Electrostatics of ions inside the nanopores and trans-membrane channels

A model of a finite cylindrical ion channel through a phospholipid membrane of width $L$ separating two electrolyte reservoirs is studied. Analytical solution of the Poisson equation is obtained for an arbitrary distribution of ions inside the trans-membrane pore. The solution is asymptotically exact in the limit of large ionic strength of electrolyte on the two sides of membrane. However, even for physiological concentrations of electrolyte, the electrostatic barrier sizes found using the theory are in excellent agreement with the numerical solution of the Poisson equation. The analytical solution is used to calculate the electrostatic potential energy profiles for pores containing charged protein residues. Availability of a semi-exact interionic potential should greatly facilitate the study of ionic transport through nanopores and ion channels

Asymptotics and local constancy of characters of p-adic groups

In this paper we study quantitative aspects of trace characters $\Theta_\pi$ of reductive $p$-adic groups when the representation $\pi$ varies. Our approach is based on the local constancy of characters and we survey some other related results. We formulate a conjecture on the behavior of $\Theta_\pi$ relative to the formal degree of $\pi$, which we are able to prove in the case where $\pi$ is a tame supercuspidal. The proof builds on J.-K.~Yu's construction and the structure of Moy-Prasad subgroups.Comment: Proceedings of Simons symposium on the trace formul

Study of Mill Island ice core (East Antarctica): A sensitive site for high resolution ocean climate signals?

第2回極域科学シンポジウム　氷床コアセッション 11月16日（水） 国立極地研究所 2階大会議

Rupture of multiple parallel molecular bonds under dynamic loading

Biological adhesion often involves several pairs of specific receptor-ligand molecules. Using rate equations, we study theoretically the rupture of such multiple parallel bonds under dynamic loading assisted by thermal activation. For a simple generic type of cooperativity, both the rupture time and force exhibit several different scaling regimes. The dependence of the rupture force on the number of bonds is predicted to be either linear, like a square root or logarithmic.Comment: 8 pages, 2 figure

The 10 sea urchin receptor for egg jelly proteins (SpREJ) are members of the polycystic kidney disease-1 (PKD1) family

<p>Abstract</p> <p>Background</p> <p>Mutations in the human polycystic kidney disease-1 (<it>hPKD1</it>) gene result in ~85% of cases of autosomal dominant polycystic kidney disease, the most frequent human monogenic disease. PKD1 proteins are large multidomain proteins involved in a variety of signal transduction mechanisms. Obtaining more information about members of the PKD1 family will help to clarify their functions. Humans have five hPKD1 proteins, whereas sea urchins have 10. The PKD1 proteins of the sea urchin, <it>Strongylocentrotus purpuratus</it>, are referred to as the Receptor for Egg Jelly, or SpREJ proteins. The SpREJ proteins form a subfamily within the PKD1 family. They frequently contain C-type lectin domains, PKD repeats, a REJ domain, a GPS domain, a PLAT/LH2 domain, 1–11 transmembrane segments and a C-terminal coiled-coil domain.</p> <p>Results</p> <p>The 10 full-length SpREJ cDNA sequences were determined. The secondary structures of their deduced proteins were predicted and compared to the five human hPKD1 proteins. The genomic structures of the 10 SpREJs show low similarity to each other. All 10 SpREJs are transcribed in either embryos or adult tissues. SpREJs show distinct patterns of expression during embryogenesis. Adult tissues show tissue-specific patterns of SpREJ expression.</p> <p>Conclusion</p> <p>Possession of a REJ domain of about 600 residues defines this family. Except for SpREJ1 and 3, that are thought to be associated with the sperm acrosome reaction, the functions of the other SpREJ proteins remain unknown. The sea urchin genome is one-fourth the size of the human genome, but sea urchins have 10 SpREJ proteins, whereas humans have five. Determination of the tissue specific function of each of these proteins will be of interest to those studying echinoderm development. Sea urchins are basal deuterostomes, the line of evolution leading to the vertebrates. The study of individual PKD1 proteins will increase our knowledge of the importance of this gene family.</p

Measurement of one-particle correlations and momentum distributions for trapped 1D gases

van Hove's theory of scattering of probe particles by a macroscopic target is generalized so as to relate the differential cross section for atomic ejection via stimulated Raman transitions to one-particle momentum-time correlations and momentum distributions of 1D trapped gases. This method is well suited to probing the longitudinal momentum distributions of 1D gases in situ, and examples are given for bosonic and fermionic atoms.Comment: 4 pages, 2 .eps figure

Irreducible characters of GSp(4, q) and dimensions of spaces of fixed vectors

In this paper, we compute the conjugacy classes and the list of irreducible characters of GSp(4,q), where q is odd. We also determine precisely which irreducible characters are non-cuspidal and which are generic. These characters are then used to compute dimensions of certain subspaces of fixed vectors of smooth admissible non-supercuspidal representations of GSp(4,F), where F is a non-archimedean local field of characteristic zero with residue field of order q.Comment: 48 pages, 21 tables. Corrected an error in Table 16 for type V* representations (theta_11 and theta_12 were switched

On the elliptic nonabelian Fourier transform for unipotent representations of p-adic groups

In this paper, we consider the relation between two nonabelian Fourier transforms. The first one is defined in terms of the Langlands-Kazhdan-Lusztig parameters for unipotent elliptic representations of a split p-adic group and the second is defined in terms of the pseudocoefficients of these representations and Lusztig's nonabelian Fourier transform for characters of finite groups of Lie type. We exemplify this relation in the case of the p-adic group of type G_2.Comment: 17 pages; v2: several minor corrections, references added; v3: corrections in the table with unipotent discrete series of G

Coherent Tunneling of Atoms from Bose-condensed Gases at Finite Temperatures

Tunneling of atoms between two trapped Bose-condensed gases at finite temperatures is explored using a many-body linear response tunneling formalism similar to that used in superconductors. To lowest order, the tunneling currents can be expressed quite generally in terms of the single-particle Green's functions of the isolated Bose gases. A coherent first-order tunneling Josephson current between two atomic Bose-condensates is found, in addition to coherent and dissipative contributions from second-order condensate-noncondensate and noncondensate-noncondensate tunneling. Our work is a generalization of Meier and Zwerger, who recently treated tunneling between uniform atomic Bose gases. We apply our formalism to the analysis of an out-coupling experiment induced by light wave fields, using a simple Bogoliubov-Popov quasiparticle approximation for the trapped Bose gas. For tunneling into the vacuum, we recover the results of Japha, Choi, Burnett and Band, who recently pointed out the usefulness of studying the spectrum of out-coupled atoms. In particular, we show that the small tunneling current of noncondensate atoms from a trapped Bose gas has a broad spectrum of energies, with a characteristic structure associated with the Bogoliubov quasiparticle u^2 and v^2 amplitudes.Comment: 26 pages, 5 figures, minor changes, to appear in PR