Phases and Transitions in Phantom Nematic Elastomer Membranes

Motivated by recently discovered unusual properties of bulk nematic elastomers, we study a phase diagram of liquid-crystalline polymerized phantom membranes, focusing on in-plane nematic order. We predict that such membranes should enerically exhibit five phases, distinguished by their conformational and in-plane orientational properties, namely isotropic-crumpled, nematic-crumpled, isotropic-flat, nematic-flat and nematic-tubule phases. In the nematic-tubule phase, the membrane is extended along the direction of {\em spontaneous} nematic order and is crumpled in the other. The associated spontaneous symmetries breaking guarantees that the nematic-tubule is characterized by a conformational-orientational soft (Goldstone) mode and the concomitant vanishing of the in-plane shear modulus. We show that long-range orientational order of the nematic-tubule is maintained even in the presence of harmonic thermal luctuations. However, it is likely that tubule's elastic properties are ualitatively modified by these fluctuations, that can be studied using a nonlinear elastic theory for the nematic tubule phase that we derive at the end of this paper.Comment: 12 pages, 4 eps figures. To appear in PR

The Poisson-Boltzmann Theory for Two Parallel Uniformly Charged Plates

We solve the nonlinear Poisson-Boltzmann equation for two parallel and likely charged plates both inside a symmetric elecrolyte, and inside a 2 : 1 asymmetric electrolyte, in terms of Weierstrass elliptic functions. From these solutions we derive the functional relation between the surface charge density, the plate separation, and the pressure between plates. For the one plate problem, we obtain exact expressions for the electrostatic potential and for the renormalized surface charge density, both in symmetric and in asymmetric electrolytes. For the two plate problems, we obtain new exact asymptotic results in various regimes.Comment: 17 pages, 9 eps figure

Universal Elasticity and Fluctuations of Nematic Gels

We study elasticity of spontaneously orientationally-ordered amorphous solids, characterized by a vanishing transverse shear modulus, as realized for example by nematic elastomers and gels. We show that local heterogeneities and elastic nonlinearities conspire to lead to anomalous nonlocal universal elasticity controlled by a nontrivial infared fixed point. Namely, at long scales, such solids are characterized by universal shear and bending moduli that, respectively, vanish and diverge at long scales, are universally incompressible and exhibit a universal negative Poisson ratio and a non-Hookean elasticity down to arbitrarily low strains. Based on expansion about five dimensions, we argue that the nematic order is stable to thermal fluctuation and local hetergeneities down to d_lc < 3.Comment: 4 RevTeX pgs, submitted to PR

Direct Voltammetric Observation of Redox Driven Changes in Axial Coordination and Intramolecular Rearrangement of the Phenylalanine-82-Histidine Variant of Yeast Iso-1-cytochrome c

Direct square-wave and cyclic voltammetric electrochemical examination of the yeast iso-1-cytochrome c Phe82His/Cys102Ser variant revealed the intricacies of redox driven changes in axial coordination, concomitant with intramolecular rearrangement. Electrochemical methods are ideally suited for such a redox study, since they provide a direct and quantitative visualization of specific dynamic events. For the iso-1-cytochrome c Phe82His/Cys102Ser variant, square-wave voltammetry showed that the primary species in the reduced state is the Met80-Fe2+-His18 coordination form, while in the oxidized state the His82-Fe3+-His18 form predominates. The addition or removal of an electron to the appropriate form of this variant serves as a switch to a new molecular form of the cytochrome. Using the 2 × 2 electrochemical mechanism, simulations were done for the cyclic voltammetry experiments at different scan rates. These, in turn, provided relative rate constants for the intramolecular rearrangement/ligand exchange and the equilibrium redox potentials of the participating coordination forms:  kb,AC = 17 s-1 for Met80-Fe3+-His18 → His82-Fe3+-His18 and kf,BD \u3e 10 s-1 for His82-Fe2+-His18 → Met80-Fe2+-His18; E0‘ = 247 mV for Met80-Fe3+/2+-His18 couple, E0‘ = 47 mV for His82-Fe3+/2+-His18 couple, and E0‘ = 176 mV for the cross-reaction couple, His82-Fe3+-His18 + e- → Met80-Fe2+-His18. Thermodynamic parameters, including the entropy of reaction, ΔS0‘Rxn, were determined for the net reduction/rearrangement reaction, His82-Fe3+-His18 + e- → Met80-Fe2+-His18, and compared to those for wild-type cytochrome, Met80-Fe3+-His18 + e- → Met80-Fe2+-His18. For the Phe82His variant mixed redox couple, ΔS0‘Rxn = −80 J/mol·K compared to ΔS0‘Rxn = −52 J/mol·K for the wild-type cyt c couple without rearrangement. Comparison of these entropies indicates that the oxidized His82-Fe3+-His18 form is highly disordered. It is proposed that this high level of disorder facilitates rapid rearrangement to Met80-Fe2+-His18 upon reduction

Soft random solids and their heterogeneous elasticity

Spatial heterogeneity in the elastic properties of soft random solids is examined via vulcanization theory. The spatial heterogeneity in the \emph{structure} of soft random solids is a result of the fluctuations locked-in at their synthesis, which also brings heterogeneity in their \emph{elastic properties}. Vulcanization theory studies semi-microscopic models of random-solid-forming systems, and applies replica field theory to deal with their quenched disorder and thermal fluctuations. The elastic deformations of soft random solids are argued to be described by the Goldstone sector of fluctuations contained in vulcanization theory, associated with a subtle form of spontaneous symmetry breaking that is associated with the liquid-to-random-solid transition. The resulting free energy of this Goldstone sector can be reinterpreted as arising from a phenomenological description of an elastic medium with quenched disorder. Through this comparison, we arrive at the statistics of the quenched disorder of the elasticity of soft random solids, in terms of residual stress and Lam\'e-coefficient fields. In particular, there are large residual stresses in the equilibrium reference state, and the disorder correlators involving the residual stress are found to be long-ranged and governed by a universal parameter that also gives the mean shear modulus.Comment: 40 pages, 7 figure

Fluctuating Nematic Elastomer Membranes: a New Universality Class

We study the flat phase of nematic elastomer membranes with rotational symmetry spontaneously broken by in-plane nematic order. Such state is characterized by a vanishing elastic modulus for simple shear and soft transverse phonons. At harmonic level, in-plane orientational (nematic) order is stable to thermal fluctuations, that lead to short-range in-plane translational (phonon) correlations. To treat thermal fluctuations and relevant elastic nonlinearities, we introduce two generalizations of two-dimensional membranes in a three dimensional space to arbitrary D-dimensional membranes embedded in a d-dimensional space, and analyze their anomalous elasticities in an expansion about D=4. We find a new stable fixed point, that controls long-scale properties of nematic elastomer membranes. It is characterized by singular in-plane elastic moduli that vanish as a power-law eta_lambda=4-D of a relevant inverse length scale (e.g., wavevector) and a finite bending rigidity. Our predictions are asymptotically exact near 4 dimensions.Comment: 18 pages, 4 eps figures. submitted to PR

Symmetries and Elasticity of Nematic Gels

A nematic liquid-crystal gel is a macroscopically homogeneous elastic medium with the rotational symmetry of a nematic liquid crystal. In this paper, we develop a general approach to the study of these gels that incorporates all underlying symmetries. After reviewing traditional elasticity and clarifying the role of broken rotational symmetries in both the reference space of points in the undistorted medium and the target space into which these points are mapped, we explore the unusual properties of nematic gels from a number of perspectives. We show how symmetries of nematic gels formed via spontaneous symmetry breaking from an isotropic gel enforce soft elastic response characterized by the vanishing of a shear modulus and the vanishing of stress up to a critical value of strain along certain directions. We also study the phase transition from isotropic to nematic gels. In addition to being fully consistent with approaches to nematic gels based on rubber elasticity, our description has the important advantages of being independent of a microscopic model, of emphasizing and clarifying the role of broken symmetries in determining elastic response, and of permitting easy incorporation of spatial variations, thermal fluctuations, and gel heterogeneity, thereby allowing a full statistical-mechanical treatment of these novel materials.Comment: 21 pages, 4 eps figure

Renormalized Surface Charge Density for a Strongly Charged Plate in Asymmetric Electrolytes: Asymptotic Exact Results in Poisson Boltzmann Theory

The Poisson-Boltzmann equation for a strongly charged plate inside a generic charge-asymmetric electrolyte is solved using the method of asymptotic matching. Both near field and far field asymptotic behaviors of the potential are systematically analyzed. Using these expansions, the renormalized surface charge density is obtained as an asymptotic series in terms of the bare surface charge density.Comment: 11 pages, 4 eps figure

Large-scale genome-wide association studies and meta-analyses of longitudinal change in adult lung function.

BACKGROUND: Genome-wide association studies (GWAS) have identified numerous loci influencing cross-sectional lung function, but less is known about genes influencing longitudinal change in lung function. METHODS: We performed GWAS of the rate of change in forced expiratory volume in the first second (FEV1) in 14 longitudinal, population-based cohort studies comprising 27,249 adults of European ancestry using linear mixed effects model and combined cohort-specific results using fixed effect meta-analysis to identify novel genetic loci associated with longitudinal change in lung function. Gene expression analyses were subsequently performed for identified genetic loci. As a secondary aim, we estimated the mean rate of decline in FEV1 by smoking pattern, irrespective of genotypes, across these 14 studies using meta-analysis. RESULTS: The overall meta-analysis produced suggestive evidence for association at the novel IL16/STARD5/TMC3 locus on chromosome 15 (P  =  5.71 × 10(-7)). In addition, meta-analysis using the five cohorts with ≥3 FEV1 measurements per participant identified the novel ME3 locus on chromosome 11 (P  =  2.18 × 10(-8)) at genome-wide significance. Neither locus was associated with FEV1 decline in two additional cohort studies. We confirmed gene expression of IL16, STARD5, and ME3 in multiple lung tissues. Publicly available microarray data confirmed differential expression of all three genes in lung samples from COPD patients compared with controls. Irrespective of genotypes, the combined estimate for FEV1 decline was 26.9, 29.2 and 35.7 mL/year in never, former, and persistent smokers, respectively. CONCLUSIONS: In this large-scale GWAS, we identified two novel genetic loci in association with the rate of change in FEV1 that harbor candidate genes with biologically plausible functional links to lung function

Fine mapping of chromosome 5p15.33 based on a targeted deep sequencing and high density genotyping identifies novel lung cancer susceptibility loci

Chromosome 5p15.33 has been identified as a lung cancer susceptibility locus, however the underlying causal mechanisms were not fully elucidated. Previous fine-mapping studies of this locus have relied on imputation or investigated a small number of known, common variants. This study represents a significant advance over previous research by investigating a large number of novel, rare variants, as well as their underlying mechanisms through telomere length. Variants for this fine-mapping study were identified through a targeted deep sequencing (average depth of coverage greater than 4000×) of 576 individuals. Subsequently, 4652 SNPs, including 1108 novel SNPs, were genotyped in 5164 cases and 5716 controls of European ancestry. After adjusting for known risk loci, rs2736100 and rs401681, we identified a new, independent lung cancer susceptibility variant in LPCAT1: rs139852726 (OR = 0.46, P = 4.73×10(–9)), and three new adenocarcinoma risk variants in TERT: rs61748181 (OR = 0.53, P = 2.64×10(–6)), rs112290073 (OR = 1.85, P = 1.27×10(–5)), rs138895564 (OR = 2.16, P = 2.06×10(–5); among young cases, OR = 3.77, P = 8.41×10(–4)). In addition, we found that rs139852726 (P = 1.44×10(–3)) was associated with telomere length in a sample of 922 healthy individuals. The gene-based SKAT-O analysis implicated TERT as the most relevant gene in the 5p15.33 region for adenocarcinoma (P = 7.84×10(–7)) and lung cancer (P = 2.37×10(–5)) risk. In this largest fine-mapping study to investigate a large number of rare and novel variants within 5p15.33, we identified novel lung and adenocarcinoma susceptibility loci with large effects and provided support for the role of telomere length as the potential underlying mechanism