Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Characterisation of the three-dimensional structure of earthworm burrow systems using image analysis and mathematical morphology

The aim of this work was to exemplify the specific contribution of both two- and three-dimensional (31)) X-ray computed tomography to characterise earthworm burrow systems. To achieve this purpose we used 3D mathematical morphology operators to characterise burrow systems resulting from the activity of an anecic (Aporrectodea noctunia), and an endogeic species (Allolobophora chlorotica), when both species were introduced either separately or together into artificial soil cores. Images of these soil cores were obtained using a medical X-ray tomography scanner. Three-dimensional reconstructions of burrow systems were obtained using a specifically developed segmentation algorithm. To study the differences between burrow systems, a set of classical tools of mathematical morphology (granulometries) were used. So-called granulometries based on different structuring elements clearly separated the different burrow systems. They enabled us to show that burrows made by the anecic species were fatter, longer, more vertical, more continuous but less sinuous than burrows of the endogeic species. The granulometry transform of the soil matrix showed that burrows made by A. nocturna were more evenly distributed than those of A. chlorotica. Although a good discrimination was possible when only one species was introduced into the soil cores, it was not possible to separate burrows of the two species from each other in cases where species were introduced into the same soil core. This limitation, partly due to the insufficient spatial resolution of the medical scanner, precluded the use of the morphological operators to study putative interactions between the two species.

A comparison of the self-association behavior of the plant cyclotides kalata B1 and kalata B2 via analytical ultracentrifugation

The recently discovered cyclotides kalata B1 and kalata B2 are miniproteins containing a head-to-tail cyclized backbone and a cystine knot motif, in which disulfide bonds and the connecting backbone segments form a ring that is penetrated by the third disulfide bond. This arrangement renders the cyclotides extremely stable against thermal and enzymatic decay, making them a possible template onto which functionalities can be grafted.We have compared the hydrodynamic properties of two prototypic cyclotides, kalata B1 and kalata B2, using analytical ultracentrifugation techniques. Direct evidence for oligomerization of kalata B2 was shown by sedimentation velocity experiments in which a method for determining size distribution of polydisperse molecules in solution was employed. The shape of the oligomers appears to be spherical. Both sedimentation velocity and equilibrium experiments indicate that in phosphate buffer kalata B1 exists mainly as a monomer, even at millimolar concentrations. In contrast, at 1.6 mM, kalata B2 exists as an equilibrium mixture of monomer (30%), tetramer (42%), octamer (25%), and possibly a small proportion of higher oligomers. The results from the sedimentation equilibrium experiments show that this self-association is concentration dependent and reversible. We link our findings to the three-dimensional structures of both cyclotides, and propose two putative interaction interfaces on opposite sides of the kalata B2 molecule, one involving a hydrophobic interaction with the Phe(6), and the second involving a charge-charge interaction with the Asp(25) residue. An understanding of the factors affecting solution aggregation is of vital importance for future pharmaceutical application of these molecules.

On S-asymptotically omega-periodic functions on Banach spaces and applications

This paper is devoted to the study of the class of continuous and bounded functions f : [0, infinity] -> X for which exists omega > 0 such that lim(t ->infinity) (f (t + omega) - f (t)) = 0 (in the sequel called S-asymptotically omega-periodic functions). We discuss qualitative properties and establish some relationships between this type of functions and the class of asymptotically omega-periodic functions. We also study the existence of S-asymptotically omega-periodic mild solutions of the first-order abstract Cauchy problem in Banach spaces. (C) 2008 Elsevier Inc. All rights reserved.

Integrability and exact solution of an electronic model with long range interactions

We present an electronic model with long range interactions. Through the quantum inverse scattering method, integrability of the model is established using a one-parameter family of typical irreducible representations of gl(211). The eigenvalues of the conserved operators are derived in terms of the Bethe ansatz, from which the energy eigenvalues of the Hamiltonian are obtained.

Estimating the potential refolding yield of recombinant proteins expressed as inclusion bodies

Recombinant protein production in bacteria is efficient except that insoluble inclusion bodies form when some gene sequences are expressed. Such proteins must undergo renaturation, which is an inefficient process due to protein aggregation on dilution from concentrated denaturant. In this study, the protein-protein interactions of eight distinct inclusion-body proteins are quantified, in different solution conditions, by measurement of protein second virial coefficients (SVCs). Protein solubility is shown to decrease as the SVC is reduced (i.e., as protein interactions become more attractive). Plots of SVC versus denaturant concentration demonstrate two clear groupings of proteins: a more aggregative group and a group having higher SVC and better solubility. A correlation of the measured SVC with protein molecular weight and hydropathicity, that is able to predict which group each of the eight proteins falls into, is presented. The inclusion of additives known to inhibit aggregation during renaturation improves solubility and increases the SVC of both protein groups. Furthermore, an estimate of maximum refolding yield (or solubility) using high-performance liquid chromatography was obtained for each protein tested, under different environmental conditions, enabling a relationship between yield and SVC to be demonstrated. Combined, the results enable an approximate estimation of the maximum refolding yield that is attainable for each of the eight proteins examined, under a selected chemical environment. Although the correlations must be tested with a far larger set of protein sequences, this work represents a significant move beyond empirical approaches for optimizing renaturation conditions. The approach moves toward the ideal of predicting maximum refolding yield using simple bioinformatic metrics that can be estimated from the gene sequence. Such a capability could potentially screen, in silico, those sequences suitable for expression in bacteria from those that must be expressed in more complex hosts. (C) 2004 Wiley Periodicals, Inc.

Signal Transduction, Plasma Membrane Calcium Movements, and Pigment Translocation in Freshwater Shrimp Chromatophores

Crustacean color change results from the differential translocation of chromatophore pigments, regulated by neurosecretory peptides like red pigment concentrating hormone (RPCH) that, in the red ovarian chromatophores of the freshwater shrimp Macrobrachium olfersi, triggers pigment aggregation via increased cytosolic cGMP and Ca(2+) of both smooth endoplasmatic reticulum (SER) and extracellular origin. However, Ca(2+) movements during RPCH signaling and the mechanisms that regulate intracellular [Ca(2+)] are enigmatic. We investigate Ca(2+) transporters in the chromatophore plasma membrane and Ca(2+) movements that occur during RPCH signal transduction. Inhibition of the plasma membrane Ca(2+)-ATPase by La(3+) and indirect inhibition of the Na(+)/Ca(2+) exchanger by ouabain induce pigment aggregation, revealing a role for both in Ca(2+) extrusion. Ca(2+) channel blockade by La(3+) or Cd(2+) strongly inhibits slow-phase RPCH-triggered aggregation during which pigments disperse spontaneously. L-type Ca(2+) channel blockade by gabapentin markedly reduces rapid-phase translocation velocity; N- or P/Q-type blockade by omega-conotoxin MVIIC strongly inhibits RPCH-triggered aggregation and reduces velocity, effects revealing RPCH-signaled influx of extracellular Ca(2+). Plasma membrane depolarization, induced by increasing external K(+) from 5 to 50 mM, produces Ca(2+)-dependent pigment aggregation, whereas removal of K(+) from the perfusate causes pigment hyperdispersion, disclosing a clear correlation between membrane depolarization and pigment aggregation; K(+) channel blockade by Ba(2+) also partially inhibits RPCH action. We suggest that, during RPCH signal transduction, Ca(2+) released from the SER, together with K(+) channel closure, causes chromatophore membrane depolarization, leading to the opening of predominantly N- and/or P/Q-type voltage-gated Ca(2+) channels, and a Ca(2+)/cGMP cascade, resulting in pigment aggregation. J. Exp. Zool. 313A:605-617, 2010. (C) 2010 Wiley-Liss, Inc.

The association of Na,K-ATPase subunits studied by circular dichroism, surface tension and dilatational elasticity

Different stoichiometries are observed between alpha and beta subunits of Na,K-ATPase that depend on the method employed to solubilize and purify the enzyme. It is not known whether this variability is due to loss of protein-protein association, or is a result of the replacement of essential phospholipids by detergent molecules. With the aim of understanding the effect of enzyme/surfactant ratio on both the catalytic activity and the enzyme structure, we have investigated the bulk and surface properties of the enzyme. The circular dichroism (CD) spectra, surface tension and dilatational surface elasticity results were compared with the residual ATPase activity of the Na,K-ATPase in different surfactant and protein concentrations. Na,K-ATPase in the (alpha beta)(2) form dissociated to the alpha beta form on dilution, and associated to the (alpha beta)(4) form when concentrated. These different stoichiometries have similar ATPase activities and are in equilibrium at C(12)E(8) concentrations below the CIVIC (0.053 mg mL(-1)). At detergent concentrations above the CIVIC the ATPase activity of all forms was abolished, which is concomitant with the dissociation of the a and subunits. (C) 2008 Elsevier Inc. All rights reserved.

Operational regimes for a simplified one-step artificial chaperone refolding method

The artificial chaperone method for protein refolding developed by Rozema et al. (Rozema, D.; Gellman, S. H. J. Am. Chem. Soc. 1995, 117 (8), 2373-2374) involves the sequential dilution of denatured protein into a buffer containing detergent (cetyltrimethylammonium bromide, CTAB) and then into a refolding buffer containing cyclodextrin WD). In this paper a simplified one-step artificial chaperone method is reported, whereby CTAB is added directly to the denatured solution, which is then diluted directly into a refolding buffer containing P-cyclodextrin (P-CD). This new method can be applied at high protein concentrations, resulting in smaller processing volumes and a more concentrated protein solution following refolding. The increase in achievable protein concentration results from the enhanced solubility of CTAB at elevated temperatures in concentrated denaturant. The refolding yields obtained for the new method were significantly higher than for control experiments lacking additives and were comparable to the yields obtained with the classical two-step approach. A study of the effect of beta-CD and CTAB concentrations on refolding yield suggested two operational regimes: slow stripping ( beta-CDXTABsimilar to1), most suited for higher protein concentrations, and fast stripping (beta-CD/CTABsimilar to2.7), best suited for lower protein concentrations. An increased chaotrope concentration resulted in higher refolding yields and an enlarged operational regime.

Dextrin-microencapsulated porphyrin - Luminescent properties

Photophysical properties of porphyrins in aqueous solutions are strongly affected by aggregation. One possible solution to this problem is to encapsulate the porphyrin into polymeric spheres, to provide an environment where the photosensitizer can be administered in its monomeric form in such treatments as photodynamic therapy. Here we report the microencapsulation of the meso-tetrakis(4-sulphonatophenyl) porphyrin (TPPS4) photosensitizer by the ultrasonic spray-drying technique. The encapsulated TPPS4 was morphologically characterized by scanning electron microscopy, and its photophysical properties were studied and compared with those of a physical blend of dextrin and TPPS4. We Successfully encapsulated TPPS4 into dextrin microspheres, and the encapsulated photosensitizer displays higher luminescence intensity than that of the prepared physical blends.

Rare Earth Doped SnO(2) Nanoscaled Powders and Coatings: Enhanced Photoluminescence in Water and Waveguiding Properties

Luminescent Eu(3+) and Er(3+) doped SnO(2) powders have been prepared by Sn(4+) hydrolysis followed by a controlled growth reaction using a particle`s surface modifier in order to avoid particles aggregation. The powders so obtained doped with up to 2 mol% rare earth ions are fully redispersable in water at pH > 8 and present the cassiterite structure. Particles size range from 3 to 10 nm as determined by Photon Correlation Spectroscopy. Rare earth ions were found to be essentially incorporated into the cassiterite structure, substituting for Sn(4+), for doping concentration smaller than 0.05 mol%. For higher concentration they are also located at the particles surface. The presence of Eu(3+) ions at the surface of the particles hinder their growth and has therefore allowed the preparation of new materials consisting of water redispersable powders coated with Eu(3+)-beta dike-tonate complexes. Enhanced UV excited photoluminescence was observed in water. SnO(2) single layers with thickness up to 200 nm and multilayer coatings were spin coated on borosilicate glass substrates from the colloidal suspensions. Waveguiding properties were evaluated by the prism coupling technique. For a 0.3 mu m planar waveguide single propagating mode was observed with attenuation coefficient of 3.5 dB/cm at 632.8 nm.

Interpretation of negative values of the interaction parameter in the adsorption equation through the effects of surface layer heterogeneity

The problem of the negative values of the interaction parameter in the equation of Frumkin has been analyzed with respect to the adsorption of nonionic molecules on energetically homogeneous surface. For this purpose, the adsorption states of a homologue series of ethoxylated nonionic surfactants on air/water interface have been determined using four different models and literature data (surface tension isotherms). The results obtained with the Frumkin adsorption isotherm imply repulsion between the adsorbed species (corresponding to negative values of the interaction parameter), while the classical lattice theory for energetically homogeneous surface (e.g., water/air) admits attraction alone. It appears that this serious contradiction can be overcome by assuming heterogeneity in the adsorption layer, that is, effects of partial condensation (formation of aggregates) on the surface. Such a phenomenon is suggested in the Fainerman-Lucassen-Reynders-Miller (FLM) 'Aggregation model'. Despite the limitations of the latter model (e.g., monodispersity of the aggregates), we have been able to estimate the sign and the order of magnitude of Frumkin's interaction parameter and the range of the aggregation numbers of the surface species. (C) 2004 Elsevier B.V All rights reserved.

Drinfield twists and alegebraic Bethe ansatz of the supersymmetric t-J model

We construct the Drinfeld twists (factorizing F-matrices) for the supersymmetric t-J model. Working in the basis provided by the F-matrix (i.e. the so-called F-basis), we obtain completely symmetric representations of the monodromy matrix and the pseudo-particle creation operators of the model. These enable us to resolve the hierarchy of the nested Bethe vectors for the gl(2\1) invariant t-J model.

Physicochemical characterization of nanoparticles formed between DNA and phosphorylcholine substituted chitosans

The interactions between phosphorylcholine-substituted chitosans (PC-CH) and calf-thymus DNA (ct-DNA) were investigated focusing on the effects of the charge ratio, the pH, and phosphorylcholine content on the size and stability of the complexes using the ethidium bromide fluorescence assay, gel electrophoresis, dynamic light scattering. and fluorescence microscopy. The size and colloidal stability of deacetylated chitosan (CH/DNA) and PC-CH/DNA complexes were strongly dependent on phosphorylcholine content, charge ratios, and pH. The interaction strengths were evaluated from ethidium bromide fluorescence, and at N/P ratios higher than 5.0, no DNA release was observed in any synthesized PC-CH/DNA polyplexes by gel electrophoresis. The PC-CH/DNA polyplexes exhibited a higher resistance to aggregation compared to deacetylated chitosan (CH) at neutral pH. At low pH values highly charged chitosan and its phosphorylcholine derivatives had strong binding affinity with DNA, whereas at higher pH Values CH formed large aggregates and only C-CH derivatives were able to form small nanoparticles with hydrodynamic radii varying from 100 to 150 nm. Nanoparticles synthesized at low ionic strength with PC-CH derivatives containing moderate degrees of substitution (DS = 20% and 40%) remained stable for weeks. Photomicroscopies also confirmed that rhodamine-labeled PC(40)CH derivative nanoparticles presented higher colloidal stability than those synthesized using deacetylated chitosan. Accordingly, due to their improved physicochemical properties these phosphorylcholine-modified chitosans provide new perspectives for controlling the properties of polyplexes. (C) 2009 Elsevier Inc. All rights reserved.

EXISTENCE RESULTS FOR ABSTRACT DEGENERATE NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract degenerate neutral functional differential equations. Some applications to partial differential equations are considered.