Hexagonal to square lattice conversion in bilayer systems

We report the results of extensive molecular dynamics simulations of the reconstructive hexagonal to square lattice conversion in bilayer colloid systems. Two types of interparticle potential were used to represent the colloid-colloid interactions in the suspension. One potential, due to Marcus and Rice, is designed to describe the interaction of sterically stabilized colloid particles. This potential has a term that represents the attraction between colloid particles when there is incipient overlap between the stabilizing brushes on their surfaces, a (soft repulsion) term that represents the entropy cost associated with interpenetration of the stabilizing brushes, and a term that represents core-core repulsion. The other potential we used is an almost hard core repulsion with continuous derivatives. Our results clearly show that the character of the reconstructive hexagonal to square lattice conversion in bilayer colloid systems is potential dependent. For a system with colloid-colloid interactions of the Marcus-Rice type, the packing of particles in the square array exhibits a large interlayer lattice spacing, with the particles located at the minima of the attractive well. In this case the hexagonal to square lattice transition is first order. For a system with hard core colloid-colloid interactions there are two degenerate stable intermediate phases, linear and zigzag rhombic, that are separated from the square lattice by strong first order transitions, and from the hexagonal lattice by either weak first or second order transitions.     

Noise measurements in bilayer lipid membranes during electroporation

A study of voltage fluctuations in bilayer lipid membranes during electroporation and under current-clamp conditions is presented. Qualitative considerations based on the electroporation theory are used in order to explain the phenomenon on long time scale. Indeed, the current-clamp condition induces a feedback mechanism on the pore formation and therefore on the macroscopic conductance. Voltage fluctuations can thus be recorded. These fluctuations are nonstationary long-living and have a flicker power spectrum over nearly four decades of frequency between about 10^-2 and 10²Hz. The study of the fluctuations in the time domain has been performed by introducing an electrical model of the system formed by the membrane and the circuit under current-clamp configuration. The analysis of the time series gives a characteristic time of 100ms for the circuitry response to the fragments of electroporation signals with characteristic times faster than 100ms. During electroporation, the response to an external periodic stimulus in the frequency range 10^-1-10Hz shows that the system behaves linearly, even if voltage fluctuations are present. Received 1 June 1999 and Received in final form 1 October 1999     

Statistical mechanics of bilayer membranes in troubled aqueous media

We consider a bilayer membrane surrounded by small impurities, assumed to be attractive or repulsive. The purpose is a quantitative study of the effects of these impurities on the statistical properties of the supported membrane. Using the replica trick combined with a variational method, we compute the membrane mean-roughness and the height correlation function for almost-flat membranes, as functions of the primitive elastic constants of the membrane and some parameter that is proportional to the volume fraction of impurities and their interaction strength. As results, the attractive impurities increase the shape fluctuations due to the membrane undulations, while repulsive ones suppress these fluctuations. Second, we compute the equilibrium diameter of (spherical) vesicles surrounded by small random particles starting from the curvature equation. Third, the study is extended to a lamellar phase composed of two parallel fluid membranes, which are separated by a finite distance. This lamellar phase undergoes an unbinding transition. We demonstrate that the attractive impurities increase the unbinding critical temperature, while repulsive ones decrease this temperature. Finally, we say that the presence of small impurities in an aqueous medium may be a mechanism to suppress or to produce an unbinding transition, even the temperature and polarizability of the aqueous medium are fixed, in lamellar phases formed by parallel lipid bilayers.     

Shapes of nearly cylindrical, axisymmetric bilayer membranes

Shapes of nearly cylindrical sections of axisymmetric phospholipid membranes are studied theoretically. Describing the shape of such sections by their deviation from a reference cylinder, the well-established shape equation for axisymmetric bilayer membranes is expanded in terms of this deviation, and it is then solved analytically. The phase diagram shows the resulting stationary shapes as functions of system parameters and external conditions, i.e., the pressure difference across the membrane, the membrane tension, the difference between the tensions of the two monolayers, and the axial force acting on the vesicle. The accuracy of the approximate analytical solution is demonstrated by comparison with numerical results. The obtained analytical solution allows to extend the analysis to include shapes where numerical methods have failed. Received 27 September 2000 and Received in final form 26 March 2001     

Superlinearity of current-voltage characteristics of oxidized cholesterol bilayer membranes

Current-voltage characteristics of bilayer oxidized cholesterol membranes were measured in 0·1 M KCl solution. The ohmic conductance was (5±3) × 10^–4–1 m^–2. To explain the superlinearity of the characteristics, a model of the ion transport through transient pores was used. Alternative diffusion barrier models could also explain the nonlinearity, but the distribution coefficients of permeable ions between the membrane hydrocarbon phase and the aqueous phase had to be taken unreasonably high.     

Application of self-consistent field theory to self-assembled bilayer membranes

Bilayer membranes self-assembled from amphiphilic molecules such as lipids, surfactants, and block copolymers are ubiquitous in biological and physiochemical systems. The shape and structure of bilayer membranes depend crucially on their mechanical properties such as surface tension, bending moduli, and line tension. Understanding how the molecular properties of the amphiphiles determine the structure and mechanics of the self-assembled bilayers requires a molecularly detailed theoretical framework. The self-consistent field theory provides such a theoretical framework, which is capable of accurately predicting the mechanical parameters of self-assembled bilayer membranes. In this mini review we summarize the formulation of the self-consistent field theory, as exemplified by a model system composed of flexible amphiphilic chains dissolved in hydrophilic polymeric solvents, and its application to the study of self-assembled bilayer membranes.     

NMR studies of carrier-mediated transport across lipid bilayer membranes

Two theoretical models are presented which show how the various kinetic steps involved in transport across lipid bilayer membranes affect NMR spectral lineshapes and relaxation times. The first model applies whenever the transported material moves across the membrane by restricted diffusion. The second model applies when the motion can be described as a jump between membrane interfaces. Both carrier-mediated and carrier-independent cases are treated. Special attention is given to the effects of relaxation in the membrane and to morphology. Exact analytical solutions for the simplest one-dimensional geometry are presented. More complicated morphologies are best treated numerically.     

Packing state in bilayer membranes of diacylphosphatidylcholines with varying acyl chain lengths under high pressures

The bilayer packing states of a series of diacylphosphatidylcholines (CnPC) containing linear saturated acyl chains were examined by a high-pressure fluorescence method. We revealed from the second derivatives of Prodan fluorescence spectra for all bilayer membranes that the Prodan molecules can be distributed into multiple sites in these bilayer membranes and move around the head-group region, depending on the phase state. The hydrophobicity of the PC molecules markedly affected the distribution quantities of the Prodan molecules between the gel and liquid crystalline phases. The distribution of the Prodan molecules into the gel phase decreased with the increasing acyl chain length while that into the liquid crystalline phase conversely increased. The present study suggests that Prodan can sensitively recognize the packing states and strengths in the bilayer membranes and becomes a good packing indicator.     

Mesoscale simulations of curvature-inducing protein partitioning on lipid bilayer membranes in the presence of mean curvature fields

The membrane-surface migration of curvature-inducing proteins in response to membrane curvature gradients has been investigated using Monte Carlo simulations of a curvilinear membrane model based on the Helfrich Hamiltonian. Consistent with theoretical and experimental data, we find the proteins that generate curvature can also sense the background membrane curvature, wherein they preferentially partition to the high curvature regions. The partitioning strength depends linearly on local membrane curvature and the slope (or the coupling constant) of the partitioning probability versus mean curvature depends on the membrane bending rigidity and instantaneous curvature field caused by different proteins. Our simulation study allows us to quantitatively characterize and identify the important factors affecting the coupling constant (slope), which may be difficult to determine in experiments. Furthermore, the membrane model is used to study budding of vesicles where it is found that in order to stabilize a mature vesicle with a stable ‘neck-region’ (or stable membrane overhangs), the area (extent) of the intrinsic curvature region needs to exceed a threshold-critical value. The migration and partitioning of curvature-inducing proteins in a budding vesicle with a stable neck (with a characteristic negative value of the Gaussian curvature) is investigated.     

Tubular lipid membranes pulled from vesicles: Dependence of system equilibrium on lipid bilayer curvature

Conditions of joint equilibrium and stability are derived for a spherical lipid vesicle and a tubular lipid membrane (TLM) pulled from this vesicle. The obtained equations establish relationships between the geometric and physical characteristics of the system and the external parameters, which have been found to be controllable in recent experiments. In particular, the proposed theory shows that, in addition to the pressure difference between internal and external regions of the system, the variable spontaneous average curvature of the lipid bilayer (forming the TLM) also influences the stability of the lipid tube. The conditions for stability of the cylindrical phase of TLMs after switching off the external force that initially formed the TLM from a vesicle are discussed. The loss of system stability under the action of a small axial force compressing the TLM is considered.     

A proton NMR study of the interactions of catecholamines with phospholipids from chicken erythrocyte membranes

Summary High-resolution NMR spectroscopy has been applied to the study of the interaction of catecholamines, norepinephrine, epinephrine, isoproterenol and their antagonists propranolol and alprenolol with sonicated phospholipids extracted from chicken erythrocyte membranes (CEM). The catecholamine molecules are immobilized by the phospholipids of CEM and the magnitude of the effect seems to depend on the alkyl substitution of their amino group. Upon introduction of alprenolol and propranolol into phospholipid vesicles a broadening of the resonances of theN-methyl alkyl chain and the terminal methyl protons was observed. The results present evidence about the specificity of the interactions of catecholamines with phospholipids from CEM.

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Riassunto La spettrografia NMR ad alta risoluzione è stata applicata allo studio dell'interazione di catecolamine, norepinefrine, epinefria, isoproterenolo e i loro antagonisti propranololo e alprenolo con fosfolipidi estratti dalle membrane di eritrocina di pollo (CEM). Le molecole di catecolamina sono immobilizzate dai fosfolipidi di CEM e la grandezza dell'effetto sembra dipendere dalla sostituzione dell'alchile nel gruppo aminico. Con l _i introduzione di alprenolo e propranololo nelle vescicole fosfolipidiche si osserva un allargamento delle risonanze della catenaN-metil alchilica e dei protoni del metil terminale. I risultati offrono prove della specificità delle interazioni delle catecolamine coi fosfolipidi del CEM.

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Резюме ЯМР спектроскопия высокого разрешения применяется для исследования взаимодействия катеколаминов с фосфолипидами, извлеченными из мембраны эритроцитов цыпленка. Молекулы катеколаминов закрепляются фосфолипидами из мембраны эритроцитов цыпленка и величина эффекта, по-видимому, зависит от замещения алкилом их аминогруппы. При введении алпренола и пропранолола в пузырьки фосфолипидов наблюдается уширение резонансов. Полученные результаты подтверждают специфичность взаимодействия катеколаминов с фосфолипидами из мембран эритроцитов цыпленка.

     

Raman Scattering in Hexagonal Diamond

Polycrystalline powder of a diamond–lonsdaleite system from the Popigai impact crater (Siberia) is studied via UV micro-Raman scattering (RS) and X-ray diffraction. A spectrum of pure lonsdaleite is obtained by subtracting two experimental Raman spectra of diamond–lonsdaleite samples with close ratios of diamond and lonsdaleite. The maximum contribution to the difference spectrum is due to the difference between the contribution from lonsdaleite, and not to the change in the bandwidth of the diamond. Deconvolution of the lonsdaleite spectrum allows isolation of all three vibrational modes (E_2g, A_1g, and E_1g) active in the first-order RS, the positions of which agree well with the results from first-principles calculations.     

Amplitude Instability in Two-Dimensional Hexagonal Clusters

The conditions for the formation of amplitude instabilities in two-dimensional Yukawa systems consisting of seven charged particles have been investigated. An analytical approach to searching for a criterion of the development of such instabilities based on the determination of the inflection point of a system’s potential energy when the particles deviate from their equilibrium positions is considered. The results obtained are compared with the melting criteria for extended two-dimensional systems.     

Hexagonal arrays in nematic liquid crystals

In this letter observations are reported which were carried out by diffraction of a laser beam, by polar diagrams of the diffracted light and by optical microscopy, being performed on a hexagonal structure which appears in nematic liquid crystals for a twist geometry.     

二维六角晶体材料中的Dirac 电子

本文综述由碳、硅、硼氮和二硫化钼等单元素或双元素构成的二维六角晶体材料中Dirac 电 子的研究成果与最新进展。文章从引言开始,接着介绍这些二维六角晶体材料的空间结构和基本 电子性质;然后探讨外场调控下这些材料在能谱和光吸收、量子输运、激子凝聚和热Josephson 效 应,以及拓扑量子相变等方面所表现出来的新奇的物理现象、简要的理论处理和可能的应用前景; 最后给出二维六角晶体材料相关研究的总结和展望。谨以本文献给南京大学建立物理学科100 周 年。     

On Hexagonal Structures in Higher Dimensional Theories

We analyze the geometrical background under which many Lie groups relevant to particle physics are endowed with a (possibly multiple) hexagonal structure. There are several groups appearing, either as special holonomy groups on the compactification process from higher dimensions, or as dynamical string gauge groups; this includes groups like SU(2), SU(3), G ₂, Spin(7), O(8) as well as E ₈ and O(32). We emphasize also the relation of these hexagonal structures with the octonion division algebra, as we expect as well eventually some role for octonions in the interpretation of symmetries in High Energy Physics.     

Hexagonal patterns in multistep optical parametric processes

The existence and competition of a novel class of hexagonal patterns in a nonlinear optical system are reported. These states are found in a mean-field model of a doubly resonant frequency divide-by-3 optical parametric oscillator (3omega?2omega+omega) in which the multistep parametric process, 2omega=omega+omega , is weakly phase matched. A generalized Swift-Hohenberg equation and a set of amplitude equations are derived to describe the coexistence of hexagonal patterns formed by the superposition of either three or six phase-locked tilted waves.     

椭圆六角分布微结构光纤中的双折射

利用全矢量有限元方法,对椭圆六角对称分布微结构光纤(MF)的双折射特性进行了理论分析,得到了双折射大小与结构参量、入射波长间的依赖关系。分析表明:合理设计结构参量可得到10-3量级大小的双折射;微结构光纤的双折射对光波波长极其敏感,并出现随波长变化快慢轴交换的现象。采用统计的方法对双折射与微结构光纤空气孔直径随机变化的统计相关性进行了理论分析,假定空气孔直径为高斯分布,获得了双折射大小的平均值和标准偏差与随机变化孔径的统计关系。结果表明,由孔径分布不规则所产生的双折射的大小主要取决于空气孔直径的平均值。     

Ferromagnetic Resonance Spectra in Single-Crystal Hexagonal Ferrites

Theoretical and experimental studies of ferromagnetic resonance in single-crystal hexagonal ferrites with different types of magnetocrystalline anisotropy (axis and plane of easy magnetization) are reported. The ferromagnetic resonance is examined in the 12–38 GHz frequency range in the state of homogeneous magnetization and in the presence of a strip domain structure inherent in materials with an axis of easy magnetization. This comprehensive ferromagnetic resonance investigation is shown to allow determination of not only anisotropy fields and g-factors but also saturation magnetization of a material from testing one sample alone. The anisotropy of g-factor of Zn₂Y is found experimentally.