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Polarization of the zygote defines the body axis during plant development. In Arabidopsis (Arabidopsis thaliana), the zygote becomes polarized and elongates in the longitudinal direction, ultimately forming the apical–basal axis of the mature plant. Despite its importance, the mechanism for this elongation remains poorly understood. Based on live-cell imaging of the zygote, we developed new image analysis methods, referred to as coordinate normalization, that appropriately fix and align positions in an image, preventing fluctuation across a temporal sequence of images. Using these methods, we discovered that the zygote elongates only at its apical tip region, similar to tip-growing cells such as pollen tubes and root hairs. We also investigated the spatiotemporal dynamics of the apical tip contour of the zygote and observed that the zygote tip retains its isotropic, hemispherical apical shape during cell elongation. By looking at the elliptical fitting of the contour over time, we further discovered that the apical cell tip becomes thinner at first and then thickens, with a transient increase in growth speed that is followed by the first cell division. We performed the same series of analyses using root hairs and established that both the hemispherical tip shape and the changes in growth rate associated with changes in tip size are specific to the zygote. In summary, the Arabidopsis zygote undergoes directional elongation as a tip-growing cell, but its tip retains an unusual isotropic shape, and the manner of growth changes with the developmental stage.

For isolated single cells on a substrate, the intracellular stiffness, which is often measured as the Young’s modulus, E, by atomic force microscopy (AFM), depends on the substrate rigidity. However, little is known about how the E of cells is influenced by the surrounding cells in a cell population system in which cells physically and tightly contact adjacent cells. In this study, we investigated the spatial heterogeneities of E in a jammed epithelial monolayer in which cell migration was highly inhibited, allowing us to precisely measure the spatial distribution of E in large-scale regions by AFM. The AFM measurements showed that E can be characterized using two spatial correlation lengths: the shorter correlation length, l(S), is within the single cell size, whereas the longer correlation length, l(L), is longer than the distance between adjacent cells and corresponds to the intercellular correlation of E. We found that l(L) decreased significantly when the actin filaments were disrupted or calcium ions were chelated using chemical treatments, and the decreased l(L) recovered to the value in the control condition after the treatments were washed out. Moreover, we found that l(L) decreased significantly when E-cadherin was knocked down. These results indicate that the observed long-range correlation of E is not fixed within the jammed state but inherently arises from the formation of a large-scale actin filament structure via E-cadherin-dependent cell-cell junctions.

Many biological systems including humans are made up of various cells. In addition, cells of a specific type gather together to form tissues, and organs are organized as an aggregate of multiple tissues. One of the tissues constituting organs is epithelial tissue. Epithelial tissue is composed of epithelial cells, and almost all the surfaces inside and outside the body is covered with epithelial tissue, many of which are monolayered. Mathematical models expressing morphogenesis of epithelial tissue have been developed by many researchers. One of the models, the cell vertex model [1] discusses tissue growth through polygonal approximation of cells, but it does not take into account the curvature of cell boundaries. Ishimoto et al., developed the bubbly vertex model [2] introducing the curvature into the model and studied the morphology of the epithelial tissue.

This paper describes the characteristics of water flow induced by the bridge oscillation of magnetic fluid between two permanent magnets subject to an external alternating magnetic field. The magnetic fluid bridge is formed in the space between a pair of identical coaxial cylindrical permanent magnets submerged in water. The direction of alternating magnetic field is parallel /antiparallel to the magnetic field produced by two permanent magnets. The magnetic fluid bridge responds to the external alternating magnetic field with harmonic oscillation. The oscillation of magnetic fluid bridge generates water flow around the bridge. Water flow is visualized using a thin milk film at the container bottom. Water flows are observed with a high-speed video camera analysis system. The experimental results show that the flow pattern induced by the bridge oscillation depends on the Keulegan–Carpenter number.

Significance Tissue morphogenesis is a dynamic process often accompanied by cell patterning and differentiation. Although how conserved growth factor signaling affects cell and tissue shapes has been actively studied, much less is known about how signaling and dynamic morphogenesis are mutually coordinated. Our study shows that BMP signaling and 3D morphogenesis of the Drosophila pupal wing are tightly coupled. These findings are highlighted by the fact that the directionality of BMP signal is changed from lateral planar during the inflation stage to interplanar after re-apposition of the dorsal and ventral wing epithelia. We suspect that the dynamic interplay between planar and interplanar signaling linked to tissue shape changes is likely to be used across species in many developing organs., At the level of organ formation, tissue morphogenesis drives developmental processes in animals, often involving the rearrangement of two-dimensional (2D) structures into more complex three-dimensional (3D) tissues. These processes can be directed by growth factor signaling pathways. However, little is known about how such morphological changes affect the spatiotemporal distribution of growth factor signaling. Here, using the Drosophila pupal wing, we address how decapentaplegic (Dpp)/bone morphogenetic protein (BMP) signaling and 3D wing morphogenesis are coordinated. Dpp, expressed in the longitudinal veins (LVs) of the pupal wing, initially diffuses laterally within both dorsal and ventral wing epithelia during the inflation stage to regulate cell proliferation. Dpp localization is then refined to the LVs within each epithelial plane, but with active interplanar signaling for vein patterning/differentiation, as the two epithelia appose. Our data further suggest that the 3D architecture of the wing epithelia and the spatial distribution of BMP signaling are tightly coupled, revealing that 3D morphogenesis is an emergent property of the interactions between extracellular signaling and tissue shape changes.

SummaryAt the level of organ formation, tissue morphogenesis drives developmental processes in animals, often involving the rearrangement of two-dimensional (2D) structures into more complex three-dimensional (3D) tissues. These processes can be directed by growth factor signaling pathways. However, little is known about how such morphological changes affect the spatiotemporal distribution of growth factor signaling. Here, using theDrosophilapupal wing, we address how Decapentaplegic (Dpp) / Bone Morphogenetic Protein (BMP) signaling and 3D wing morphogenesis are coupled. Dpp, expressed in the longitudinal veins (LVs) of the pupal wing, initially diffuses laterally during the inflation stage to regulate cell proliferation. Dpp localization is then refined to the LVs within each epithelial plane, but with active interplanar signaling for vein patterning, as the two epithelia appose. Our data further suggest that the 3D architecture of the wing epithelia directs the spatial distribution of BMP signaling, revealing how 3D morphogenesis is an emergent property of the interactions between extracellular signaling and tissue shape changes.

In the olfactory epithelium (OE), olfactory cells (OCs) and supporting cells (SCs), which express different cadherins, are arranged in a characteristic mosaic pattern in which OCs are enclosed by SCs. However, the mechanism underlying this cellular patterning is unclear. Here, we show that the cellular pattern of the OE is established by cellular rearrangements during development. In the OE, OCs express nectin-2 and N-cadherin, and SCs express nectin-2, nectin-3, E-cadherin, and N-cadherin. Heterophilic trans-interaction between nectin-2 on OCs and nectin-3 on SCs preferentially recruits cadherin via α-catenin to heterotypic junctions, and the differential distributions of cadherins between junctions promote cellular intercalations, resulting in the formation of the mosaic pattern. These observations are confirmed by model cell systems, and various cellular patterns are generated by the combinatorial expression of nectins and cadherins. Collectively, the synergistic action of nectins and cadherins generates mosaic pattern, which cannot be achieved by a single mechanism.

The morphologies of ectodermal organs are shaped by appropriate combinations of several deformation modes, such as invagination and anisotropic tissue elongation. However, how multicellular dynamics are coordinated during deformation processes remains to be elucidated. Here, we developed a four-dimensional (4D) analysis system for tracking cell movement and division at a single-cell resolution in developing tooth epithelium. The expression patterns of a Fucci probe clarified the region- and stage-specific cell cycle patterns within the tooth germ, which were in good agreement with the pattern of the volume growth rate estimated from tissue-level deformation analysis. Cellular motility was higher in the regions with higher growth rates, while the mitotic orientation was significantly biased along the direction of tissue elongation in the epithelium. Further, these spatio-temporal patterns of cellular dynamics and tissue-level deformation were highly correlated with that of the activity of cofilin, which is an actin depolymerization factor, suggesting that the coordination of cellular dynamics via actin remodeling plays an important role in tooth epithelial morphogenesis. Our system enhances the understanding of how cellular behaviors are coordinated during ectodermal organogenesis, which cannot be observed from histological analyses.

We consider moduli integrals appearing in four-point correlation functions of the (p, q) minimal models coupled to Liouville gravity on a sphere, which is sometimes called 2D minimal gravity or minimal string theory on a sphere. Liouville gravity on a sphere is the quantized metric of the spherical topology in the conformal gauge. Reviewing the previous results on such four-point functions (Y. Ishimoto and Sh. Yamaguchi: Phys. Lett. B607 (2005) 172), we show logarithmic correlation functions of ‘tachyons’ in the Liouville sector, and its moduli integrals of the full correlation functions, in particular in the Majorana fermion model coupled to 2D gravity. Further discussions and related results are given in the final section and in Y. Ishimoto and Al. Zamolodchikov: Theor. Math. Phys.147 (2006) 755.

We consider the partition function of the two-dimensional free massive Majorana fermion coupled to the quantized metric of the spherical topology. By adding an arbitrary conformal “spectator” matter, we gain control over the total matter central charge. This provides an interesting continuously parameterized family of critical points and also allows making a connection with the semiclassical limit. We use the Liouville field theory as the effective description of the quantized gravity. The spherical scaling function is calculated approximately, but (we believe) to a good numerical precision, in almost the whole domain of the spectator parameter. An impressive comparison with the predictions of the exactly solvable matrix model yields a more general model of random-lattice statistics, which is most probably not solvable by the matrix-model technique but reveals a more general pattern of critical behavior. We hope that numerical simulations or series extrapolation will be able to reveal our family of scaling functions.

It is well known that LCFT generally contains Jordan cell structure and, in our previous paper, we have proposed a conjecture that one and only one boundary sate is allowed in the rank-2 cell. With these states in c=-2 rational LCFT, we can express boundary states in the closed string picture, in regard to corresponding boundary conditions in the open string picture. In this paper, We briefly review our previous paper on boundary states in LCFTs. We also add one more proof which supports the conjecture, and confirm this doesn't change our previous results. This paper is based on the talk given at School & Workshop On Logarithmic Conformal Field Theory and Its Applications held in Tehran, Iran.

This paper describes microstreaming flows generated by oscillating interface of magnetic fluid adsorbed on a circular cylindrical permanent magnet in alternating magnetic field. The interface of magnetic fluid adsorbed on the NdFeB magnet responds to the external alternating magnetic flied as harmonic oscillation. The directions of alternating magnetic field are parallel and antiparallel to the magnetic field of permanent magnet. The oscillation of magnetic fluid interface generates streaming flow around the magnet-magnetic fluid element in water. Microstreaming flows are observed with a high-speed video camera analysis system. The flow pattern generated by magnetic fluid motion depends on the Keulegan–Carpenter number and the Reynolds number.

In order to describe two-dimensionally packed cells in epithelial tissues both mathematically and physically, there have been developed several sorts of geometrical models, such as the vertex model, the finite element model, the cell-centered model, the cellular Potts model. So far, in any case, pressures have not neatly been dealt with and curvatures of the cell boundaries have been even omitted through their approximations. We focus on these quantities and formulate them on the vertex model. Thus, a model with the curvatures is constructed and its algorithm is given for simulation. Its possible extensions and applications will also be discussed., Comment: REVTex4.1, 25 pages in double column, 15 figures; revised explanations in Sec 2 with 3 figures (1 added, 2 revised), results unchanged, corrected typos, added references

There exist logarithmic CFTs(LCFTs) such as the $c_{p,1}$ models. It is also well known that it generally contains Jordan cell structure. In this paper, we obtain the boundary Ishibashi state for a rank-2 Jordan cell structure and, with these states in $c=-2$ rational LCFT, we derive boundary states in the closed string picture, which correspond to boundary conditions in the open string picture. We also discuss the Verlinde formula for LCFT and possible applications to string theory., Comment: LaTeX, 21 pages; a reference added

The $N=4$ SU(2)$_k$ superconformal algebra has the global automorphism of SO(4) $\approx$ SU(2)$\times$SU(2) with the {\it left} factor as the Kac-Moody gauge symmetry. As a consequence, an infinite set of independent algebras labeled by $\rho$ corresponding to the conjugate classes of the {\it outer} automorphism group SO(4)/SU(2)=SU(2) are obtained \`a la Schwimmer and Seiberg. We construct Feigin-Fuchs representations with the $\rho$ parameter embedded for the infinite set of the $N=4$ nonequivalent algebras. In our construction the extended global SU(2) algebras labeled by $\rho$ are self-consistently represented by fermion fields with appropriate boundary conditions., Comment: 19 pages, LaTeX file

A family of models of liquid on a two-dimensional lattice (2D lattice liquid models) have been proposed as primitive models of soft-material membrane. As a first step, we have formulated them as single-component, single-layered, classical particle systems on a two-dimensional surface with no explicit viscosity. Among the family of the models, we have shown and constructed two stochastic models, a vicious walk model and a flow model, on an isotropic regular lattice and on some honeycomb lattices of various sizes. In both cases, the dynamics is governed by the nature of the frustration of the particle movements. By simulations, we have found the approximate functional form of the frustration probability and peculiar anomalous diffusions in their time-averaged mean-square displacements in the flow model. The relations to other existing statistical models and possible extensions of the models are also discussed.

Based on our previous paper [cond-mat/0507477], we establish a general model for the whip-toroid transitions of a semiflexible homopolymer chain using the path integral method and the O(3) nonlinear sigma model on a line segment with the local inextensibility constraint. We exactly solve the energy levels of classical solutions, and show that some of its classical configurations exhibit toroidal forms, and the system has phase transitions from a whip to toroidal states with a conformation parameter $c=\frac{W}{2 l} (\frac{L}{2\pi})^2$. We also discuss the stability of the toroid states and propose the low-energy effective Green function. Finally, with the finite size effect on the toroid states, predicted toroidal properties are successfully compared to experimental results of DNA condensation., Comment: final version: RevTeX4 double column, 15 pages, 6 figures (colour), some typos fixed, to appear in Journal of Chemical Physics

Amongst conformal field theories, there exist logarithmic conformal field theories such as $c_{p,1}$ models. We have investigated $c_{p,q}$ models with a boundary in search of logarithmic theories and have found logarithmic solutions of two-point functions in the context of the Coulomb gas picture. We have also found the relations between coefficients in the two-point functions and correlation functions of logarithmic boundary operators, and have confirmed the solutions in [hep-th/0003184]. Other two-point functions and boundary operators have also been studied in the free boson construction of boundary CFT with $SU(2)_k$ symmetry in regard to logarithmic theories. This paper is based on a part of D. Phil. Thesis [hep-th/0312160]., Comment: Latex2e JHEP style, 22 pages, 4 figures, based on hep-th/0312160; typo fixed

3d Chern-Simons gauge theory has a strong connection with 2d CFT and link invariants in knot theory. We impose some constraints on the $D(2|1;\alpha)$ CS theory in the similar context of the hamiltonian reduction of 2d superconformal algebras. There Hilbert states in $D(2|1;\alpha)$ CS theory are partly identified with characters of the large N=4 SCFT by their transformation properties., Comment: LaTeX 13 pages, 1 figure; one reference added, some improvements mainly in section 4

We investigate how different microscopic interactions between semiflexible chain segments can qualitatively alter the physical properties of the condensed toroid. We propose a general form of the Hamiltonian of the toroid and discuss its analytic properties. For different interactions, the theory predicts different scaling behaviours of the mean toroidal and cross sectional radii, $r_c$ and $r_{cross}$, as functions of the contour length L: $(r_c, r_{cross}) \sim L^{\nu(N_c)}$ with $\nu=(1/5, 2/5)$ for the van der Waals type, $\nu=(-1/3, 2/3)$ for the Coulomb type, $\nu=(-1, 1)$ for the delta function type attractions in the asymptotic limit. For the toroids with finite winding number $N_c=100 \sim 400$, we find $\nu \simeq 0$ for the Yukawa interaction with screening parameter $\kappa=0.5 \sim 1.0$, and $\nu=0.1 \sim 0.13$ for the van der Waals type interactions. These findings could provide possible explanation for the experimentally well known observation $\nu \simeq 0$ of the condensed DNA toroids. Conformational transitions are also discussed.

We study a Wess-Zumino-Witten model with target space AdS_3 x (S^3 x S^3 x S^1)/Z_2. This allows us to construct space-time N=3 superconformal theories. By combining left-, and right-moving parts through a GSO and a Z_2 projections, a new asymmetric (N,\bar{N})=(3,1) model is obtained. It has an extra gauge (affine) SU(2) symmetry in the target space of the type IIA string. An associated configuration is realized as slantwise intersecting M5-M2 branes with a Z_2-fixed plane in the M-theory viewpoint., 27 pages, 1 figure, final version

We study the simplest examples of minimal string theory whose worldsheet description is the unitary (p,q) minimal model coupled to two-dimensional gravity (Liouville field theory). In the Liouville sector, we show that four-point correlation functions of `tachyons' exhibit logarithmic singularities, and that the theory turns out to be logarithmic. The relation with Zamolodchikov's logarithmic degenerate fields is also discussed. Our result holds for generic values of (p,q)., Comment: Latex2e 13 pages; v.2: minor corrections, typos fixed