Monotonicity of zeros of Jacobi polynomials

Denote by x(nk)(alpha, beta), k = 1...., n, the zeros of the Jacobi polynornial P-n((alpha,beta)) (x). It is well known that x(nk)(alpha, beta) are increasing functions of beta and decreasing functions of alpha. In this paper we investigate the question of how fast the functions 1 - x(nk)(alpha, beta) decrease as beta increases. We prove that the products t(nk)(alpha, beta) := f(n)(alpha, beta) (1 - x(nk)(alpha, beta), where f(n)(alpha, beta) = 2n(2) + 2n(alpha + beta + 1) + (alpha + 1)(beta + 1) are already increasing functions of beta and that, for any fixed alpha > - 1, f(n)(alpha, beta) is the asymptotically extremal, with respect to n, function of beta that forces the products t(nk)(alpha, beta) to increase. (c) 2007 Elsevier B.V. All rights reserved.

Almost strict total positivity and a class of Hurwitz polynomials

We establish sufficient conditions for a matrix to be almost totally positive, thus extending a result of Craven and Csordas who proved that the corresponding conditions guarantee that a matrix is strictly totally positive. Then we apply our main result in order to obtain a new criteria for a real algebraic polynomial to be a Hurwitz one. The properties of the corresponding extremal Hurwitz polynomials are discussed. (C) 2004 Elsevier B.V. All rights reserved.

On the behaviour of zeros of Jacobi polynomials

Denote by x(n,k)(alpha, beta) and x(n,k) (lambda) = x(n,k) (lambda - 1/2, lambda - 1/2) the zeros, in decreasing order, of the Jacobi polynomial P-n((alpha, beta))(x) and of the ultraspherical (Gegenbauer) polynomial C-n(lambda)(x), respectively. The monotonicity of x(n,k)(alpha, beta) as functions of a and beta, alpha, beta > - 1, is investigated. Necessary conditions such that the zeros of P-n((a, b)) (x) are smaller (greater) than the zeros of P-n((alpha, beta))(x) are provided. A. Markov proved that x(n,k) (a, b) < x(n,k)(α, β) (x(n,k)(a, b) > x(n,k)(alpha, beta)) for every n is an element of N and each k, 1 less than or equal to k less than or equal to n if a > alpha and b < β (a < alpha and b > beta). We prove the converse statement of Markov's theorem. The question of how large the function could be such that the products f(n)(lambda) x(n,k)(lambda), k = 1,..., [n/2] are increasing functions of lambda, for lambda > - 1/2, is also discussed. Elbert and Siafarikas proved that f(n)(lambda) = (lambda + (2n(2) + 1)/ (4n + 2))(1/2) obeys this property. We establish the sharpness of their result. (C) 2002 Elsevier B.V. (USA).

Characterization of generalized Bessel polynomials in terms of polynomial inequalities

Generalized Bessel polynomials (GBPs) are characterized as the extremal polynomials in certain inequalities in L-2 norm of Markov type. (C) 1998 Academic Press.

Monotonicity of zeros of Laguerre-Sobolev-type orthogonal polynomials

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Sharp bounds for the extreme zeros of classical orthogonal polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Updated Brazilian database on food carotenoids: Factors affecting carotenoid composition

This article updates the Brazilian database on food carotenoids. Emphasis is on carotenoids that have been demonstrated important to human health: alpha-carotene, beta-carotene, beta-cryptoxanthin, lycopene, lutein and zeaxanthin. The sampling and sample preparation strategies and the analytical methodology are presented. Possible sources of analytical errors, as well as the measures taken to avoid them, are discussed. Compositional variation due to such factors as variety/cultivar, stage of maturity, part of the plant utilized, climate or season and production technique are demonstrated. The effects of post-harvest handling, preparation, processing and storage of food on the carotenoid composition are also discussed. The importance of biodiversity is manifested by the variety of carotenoid sources and the higher levels of carotenoids in native, uncultivated or semi-cultivated fruits and vegetables in comparison to commercially produced crops. (C) 2008 Elsevier B.V. All rights reserved.

Total and individual carotenoid profiles in Solanum phureja of cultivated potatoes: I. Concentrations and relationships as determined by spectrophotometry and HPLC

Total and individual carotenoid concentrations were determined by spectro photometry and HPLC, in raw tubers of a sample of 23 accessions of Solanum phureja potatoes taken at random from the world germplasm collection following its stratification on tuber flesh color. Lutein, zeaxanthin, violaxanthin, antheraxanthin and beta-carotene were detected in all accessions and three distinct patterns of carotenoid accumulation were evidenced by cluster analysis. Accessions in group 1 showed the highest concentrations of total carotenoids (1258-1840 mu g 100 g(-1) FW) comprised largely of zeaxanthin (658-1290 mu g 100 g(-1) FW) with very low or no presence of beta-carotene (below 5.4 mu g 100 g(-1) FW). Accessions in group 2 presented moderate total carotenoid concentrations with violaxanthin, antheraxanthin, lutein and zeaxanthin as the major carotenoids. Accessions in group 3 showed low concentrations of total carotenoids (97-262 mu g 100 g(-1) FW) and very low or no zeaxanthin, with lutein and violaxanthin as the predominant carotenoids and relatively high concentrations of beta-carotene(up to 27 mu g 100 g(-1) FW). Five accessions with significant concentrations of zeaxanthin were identified with the accession 703566 showing the highest concentration (1290 p g 100 g(-1) FW). This value is to our knowledge higher than any value previously reported for potatoes, including those achieved through genetic modification. For the 23 S. phureja accessions, total carotenoid concentration was positively and significantly correlated with antheraxanthin and zeaxanthin concentrations, and negatively and significantly correlated with beta-carotene concentration. (C) 2008 Elsevier B.V. All rights reserved.

Refolding and purification of bothropstoxin-1, a Lys49 - Phospholipase A(2) homologue, expressed as inclusion bodies in Escherichia coli

Hydrolysis of phospholipids by Group II phospholipase A(2) enzymes involves a nucleophilic attack on the sn-2 ester bond by the His48 residue and stabilization of the reaction intermediate by a Ca2+ ion cofactor bound to the Asp49 residue in the protein active site region, Bothropstoxin-I (BthTX-I) is a PLA, variant present in the venom of the snake Bothrops jararacussu which shows a Asp49 to Lys substitution and which lacks hydrolytic activity yet damages artificial membranes by a noncatalytic Ca2+-independent mechanism. In order to better characterize this unusual mechanism of membrane damage, we have established an expression system for BthTX-I in Escherichia coli. The DNA-coding sequence for BthTX-I was subcloned into the vector pET11-d, and the BthTX-I was expressed as inclusion bodies in E, coli BL21(DE3). The native BthTX-I contains seven disulfide bonds, and a straightforward protocol has been developed to refold the recombinant protein at high protein concentration in the presence of surfactants using a size-exclusion chromatography matrix. After refolding, recovery yields of 2.5% (corresponding to 4-5 mg of refolded recombinant BthTX-I per liter of bacterial culture) were routinely obtained. After refolding, identical fluorescent and circular dichroism spectra were obtained for the recombinant BthTX-I compared to those of the native protein. Furthermore, the native and refolded recombinant protein demonstrated identical membrane-damaging properties as evaluated by measuring the release of an entrapped fluorescent marker from liposomes, (C) 2001 Academic Press.

Tertiary structural changes of the alpha-hemolysin from Staphylococcus aureus on association with liposome membranes

The interaction of alpha-hemolysin (also called alpha-toxin) from Staphylococcus aureus with mixed egg-yolk phosphatidylcholine/cholesterol liposomes has been investigated using the intrinsic tryptophan fluorescence emission (ITFE) signal. The ITFE intensity of alpha-hemolysin, which was obtained using a novel purification protocol, showed a triphasic increase on incubation with liposomes at low protein/lipid ratios. The first, rapid phase results in an increase in ITFE of 10%, which reflects rapid conformation changes in the alpha-hemolysin on association with the liposome membrane, the second phase of the ITFE increase is associated with a red shift from 334 to 339 nm in the maximum emission wavelength, suggesting the transition to a partially unfolded intermediate in the oligomerization process. The third phase of the ITFE intensity change demonstrates a temporal correlation with the appearance of SDS-stable oligomers. The results demonstrate the feasibility of identification of intermediate protein conformations in complex membrane-associated processes by manipulation of the liposomal membrane composition. (C) 1998 Academic Press.

Crystal structure of the platelet activator convulxin, a disulfide-linked alpha(4)beta(4) cyclic tetramer from the venom of Crotalus durissus terrificus

Convulxin (CVX), a C-type lectin, isolated from the venom of the South American rattlesnake Crotalus durissus terrificus, causes cardiovascular and respiratory disturbances and is a potent platelet activator which hinds to platelet glycoprotein GPVI. The structure of CVX has been solved at 2.4 Angstrom resolution to a crystallographic residual of 18.6% (R-free =26.4%). CVX is a disulfide linked heterodimer consisting of homologous alpha and beta chains. The heterodimers are additionally linked by disulfide bridges to form cyclic alpha(4)beta(4)heterotetramers. These domains exhibit significant homology to the carbohydrate-binding domains of C-type lectins, to the factor IX-binding protein (IX-bp), and to flavocetin-A (Fl-A) but sequence and Structural differences are observed in both the domains in the putative Ca2+ and carbohydrate binding regions. (C) 2003 Elsevier B.V. All rights reserved.

Activation of Ca2+-independent membrane-damaging activity in Lys49-phospholipase A(2) promoted by amphiphilic molecules

Association of class-II phospholipase A(2) (PLA(2)) with aggregated phospholipid substrate results in elevated levels of the Ca2+-dependent hydrolytic activity. The Asp49 residue participates in coordination of the Ca2+ ion cofactor, however, in Lys49-PLA(2) homologues (Lys49-PLA(2)S), substitution of the Asp49 by Lys results in loss of Ca2+ binding and lack of detectable phospholipid hydrolysis. Nevertheless, Lys49-PLA2S cause Ca2+-independent damage of liposome membranes. Bothropstoxin-I is a homodimeric Lys49-PLA(2) from the venom of Bothrops jararacussu, and in fluorescent marker release and dynamic light scattering experiments with DPPC liposomes we demonstrate activation of the Ca2+-independent membrane damaging activity by similar to4 molecules of sodium dodecyl sulphate (SDS) per protein monomer. Activation is accomparlied by significant changes in the intrinsic tryptophan fluorescence emission (ITFE) and near UV circular dichroism (UVCD) spectra of the protein. Subsequent binding of 7-10 SDS molecules results in further alterations in the ITFE and far UVCD spectra. Reduction in the rate of N-bromosuccinimide modification of Trp77 at the dimer interface suggests that initial binding of SDS to this region accompanies the activation of the membrane damaging activity. 1-anilinonaphthalene-8-sulphonic acid binding studies indicate that subsequent SDS binding to the active site is concomitant with the second structural transition. These results provide insights in the structural basis of amphiphile/protein coupling in class-II PLA(2)s. (C) 2004 Published by Elsevier B.V.

Structural insights into the catalytic mechanism of sphingomyelinases D and evolutionary relationship to glycerophosphodiester phosphodiesterases

Spider venom sphingomyelinases D catalyze the hydrolysis of sphingomyelin via an Mg2+ ion-dependent acid-base catalytic mechanism which involves two histidines. In the crystal structure of the sulfate free enzyme determined at 1.85 angstrom resolution, the metal ion is tetrahedrally coordinated instead of the trigonal-bipyramidal coordination observed in the sulfate bound form. The observed hyperpolarized state of His47 requires a revision of the previously suggested catalytic mechanism. Molecular modeling indicates that the fundamental structural features important for catalysis are fully conserved in both classes of SMases D and that the Class II SMases D contain an additional intra-chain disulphide bridge (Cys53-Cys201). Structural analysis suggests that the highly homologous enzyme from Loxosceles bonetti is unable to hydrolyze sphingomyelin due to the 95G1y -> Asn and 134Pro -> Glu mutations that modify the local charge and hydrophobicity of the interfacial face. Structural and sequence comparisons confirm the evolutionary relationship between sphingomyelinases D and the glicerophosphodiester phosphoesterases which utilize a similar catalytic mechanism. (c) 2006 Elsevier B.V. All rights reserved.

An ultraviolet photoacoustic spectroscopy study of the interaction between Lys49-phospholipase A(2) and amphiphilic molecules

We have used near ultraviolet photoacoustic spectroscopy (PAS) over the wavelength range 240-320 nm to investigate the complex formed between the homodimeric bothropstoxin-I, a lysine-49-phospholipase A(2) from the venom of Bothrops jararacussu (BthTx-I), with the anionic amphiphile sodium dodecyl sulfate (SDS). At molar ratios > 10, the complex developed a significant light scatter, accompanied by a decrease in the intrinsic tryptophan fluorescence intensity emission (ITFE) of the protein, and an increase in the near UV-PAS signal. Difference PAS spectroscopy at SDS/BthTx-I ratios < 8 were limited to the region 280-290 nm, suggesting initial SDS binding to the tryptophan 77 located at the dimer interface. At SDS/BthTx-I ratios > 10, the intensity between 260 and 320 nm increases demonstrating that the more widespread tyrosine and phenylalanine residues contribute to the SDS/BthTx-I interaction. PAS signal phase changes at wavelengths specific for each aromatic residue suggest that the Trp77 becomes more buried on SDS binding, and that protein structural changes and dehydration may alter the microenvironments of Tyr and Phe residues. These results demonstrate the potential of near UV-PAS for the investigation of membrane proteins/detergent complexes in which light scatter is significant. (c) 2006 Elsevier B.V. All rights reserved.