Yang-Mills and Dirac Fields with Inhomogeneous Boundary Conditions

Finite time existence and uniqueness of solutions of the evolution equations of minimally coupled Yang-Mills and Dirac systems are proved for inhomogeneous boundary conditions. A characterization of the space of solutions of minimally coupled Yang-Mills and Dirac equations is obtained in terms of the boundary data and the Cauchy data satisfying the constraint equation. The proof is based on a special gauge fixing and a singular perturbation result for the existence of continuous semigroups. Received: 18 April 1996 / Accepted: 3 March 1997     

Movement of proteins in an environment crowded by surfactant micelles: anomalous versus normal diffusion

Small proteins move in crowded cell compartments by anomalous diffusion. In many of them, e.g., the endoplasmic reticulum, the proteins move between lipid membranes in the aqueous lumen. Molecular crowding in vitro offers a systematic way to study anomalous and normal diffusion in a well controlled environment not accessible in vivo. We prepared a crowded environment in vitro consisting of hexaethylene glycol monododecyl ether (C(12)E(6)) nonionic surfactant and water and observed lysozyme diffusion between elongated micelles. We have fitted the data obtained in fluorescence correlation spectroscopy using an anomalous diffusion model and a two-component normal diffusion model. For a small concentration of surfactant (below 4 wt %) the data can be fitted by single-component normal diffusion. For larger concentrations the normal diffusion fit gave two components: one very slow and one fast. The amplitude of the slow component grows with C(12)E(6) concentration. The ratio of diffusion coefficients (slow to fast) is on the order of 0.1 for all concentrations of surfactant in the solution. The fast diffusion is due to free proteins while the slow one is due to the protein-micelle complexes. The protein-micelle interaction is weak since even in a highly concentrated solution (35% of C(12)E(6)) the amplitude of the slow mode is only 10%, despite the fact that the average distance between the micelles is the same as the size of the protein. The anomalous diffusion model gave the anomaly index (r(2)(t) approximately t(alpha)), alpha monotonically decreasing from alpha = 1 (at 4% surfactant) to alpha = 0.88 (at 37% surfactant). The fits for two-component normal diffusion and anomalous diffusion were of equally good quality, but the physical interpretation was only straightforward for the former.     

Programmed metalloporphyrins for self-assembly within light-harvesting stacks: (5,15-dicyano-10,20-bis(3,5-di-tert-butylphenyl)porphyrinato)zinc(II) and its push-pull 15-N,N-dialkylamino-5-cyano congeners obtained by a facile direct amination

The title dicyano compound was synthesized via cyanation and it self-assembles in nonpolar solvents giving red-shifted and broad absorption maxima just as the bacteriochlorophylls which are encountered in the light-harvesting organelles of early photosynthetic bacteria. In the crystal, stacks are formed through a hierarchic combination of pi-stacking and a CN-Zn electrostatic interaction. Push-pull 15-N,N-dialkylamino-5-cyano congeners could be obtained in high yields using a solvent- and catalyst-free direct amination of meso-bromoporphyrins. Importantly, the fluorescence of the self-assembled species due to the very orderly manner in which the chromophores are arranged is not entirely quenched and has a surprisingly long lifetime of over 1 ns. This lends hope of using the trapped energy in biomimetic hybrid solar cells.     

Stability of equilibrium points of demand-inventory model with stock-dependent demand

A model of demand and inventory of a product in one echelon of supply chain is considered. The model is formulated as a system of difference equations, in which every equilibrium point is nonhyperbolic. A positive invariant set of the system is constructed. An analysis of properties of equilibrium points of the system is based on the Lyapunov method or reducing it to the family of systems of difference equations with hyperbolic equilibrium points.     

A new catalytic route to boryl- and borylsilyl-substituted buta-1,3-dienes

Vinyl-substituted boronates in the presence of complexes containing Ru-H bonds (preferably [Ru(CO)ClH(PCy(3))(2)], Cy: cyclohexyl) react regioselectively with terminal ethynes (involving silylethynes), albeit with the exception of phenylacetylene, to produce boryl- and borylsilyl-substituted buta-1,3-dienes with a preference for E,E-diene. The reaction opens a new catalytic route for the preparation of dienylboronates, and particularly dienylsilylboronates, that are functionalised building blocks in the synthesis of organic and natural products. The mechanism of this new reaction was proved to involve an insertion of alkyne into Ru-H bonds followed by an insertion of coordinated vinyl boronate into the Ru-C= bond and beta-hydrogen transfer to the metal to eliminate boryldiene or borylsilyldiene.     

Net charge and electrophoretic mobility of lysozyme charge ladders in solutions of nonionic surfactant

We report on the electrophoretic mobility and on the thermal diffusion of lysozyme proteins dissolved in aqueous solutions of a nonionic surfactant (C12E6) at a wide range of concentrations of the surfactant (0-20% by weight). We want to estimate the influence of a dense network of elongated micelles of C12E6 on the effective charge of the proteins as observed in the capillary electrophoresis experiments. The possible mechanism leading to the change in the effective charge of protein could involve the deformation of the cloud of counterions around the protein when it squeezes through the narrow (of the order of a protein diameter) aqueous channels formed in the solution of elongated micelles. The combination of independent measurements of the electrophoretic mobility of a family of modified proteins (lysozyme charge ladder [Colton et al. J. Am. Chem. Soc. 1997, 119, 12701]), of the microviscosity of the solutions of surfactant (obtained via fluorescence correlation spectroscopy), and of the hydrodynamic radius of the proteins (photon correlation spectroscopy) allow us to conclude that the effective charge of the proteins is not affected by the presence of surfactant, even at high concentrations.