5 and K10 residues. The result is based on simulated annealing and molecular dynamics simulation studies on SPF and its four analogues with K10E, K10D, E5K, and E5K & K10E substitutions. It showed that K10 residue has a critical role in maintaining the highest helical content and the positions of charged residues are also very important for maintaining the helical structure of the SPF peptide. Formation of some new long-range hydrogen bonds and the rupture of some shortrange hydrogen bonds involving the tenth residue led to the disruption of helical structure of SPF peptide when E5 and K10 residues are interchanged.