Formation of Supramolecular Nanostructures through in Situ Self-Assembly and Post-Assembly Modification of a Biocatalytically Constructed Dipeptide Hydrazide**

Aqueous self-assembly of short peptides has attracted growing attention for the construction of supramolecular materials for various bioapplications. Herein, we describe how the thermolysin-assisted biocatalytic construction of a dipeptide hydrazide from an N-protected amino acid and an amino acid hydrazide leads to the formation of thermally stable supramolecular hydrogels. In addition, we demonstrate the post-assembly modification of the supramolecular architectures constructed in situ tethering hydrazide groups as a chemical handle by means of fluorescence imaging.     

Anisotropic friction model of DNA electrophoresis in polymer solutions: Comparison with direct observations

The electrophoresis of DNA chains in uncrosslinked polymer solutions with a Brownian dynamics simulation with an anisotropic friction tensor was analyzed. According to the degree of anisotropy, three types of migration behavior are obtained: fluctuation without or with periodicity between U‐shaped and compact conformations, or migration with linear conformation. We found good agreement between our simulation results and the direct observations of DNA by fluorescence microscopy. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1316–1322, 2003     

RSOS Models and Jantzen–Seitz Representations of Hecke Algebras at Roots of Unity

A special family of partitions occurs in two apparently unrelated contexts: the evaluation of one-dimensional configuration sums of certain RSOS models, and the modular representation theory of symmetric groups or their Hecke algebras H_m. We provide an explanation of this coincidence by showing how the irreducible H_m-modules which remain irreducible under restriction to H_{m_1} (Jantzen–Seitz modules) can be determined from the decomposition of a tensor product of representations sl_n.     

Validation of a method for predicting the precision, limit of detection and range of quantitation in competitive ELISA.

The mathematical model for predicting the precision, limit of detection (LOD) and range of quantitation (ROQ) in a competitive enzyme-linked immunosorbent assay (ELISA) proposed by Hayashi et al. (Anal. Chem., 2004, 76, 1295) was validated. The model describes the relative standard deviation (RSD) of concentration estimates by the RSDs of pipetting volumes of analyte, enzyme-conjugated antigen, antibody and substrate solutions, and the standard deviation (SD) of inherent absorbances between the wells in an ELISA plate. For 6 kinds of direct competitive ELISA kits, the LOD and ROQ predicted by the model agreed well with those obtained by experiments with real samples. It was also confirmed that the model is applicable to the prediction of uncertainty that depends on the pipetting error of the viscous antiserum solution. The model was demonstrated to be useful for estimating the LOD and ROQ of competitive ELISA.     

Stable marker-particle method for the Voronoi diagram in a flow field

The Voronoi diagram in a flow field is a tessellation of water surface into regions according to the nearest island in the sense of a “boat-sail distance”, which is a mathematical model of the shortest time for a boat to move from one point to another against the flow of water. The computation of the diagram is not easy, because the equi-distance curves have singularities. To overcome the difficulty, this paper derives a new system of equations that describes the motion of a particle along the shortest path starting at a given point on the boundary of an island, and thus gives a new variant of the marker-particle method. In the proposed method, each particle can be traced independently, and hence the computation can be done stably even though the equi-distance curves have singular points.     

Electron spin resonance studies of plasma-induced polystyrene radicals

Plasma-induced polystyrene radicals were first studied by electron spin resonance (ESR). The room temperature ESR spectrum was compared with those obtained by γ-irradiation, UV-irradiation, and mechanical fracture. It was found that even less than a few seconds of plasma-irradiation gave rise to a large amount of polystyrene radicals and the ESR spectrum consisted of two types of spectra, a triplet and a single broad line. The spectral feature of the triplet was nearly identical with that of γ-irradiated polystyrene. Thus, it was assigned to the structure of a cyclohexadienyl-type radical formed by a nearly random addition of a hydrogen atom to the aromatic ring. The single broad line, thought to be an outline of multicomponent spectrum, was assigned to an immobilized dangling-bond sites at the plasma-induced crosslinked portion of the polystyrene surface.     

Preparation and condensation reactions of a new light-fluorous Mukaiyama reagent: reliable purification with fluorous solid phase extraction for esters and amides

A modified light-fluorous Mukaiyama reagent bearing a C₈F₁₇ tag was prepared and examined in ester and amide forming condensation reactions. Following the reactions, the desired product was effectively separated from the fluorous pyridone by-product using a simple fluorous solid phase extraction.     

Non-existence of phase transition of oriented percolation on Sierpinski carpet lattices

 A percolation problem on Sierpinski carpet lattices is considered. It is obtained that the critical probability of oriented percolation is equal to 1. In contrast it was already shown that the critical probability p _c of percolation is strictly less than 1 in Kumagai [9]. This result shows a difference between fractal-like lattice and ℤ ^d lattice. Received: 15 May 2002 / Revised version: 11 October 2002 / Published online: 21 February 2003 Mathematics Subject Classification (2000): Primary: 60K35, 82B43; Secondary: 82B26     

The Heat Kernel on Hyperbolic Space

The purpose of this note is to provide a new proof for the explicitformulas of the heat kernel on hyperbolic space. By definition,the hyperbolic space Hⁿ is a (unique) simply connected completen-dimensional Riemannian manifold with a constant negative sectionalcurvature –1. 1991 Mathematics Subject Classification58G32, 58G11.