Isotropic random walks in a tree

Summary Let T be an infinite homogeneous tree of order a+1. We study Markov chains {X _n} in T whose transition functions p(x, y)=A[d(x,y)] depend only on the shortest distance between x and y in the graph. The graph T can be represented as a symmetric space of a p-adic matrix group; we prove a series of results using essentially the spherical functions of this symmetric space. Theorem 1. d(X _n,x) n a.s., where >0 if A(0) 1, X ₀=x. Assuming {X _n} is strongly aperiodic, Theorem 2. p ₂(x, y)CRⁿ/n^3/2 for fixed x, y where R=(d) A(d)<1, and if E[d(X₁, X₀)²]<, Theorem 3. R(1–u, x, y) = (1–u)ⁿp_n(x, y)=Ca^–d[exp(–du/)+o_d(1)] as d=d(x,y) uniformly for 0u2. Using Theorem 3, we calculate the Martin boundary Dirichlet kernel of p(x, y) on T, which turns out to be independent of {itA(d)}. We also consider a stepping-stone model of a randomly-mating-and-migrating population on the nodes of T. If initially all individuals are distinct, then in generation n approximately half of the individuals of a given type are within n of a typical one and essentially all are within 2n.This work was partially supported by the National Science Foundation under grant number MCS 75-08098-A01For the academic year 1977–78: Department of Mathematics GN-50, University of Washington, Seattle, Washington 98195 USA     

Some Asymptotic Results on <Emphasis Type="Italic">q</Emphasis>-Binomial Coefficients

We look at the asymptotic behavior of the coefficients of the q-binomial coefficients (or Gaussian polynomials) \({\left(\begin{array}{c}{a+k}\\{k}\end{array}\right)_{q}}\), when k is fixed. We give a number of results in this direction, some of which involve Eulerian polynomials and their generalizations.     

Comparison of "Polarization inversion with spin exchange at magic angle" and "geometric analysis of labeled alanines" methods for transmembrane helix alignment

Using the model alpha-helical peptide acetyl-GGALW5LALALALALALALW19LAGA-ethanolamide ("GWALP23"), we have compared the polarization inversion with spin exchange at magic angle method and geometric analysis of labeled alanines method for estimating the transmembrane helix orientation. For GWALP23 in bilayers of a short lipid, dilauroylphosphatidylcholine, we find general agreement between the two methods, with a static helix tilt of about 11degrees-13degrees with respect to the bilayer normal.     

Viscosity of dilute colloidal dispersions involving polysaccharide-based stabilizers

The viscosity of oil-in-water emulsions stabilized by amphiphilic derivatives of dextran (a neutral bacterial polysaccharide) was studied. The oil volume fraction was kept lower than 20% and the mean droplet diameter remained between 200 and 300 nm. The effects of temperature and oil volume fraction on emulsion viscosity were examined using a capillary viscometer. Andrade equation was shown to conveniently account for the variation of viscosity with temperature. Semiempirical equations were derived for the variation of activation energy with oil volume fraction. The established equations were extended to other emulsions using literature data.     

New approaches in the design of ceramic and hybrid membranes

This paper describes approaches developed for the preparation and also the characterization of innovative inorganic or hybrid membrane materials. Soft chemistry routes, sol–gel methods and plasma-enhanced chemical vapour deposition (PECVD) are used to get tailor-made layers with different architectures. The infiltrated composite membranes are first examined. They exhibit a good thermo-mechanical resistance, a low sensitivity to the presence of defects, a relatively high flow resistance and are attractive for catalytic contactor applications. Preliminary results on supported ceramic membranes with a hierarchical porosity are then presented. Finally, examples are given to illustrate the interest of the PECVD route and of plasma post-treatments for preparing very thin hybrid separative layers.     

Glucose-based amphiphilic telomers designed to keep membrane proteins soluble in aqueous solutions: synthesis and physicochemical characterization

A novel class of nonionic amphipols (NAPols) designed to handle membrane proteins in aqueous solutions has been synthesized, and its solution properties have been examined. These were synthesized through free radical cotelomerization of glucose-based hydrophilic and amphiphilic monomers derived from tris(hydroxymethyl)acrylamidomethane using azobisisobutyronitrile as the initiator and thiol as the transfer agent. The molecular weight and the hydrophilic/lipophilic balance of the cotelomers were modulated by varying the thiol/monomers and the hydrophilic monomer/amphiphilic monomer ratios, respectively, and were characterized by 'H NMR, UV, gel permeation chromatography, and Fourier transform infrared spectroscopy. Their physicochemical properties in aqueous solution were studied by dynamic light scattering, aqueous size-exclusion chromatography, analytical ultracentrifugation, and surface-tension measurements. NAPols are highly soluble in water and form, within a large concentration range, well-defined supramolecular assemblies with a diameter of approximately 6-7 nm, a narrow particle size distribution, and an average molecular weight close to 50 x 10(3) g x mol(-1). Varying the hydrophilic/amphiphilic monomer ratio of NAPols in the range of 3.0-4.9, the degree of polymerization in the range of 51-78, and the resulting average molar mass in the range of 20-29 x 10(3) g x mol(-1) has little incidence on their solution properties. Glucose-based NAPols efficiently kept soluble in aqueous solutions two test membrane proteins: bacteriorhodopsin and the transmembrane domain of Escherichia coli's outer membrane protein A.     

High-relaxivity magnetic resonance imaging (MRI) contrast agent based on supramolecular assembly between a gadolinium chelate, a modified dextran, and poly-beta-cyclodextrin

Nanosized contrast agents have great potential in magnetic resonance molecular imaging applications for clinical diagnosis. This study proposes new nanoparticles spontaneously formed under mild conditions and composed of a noncovalent adduct between a gadolinium complex, a polymer of beta-cyclodextrin (pbetaCD: MW 1.5 x 10(6) g mol(-1)) and a dextran grafted with alkyl chains (MD). The formation of this supramolecular nanoassembly is based upon a "lock-and-key" recognition process in which the hydrophobic alkyl chains of MD and the adamantyl moieties of macrocyclic Gd(III) chelates are included in the cavities of pbetaCD. The large number of betaCDs contained in the pbetaCD resulted in the formation of 200 nm diameter nanoparticles, each entrapping 1.8 x 10(5) molecules of a low-molecular-weight Gd complex. This system, which exhibits a great relaxivity enhancement (48.4 mM(-1) s(-1), at 20 MHz and 37 degrees C) compared to the Gd(III) chelate itself (5.2 mM(-1) s(-1)), appears to be a promising strategy for the in vivo targeted delivery of Gd(III) complexes. The mechanisms of particle formation, conjugation strategies, and relaxometric characterizations in the field of contrast-enhanced magnetic resonance imaging are discussed.     

Induction of persistent double strand breaks following multiphoton irradiation of cycling and G1-arrested mammalian cells-replication-induced double strand breaks

DNA double strand breaks (DSBs) are amongst the most deleterious lesions induced within the cell following exposure to ionizing radiation. Mammalian cells repair these breaks predominantly via the nonhomologous end joining pathway which is active throughout the cell cycle and is error prone. The alternative pathway for repair of DSBs is homologous recombination (HR) which is error free and active during S- and G2/M-phases of the cell cycle. We have utilized near-infrared laser radiation to induce DNA damage in individual mammalian cells through multiphoton excitation processes to investigate the dynamics of single cell DNA damage processing. We have used immunofluorescent imaging of gamma-H2AX (a marker for DSBs) in mammalian cells and investigated the colocalization of this protein with ATM, p53 binding protein 1 and RAD51, an integral protein of the HR DNA repair pathway. We have observed persistent DSBs at later times postlaser irradiation which are indicative of DSBs arising at replication, presumably from UV photoproducts or clustered damage containing single strand breaks. Cell cycle studies have shown that in G1 cells, a significant fraction of multiphoton laser-induced prompt DSBs persists for > 4 h in addition to those induced at replication.     

Measurement of Acetylcholine in Rat Brain Microdialysates by LC–Isotope Dilution Tandem MS

An LC–MS–MS method was developed for measuring acetylcholine (ACh) in an aqueous medium using reversed-phase ion-pair chromatography, electrospray ionization on a quadrupole ion trap instrument and a tetradeuterated analogue (ACh-1,1,2,2-d₄) as an internal standard. A rapid separation was achieved on a 5-cm long octadecylsilica column (2.1 mm i.d.) by employing heptafluorobutyric acid (0.1% v/v) as an ion-pairing agent and requiring 10% v/v acetonitrile in 20 mM ammonium formate buffer under isocratic elution at 200 μl min⁻¹ flow rate. The instrument’s response was calibrated with samples containing known mole ratios of ACh and ACh-1,1,2,2-d₄ in an artificial cerebrospinal fluid, which afforded the conclusion that analyte concentrations could be determined by multiplying the measured analyte to internal standard ion-current ratio with the known molar concentration of the ACh-1,1,2,2-d₄ added. The rapid and simple assay was tested by measuring the basal neurotransmitter concentration in rat brain microdialysates without the use of a cholinesterase inhibitor upon sample collection.