Left-handed Twists Research Articles

Chiral Nucleating Agents Affecting the Handedness of Lamellar Twist in the Banded Spherulites in Poly(ε-Caprolactone)/Poly(Vinyl Butyral) Blends.

Chiral silica, which acts as a nucleating agent of poly(ε-caprolactone) (PCL), was demonstrated to induce excess handedness of lamellar twist in the banded spherulites of PCL blended with poly(vinyl butyral). The d- and l-forms of silica enhanced the right- and left-handed twists, respectively. The influences of chiral silica on the twist handedness were statistically significant. These results indicate that the handedness of twisting can be controlled upon primary nucleation. The organic substances used as chiral templates of silica had no effect on the handedness; silica was shown to govern the handedness. The possible mechanisms of the chirality transfer are discussed.

Majorana vortex photons a form of entangled photons propagation through brain tissue.

This paper extends the concept of entangled vector vortex beams as a form of Majorana-like photons. Majorana photon quasi particles are introduced and attributed to a class of entangled vector beams and show higher transmission. These photons and the antiphotons are identical. A Majorana photon has within itself both right and left handed twists. These majorana beams travel at speeds other than speed of light, c in free space. Light transmission of Majorana photon vortex beams with orbital angular momentum (OAM) are investigated in a mouse brain at different local regions showing enhanced transmission and properties of being entangled. This work is new interpretation of our past paper of mixed photon beam states. The transmission change observed with Majorana structured light other than linear polarization is attributed to the nonseparable and mixed nature of radial and azimuthal polarizations with OAM and the handedness of the light passing through chiral brain media. These mixed nonhomogeneous beams are entangled in OAM and polarization. Majorana photons may play an important role in the future for quantum and optical computing and sub and super luminal speeds due to its traversal wave vector, k.

ROOTS OF DEHN TWISTS ABOUT MULTICURVES

AbstractA multicurve${\mathcal{C}}$ in a closed orientable surface Sg of genus g is defined to be a finite collection of disjoint non-isotopic essential simple closed curves. A left-handed Dehn twist$t_{\mathcal{C}}$about${\mathcal{C}}$ is the product of left-handed Dehn twists about the individual curves in ${\mathcal{C}}$. In this paper, we derive necessary and sufficient conditions for the existence of a root of $t_{\mathcal{C}}$ in the mapping class group Mod(Sg). Using these conditions, we obtain combinatorial data that correspond to roots, and use it to determine upper bounds on the degree of a root. As an application of our theory, we classify all such roots up to conjugacy in Mod(S4). Finally, we establish that no such root can lie in the level m congruence subgroup of Mod(Sg), for m ≥ 3.

The untwisting number of a knot

The unknotting number of a knot is the minimum number of crossings one must change to turn that knot into the unknot. The algebraic unknotting number is the minimum number of crossing changes needed to transform a knot into an Alexander polynomial-one knot. We work with a generalization of unknotting number due to Mathieu-Domergue, which we call the untwisting number. The untwisting number is the minimum number (over all diagrams of a knot) of right- or left-handed twists on even numbers of strands of a knot, with half of the strands oriented in each direction, necessary to transform that knot into the unknot. We show that the algebraic untwisting number is equal to the algebraic unknotting number. However, we also exhibit several families of knots for which the difference between the unknotting and untwisting numbers is arbitrarily large, even when we only allow twists on a fixed number of strands or fewer.

Non-fillable invariant contact structures on principal circle bundles and left-handed twists

We define symplectic fractional twists, which subsume Dehn twists and fibered twists and use these in open books to investigate contact structures. The resulting contact structures are invariant under a circle action, and share several similarities with the invariant contact structures that were studied by Lutz and Giroux. We show that left-handed fractional twists often give rise to “algebraically overtwisted” contact manifolds, a certain class of non-fillable contact manifolds.

Geometrical criteria for left-handed twists within protein beta-strands

Using a statistical analysis on beta-sheet structures from the Protein Data Bank, characteristic angles within beta-strands were correlated to the nature of the side chains. The twists were computed from the atomic coordinates of five consecutive amino acids’ alpha carbons from single beta-strand sequences. Conditions on the angles for twists to be mainly left-handed are given together with the frequency of occurrence for these non-standard geometrical properties within protein beta-strands. Applications in protein structure prediction and CASP challenges in particular are envisioned by making use of the probabilities of occurrence in protein structures of angle value ranges for given amino acids.

Vibrational Circular Dichroism as a Probe of Fibrillogenesis: The Origin of the Anomalous Intensity Enhancement of Amyloid-like Fibrils

Amyloid fibrils are affiliated with various human pathologies. Knowledge of their molecular architecture is necessary for a detailed understanding of the mechanism of fibril formation. Vibrational circular dichroism (VCD) spectroscopy has recently shown sensitivity to amyloid fibrils [Ma et al. J. Am. Chem. Soc. 2007, 129, 12364 and Measey et al. J. Am. Chem. Soc. 2009, 131, 18218]. In particular, amyloid fibrils give rise to an intensity enhanced signal in the amide I band region of the corresponding VCD spectrum, offering promise of utilizing such a method for probing fibrillogenesis and the chiral structure of fibrils. Herein, we further investigate this phenomenon and demonstrate the use of VCD to probe the fibril formation kinetics of a short alanine-rich peptide. To elucidate the origin of the anomalous VCD intensity enhancement, we use an excitonic coupling model to simulate the VCD spectrum of stacked β-sheets containing one (Ising-like model) and two amide I oscillators per strand, as models for the underlying amyloid-fibril secondary structure. With this simple model, we show that the VCD intensity enhancement of amyloid-like fibrils results from intrasheet and, to a more limited extent, also from intersheet vibrational coupling between stacked β-sheets. The enhancement requires helically twisted sheets and is most pronounced for arrangements with parallel-oriented strands. Both the intersheet distance and the orientation of the amide I transition dipole moments of neighboring sheets are found to modulate the intensity enhancement of the amide I VCD signal. Moreover, our simulations suggest that, depending on the three-dimensional arrangement of the β-strands, the sign of the VCD signal of amyloid-like fibrils can be used to distinguish between right- and left-handed helical twists of parallel-oriented β-sheets. We compare the results of our simulation to experimental spectra of two short peptides, GNNQQNY, the N-terminal peptide fragment of the yeast prion protein Sup35, and an amyloidogenic alanine-rich peptide, AKY8. Our results demonstrate the advantages of using VCD spectroscopy to probe the kinetics of peptide and protein aggregation as well as the chirality of the resulting supramolecular structure.

OBSERVATIONAL EVIDENCE OF UNWINDING AND CHIRALITY CHANGING IN PENUMBRAL FILAMENTS BYHINODE

In this paper, we present a very important and quite controversial observational property of penumbral filaments that may exhibit twisting motions and change their chirality. Using high-resolution observations from the Solar Optical Telescope on board Hinode, we study the unwinding and twisting motions in the penumbral filaments of active region NOAA 10930. Penumbral filaments, including those to the northwest of the magnetic polarity inversion line (PIL) and those inside the PIL region, are found to make unwinding motions associated with the decrease of their right-handed twists. After unwinding, the filaments inside the PIL region are found to twist continuously to develop left-handed twists in them. Moreover, we find the filament elongating, expanding, splitting, and the screw pitch decreasing in the unwinding process and, getting shorter, shrinking, merging, and the screw pitch increasing in the twisting process. These observational results indicate that penumbral filaments are more inclined to be twisted magnetic flux tubes in nature.

On the possibility of the violation of the Curie-Neumann principle in anisotropic media with dissymmetry

The dynamics of defects and their mutual transformation and annihilation in drops of a nematic-cholesteric mixture in the presence of quasistatic electric fields has been investigated by the birefringence method. Three basic independent configurations of the director distribution—static and dynamic with the right and left-handed twists of cholesteric layers around the axis parallel to the field—are formed above the threshold field. The possible mechanisms of the observed processes have been discussed. It has been shown that a certain symmetry of the causes (the nematic-cholesteric liquid crystal and field) does not necessarily lead to the corresponding symmetry of the induced structures and mechanical processes. An anisotropic distribution of the orientation of rotating spiral structures with respect to the normal to the nematic-cholesteric liquid crystal layer has been revealed.

Ultrastructures and strain comparison of under-glycosylated scrapie prion fibrils

Prions, composed primarily of misfolded, often fibrillar, polymers of prion protein, have poorly understood structures. Heavy surface glycosylation may obscure visualization of their fibrillar cores, so we purified severely under-glycosylated prion protein fibrils from scrapie-infected transgenic mice expressing anchorless prion protein. Using electron and atomic force microscopy, we obtained dimensions and morphological information about prion protein core protofilaments which variably intertwined to form scrapie fibrils. Occasional isolated protofilaments were observed, suggesting that the lateral association of protofilaments is neither essential nor invariant in prion protein polymerization. Strain comparisons suggested basic structural differences; ME7 and 22L fibrils contained thinner protofilaments, 22L fibrils preferred left-handed twists, and 22L fibril periodicities averaged 106nm per half-turn, compared with 64 and 66nm for RML and ME7 fibrils, respectively. The strains displayed overlapping fibril morphologies, providing evidence that prion fibril morphology is influenced, but not dictated, by strain-dependent differences in protofilament structure. These measurements of the amyloid core of scrapie fibrils should aid development of models of prion structure and strain determination.

Five-Dimensional Contact SU(2)- and SO(3)-Manifolds and Dehn Twists

In the first part of this paper the five-dimensional contact SO(3)-manifolds are classified up to equivariant coorientation preserving contactomorphisms. The construction of such manifolds with singular orbits requires the use of generalized Dehn twists. We show as an application that all simply connected 5-manifolds with singular orbits are realized by a Brieskorn manifold with exponents (k,2,2,2). The standard contact structure on such a manifold gives right-handed Dehn twists, and a second contact structure defined in the article gives left-handed twists. In an appendix we also describe the classification of five-dimensional contact SU(2)-manifolds.

Left-handed helical twists in "mixed beta-peptides" derived from alternating C-linked carbo-beta3-amino acids and beta-hGly units.

Ambidextrous peptides: Novel mixed β-peptides were synthesized from alternating C-linked carbo-β3-amino acid and β-homoglycine residues. The peptides form unprecedented left-handed 10/12 and 12/10 helices (see picture) in addition to the corresponding right-handed helices. Supporting information for this article is available on the WWW under http://www.wiley-vch.de/contents/jc_2002/2004/z53467_s.pdf or from the author. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.

Chiral Fluctuations and Structures

Abstract Chiral molecules form a number of non-chiral structures, the simplest being an isotropic fluid phase. In a mesophase of achiral molecules the fluctuations will on an average be achiral as well: left-handed twists and right-handed twists will occur with the same probability. In a system composed of chiral molecules, however, the fluctuations will be biased in one direction or the other, and there will be optical effects such as a non-zero fluctuation induced rotary power in addition to the molecular rotary power of the individual molecules. We discuss this effect in a number of contexts, including lyotropic lamellar phases. When the tendency to twist is strong enough or the line energy of having an exposed edge is small enough, a new, defect riddled ground state of a lyotropic lamella, akin to the Renn-Lubensky twist-grain-boundary phase of thermotropic smectics, can occur.

Study of polyethylene spherulites using scanning electron microscopy

A detailed scanning electron microscopy study has been made of spherulites in meltcrystallized polyethylene. In particular, unetched, ion etched, nitric acid etched and plastically deformed polyethylene samples have been examined. It appears that the spherulites visible on the surface of these samples consist of lamellae which possess alternate right- and left-handed partial twists. It is quite possible that enough material was removed from the surfaces of the samples by ion etching that the spherulites visible on etched samples could be representative of bulk samples. While questions remain both about the half twist model and about the current full twist model, the half twist model deserves consideration as an alternate model for spherulite structure.