Twisted Ribbons Research Articles

Helicoids, Wrinkles, and Loops in Twisted Ribbons

We investigate the instabilities of a flat elastic ribbon subject to twist under tension and develop an integrated phase diagram of the observed shapes and transitions. We find that the primary buckling mode switches from being localized longitudinally along the length of the ribbon to transverse above a triple point characterized by a crossover tension that scales with ribbon elasticity and aspect ratio. Far from threshold, the longitudinally buckled ribbon evolves continuously into a self-creased helicoid with focusing of the curvature along the triangular edges. Further twist causes an anomalous transition to loops compared with rods due to the self-rigidity induced by the creases. When the ribbon is twisted under high tension, transverse wrinkles are observed due to the development of compressive stresses with higher harmonics for greater width-to-length ratios. Our results can be used to develop functional structures using a wide range of elastic materials and length scales.

Rings and ribbons in protein structures: Characterization using helical parameters and Ramachandran plots for repeating dipeptides

Helical parameters displayed on a Ramachandran plot allow peptide structures with successive residues having identical main chain conformations to be studied. We investigate repeating dipeptide main chain conformations and present Ramachandran plots encompassing the range of possible structures. Repeating dipeptides fall into the categories: rings, ribbons, and helices. Partial rings occur in the form of "nests" and "catgrips"; many nests are bridged by an oxygen atom hydrogen bonding to the main chain NH groups of alternate residues, an interaction optimized by the ring structure of the nest. A novel recurring feature is identified that we name unpleated β, often situated at the ends of a β-sheet strand. Some are partial rings causing the polypeptide to curve gently away from the sheet; some are straight. They lack β-pleat and almost all incorporate a glycine. An example is the first glycine in the GxxxxGK motif of P-loop proteins. Ribbons in repeating dipeptides can be either flat, as seen in repeated type II and type II' β-turns, or twisted, as in multiple type I and type I' β-turns. Hexa- and octa-peptides in such twisted ribbons occur frequently in proteins, predominantly with type I β-turns, and are the same as the "β-bend ribbons" hitherto identified only in short peptides. One is seen in the GTPase-activating protein for Rho in the active, but not the inactive, form of the enzyme. It forms a β-bend ribbon, which incorporates the catalytic arginine, allowing its side chain guanidino group to approach the active site and enhance enzyme activity.

Statistical mechanics of ribbons under bending and twisting torques

We present an analytical study of ribbons subjected to an external torque. We first describe the elastic response of a ribbon within a purely mechanical framework. We then study the role of thermal fluctuations in modifying its elastic response. We predict the moment–angle relation of bent and twisted ribbons. Such a study is expected to shed light on the role of twist in DNA looping and on bending elasticity of twisted graphene ribbons. Our quantitative predictions can be tested against future single molecule experiments.

Helical Nanostructure of Achiral Silver p-Tolylacetylide Molecules

Silver p-tolylacetylide is an achiral molecule; however, its nanostructure has been found to consist of twisted nanoribbons. The twisted ribbon is a helicoid that combines translation and perpendicular rotation along the ribbon axis. A helix, a typical chiral structure, can be created by the aggregation of achiral molecules, and the recrystallization conditions control the twist of the nanoribbons. Therefore, the recrystallization controls the chirality.

Instability of flat disks with respect to the formation of twisted ribbons in smectic-A*monolayers

Smectic-A* monolayers self-assembled from aqueous solutions of chiral fd viruses and a polymer depletant can assume a variety of shapes such as flat disks and twisted ribbons. A first order phase transition from a flat disk to a ribbon occurs upon lowering the concentration of polymer depletant or the temperature. A theoretical model based on the de Gennes model for the smectic-A phase, the Helfrich model of membrane elasticity, and a simple edge energy has been previously used to calculate the disk-ribbon phase diagram. In this paper we apply this model to the nucleation process of ribbons. First, we study the "rippled disks" that have been observed as precursors of ribbons. Using a model shape proposed by Meyer which includes rippling in both the in-plane and out-of-plane directions, we study the energetics of the disks as functions of the edge energy modulus (a measure of the polymer concentration) and the mean curvature modulus k. We find that as the edge energy modulus is reduced the radial size of the ripples grows rapidly in agreement with experimental observations. For small enough k we find that the out-of-plane size of the ripples grows but its value saturates at a fraction of the twist penetration depth, too small to be experimentally observable. For large k the membrane remains flat though rippled in the radial direction. Such membranes do not have negative Gaussian curvature and thus will not likely spawn twisted ribbons. We also study the creation of twisted ribbons produced by stretching the edge of a flat membrane in a localized region. In experiments using a pair of optical traps it has been observed that once the membrane has been sufficiently stretched a ribbon forms on the stretched edge. We study this process theoretically using a free energy consisting of the Helfrich and edge energies alone. We add a small ribbonlike perturbation to the protrusion produced by stretching and determine whether it is energetically favorable as a function of the size of the protrusion. In qualitative agreement with experiment we find a nonzero value for the critical size of the protrusion needed to make a ribbon energetically favorable, though the value we find is an order of magnitude lower than the experimental value possibly due to our neglect of the director field. As in the case of the rippled disks we find that the mean curvature energy acts as a barrier between the disk and twisted ribbon structures.

Sperm Trajectories Form Chiral Ribbons

We report the discovery of an entirely new three-dimensional (3D) swimming pattern observed in human and horse sperms. This motion is in the form of ‘chiral ribbons’, where the planar swing of the sperm head occurs on an osculating plane creating in some cases a helical ribbon and in some others a twisted ribbon. The latter, i.e., the twisted ribbon trajectory, also defines a minimal surface, exhibiting zero mean curvature for all the points on its surface. These chiral ribbon swimming patterns cannot be represented or understood by already known patterns of sperms or other micro-swimmers. The discovery of these unique patterns is enabled by holographic on-chip imaging of >33,700 sperm trajectories at >90–140 frames/sec, which revealed that only ~1.7% of human sperms exhibit chiral ribbons, whereas it increases to ~27.3% for horse sperms. These results might shed more light onto the statistics and biophysics of various micro-swimmers' 3D motion.

Propulsion Efficiency of a Dynamic Self-Assembled Helical Ribbon

We study the dynamic self-assembly and propulsion of a ribbon formed from paramagnetic colloids in a dynamic magnetic field. The sedimented ribbon assembles due to time averaged dipolar interactions between the beads. The time dependence of the dipolar interactions together with hydrodynamic interactions cause a twisted ribbon conformation. Domain walls of high twist connect domains of nearly constant orientation and negligible twist and travel through the ribbon. The particular form of the domain walls can be controlled via the frequency and the eccentricity of the modulation. The flux of twist walls-a true ribbon property absent in slender bodies-provides the thrust onto the surrounding liquid that propels this biomimetic flagellum into the opposite direction. The propulsion efficiency increases with frequency and ceases abruptly at a critical frequency where the conformation changes discontinuously to a flat standing ribbon conformation.

Self‐Assembly of Racemic Alanine Derivatives: Unexpected Chiral Twist and Enhanced Capacity for the Discrimination of Chiral Species

Twisted ribbons were formed by the self-assembly of racemic alanine derivatives (middle picture), whereas only flat nanostructures were obtained from the individual enantiomers (left). The twist was sensitive to a slight enantiomeric excess and showed remarkable macroscopic chirality. Moreover, it could discriminate various amino acid derivatives (right) and even enabled the determination of the ee value of a mixed system.

Coexistence of ribbon and helical fibrils originating from hIAPP 20–29 revealed by quantitative nanomechanical atomic force microscopy

Uncontrolled misfolding of proteins leading to the formation of amyloid deposits is associated with more than 40 types of diseases, such as neurodegenerative diseases and type-2 diabetes. These irreversible amyloid fibrils typically assemble in distinct stages. Transitions among the various intermediate stages are the subject of many studies but are not yet fully elucidated. Here, we combine high-resolution atomic force microscopy and quantitative nanomechanical mapping to determine the self-assembled structures of the decapeptide hIAPP(20-29), which is considered to be the fibrillating core fragment of the human islet amyloid polypeptide (hIAPP) involved in type-2 diabetes. We successfully follow the evolution of hIAPP(20-29) nanostructures over time, calculate the average thickening speed of small ribbon-like structures, and provide evidence of the coexistence of ribbon and helical fibrils, highlighting a key step within the self-assembly model. In addition, the mutations of individual side chains of wide-type hIAPP(20-29) shift this balance and destabilize the helical fibrils sufficiently relative to the twisted ribbons to lead to their complete elimination. We combine atomic force microscopy structures, mechanical properties, and solid-state NMR structural information to build a molecular model containing β sheets in cross-β motifs as the basis of self-assembled amyloids.

146 Amyloid fibril polymorphism probed by advanced vibrational spectroscopy

Amyloid fibrils are associated with many neurodegenerative diseases. All known amyloids including pathogenic and nonpathogenic forms display functional and structural heterogeneity (polymorphism) which determines the level of their toxicity. Despite a significant biological and biomedical importance, the nature of the amyloid fibril polymorphism remains elusive. We utilized for the first time three most advanced vibrational techniques to probe the core, the surface, and supramolecular chirality of fibril polymorphs. A new type of folding, aggregation phenomenon, spontaneous refolding from one polymorph to another, was discovered (Kurouski, Lauro et al., 2010). Hydrogen–deuterium exchange deep UV resonance Raman spectroscopy (Oladepo, Xiong et al., 2012) combined with advanced statistical analysis (Shashilov & Lednev, 2010) allowed for structural characterization of the highly ordered cross-β core of amyloid fibrils. We reported several examples showing significant variations in the core structure for fibril polymorphs. Amyloid fibrils are generally composed of several protofibrils and may adopt variable morphologies, such as twisted ribbons or flat-like sheets. We discovered the existence of another level of amyloid polymorphism, namely, that associated with fibril supramolecular chirality. Two chiral polymorphs of insulin, which can be controllably grown by means of small pH variations, exhibit opposite signs of vibrational circular dichroism (VCD) spectra (Kurouski, Dukor et al. 2012). VCD supramolecular chirality is correlated not only by the apparent fibril handedness but also by the sense of supramolecular chirality from a deeper level of chiral organization at the protofilament level of fibril structure. A small pH change initiates spontaneous transformation of insulin fibrils from one polymorph to another. As a result, fibril supramolecular chirality overturns both accompanying morphological and structural changes (Kurouski, Dukor et al. 2012). No conventional methods could probe the fibril surface despite its significant role in the biological activity. We utilized tip-enhanced Raman spectroscopy (TERS) to characterize the surface structure of an individual fibril due to a high depth and lateral spatial resolution of the method in the nanometer range (Kurouski, Deckert-Gaudig et al. 2012). It was found that the surface is strongly heterogeneous and consists of clusters with various protein conformations and amino acid composition.

Analytical model and multiscale simulations of Aβ peptide aggregation in lipid membranes: towards a unifying description of conformational transitions, oligomerization and membrane damage

The mechanisms underlying the formation of extracellular amyloid plaques on neuronal membranes, a major hallmark of Alzheimer's disease, are the subject of intense debate. Here we use multiscale simulations and analytical theory to unveil the early steps of the spontaneous self-assembly of membrane-embedded α-helical Aβ (1-40) peptides. Based on a simple analytical model describing the electrostatic repulsions among water-exposed charged residues, the presence of distorted structures called "frustrated helices" is predicted. Large scale (20 μs) Coarse Grained simulations of 36 replicas of Aβ (1-40) performed within a POPC lipid matrix confirmed the formation of supramolecular assemblies which resemble a twisted ribbon. Fully atomistic simulations have demonstrated the stability of these helical structures. Concomitant to the formation of these large assemblies, CG simulations evidenced membrane curvature and substantiate the view that these assemblies may entail mechanical stress on membrane structure. We think that these findings provide an alternative view to the traditional models that consider a conformational transition towards β-sheet rich structures as a prerequisite for triggering membrane damage and, eventually, neurotoxicity.

Geometrical edgeactants control interfacial bending rigidity of colloidal membranes

A colloidal membrane is a one rod-length thick monolayer of aligned rods which spontaneously assembles in a mixture of rod-like viruses and non-adsorbing polymer. The complex structure of the monolayer edge modifies its fluctuations, effectively smoothing out the interface. We demonstrate that long filaments such as F-actin or flagella preferentially dissolve in the membrane's edge and can be used to control its interfacial properties. This effect is not driven by energetic interactions, but is rather a direct consequence of the intrinsic geometry of the constituent particles; hence we call such filaments geometrical edgeactants. Using optical manipulation techniques we adsorb individual filaments onto the edge of the colloidal membrane and measure their influence on the edge fluctuations. Edgeactants stiffen the interface, increasing its bending rigidity by up to an order of magnitude. Furthermore, they also locally suppress a polymorphic transition into twisted ribbons inherent to colloidal membranes. These results demonstrate new ways to control soft materials in which the final structure is only determined by the geometry of the constituent objects.

Formation of Highly Twisted Ribbons in a Carboxymethylcellulase Gene-Disrupted Strain of a Cellulose-Producing Bacterium

Cellulases are enzymes that normally digest cellulose; however, some are known to play essential roles in cellulose biosynthesis. Although some endogenous cellulases of plants and cellulose-producing bacteria are reportedly involved in cellulose production, their functions in cellulose production are unknown. In this study, we demonstrated that disruption of the cellulase (carboxymethylcellulase) gene causes irregular packing of de novo-synthesized fibrils in Gluconacetobacter xylinus, a cellulose-producing bacterium. Cellulose production was remarkably reduced and small amounts of particulate material were accumulated in the culture of a cmcax-disrupted G. xylinus strain (F2-2). The particulate material was shown to contain cellulose by both solid-state (13)C nuclear magnetic resonance analysis and Fourier transform infrared spectroscopy analysis. Electron microscopy revealed that the cellulose fibrils produced by the F2-2 cells were highly twisted compared with those produced by control cells. This hypertwisting of the fibrils may reduce cellulose synthesis in the F2-2 strains.

CdTe 나노입자의 자기조립과정을 통한 나노리본 합성

CdTe 나노입자로부터 형성된 나노리본은 독특한 광학적 특성을 나타낸다. 용액 내 CdTe의 <TEX>$Te^{2-}$</TEX> 이온의 산화는 나노입자에 불규칙적인 결함을 유발하며 이때 여러 층의 나노결정으로 구성된 나노리본을 형성하게 된다. 본 연구에서는 자기조립 된 CdTe 나노입자가 나노리본을 형성하는 과정에서 빛을 조사하였다. 빛은 용액 내 CdTe 나노입자의 표면에 위치한 <TEX>$Te^{2-}$</TEX>의 산화를 촉진시키는 촉매 역할을 수행한다. 합성된 3차원 나노리본의 형태와 특성을 투과전자현미경(TEM)으로 조사하였다. TEM 결과 안정제가 완전히 제거된 부분에서 부분적으로 접힌 꼬인 형태의 다결정 나노리본을 관찰할 수 있었다. Photoluminescence (PL) 측정 결과 550 nm에서 544 nm로 나노입자가 나노리본으로 형성될 때 Blue shift 되었음을 확인하였다. 본 연구에서 제안된 새로운 합성법은 나노물질을 합성하는 새로운 대안을 제시한다. CdTe nanoribbons feature their unique optical properties compared with CdTe nanoparticles. Slow oxidation of tellurium ions on CdTe nanoparticles resulted in the organization of individual nanoparticle into nanoribbons. The light-controlled self-assembly of CdTe nanoparticles led to twisted ribbons. It was found that irradiation improved the oxidation of tellurium ions. Transmission electron microscopy (TEM) were performed to characterize the synthesized nanostructures and showed nanowires were twisted after self-assembly. The photoluminescence was slightly blue-shifted from 550 to 544 nm. This synthetic procedure could potentially provide a key step toward the fabrication of nanowires.

Normal and Reversed Supramolecular Chirality of Insulin Fibrils Probed by Vibrational Circular Dichroism at the Protofilament Level of Fibril Structure

Fibrils are β-sheet-rich aggregates that are generally composed of several protofibrils and may adopt variable morphologies, such as twisted ribbons or flat-like sheets. This polymorphism is observed for many different amyloid associated proteins and polypeptides. In a previous study we proposed the existence of another level of amyloid polymorphism, namely, that associated with fibril supramolecular chirality. Two chiral polymorphs of insulin, which can be controllably grown by means of small pH variations, exhibit opposite signs of vibrational circular dichroism (VCD) spectra. Herein, using atomic force microscopy (AFM) and scanning electron microscopy (SEM), we demonstrate that indeed VCD supramolecular chirality is correlated not only by the apparent fibril handedness but also by the sense of supramolecular chirality from a deeper level of chiral organization at the protofilament level of fibril structure. Our microscopic examination indicates that normal VCD fibrils have a left-handed twist, whereas reversed VCD fibrils are flat-like aggregates with no obvious helical twist as imaged by atomic force microscopy or scanning electron microscopy. A scheme is proposed consistent with observed data that features a dynamic equilibrium controlled by pH at the protofilament level between left- and right-twist fibril structures with distinctly different aggregation pathways for left- and right-twisted protofilaments.

Hierarchical Superstructures with Control of Helicity from the Self‐Assembly of Chiral Bent‐Core Molecules

Herein, two asymmetric chiral bent-core molecules, 3-[(4-{[4-(heptyloxy)benzoyl]oxy}benzoyl)oxy]-phenyl-4-[(4-{[(1R)-1-methylheptyl]oxy}benzoyl)oxy] benzoate (BC7R) and 3-[(4-{[4-(heptyloxy)benzoyl]oxy}benzoyl)oxy]-phenyl-4-[(4-{[(1S)-1-methylheptyl]oxy}benzoyl)oxy] benzoate (BC7S), were synthesized to demonstrate control of the helicity of their self-assembled hierarchical superstructures. Mirror-imaged CD spectra showed a split-type Cotton effect after the formation of self-assembled aggregates of BC7R and BC7S, thereby suggesting the formation of intermolecular exciton couplets with opposite optical activities. Both twisted and helical ribbons with preferential helicity that corresponded to the twisting character of the intermolecular exciton couplet were found in the aggregates. The formation of helical ribbons was attributed to the merging of twisted ribbons through an increase in width to improve morphological stability. As a result, control of the helicity of hierarchical superstructures from the self-assembly of bent-core molecules could be achieved by taking advantage of the transfer of chiral information from the molecular level onto the hierarchical scale.

Controlled Transformation of CdTe Nanoparticles Into Nanoribbons via Self-Assembling Process

CdTe nanorribons were successfully synthesized from individual nanoparticle. Slow oxidation of Te(2-) in CdTe nanoparticles resulted in the assembly of ribbons consisting of several layers of individual nanocrystals. The light-controlled self-assembly of CdTe nanoparticles led to twisted ribbons with variable pitch. Transmission electron microscopy, scanning electron microscopy, and atomic force microscopy were performed to characterize the synthesized nanostructures. The suggested synthetic procedure provides a viable pathway for the fabrication of nanomaterials with helical conformations.

Cardiac safety, drug‐induced QT prolongation and torsade de pointes (TdP)

Torquere is Latin for ‘to twist’ and gave rise to ‘torque’ in English and, in French, to ‘torsade’ a ‘twisted fringe, cord or ribbon’. Torsade de pointes (TdP) is a ballet sequence in which the dancer twists around her ‘pointes’ (dancing en pointe means ‘on the tip’ and is a classical ballet technique, usually performed using special shoes called pointes). Dessertenne used this phrase to describe a distinctive form of ventricular tachycardia in an elderly woman, because the electrical axis of the ventricular complexes varied cyclically giving the electrocardiogram (ECG) a twisted appearance (Figure 1) [1]. Similar polymorphic ventricular tachycardia had previously been identified as the cause of loss of consciousness during quinidine therapy (‘quinidine syncope’) [2]. TdP can be fatal and occurs in several clinical settings associated with prolongation of the ventricular action potential, notably drug treatment and inherited abnormalities of cardiac ion channels [3]. Prolongation of the ventricular action potential is recognized non-invasively by QT segment prolongation on the ECG (a useful but tricky surrogate end-point for risk of clinically important TdP – see below).We have commented previously on druginduced QT prolongation and its importance in drug development [4–7]. Several antidysrhythmic drugs, for example disopyramide and procainamide, as well as quinidine, cause TdP including some (flecainide, encainide and D-sotalol) that have increased mortality in randomized controlled trials [8, 9].Several non-cardiac drugs can also, albeit less frequently cause TdP. These include domperidone (in high dose intravenously – see below), methadone, arsenic trioxide, and several antihistamines, antipsychotic drugs and antiinfective drugs [3]. Not only do drugs differ in their potential to cause TdP, but several patient factors also strongly influence the risk [3]. One of the strongest of these is female sex [10] perhaps because testosterone, which shortens QT interval [11], is lower in women than in men. Several other susceptibility factors can be understood in terms of their influence on cardiac repolarization. These include poor left ventricular function, hypokalaemia, severe hypomagnesaemia and genetic polymorphisms in cardiac ion channels associated with inherited long QT syndromes (LQTS). Drug–drug interactions are clinically important, notably the interaction between ketoconazole (a potent inhibitor of CYP3A) and terfenadine [12], which contributed to the withdrawal of terfenadine from the market after several years of use, including over the counter sales. Diet (especially fruit juice consumption) also influences drug disposition in complex ways [13] underscoring the difficulties for regulators concerned about the potential for low frequency but severe drug harms.

Self-Assembly of Aβ-Based Peptide Amphiphiles with Double Hydrophobic Chains

Two peptide-amphiphiles (PAs), 2C(12)-Lys-Aβ(12-17) and C(12)-Aβ(11-17)-C(12), were constructed with two alkyl chains attached to a key fragment of amyloid β-peptide (Aβ(11-17)) at different positions. The two alkyl chains of 2C(12)-Lys-Aβ(12-17) were attached to the same terminus of Aβ(12-17), while the two alkyl chains of C(12)-Aβ(11-17)-C(12) were separately attached to each terminus of Aβ(11-17). The self-assembly behavior of both the PAs in aqueous solutions was studied at 25 °C and at pHs 3.0, 4.5, 8.5, and 11.0, focusing on the effects of the attached positions of hydrophobic chains to Aβ(11-17) and the net charge quantity of the Aβ(11-17) headgroup. Cryogenic transmission electron microscopy and atomic force microscopy show that 2C(12)-Lys-Aβ(12-17) self-assembles into long stable fibrils over the entire pH range, while C(12)-Aβ(11-17)-C(12) forms short twisted ribbons and lamellae by adjusting pHs. The above fibrils, ribbons, and lamellae are generated by the lateral association of nanofibrils. Circular dichroism spectroscopy suggests the formation of β-sheet structure with twist and disorder to different extents in the aggregates of both the PAs. Some of the C(12)-Aβ(11-17)-C(12) molecules adopt turn conformation with the weakly charged peptide sequence, and the Fourier transform infrared spectroscopy indicates that the turn content increases with the pH increase. This work provides additional basis for the manipulations of the PA's nanostructures and will lead to the development of tunable nanostructure materials.

Handedness Inversion of Chiral Amphiphilic Molecular Assemblies Evidenced by Supramolecular Chiral Imprinting in Mesoporous Silica Assemblies

Antipodal twisted helical ribbons with lamellar bilayer structure were obtained by self-assembly of chiral amphiphilic molecules in water and water/ethanol. The handedness inversion of the molecular arrangement in these antipodal helical ribbons was investigated by using chiroptical spectroscopy and molecular probes in their antipodal mesoporous silica assemblies synthesized through pairing interaction between the head group of the chiral amphiphilic molecules and a co-structure-directing agent. The supramolecular chirality is imprinted in the pore surface through the organic group of the co-structure-directing agent. The mirror-image diffuse-reflectance circular dichroism spectra of the conjugated discotic probing molecule introduced into their supramolecular chiral imprinted mesoporous silica demonstrated the origin of inverse chirality from the antipodal helical stacking of the molecules.