111In–L–LDL and 153Gd–L–LDL as radiotracers for detection of AR4‐2J rat pancreatic tumors

Pancreatic cancer has an extremely poor prognosis, due, in part, to lack of methods for early diagnosis. The present study was designed to evaluate the potential of labeling low‐density lipoprotein (LDL) with a radionuclide using a lipid chelating agent, bis(stearylamide) of diethylenetriaminepentaacetic acid (L), to detect pancreatic tumors by gamma‐scintigraphy. Previous studies indicated that the difficulty of visualization of pancreatic tumors was due to their poor vascularization. This study compares the ability of two radiotracers, ¹¹¹In–L–LDL and ¹⁵³Gd–L–LDL to target highly vascularized rat pancreatic tumors (AR4‐2J) implanted in nude mice. Biodistribution studies showed that the tumor uptake of ¹¹¹In–L–LDL and ¹⁵³Gd–L–LDL tracers was twofold and fivefold higher respectively than with the controls (¹¹¹In citrate and ¹⁵³Gd citrate respectively). These tracers would thus be suitable for scintigraphic imaging. We show here that LDL could be employed as a delivery system for tracers such as ¹¹¹In or ¹⁵³Gd when these two radionuclides are complexed by a lipid‐chelating anchor, and that ¹¹¹In–L–LDL and ¹⁵³Gd–L–LDL enabled better visualization of the pancreatic tumor tissues, with a better result with ¹⁵³Gd–L–LDL. Copyright © 2004 John Wiley & Sons, Ltd.     

Metallo‐supramolecular micelles: Studies by analytical ultracentrifugation and electron microscopy

In aqueous solutions, amphiphilic block copolymers in which a polystyrene (PS) segment is connected to a poly(ethylene oxide) (PEO) block via a bis(2,2′:6′,2″‐ terpyridine ruthenium) complex can form micelles. Such micelles of the protomer type PS₂₀‐[Ru]‐PEO₇₀, according to the preparation procedure representing frozen micelles, were studied by sedimentation velocity and sedimentation equilibrium analysis in an analytical ultracentrifuge and by transmission electron microscopy, with different techniques applied for the sample preparation. The particles obtained were surprisingly multifarious in size. In ultracentrifugation experiments performed at relatively low salt concentrations, the distributions of the sedimentation coefficient s_20,w showed a pronounced peak at 9.6 S and a broad, only partly separated second peak around 14 S. The molar mass of the particles at the peak was around 430,000 g/mol, corresponding to an aggregation number of approximately 85. The average hydrodynamic diameter of the particles in the peak fraction was approximately 13 nm. In electron micrographs of negatively stained samples, spheres of diameters between 10 and 25 nm were the most abundant particles, but larger ones with a wide size range were also visible. The latter particles apparently were composed of smaller ones. The data from both sedimentation analysis and electron microscopy showed that (1) the studied compound formed primary micelles of diameters around 20 nm and (2) the primary micelles had a tendency toward aggregation. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3159–3168, 2003     

Boundary blow-up for differential equations with indefinite weight

We obtain results of existence and multiplicity of solutions for the second-order equation x″+q(t)g(x)=0, with x(t) defined for all t∈]0,1[ and such that x(t)→+∞ as t→0⁺ and t→1⁻. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0,1].     

Convergence in probability for perturbed stochastic integral equations

Summary In this work, one considers two stochastic integral equations indexed by some parameter and one studies the contiguity of their solutions when the parameter converges to some ₀. Two types of behaviour are described; they lead to the notion of regular and singular perturbations. The method which is used also enables a study of the rate of convergence. Applications to time discretization of equations are given.     

The investigation of critical parameters in the glycolytic response of single living cells by rapid microspectrofluorometric analysis

Summary NAD(P)H fluorescence emission spectra are recorded from single living cells, by a recently developed multichannel microspectrofluorometric technique, in correlation with the intracellular microelectrophoretic addition of substrate (i. e., glucose-6-P). These spectra may be used as a reference basis in establishing the critical parameters to be followed when the same studies are extended to a variety of cells, submitted to various drug effects or physical treatments. The sum-spectra corresponding to channel by channel (wavelength by wavelength) summation of spectra obtained from various cells within a series, before and after addition of substrate, and their difference spectrum may be normalized and evaluated comparatively. The NAD(P)H emission maximum prior to addition of substrate seems to present a mixture of dehydrogenase-bound and free coenzyme. There is a suggestion that immediately after substrate, i. e., at 5 sec, an increase in free NADH is first observed. While the overall changes in fluorescence intensity associated with substrate are quite large (50–150% increase), the counts (i. e., an expression of photons) associated with shifts in the emission maximum (free vs. bound NAD(P)H changes) are at times barely above noise. Rapid microspectrofluorometry provides in principle the most direct approach for the identification of coenzyme bound to various dehydrogenases in single living cells, but further improvements in spectral resolution and signal-to-noise ratio are required, for a better definition of the spectral shifts which may be observed.

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Zusammenfassung Mit Hilfe einer kürzlich entwickelten Mehrkanal-Mikrospektrofluorometer-Methode wurden von einzelnen lebenden Zellen nach intrazellulär mikroelektrophoretischer Substratzugabe (z. B. Glucose-6-P) NAD(P)H Fluoreszenz-Emissionsspektren aufgenommen. Diese Spektren können als Vergleichsbasis bei der Festsetzung der entscheidenden Parameter verwendet werden, wenn die gleichen Untersuchungen auf eine Reihe von Zellen ausgedehnt werden sollen, die verschiedenen Medikamenteffekten oder physikalischer Behandlung ausgesetzt werden. Die Summenspektren, die der kanalmäßigen (wellenlängenmäßigen) Summierung der Spektren von verschiedenen Zellen innerhalb einer Serie, vor und nach Substratzugabe entsprechen, sowie ihre Differenzspektren können normalisiert und vergleichsweise ausgewertet werden. Das NAD(P)H-Emissionsmaximum vor der Substratzugabe scheint ein Gemisch von freiem und dehydrogenasegebundenem Coenzym darzustellen. Unmittelbar nach Substratzugabe (d. h. nach 5 sec) ist ein Anstieg an freiem NADH das erste Mal zu beobachten. Während die mit dem Substrat einhergehenden Gesamtveränderungen der Fluoreszenzintensität recht groß sind (50–150% Anstieg), sind die Impulse (als Effekt der Photonen), die mit einer Verschiebung im Emissionsmaximum verbunden sind (Veränderungen von freiem und gebundenem NAD(P)H) zu manchen Zeiten kaum höher als das Rauschen. Die rasche Mikrospektrofluorometrie stellt im Prinzip die direkteste Methode zur Identifizierung von Coenzymen dar, die an verschiedenen Dehydrogenasen in einzelnen lebenden Zellen gebunden sind. Weitere Verbesserungen der Spektralauflösung und der Empfindlichkeit (signal-to-noise ratio) sind notwendig, um die Spektralverschiebungen, die beobachtet werden, besser auswerten zu können.

     

A systematic formula for the asymptotic expansion of singular integrals

Asymptotic theories like the lifting-line, the slender body or the slender ship lead to lineintegrals with singular kernels. Sometimes these integrals are improper, that is to say that they are defined only by their Finite Part. To find asymptotic expansions of these integrals, the Matched Asymptotic Expansion Method is widely used along with other more specific methods depending on the kernel type. The first method is laborious and not systematic, and the other methods are sometimes too much specific to treat general cases. Moreover, all of them are not well adapted to deal with Finite Part integrals.Here, a new method is proposed to avoid the previous difficulties. This method is systematic for homogeneous kernels and gives approximations up to any order, as long as the derivative of the weight function exists at this given order. Moreover the occurrence of logarithmic terms in the expansion is explained and easily predictable. An elliptic integral and the classical lifting-line theory are treated to illustrate the ease of this method.

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Résumé Les théories asymptotiques telles que la ligne portante, le corps élancé ou le navire de grand allongement conduisent à des intégrales curvilignes à noyaux singuliers. Parfois, ces intégrales sont impropres c'est à dire qu'elles sont définies en Parties Finies. Différentes méthodes ont été mises au point pour trouver les développements asymptotiques de ces intégrales. Généralement elles dépendent fortement de la nature du noyau, et c'est finalement la méthode des développements raccordés qui est utilisées quand le noyau est trop compliqué. Cependant, cette méthode est laborieuse et comme les précèdentes non adaptée aux intégrales défines par leur Partie Finie.Une nouvelle méthode est proposée pour surmonter ces difficultés. Cette méthode est systématique pour les noyaux homogènes et donne les approximations à tout ordre pourvu que les dérivées de la fonction poids existent jusqu'à cet ordre. De plus la présence de termes logarithmiques dans le développement est expliquée et aisément prédictible.Une intégrale elliptique, ainsi que la fameuse théorie de la ligne portante sont traités pour illustrer les possibilités de la méthode.

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Nomenclature D domain of integration - f(x) weight function - FP Finite Part - h(x) weight function - I ,I _o bounded intervals - j, J integers - K(x, ) singular kernel - L, L integers - M integer defining the approximation order - P _k (x) Legendre polynomial - R set of real numbers - R(ß) equals 1 if is an integer and 0 if not - R _{f, J} ,R _{K, L} remainders of Taylor developments - S () equals either 1 or the sign function:sgn() - t, u, v, x variable of integration - , real numbers - homogeneity order of the kernel - F () Euler's integral (gamma function) - small parameter - [.] integer part of