Fibril stability in solutions of twisted -sheet peptides: a new kind of micellization in chiral systems

The problem of fibril (fibre) formation in chiral systems is explored theoretically being supported by experiments on synthetic de novo 11-mer peptide forming self-assembled -sheet tapes. Experimental data unambiguously indicate that the tapes form fibrils of nearly monodisperse thickness ca . 8-10 nm. Fibril formation and stabilisation are attributed to inter-tape face-to-face attraction and their intrinsic twist, correspondingly. The proposed theory is capable of predicting the fibril aggregation number and its equilibrium twist in terms of molecular parameters of the primary tapes. The suggested novel mechanism of twist stabilisation of finite aggregates (fibrils) is different to the well-known stabilisation of micelles in amphiphilic systems, and it is likely to explain the formation and stability of fibrils in a wide variety of systems including proteinaceous amyloid fibres, sickle-cell hemoglobin fibres responsible for HbS anemia, corkscrew threads found in chromonics in the presence of chiral additives and native cellulose microfibrillar crystallites. The theory also makes it possible to extract the basic molecular parameters of primary tapes (inter-tape attraction energy, helical twist step, elastic moduli) from the experimental data. Received 7 May 1999 and Received in final form 15 February 2000     

Helix coil mixing in twist-storing polymers

Twist-storing polymers respond with elastic energy penalty to coherent or random twisting along the local chain axis away from its equilibrium, which can be straight (as in “ribbons”) or helical (as in DNA and other biopolymers). Here we study the equilibrium conformation of such polymers, focusing on the thermodynamic balance between twist and writhe, resulting from the competition between the random coil entropy and the potential energy stored in superhelical portions of the polymer chain. Two macroscopic variables characterise such a chain, the end-to-end distance R and the link number Lk, which is a topological invariant of a given polymer with clamped ends. We find that with increasing link number Lk, the chain accommodates its excess twist in growing plectonemes, unless forced out of this state by stretching its end-to-end distance R. We calculate the force-extension relation, which exhibits crossovers between different deformation regimes. Received 16 November 2000 and Received in final form 6 February 2001     

Revisit of the shape and orientation of precipitates with tetragonal transformation strains that minimise the elastic energy

ABSTRACT

The selection of the shape and orientation of precipitates with tetragonal misfit (transformation) strains that minimise the elastic energy is revisited. The complex map of preferred shapes suggested by Kaganova and Roitburd for inhomogeneous isotropic materials is extended to materials with cubic symmetry and for systems that compromise with the surface energy of close-packed planes. Several shape transitions are explained from the kinematics of precipitates with tetragonal transformation strains in solid matrices. Plate shaped precipitates are associated with minimum elastic energy in homogenous systems and for soft precipitates, in accordance with the theorem of Khachaturyan. We explain how compact shapes like rods and spheres arise when the matrix is softer than the precipitate. Analytic estimations are derived to determine the preferred shapes based on the difference between the elastic stiffness of the matrix and the precipitate. When the transformation strains differ in sign, they give rise to a large lattice rotation. This lattice rotation is necessary for the formation of twins by equivalent variants of the transformation strain.     

Shapes of lipid monolayer domains: Solutions using elliptic functions

Solid lipid monolayer domains surrounded by a fluid phase at an air-water interface exhibit complex shapes. These intriguing shapes can be understood in terms of a competition between line tension and long-range dipole-dipole interaction. The dipolar energy has recently been relevant to a negative line tension and a positive curvature energy at the boundary, and a corresponding shape equation was derived by the variation of the approximated domain energy (Phys. Rev. Lett. 93, 206101 (2004)). Here we further incorporate surface pressure into the shape equation and show that the equation can be analytically solved: the curvature of the domain boundary is exactly obtained as an elliptic function of arc-length. We find that a circular domain can grow into bean-and peach-like domains with pressure, i.e., dipping and cuspidal transitions of circle by compression. The comparison with the experimental observation shows nice agreement.     

Configuration of a chiral smectic-C film with a circular inclusion

It was shown experimentally (P.V. Dolganov et al., Europhys. Lett. 76, 250 (2006)) and by numerical calculations (C. Bohley, R. Stannarius, Eur. Phys. J. E 23, 25 (2007)) that the c -director profile of a two-dimensional chiral smectic-C (SmC) film around a circular inclusion adopts dipolar rather than quadrupolar configuration observed in achiral SmC films. We give an analytical argument on how spontaneous bend inherent in chiral SmC liquid crystals influences the configuration of a SmC liquid crystal film around a circular inclusion imposing tangential anchoring. We find how the angle α between two surface defects seen from the center of the inclusion depends on the radius of the inclusion R and the strength of the spontaneous bend q . We show, however, that the contribution of the spontaneous bend to the free energy suffers from mathematical ambiguity; it depends on the mathematical treatment of the outer boundary even when it is at infinity. This might indicate that the shape as well as the treatment of the outer boundary of the film can significantly influence the equilibrium configuration of the c -director and the position of the surface defects.     

受拉扭弹性细杆超螺旋形态的定性分析

基于弹性杆的Kirchhoff模型讨论受拉扭弹性细杆的超螺旋形态.导出细长螺旋杆的等效抗弯和抗扭刚度.分析受拉扭弹性细杆的稳定性和分岔,且利用等效刚度概念将弹性杆的稳定性条件应用于对细长螺旋杆稳定性的判断.在扭矩不变条件下增加拉力至极限值时,直杆平衡状态失稳转为螺旋杆状态.继续增加拉力,直螺旋杆平衡状态失稳卷绕为超螺旋杆.从而对Thompson/Champney实验中受拉扭弹性细杆形成超螺旋形态的多次卷绕现象作出定性的理论解释. 关键词： 弹性细杆 Kirchhoff动力学比拟 等效刚度 超螺旋形态     

Three-body interaction-induced light scattering in krypton gas: a computer simulation of the spectral line shapes

The two-, three- and four-body effective collision induced scattering spectral line shapes are calculated for dense gaseous krypton using the pairwise additivity (PA) approximation and different polarizability models. These spectra and several interaction induced spectra calculated at various densities are compared with the experimental measurements of Barocchi et al. [1988, Europhys. Lett., 5, 607]. The potential effect on the spectrum is found to be weak. The results obtained with the Meinander et al. [1986, J. chem. Phys., 84, 3005] empirical polarizability model and molecular dynamics fit well the experimental two- and three-body spectral shapes. The irreducible contribution to the spectral shape is evaluated using the dipole induced dipole irreducible polarizability [buckingham, A. D., and Hands, I. D., 1991, Chem. Phys. Lett., 185, 544]. This contribution is found to be relatively weak for the anisotropic spectra in the frequency and density range studied, explaining the good agreement between the pairwise approximation calculations and the experimental data. The spectra radiated by the quasi-molecules Kr₂, Kr₃, and Kr₄ (the total spectrum within the PA approximation) are also simulated.     

Arrays of Charged (±2π)-Twist Disclinations in Ferroelectric Liquid Crystals

The notion of an electrostatic charge of (±2)-twist disclinations is used to approximate the evaluation of the electrostatic interaction energy among disclinations forming arrays in finite samples of ferroelectric chiral smectic C liquid crystals. Screening effects of free charges in a material surrounding the disclination are taken into account by introducing a phenomenological depolarisation factor.The electrostatic interaction energy is important in chiral smectic C materials with high values of the spontaneous polarisation when screening effects of free charges are small. Then the electrostatic interaction leads to elimination of disclinations from the sample. When there is a high concentration of free charges in the sample (smaller value of depolarisation factor), the electrostatic interaction energy is of the order of the elastic interaction energy of disclinations what influences the equilibrium of disclination arrays in the sample. Two disclination configurations are considered. In the Brunet-Williams configuration the disclinations of opposite topological charge have also the opposite electrostatic charge so their attraction is augmented. This attraction can be balanced by the helical structure in the central part of the sample when the sample thickness is rather high.On the contrary, in the Glogarová-Pavel configuration the disclinations of opposite topological charge have the electrostatic charge of the same sign. The equilibrium in this configuration is either a balance of elastic attraction and electrostatic repulsion if elastic and Coulomb forces are of the same order or it is governed by the value of the anchoring energy when electrostatic interaction prevails over the elastic one.     

Macroscopic torsional strain and induced molecular conformational deracemization

A macroscopic helical twist is imposed on an achiral nematic liquid crystal by controlling the azimuthal alignment directions at the two substrates. On application of an electric field the director rotates in the substrate plane. This electroclinic effect, which requires the presence of chirality, is strongest at the two substrates and increases with increasing imposed twist distortion. We present a simple model involving a trade-off among bulk elastic energy, surface anchoring energy, and deracemization entropy that suggests the large equilibrium director rotation induces a deracemization of chiral conformations in the molecules-effectively "top-down" chiral induction-quantitatively consistent with experiment.     

Force-extension curves of bacterial flagella

Bacterial flagella assume different helical shapes during the tumbling phase of a bacterium but also in response to varying environmental conditions. Force-extension measurements by Darnton and Berg explicitly demonstrate a transformation from the coiled to the normal helical state (N.C. Darnton, H.C. Berg, Biophys. J. 92, 2230 (2007)). We here develop an elastic model for the flagellum based on Kirchhoff's theory of an elastic rod that describes such a polymorphic transformation and use resistive force theory to couple the flagellum to the aqueous environment. We present Brownian-dynamics simulations that quantitatively reproduce the force-extension curves and study how the ratio G \Gamma of torsional to bending rigidity and the extensional rate influence the response of the flagellum. An upper bound for G \Gamma is given. Using clamped flagella, we show in an adiabatic approximation that the mean extension, where a local coiled-to-normal transition occurs first, depends on the logarithm of the extensional rate.     

Elasticity theory of a twisted stack of plates

We present an elastic model of B-form DNA as a stack of thin, rigid plates or base pairs that are not permitted to deform. The symmetry of DNA and the constraint of plate rigidity limit the number of bulk elastic constants contributing to a macroscopic elasticity theory of DNA to four. We derive an effective twist-stretch energy in terms of the macroscopic stretch along and relative excess twist about the DNA molecular axis. In addition to the bulk stretch and twist moduli found previously, we obtain a twist-stretch modulus with the following remarkable properties: 1) it vanishes when the radius of the helical curve following the geometric center of each plate is zero, 2) it vanishes with the elastic constant K₂₃ that couples compression normal to the plates to a shear strain, if the plates are perpendicular to the molecular axis, and 3) it is nonzero if the plates are tilted relative to the molecular axis. This implies that a laminated helical structure carved out of an isotropic elastic medium will not twist in response to a stretching force, but an isotropic material will twist if it is bent into the shape of a helix. Received: 4 July 1997 / Received in final form: 16 October 1997 / Accepted: 21 October 1997     

Equilibrium morphologies of epitaxially strained islands

An analytical expression of the free energy consisting of the strain energy, surface energy and interfacial energy for the coherent island/substrate system, as well as the evolving relations of aspect ratio against volume of the island, and misfit of the system, which provides a broad perspective on island behavior, is obtained, and used to study the equilibrium shapes of the systems. A two-dimensional model assuming linear elastic behavior is used to analyze an isolated island with elastic properties similar to those of the substrate. The results show that in order to minimize the total free energy, a coherent island will adopt a particular shape and height-to-width aspect ratio that are a function of only the island volume. The effect of a misfit dislocation on the equilibrium shape of an island is in passing examined. These can serve as a basis for interpretation of experiments.     

Properties and symmetry of the solid cluster phase of protein

To date, only one solid crystalline form of protein has been discovered and studied. At the same time, we have experimentally found that the solid protein phase may have fundamentally different properties, as well as various types and scales of symmetry, depending on condensation conditions in the water-protein system. The key issue here is the condensation kinetics. For example, in an open system under the equilibrium conditions (low process rate), the equilibrium long-range crystalline protein lattice forms at the microlevel. In a nonequilibrium (high process rate) protein-water system, an autowave process with nonlinear irregular dynamics is established and a polyfilm solid phase with a set of three-dimensional dissipative nanostructures occurs. The type and scale of symmetry change. The crystal order at the microlevel disappears, and the material becomes amorphous. A new allotropic modification of the solid nonequilibrium protein film arises. This modification has the highly ordered (on the nano-to macroscale) superlattice with straight, helical, chiral, mirror, or rotation symmetry. This kind of protein has been identified both in vitro and in vivo and has been called “protos.”.     

Textural analysis of a mesophase with banana shaped molecules

Observed under the polarizing microscope, the phase in the banana compound D14F3 [J.P. Bedel et al., Liq. Cryst. 27, 1411 (2000)] displays two types of textures of defects, namely (a): helical ribbons, that nucleate in large quantities when the samples are quenched from a sufficiently high temperature in the isotropic phase (b)- shapes with no helicity having the structure of developable domains much akin to those observed in columnar phases, either resulting from the annealing of the helical ribbons or nucleating under slow cooling processes. The existence of these two kinds of defects points toward the complex nature of the structure of the B7 phase, which is at the same time a columnar and a smectic phase. Our observations fit the model [M. Kleman, J. Phys. France 46, 1193 (1985)] according to which the geometry of a helical ribbon is that one of the central region of a screw dislocation with a giant Burgers vector, split into two helical disclination lines of strength k = 1/2 which bound the ribbon. Textures and defects, already partly documented, and growth features and annealing processes, not yet reported in the literature, are analyzed. We conclude that the helical ribbons and the developable domains with no helicity are textures of two different B7 states, namely a metastable state and the ground state respectively. Comparative textural analysis is performed for two other banana compounds exhibiting B2 phases.Received: 8 November 2003, Published online: 5 February 2004PACS: 61.30.Jf Defects in liquid crystals - 61.72.Bb Theories and models of crystal defects - 64.60.My Metastable phases     

Helical instability of a straight Abrikosov vortex in an anisotropic superconductor

Because of attraction of the parallel currents forming an Abrikosov vortex, the vortex energy per unit length decreases, under bending of the vortex, by a quantity proportional to the square of the curvature. Solving the London equation in an approximation allowing for this effect makes it possible to calculate the energy of an Abrikosov vortex in the form of a helix whose length and pitch are much larger than the correlation length, whose curvature is small compared to the reciprocal London length, and whose slope in relation to an axis coinciding with the direction in which the vortex energy is the highest is also small. When the anisotropy is large, which is characteristic of high-T _c superconductors, the energy of such an Abrikosov vortex is lower than that of a straight Abrikosov vortex. Certain consequences of the fact that the Abrikosov vortices in a high-T _c superconductor are helical are discussed. Among these is a phase transition that breaks the symmetry between Abrikosov vortices shaped like right-and left-hand helixes in relation to the magnetic field. Zh. éksp. Teor. Fiz. 111, 1869–1878 (May 1997)     

Elastic scattering of electrons from tetrahydrofurfuryl alcohol

Differential cross-sections (DCSs) for elastic scattering of electrons from tetrahydrofurfuryl alcohol (THFA), which can be considered as an analogue molecule to DNA sugar deoxyribose, were determined using crossed beam measurements for incident energies from 40 eV to 300 eV and scattering angles from 30° to 110°. The relative DCSs were measured both as a function of incident electron energy and scattering angle, allowing absolute calibration of the whole data set via normalization to a single point. The absolute calibration has been performed according to calculated absolute DCSs obtained by the corrected independent atom method using an improved quasifree absorption model. The calculated data-set includes DCSs and integral elastic and inelastic cross-sections in the incident energy range from 5 eV to 5000 eV. The theoretical results agree very well with the experimental ones, regarding the shape of DCSs. Moreover, the same theoretical procedure has been used to obtain DCSs for elastic electron scattering from a simpler deoxyribose analogue tetrahydrofuran (THF), which agree very well, both in shape and on the absolute scale, with the recent experimentally obtained absolute DCSs [A.R. Milosavljević et al., Eur. Phys. J. D 35, 411 (2005)]. The present results are also compared with the recent theoretical data for THF and THFA. Finally, according to both experimental and theoretical data, the DCSs for elastic electron scattering from THFA and THF molecules appear to be very similar both in shape and absolute scale.     

Stability diagram for elastic domains in epitaxial ferroelectric thin films

The statics of isolated elastic domains (twins) in epitaxial thin tetragonal films grown on a cubic substrate is investigated theoretically. Different possible variants of the geometric shape of a domain are studied: plate, trapezoidal, and triangular. The nonuniform internal stresses, which also exist in polydomain epitaxial systems, are calculated by the effective-dislocation method. Hence the elastic energies stored in heterostructures with different domains are determined. The equilibrium width of a domain is calculated by minimizing the total internal energy of the heterostructure. Next, the stability diagram for isolated domains in epitaxial films is constructed from energy considerations. It is shown that in a large part of this diagram trapezoidal domains are energetically more advantageous than plate-shaped domains. The effect of an external electric field on the stability of 90° domains in epitaxial ferroelectric films is investigated. Fiz. Tverd. Tela (St. Petersburg) 39, 127–134 (January 1997)     

Computer Simulation of a 3-D Sensing System with Structured Illumination

A computer simulation system of three-dimensional sensing with structured illumination is presented. It includes the generation of deformed fringe patterns from 3-D shapes and the reconstruction of 3-D shapes, conversely. Some experimental results of the deformed fringe pattern and the reconstructed object shapes are presented. We have also discussed the effect of some major system parameters on the measurement results and considered how to correct these parameters according to the measurement result of the standard plane. Using this simulation system, the major system parameters: environmental conditions, measurement accuracy and algorithm evaluation of the 3-D shape measurement system based on PMP, FTP, SPM, etc., can be researched. © 1997 Elsevier Science Ltd. All rights reserved.     

CONFORMATIONAL ANALYSIS AND MOLECULAR MODELING OF CHOLESTERIC LIQUID CRYSTAL POLYESTERS BASED ON XRD,RAMAN, AND TRANSITION THERMAL ANALYSIS

Molecular modeling of the cholesteric liquid crystal polyester poly[oxy(1,2 - dodecane)oxycarbonyl-1,4-phenyleneoxycarbonyl-1,4-phenylenecarbonyloxy-1,4-phenylenecarbonyl] (PTOBDME), [C₃₄H₃₆O₈] _n , synthesized in our laboratory and thermally characterized by differential scanning calorimetry (DSC), was performed to explain both its cholesteric mesophase and 3D crystalline structure. Conformational analysis (CA) was run for the monomer both by systematic search and with molecular dynamics (MD) simulations. Minima energy conformers were “polymerized” with Cerius² and helical, cholesteric molecules were obtained in all cases. Our models agree with the chiral behavior observed by X-ray diffraction (XRD), thermooptical analysis (TOA) and circular dichroism (CD) experiments. Crystal packing of the polymer molecules were simulated in cells with parameters a and b obtained from experimental powder X-ray diffraction patterns and c calculated from the translational repetitive unit during the theoretical polymerization. Recalculated X-ray powder diffraction patterns of our models matched the observed ones. Morphology simulation from those crystal models is in good agreement with the crystals observed by optical microscopy. We have also modeled the self-associating nature of those polyesters when dispersed in aqueous media. Simulation of our models surrounded by different solvents, such as water and chloroform, were performed by calculating their interaction energies, coordination numbers, and mixing energies, applying Monte Carlo simulation techniques based on the Flory-Huggins theory. These results were compared with their experimental vibrational Fourier transform (FT)–Raman spectra in the regions in which structural marker bands of the polymer appear.