Large deformation of spherical vesicle studied by perturbation theory and Surface evolver

With tangent angle perturbation approach the axial symmetry deformation of a spherical vesicle in large under the pressure changes is studied by the elasticity theory of Helfrich spontaneous curvature model.Three main results in axial symmetry shape: biconcave shape, peanut shape, and one type of myelin are obtained. These axial symmetry morphology deformations are in agreement with those observed in lipsome experiments by dark-field light microscopy [Hotani, J. Mol. Biol. 178, (1984) 113] and in the red blood cell with two thin filaments (myelin) observed in living state (see, Bessis, Living Blood Cells and Their Ultrastructure, Springer-Verlag, 1973). Furthermore, the biconcave shape and peanut shape can be simulated with the help of a powerful software, Surface Evolver [Brakke, Exp. Math. 1, 141 (1992) 141], in which the spontaneous curvature can be easy taken into account.Comment: 16 pages, 6 EPS figures and 2 PS figure

Spheres and Prolate and Oblate Ellipsoids from an Analytical Solution of Spontaneous Curvature Fluid Membrane Model

An analytic solution for Helfrich spontaneous curvature membrane model (H. Naito, M.Okuda and Ou-Yang Zhong-Can, Phys. Rev. E {\bf 48}, 2304 (1993); {\bf 54}, 2816 (1996)), which has a conspicuous feature of representing the circular biconcave shape, is studied. Results show that the solution in fact describes a family of shapes, which can be classified as: i) the flat plane (trivial case), ii) the sphere, iii) the prolate ellipsoid, iv) the capped cylinder, v) the oblate ellipsoid, vi) the circular biconcave shape, vii) the self-intersecting inverted circular biconcave shape, and viii) the self-intersecting nodoidlike cylinder. Among the closed shapes (ii)-(vii), a circular biconcave shape is the one with the minimum of local curvature energy.Comment: 11 pages, 11 figures. Phys. Rev. E (to appear in Sept. 1999

A model for the force stretching double-stranded chain molecules

We modify and extend the recently developed statistical mechanical model for predicting the thermodynamic properties of chain molecules having noncovalent double-stranded conformations, as in RNA or ssDNA, and $\beta-$sheets in protein, by including the constant force stretching at one end of molecules as in a typical single-molecule experiment. The conformations of double-stranded regions of the chain are calculated based on polymer graph-theoretic approach [S-J. Chen and K. A. Dill, J. Chem. Phys. {\bf109}, 4602(1998)], while the unpaired single-stranded regions are treated as self-avoiding walks. Sequence dependence and excluded volume interaction are taken into account explicitly. Two classes of conformations, hairpin and RNA secondary structure are explored. For the hairpin conformations, all possible end-to-end distances corresponding to the different types of double-stranded regions are enumerated exactly. For the RNA secondary structure conformations, a new recursive formula incorporating the secondary structure and end-to-end distribution has been derived. Using the model, we investigate the extension-force curves, contact and population distributions and re-entering phenomena, respectively. we find that the force stretching homogeneous chains of hairpin and secondary structure conformations are very different: the unfolding of hairpins is two-state, while unfolding the latter is one-state. In addition, re-entering transitions only present in hairpin conformations, but are not observed in secondary structure conformations.Comment: 19 pages, 28 figure

Expression of glypican 3 in placental site trophoblastic tumor

<p>Abstract</p> <p>Background</p> <p>Glypican-3 (GPC3) is a membrane-bound heparan sulfate proteoglycan that functions in embryonic cell growth and differentiation and is highly expressed in the placenta. GPC3 is mutated in Simpson-Golabi-Behmel syndrome, which is characterized by tissue overgrowth and an increased risk of embryonal malignancies. GPC3 has also been implicated in sporadic cancer, particularly hepatocellular carcinoma, for which it has been shown to be a useful diagnostic marker. Although GPC3 expression has been studied in non-neoplastic placental tissue, its presence in gestational trophoblastic diseases has not been previously explored. The purpose of this study was to investigate the immunohistochemical expression of GPC3 in placental site trophoblastic tumor (PSTT), a very rare gestational trophoblastic neoplasm which may be morphologically confused with non-trophoblastic tumors, and to assess its possible utility as a diagnostic marker.</p> <p>Methods</p> <p>Fifteen cases of PSTT, as well as samples from placental site nodule (PSN) (n = 2), leiomyosarcoma (n = 1), leiomyoma (n = 1), invasive cervical squamous cell carcinoma (n = 7) and endometrial adenocarcinoma (n = 11) were examined. Immunoreactivity was semi-quantitatively evaluated as negative (0, < 5% of cells stained), focally positive (1+, 5-10% of cells stained), positive (2+, 11-50% of cells stained) or diffusely positive (3+, > 50% of cells stained). Staining intensity for each subtype was graded from 0 to 3 and a mean intensity was calculated.</p> <p>Results</p> <p>Eighty percent of PSTT (12/15) were immunoreactive for GPC3 (0, 20; 1+, 20%; 2+, 40%; 3+, 20%) with a mean intensity of 1.3. Stronger, predominately cytoplasmic staining was seen in larger multi- and mononucleated cells with smaller mononucleate cells showing weak muddy cytoplasmic staining. Both PSN cases were positive (1+, 50%; 2+, 50%) and two of nine invasive cervical squamous cell carcinomas showed staining (0, 57%; 1+, 29%; 2+, 14%), predominately in a basal distribution. Other uterine tumors and non-neoplastic tissues were negative.</p> <p>Conclusions</p> <p>Identification of GPC3 in PSTT and PSN is consistent with the derivation of these lesions from intermediate trophoblasts, which have been described to express GPC3. GPC3 may be a useful adjunct immunohistochemical marker in differentiating PSTT from non-trophoblastic tumors.</p

Area-Constrained Planar Elastica

We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties: not only can the Euler-Lagrange equation be integrated to provide a quadrature for the curvature but, in addition, the embedding itself can be expressed as a local function of the curvature. The configuration space is shown to be essentially one-dimensional, with surprisingly rich structure. Distinct branches of integer-indexed equilibria exhibit self-intersections and bifurcations -- a gallery of plots is provided to highlight these findings. Perturbations connecting equilibria are shown to satisfy a first order ODE which is readily solved. We also obtain analytical expressions for the energy as a function of the area in some limiting regimes.Comment: 23 pages, several figures. Version 2: New title. Changes in the introduction, addition of a new section with conclusions. Figure 14 corrected and one reference added. Version to appear in PR

SU(2)-in-SU(1,1) Nested Interferometer for Highly Sensitive, Loss-Tolerant Quantum Metrology

We present experimental and theoretical results on a new interferometer topology that nests a SU(2) interferometer, e.g., a Mach-Zehnder or Michelson interferometer, inside a SU(1,1) interferometer, i.e., a Mach-Zehnder interferometer with parametric amplifiers in place of beam splitters. This SU(2)-in-SU(1,1) nested interferometer (SISNI) simultaneously achieves high signal-to-noise ratio (SNR), sensitivity beyond the standard quantum limit (SQL) and tolerance to photon losses external to the interferometer, e.g., in detectors. We implement a SISNI using parametric amplification by four-wave mixing (FWM) in Rb vapor and a laser-fed Mach-Zehnder SU(2) interferometer. We observe path-length sensitivity with SNR 2.2 dB beyond the SQL at power levels (and thus SNR) 2 orders of magnitude beyond those of previous loss-tolerant interferometers. We find experimentally the optimal FWM gains and find agreement with a minimal quantum noise model for the FWM process. The results suggest ways to boost the in-practice sensitivity of high-power interferometers, e.g., gravitational wave interferometers, and may enable high-sensitivity, quantum-enhanced interferometry at wavelengths for which efficient detectors are not available.Comment: 6 pages + 4 of supplemental material, 5 figure

Numerical observation of non-axisymmetric vesicles in fluid membranes

By means of Surface Evolver (Exp. Math,1,141 1992), a software package of brute-force energy minimization over a triangulated surface developed by the geometry center of University of Minnesota, we have numerically searched the non-axisymmetric shapes under the Helfrich spontaneous curvature (SC) energy model. We show for the first time there are abundant mechanically stable non-axisymmetric vesicles in SC model, including regular ones with intrinsic geometric symmetry and complex irregular ones. We report in this paper several interesting shapes including a corniculate shape with six corns, a quadri-concave shape, a shape resembling sickle cells, and a shape resembling acanthocytes. As far as we know, these shapes have not been theoretically obtained by any curvature model before. In addition, the role of the spontaneous curvature in the formation of irregular crenated vesicles has been studied. The results shows a positive spontaneous curvature may be a necessary condition to keep an irregular crenated shape being mechanically stable.Comment: RevTex, 14 pages. A hard copy of 8 figures is available on reques

Concise theory of chiral lipid membranes

A theory of chiral lipid membranes is proposed on the basis of a concise free energy density which includes the contributions of the bending and the surface tension of membranes, as well as the chirality and orientational variation of tilting molecules. This theory is consistent with the previous experiments [J.M. Schnur \textit{et al.}, Science \textbf{264}, 945 (1994); M.S. Spector \textit{et al.}, Langmuir \textbf{14}, 3493 (1998); Y. Zhao, \textit{et al.}, Proc. Natl. Acad. Sci. USA \textbf{102}, 7438 (2005)] on self-assembled chiral lipid membranes of DC$_{8,9}$PC. A torus with the ratio between its two generated radii larger than $\sqrt{2}$ is predicted from the Euler-Lagrange equations. It is found that tubules with helically modulated tilting state are not admitted by the Euler-Lagrange equations, and that they are less energetically favorable than helical ripples in tubules. The pitch angles of helical ripples are theoretically estimated to be about 0$^\circ$ and 35$^\circ$, which are close to the most frequent values 5$^\circ$ and 28$^\circ$ observed in the experiment [N. Mahajan \textit{et al.}, Langmuir \textbf{22}, 1973 (2006)]. Additionally, the present theory can explain twisted ribbons of achiral cationic amphiphiles interacting with chiral tartrate counterions. The ratio between the width and pitch of twisted ribbons is predicted to be proportional to the relative concentration difference of left- and right-handed enantiomers in the low relative concentration difference region, which is in good agreement with the experiment [R. Oda \textit{et al.}, Nature (London) \textbf{399}, 566 (1999)].Comment: 14 pages, 7 figure