HELFIT: Helix fitting by a total least squares method

The problem of fitting a helix to data arises in analysis of protein structure, in nuclear physics, and in engineering. A continuous helix is described by five parameters: helix axis, helix radius, and helix pitch. One of these helix parameters is frequently predefined in the helix fitting. Other algorithms find only the helix axis or determine separately the helix axis, the helix radius, or the helix pitch. Here we describe a total least squares method, HELFIT, for helix fitting. HELFIT enables one to calculate simultaneously all five of the helix parameters with high accuracy. The minimum number of data points required for the analysis is only four. HELFIT is very insensitive to noise even in short helices. HELFIT also calculates a parameter, p = rmsd/(N − 1)^1/2, which estimates the regularity of helical structures independent of the number of data points, where rmsd is the root mean square distance from the best-fit helix to data points and N is the number of data points. It should become a basic tool of structural bioinformatics.     

Parallel Homochiral and Anti‐Parallel Heterochiral Hydrogen‐Bonding Interfaces in Multi‐Helical Abiotic Foldamers

A hydrogen‐bonding interface between helical aromatic oligoamide foldamers has been designed to promote the folding of a helix‐turn‐helix motif with a head‐to‐tail arrangement of two helices of opposite handedness. This design complements an earlier helix‐turn‐helix motif with a head‐to‐head arrangement of two helices of identical handedness interface. The two motifs were shown to have comparable stability and were combined in a unimolecular tetra‐helix fold constituting the largest abiotic tertiary structure to date.     

Characterization of the dynamics of an essential helix in the U1A protein by time-resolved fluorescence measurements

The RNA recognition motif (RRM), one of the most common RNA-binding domains, recognizes single-stranded RNA. A C-terminal helix that undergoes conformational changes upon binding is often an important contributor to RNA recognition. The N-terminal RRM of the U1A protein contains a C-terminal helix (helix C) that interacts with the RNA-binding surface of a beta-sheet in the free protein (closed conformation), but is directed away from this beta-sheet in the complex with RNA (open conformation). The dynamics of helix C in the free protein have been proposed to contribute to binding affinity and specificity. We report here a direct investigation of the dynamics of helix C in the free U1A protein on the nanosecond time scale using time-resolved fluorescence anisotropy. The results indicate that helix C is dynamic on a 2-3 ns time scale within a 20 degrees range of motion. Steady-state fluorescence experiments and molecular dynamics simulations suggest that the dynamical motion of helix C occurs within the closed conformation. Mutation of a residue on the beta-sheet that contacts helix C in the closed conformation dramatically destabilizes the complex (Phe56Ala) and alters the steady-state fluorescence, but not the time-resolved fluorescence anisotropy, of a Trp in helix C. Mutation of Asp90 in the hinge region between helix C and the remainder of the protein to Ala or Gly subtly alters the dynamics of the U1A protein and destabilizes the complex. Together these results show that helix C maintains a dynamic closed conformation that is stable to these targeted protein modifications and does not equilibrate with the open conformation on the nanosecond time scale.     

Probing helix formation in unsolvated peptides

Ion mobility measurements have been used to examine helix formation in unsolvated glycine-based peptides containing three alanine residues. Nine sequence isomers of Ac-[12G3A]K+H(+) were studied (Ac = acetyl, G = glycine, A = alanine, and K = lysine). The amount of helix present for each peptide was examined using two metrics, and it is strongly dependent on the proximity and the location of the alanine residues. Peptides with three adjacent alanines have the highest helix abundances, and those with well-separated alanines have the lowest. The helix abundances for most of the peptides can be fit reasonably well using a modified Lifson-Roig theory. However, Lifson-Roig theory fails to account for several key features of the experimental results. The most likely explanation for the correlation between helix abundances and the number of adjacent alanines is that neighboring alanines promote helix nucleation.     

Unprecedented Chain‐Length‐Dependent Conformational Conversion Between 11/9 and 18/16 Helix in α/β‐Hybrid Peptides

α,β‐Hybrid oligomers of varying lengths with alternating proteogenic α‐amino acid and the rigid β^2,3,3‐trisubstituted bicyclic amino acid ABOC residues were studied using both X‐ray crystal and NMR solution structures. While only an 11/9 helix was obtained in the solid state regardless of the length of the oligomers, conformational polymorphism as a chain‐length‐dependent phenomenon was observed in solution. Consistent with DFT calculations, we established that short oligomers adopted an 11/9 helix, whereas an 18/16 helix was favored for longer oligomers in solution. A rapid interconversion between the 11/9 helix and the 18/16 helix occurred for oligomers of intermediate length.     

Induction of a heterochiral helix through the covalent chiral domino effect originating in the "Schellman motif"

We report unique phenomena where the transition from a homochiral helix to a heterochiral helix occurs by increasing the chain length of the l-sequence. Peptides composed of the l-Leu sequences with different lengths and the achiral nona-sequence at the C-terminal side were used here. Conformation of their peptides in solution was investigated mainly by using CD analysis in various solvents, or additionally by IR and NMR. When the l-sequence has a sufficient length, a left-handed helicity was induced in the achiral sequence. Notably, the polymeric l-sequence produced a heterochiral helix that switches the helix sense around the boundary of the chiral/achiral sequence. Energy calculation demonstrated that a stable heterochiral helix favors a bending form, while a homochiral helix takes a relatively straight form. Such a bending form was suggested to be advantageous to solvent effects. The "Schellman motif" has been recognized as a local heterochiral structure in protein helices. We propose a nucleation model of a heterochiral helix through the covalent chiral domino effect derived from the Schellman motif. The present findings not only offer us novel design of a heterochiral helix but also support an elementary model for the origins of homochiral-heterochiral structures from primitive chiral/achiral sequences.     

Control of peptide helix sense by temperature tuning of noncovalent chiral domino effect

We have investigated temperature effect on control of a peptide helix sense through the noncovalent chiral domino effect (NCDE: Inai, Y. et al., J. Am. Chem. Soc. 2003, 125, 8151-8162). Nonapeptide (1: Inai, Y.; Komori, H. Biomacromolecules 2004, 5, 1231-1240), which alone prefers a right-handed helix, maintained a screw-sense balance or a small imbalance at room temperature in the presence of Boc-d-amino acid. Cooling of the solution induced a left-handed helix more clearly. Conversely, heating from room temperature recovered the original right-handed sense. This helix-helix transition was essentially reversible in cooling-heating cycles. An increase in the Boc-d-amino acid concentration elevated temperature for switching CD signs based on the conformational transition. A similar thermal-driven inversion of helix sense was observed for 1 at other initial concentrations, suggesting that this behavior is insensitive to some peptide aggregation. NMR study provided direct evidence for the domino-type control of helix sense, in which Boc-Leu-OH is mainly located at the N-terminal segment. In addition, a left-handed helix induced by the d-isomer was shown to participate in equilibrium with a right-handed helix, whereas the right-handed helix was predominant in the presence of l-isomer. Consequently, we here have proposed a model for controlling a peptide helix sense (or its screw-sense bias) through temperature tuning of the external chiral interaction specific to the N-terminal sequence.     

Cross-linking-induced permanently perpendicular helix orientation in surface-grafted polyglutamate films

Using a chemical cross-linking procedure, surface-grafted polyglutamate films with a permanently perpendicular helix orientation were prepared. A surface-grafted alpha-helical polyglutamate film containing polymerizable side groups was synthesized by ring-opening terpolymerization of 50 molar% gamma-methyl-L-glutamate N-carboxyanhydride (NCA), 30% gamma-stearyl-L-glutamate NCA and 20% gamma-4-vinylbenzyl-L-glutamate NCA initiated from a silicon substrate functionalized with primary amino groups. The average tilt angle of the end-grafted helices in this film is approximately 66 degrees , indicating a nearly parallel helix orientation with respect to the substrate surface. After swelling of the grafted terpolyglutamate film in stearyl methacrylate and subsequent radical cross-linking, the average helix tilt angle decreases to about 11 degrees, indicating an almost perpendicular helix orientation. The film thickness increases accordingly from 151 A before to approximately 390 A after cross-linking. Extensive solvent treatment of the cross-linked film shows that the perpendicular helix orientation is permanent.     

Building β-peptide H10/12 foldamer helices with six-membered cyclic side-chains: fine-tuning of folding and self-assembly

The ability of the β-peptidic H10/12 helix to tolerate side-chains containing six-membered alicyclic rings was studied. cis-2-Aminocyclohex-3-ene carboxylic acid (cis-ACHEC) residues afforded H10/12 helix formation with alternating backbone configuration. Conformational polymorphism was observed for the alternating cis-ACHC hexamer, where chemical exchange takes place between the major left-handed H10/12 helix and a minor folded conformation. The hydrophobically driven self-assembly was achieved for the cis-ACHC-containing helix which was observed as vesicles ~100 nm in diameter.     

Interplay of secondary structures and side-chain contacts in the denatured state of BBA1

The denatured state of a miniprotein BBA1 is studied under the native condition with the AMBER/Poisson-Boltzmann energy model and with the self-guided enhanced sampling technique. Forty independent trajectories are collected to sample the highly diversified denatured structures. Our simulation data show that the denatured BBA1 contains high percentage of native helix and native turn, but low percentage of native hairpin. Conditional population analysis indicates that the native helix formation and the native hairpin formation are not cooperative in the denatured state. Side-chain analysis shows that the native hydrophobic contacts are more preferred than the non-native hydrophobic contacts in the denatured BBA1. In contrast, the salt-bridge contacts are more or less nonspecific even if their populations are higher than those of hydrophobic contacts. Analysis of the trajectories shows that the native helix mostly initiates near the N terminus and propagates to the C terminus, and mostly forms from 3(10)-helix/turn to alpha helix. The same analysis shows that the native turn is important but not necessary in its formation in the denatured BBA1. In addition, the formations of the two strands in the native hairpin are rather asymmetric, demonstrating the likely influence of the protein environment. Energetic analysis shows that the native helix formation is largely driven by electrostatic interactions in denatured BBA1. Further, the native helix formation is associated with the breakup of non-native salt-bridge contacts and the accumulation of native salt-bridge contacts. However, the native hydrophobic contacts only show a small increase upon the native helix formation while the non-native hydrophobic contacts stay essentially the same, different from the evolution of hydrophobic contacts observed in an isolated helix folding.     

Optical rotatory dispersion and circular dichroism studies of copoly(propyl-L-aspartate-benzyl-L-aspartate)

Copoly(propyl-L -aspartate-benzyl-L -aspartate)s with various compositions were synthesized by propylation of a parent poly(β-benzyl-L -Aspartate). The variation of helix sense of copolyaspartate obtained against a degree of propylation and temperature was examined by optical rotatory dispersion and circular dichroism method. Copolyaspartate of propylation less than about 70% is in a left-handed α helix conformation and its Moffitt parameter b₀ and molecular ellipticity [θ]₂₂₂ decreased gradually with increasing propylation. On the other hand, a different temperature dependence of b₀ and [θ]₂₂₂ was observed for copolyaspartate of propylation more than about 80%, i.e., the reversible transition of the helix sense from right- to left-handed α helix took place by temperature increasing. These features were basically similar to the variation in helix sense of copoly(ethyl-L -aspartate-benzyl-L -aspartate), although a slight difference was seen for copoly(propyl-L -aspartate-benzyl-L -aspartate). The thermodynamic treatment indicating larger entropy of right-handed α helix suggests much mobile side chain of the right-handed α helix than the left handed one.     

Iso-energy contour maps for the interaction of water with DNA double helix in the B conformation

The interaction energy between water with B-DNA double helix is computed for few cylindrical surfaces (enclosing the helix) using analytical pair potentials. The iso-energy contour maps indicate a strong attraction for water extending to three water layers surrounding DNA and very stable bridging structure of water molecules connecting two successive phosphate groups along a single helix in the innermost layer.     

Energy calculations on helical polypeptides: Structure of polyglycine II

Single chain and packing energy calculations have been made on polyglycine (threefold and fourfold helical structures) with interchain NH…?O hydrogen bonds. In conformation A of polyglycine, in which the NH groups point away from the helix axis and the CO groups are nearer to the helix axis, the conformational energy is nearly the same for threefold and fourfold structures. However, the minimum energy conformation corresponds to a threefold structure of polyglycine with peptide configurations in conformation B in which the CO groups point away from the helix axis and NH groups are nearer to the helix axis. This structure is consistent with the polyglycine II x-ray diffraction data.     

Laser emission at the second-order photonic band gap in an electric-field-distorted cholesteric liquid crystal

ABSTRACT

We study the optical properties of a cholesteric liquid crystal doped with a fluorescent dye in the regime of highly distorted helix without full helix unwinding. The distortion was achieved by applying a pulsed AC electric field, perpendicular to the helix axis. If the pulse is in the millisecond range, the helix is deformed but keeps its original pitch even for electric fields higher than the theoretical critical field for helix unwinding. In this field regime, very pronounced high-order photonic band gaps are observed, in agreement with our calculations. We theoretically explore the possibility of obtaining viable laser emission at the second-order photonic band gap, and experimentally find that lasing is not only possible but has a figure of merit similar to that of the usual laser at the main-gap region. Therefore, electric-field-induced high-order photonic band gaps are potentially useful for multiline laser applications.     

Mechanism of helix nucleation and propagation: microscopic view from microsecond time scale MD simulations

Microsecond time scale molecular dynamics simulations of the 13-residue peptide RN24 were carried out to investigate the mechanism of helix nucleation and propagation. An extended and an ideal alpha-helical conformation were used as starting structures. NOE-derived interatomic distances were compared with distances calculated from the simulations, showing good agreement between experimental and simulation results. Based on almost 200 helix nucleation events observed, beta-turn and 3(10)-helix play an important role in helix nucleation; in most cases, helix nucleation is preceded by the formation of a short-lived beta-turn (60% probability) or 3(10)-helix (20% probability), and the conversion from beta-turn to alpha-turn involves bifurcated hydrogen bonds. Helix propagation in RN24 appears to occur preferentially from the N-terminus to the C-terminus, and helix unfolding preferentially in the opposite direction.     

Tricks of Light on Helices: Transformation of Helical Polymers by Photoirradiation

The following polymer structural transitions were achieved using light: preferred‐handed helix formation for poly(9,9‐di‐n‐octylfluoren‐2,7‐diyl), helix racemization (helix–helix transition) for poly(2,7‐bis(4‐t‐butylphenyl)fluoren‐9‐yl acrylate) and poly(2,5‐bis[4‐((S)‐2‐methylbutyloxy)phenyl]styrene), and helix decomposition for poly(2,7‐bis(4‐t‐butylphenyl)‐9‐methylfluoren‐9‐yl acrylate) and poly(2,7‐bis(4‐t‐butylphenyl)fluoren‐9‐ylmethyl methacrylate). Although these types of transitions and chemical transformations have been studied mainly using heat or chemicals as stimuli, light can also cause these structural alterations. In the helix construction and the helix–helix transition, a key transition is a twist‐coplanar conformational change of a biphenyl or an aryl–aryl unit in the side chain or the main chain of the polymer. Furthermore, the helix–helix transition was caused only by light and not by heat. The examples discussed in this review are expected to trigger off a new direction in synthesis and reaction of chiral polymers.     

Left-handed and ambidextrous helices in the gas phase

We have used ion mobility mass spectrometry to study the effect of d-residues on helix formation in unsolvated alanine-based peptides. The right-handed helix of AC-A15K + H+ is significantly disrupted when five or more of the natural L-residues are randomly replaced with D-residues. On the other hand, when a block of L-residues is replaced with D-residues, an unusual ambidextrous structure with helical segments of opposite chirality is formed. A peptide with all D-residues forms a left-handed helix.     

Equilibrium Shift in Solution: Molecular Shape Recognition and Precipitation of a Synthetic Double Helix Using Helicene‐Grafted Silica Nanoparticles

Chiral silica nanoparticles (70 nm) grafted with (P)‐helicene recognized the molecular shape of double helix and random coil (P)‐ethynylhelicene oligomers in solution. A mixture of the (P)‐nanoparticles and double helix precipitated much faster than a mixture of the (P)‐nanoparticles and random coil, and the precipitate contained only the double helix. The mixture of the (P)‐nanoparticles and (P)‐ethynylhelicene pentamer reversibly dispersed in trifluoromethylbenzene upon heating at 70 °C and precipitated upon cooling at 25 °C. When a 10:90 equilibrium mixture of the double helix and random coil in solution was treated with the (P)‐nanoparticles, the double helix was precipitated in 53 % yield and was accompanied by equilibrium shift.     

Cholesteric polymers in electric fields

The main peculiarities of electric field-induced structural transformations in cholesterol containing comb-shaped polymers are discussed. As for low molar mass cholesterics both the changes in the texture and the untwisting of the helix can be observed. In cholesteric copolymers with a layered order of the side chains the untwisting of the helix results in the formation of a smectic-like structure. The dynamics of the helix untwisting is shown to be controlled by the mobility of the backbone.