Determinant Structure of the Rational Solutions for the Painlev\'e IV Equation

Rational solutions for the Painlev\'e IV equation are investigated by Hirota bilinear formalism. It is shown that the solutions in one hierarchy are expressed by 3-reduced Schur functions, and those in another two hierarchies by Casorati determinant of the Hermite polynomials, or by special case of the Schur polynomials.Comment: 19 pages, Latex, using theorem.st

Confined diffusion of transmembrane proteins and lipids induced by the same actin meshwork lining the plasma membrane.

The mechanisms by which the diffusion rate in the plasma membrane (PM) is regulated remain unresolved, despite their importance in spatially regulating the reaction rates in the PM. Proposed models include entrapment in nanoscale noncontiguous domains found in PtK2 cells, slow diffusion due to crowding, and actin-induced compartmentalization. Here, by applying single-particle tracking at high time resolutions, mainly to the PtK2-cell PM, we found confined diffusion plus hop movements (termed "hop diffusion") for both a nonraft phospholipid and a transmembrane protein, transferrin receptor, and equal compartment sizes for these two molecules in all five of the cell lines used here (actual sizes were cell dependent), even after treatment with actin-modulating drugs. The cross-section size and the cytoplasmic domain size both affected the hop frequency. Electron tomography identified the actin-based membrane skeleton (MSK) located within 8.8 nm from the PM cytoplasmic surface of PtK2 cells and demonstrated that the MSK mesh size was the same as the compartment size for PM molecular diffusion. The extracellular matrix and extracellular domains of membrane proteins were not involved in hop diffusion. These results support a model of anchored TM-protein pickets lining actin-based MSK as a major mechanism for regulating diffusion

The End of the Reionization Epoch Probed by Ly-alpha Emitters at z=6.5 in the Subaru Deep Field

We report an extensive search for Lyman-alpha emitters (LAEs) at z=6.5 in the Subaru Deep Field. Subsequent spectroscopy with Subaru and Keck identified eight more LAEs, giving a total of 17 spectroscopically confirmed LAEs at z=6.5. Based on this spectroscopic sample of 17, complemented by a photometric sample of 58 LAEs, we have derived a more accurate Lyman-alpha luminosity function of LAEs at z=6.5, which reveals an apparent deficit at the bright end of ~0.75 mag fainter L*, compared with that observed at z=5.7. The difference in the LAE luminosity functions between z=5.7 and 6.5 is significant at the 3-sigma level, which is reduced to 2-sigma when cosmic variance is taken into account. This result may imply that the reionization of the universe has not been completed at z=6.5. We found that the spatial distribution of LAEs at z=6.5 was homogeneous over the field. We discuss the implications of these results for the reionization of the universe.Comment: To appear in APJ vol.648. Only minor corrections have been made. Black&White version is available at http://zone.mtk.nao.ac.jp/~kashik/sdf/z6p5lae/paper/sdf_z6p5lae_bw.pd

A Search for Lyman alpha Emitters at Redshift 3.7

We present the results of a survey for emission-line objects based on optical intermediate-band ($\lambda_{\rm c}$ = 5736 \AA ~ and $\Delta\lambda$ = 280 \AA) and broad-band ($B$, $V$, $R$, and $i^\prime$) observations of the Subaru/XMM-Newton Deep Field on the 8.2 m Subaru telescope with the Subaru Prime Focus Camera, Suprime-Cam. All the data were obtained during the guaranteed time observations of the Suprime-Cam instrument. The intermediate-band image covered a sky area with 10\minpoint62 \times 12\minpoint40 \approx 132 arcmin$^2$ in the Subaru/XMM-Newton Deep Field (Ouchi et al.). Using this image, we have found 23 emission-line sources whose observed emission-line equivalent widths are greater than 250 \AA. Their optical multicolor properties indicate that six emission-line sources are Ly$\alpha$ emitters at $z \approx$ 3.7 ($\Delta z \approx 0.22$). They are either intense starburst galaxies or active galactic nuclei like quasars at $z \approx$ 3.7. Two more emission-line sources may also be Ly$\alpha$ emitters at $z \approx$ 3.7 although their multicolor properties are marginal. Among the remaining 15 emission-line objects, eight objects appear strong emission-line galaxies at lower redshift; e.g., [O {\sc ii}] $\lambda$3727 emitters at $z \approx 0.54$, H$\beta$ at $z \approx 0.18$, or [O {\sc iii}]$\lambda$5007 emitters at $z \approx 0.15$. The remaining seven objects are unclassified because they are too faint to be detected in broad-band images. We discuss observational properties of these strong emission-line sources. In particular, our data allow us to estimate the star formation density at $z \approx 3.7$ for the first time.Comment: Accepted for publication in AJ;14 pages, 26 figures (all figures are JPEG file

Both MHC Class II and its GPI-Anchored Form Undergo Hop Diffusion as Observed by Single-Molecule Tracking

Previously, investigations using single-fluorescent-molecule tracking at frame rates of up to 65 Hz, showed that the transmembrane MHC class II protein and its GPI-anchored modified form expressed in CHO cells undergo simple Brownian diffusion, without any influence of actin depolymerization with cytochalasin D. These results are at apparent variance with the view that GPI-anchored proteins stay with cholesterol-enriched raft domains, as well as with the observation that both lipids and transmembrane proteins undergo short-term confined diffusion within a compartment and long-term hop diffusion between compartments. Here, this apparent discrepancy has been resolved by reexamining the same paradigm, by using both high-speed single-particle tracking (50 kHz) and single fluorescent-molecule tracking (30 Hz). Both molecules exhibited rapid hop diffusion between 40-nm compartments, with an average dwell time of 1–3 ms in each compartment. Cytochalasin D hardly affected the hop diffusion, consistent with previous observations, whereas latrunculin A increased the compartment sizes with concomitant decreases of the hop rates, which led to an ∼50% increase in the median macroscopic diffusion coefficient. These results indicate that the actin-based membrane skeleton influences the diffusion of both transmembrane and GPI-anchored proteins

NRFL-1, the C. elegans NHERF orthologue, interacts with amino acid transporter 6 (AAT-6) for age-dependent maintenance of AAT-6 on the membrane.

The NHERF (Na(+)/H(+) exchanger regulatory factor) family has been proposed to play a key role in regulating transmembrane protein localization and retention at the plasma membrane. Due to the high homology between the family members, potential functional compensations have been a concern in sorting out the function of individual NHERF numbers. Here, we studied C. elegans NRFL-1 (C01F6.6) (nherf-like protein 1), the sole C. elegans orthologue of the NHERF family, which makes worm a model with low genetic redundancy of NHERF homologues. Integrating bioinformatic knowledge of C. elegans proteins into yeast two-hybrid scheme, we identified NRFL-1 as an interactor of AAT-6, a member of the C. elegans AAT (amino acid transporter) family. A combination of GST pull-down assay, localization study, and co-immunoprecipitation confirmed the binding and characterized the PDZ interaction. AAT-6 localizes to the luminal membrane even in the absence of NRFL-1 when the worm is up to four-day old. A fluorescence recovery after photobleaching (FRAP) analysis suggested that NRFL-1 immobilizes AAT-6 at the luminal membrane. When the nrfl-1 deficient worm is six-day or older, in contrast, the membranous localization of AAT-6 is not observed, whereas AAT-6 tightly localizes to the membrane in worms with NRFL-1. Sorting out the in vivo functions of the C. elegans NHERF protein, we found that NRFL-1, a PDZ-interactor of AAT-6, is responsible for the immobilization and the age-dependent maintenance of AAT-6 on the intestinal luminal membrane