Multipulse Phases in k-Mixtures of Bose–Einstein Condensates

For the system

$-\Delta U_i+ U_i=U_i^3-\beta U_i\sum_{j\neq i}U_j^2,\quad i=1,\dots,k,$

(with k ≧ 3), we prove the existence for β large of positive radial solutions on \({\mathbb R^N}\) . We show that as β →  + ∞, the profile of each component U _i separates, in many pulses, from the others. Moreover, we can prescribe the location of such pulses in terms of the oscillations of the changing-sign solutions of the scalar equation  ? ΔW  +  W  =  W³. Within an Hartree–Fock approximation, this provides a theoretical indication of phase separation into many nodal domains for the k-mixtures of Bose–Einstein condensates.

     

Radial Solutions of¶Superlinear Equations on ℝN¶Part II: The Forced Case

We study the effect of a forcing term in the context of the search of multiple nodal solutions u∈h ¹(? ^N ) to a class of elliptic equations of type¶?Δu(x)=f(|x|,u(x))+h(|x|), x∈? ^N ,¶where f(|x|≡0 and f is superlinear but subcritical at infinity.     

Ultrafast and selective labeling of endogenous proteins using affinity-based benzotriazole chemistry

Chemical modification of proteins is enormously useful for characterizing protein function in complex biological systems and for drug development. Selective labeling of native or endogenous proteins is challenging owing to the existence of distinct functional groups in proteins and in living systems. Chemistry for rapid and selective labeling of proteins remains in high demand. Here we have developed novel affinity labeling probes using benzotriazole (BTA) chemistry. We showed that affinity-based BTA probes selectively and covalently label a lysine residue in the vicinity of the ligand binding site of a target protein with a reaction half-time of 28 s. The reaction rate constant is comparable to the fastest biorthogonal chemistry. This approach was used to selectively label different cytosolic and membrane proteins in vitro and in live cells. BTA chemistry could be widely useful for labeling of native/endogenous proteins, target identification and development of covalent inhibitors.

Affinity-based benzotriazole (BTA) probes selectively and covalently label native proteins or endogenous proteins in cells with a fast reaction rate. It is enormously useful for characterizing protein function in biological systems and for drug development.     

An age‐dependent population equation with delayed birth process

Within a semigroup framework, we discuss well posedness and qualitative behaviour of an age‐dependent population equation with delay in the birth process. Using positivity and Perron–Frobenius theory we obtain an explicit stability criterion. Copyright © 2004 John Wiley & Sons, Ltd.     

Hierarchical decomposition of domains with fractures

We consider the efficient and robust numerical solution of elliptic problems with jumping coefficients occurring on a network of thin fractures. We present an iterative solution concept based on a hierarchical separation of the fractures and the surrounding rock matrix. Upper estimates for the convergence rates are independent of the width of the fractures and of the jumps of the coefficients. Inexact solution of the local subproblems is also considered. The theoretical results are illustrated by numerical experiments.

     

Binding affinities of host-guest, protein-ligand, and protein-transition-state complexes

The affinities of hosts-ranging from small synthetic cavitands to large proteins-for organic molecules are well documented. The average association constants for the binding of organic molecules by cyclodextrins, synthetic hosts, and albumins in water, as well as of catalytic antibodies or enzymes for substrates are 10(3.5+/-2.5) M(-1). Binding affinities are elevated to 10(8+/-2) M(-1) for the complexation of transition states and biological antigens by antibodies or inhibitors by enzymes, and to 10(16+/-4) M(-1) for transition states with enzymes. The origins of the distributions of association constants observed for the broad range of host-guest systems are explored in this Review, and typical approaches to compute and analyze host-guest binding in solution are discussed. In many classes of complexes a rough correlation is found between the binding affinity and the surface area that is buried upon complexation. Enzymes transcend this effect and achieve transition-state binding much greater than is expected from the surface areas.     

New designer drug, 2,5-dimethoxy-4-propylthio-beta-phenethylamine (2C-T-7): studies on its metabolism and toxicological detection in rat urine using gas chromatography/mass spectrometry

Studies are described on the metabolism and toxicological analysis of the phenethylamine-derived designer drug 2,5-dimethoxy-4-propylthio-beta-phenethylamine (2C-T-7) in rat urine using gas chromatography/mass spectrometry (GC/MS). The identified metabolites indicated that 2C-T-7 was metabolized by hydroxylation of the propyl side chain followed by N-acetylation and sulfoxidation and also by deamination followed by oxidation to the corresponding acid or by reduction to the corresponding alcohol. To a minor extent, 2C-T-7 was also metabolized by S-dealkylation followed by N-acetylation, S-methylation and sulfoxidation. The authors' systematic toxicological analysis (STA) procedure using full-scan GC/MS after acid hydrolysis, liquid-liquid extraction microwave-assisted acetylation allowed the detection of an intake of a dose of 2C-T-7 in rat urine that corresponds to a common drug users' dose. Assuming similar metabolism, the described STA procedure should be suitable for proof of an intake of 2C-T-7 in human urine.     

Overcharging of polyelectrolyte complexes by the guest polyelectrolyte studied by fluorescence spectroscopy

Polyion complexes (PICs) of anionic block copolymer poly(ethylene oxide)-block-poly(sodium methacrylate), PEO-block-(PMA)Na, and a cationic homopolymer, poly((methacryloyloxyethyl)trimethylammonium chloride), PMOTAC, have been studied by fluorescence spectroscopy. Pyrene and naphthalene singly labeled block copolymers were used with two different sodium methacrylate block lengths. The chain exchange between the stoichiometric PICs at the equilibrium state and the formation of the negatively charged PICs on addition of excess PEO-block-(PMA)Na to stoichiometric PIC solution were of interest. The chain exchange between the stoichiometric complexes was observed to occur via two mechanisms. The faster chain exchange occurs via insertion and expulsion of single chains, while merging and splitting of the PIC particles is behind the slower chain exchange event. Incorporation of an excess amount of the guest polyion into a stoichiometric PIC took place on further addition of the PEO-block-(PMA)Na. The same mechanisms were recognized in the overcharging process of the PICs as in the chain exchange between the stoichiometric PICs.