The postage stamp problem and arithmetic in base <Emphasis Type="Italic">r</Emphasis>

Let h, k be fixed positive integers, and let A be any set of positive integers. Let hA ≔ {a ₁ + a ₂ + ... + a _r : a _i ∈ A, r ⩽ h} denote the set of all integers representable as a sum of no more than h elements of A, and let n(h, A) denote the largest integer n such that {1, 2,...,n} ⊆ hA. Let n(h, k) := : n(h, A), where the maximum is taken over all sets A with k elements. We determine n(h, A) when the elements of A are in geometric progression. In particular, this results in the evaluation of n(h, 2) and yields surprisingly sharp lower bounds for n(h, k), particularly for k = 3.     

Energy transfer between Er3+:Sm3+codoped TeO2-Li2O glass

The energy transfer in Er3+: Sm3+ codoped binary TeO2-Li2O (TLO) glass has been studied using 532 nm laser radiation on the basis of fluorescence intensity and the lifetime measurements. It is observed that the trace of erbium ion can be utilized to sensitize the samarium. The mechanism involved in the present case is found to be dipole-dipole. The energy transfer efficiencies, probabilities of energy transfer and the average donor acceptor distance has been evaluated.     

Effect of pyridine on infrared absorption spectra of copper phthalocyanine

Infrared absorption spectra of copper phthalocyanine in KBr pellet and pyridine solution in 400-1625 and 2900-3200 cm(-1)regions are reported. In the IR spectra of solid sample, presence of weak bands, which are forbidden according to the selection rules of D4h point group, is explained on the basis of distortion in the copper phthalocyanine molecule caused by the crystal packing effects. Observation of a new band at 1511 cm(-1) and change in intensity of some other bands in pyridine are interpreted on the basis of coordination of the solvent molecule with the central copper ion.     

Halogen-containing tetrametallic aluminium alkoxides

New halogen-containing tetrametallic aluminium alkoxides of formula [Al{(mu-OEt)2AlMeCl}3] ( 2-cis; 2-trans), and [Al{(mu-OEt)2AlBr2}3] ( 4), have been synthesized by combining Al(OEt)3 and Me2AlCl (for 2) or EtAlBr2 (for 4). They were fully characterized by (1H, 27Al) NMR, IR, mp, elemental analysis, and single-crystal X-ray diffractometry. The chloride analogue of 4, [Al{(mu-OEt)2AlCl2}3] ( 3), prepared previously using a different route, was also prepared here by combining Al(OEt)3 and EtAlCl2.     

Monitoring orientation and dynamics of membrane-bound melittin utilizing dansyl fluorescence

Melittin is a cationic hemolytic peptide isolated from the European honey bee, Apis mellifera. In spite of a number of studies, there is no consensus regarding the orientation of melittin in membranes. In this study, we used a melittin analogue that is covalently labeled at its amino terminal (Gly-1) with the environment-sensitive 1-dimethylamino-5-sulfonylnaphthalene (dansyl) group to obtain information regarding the orientation and dynamics of the amino terminal region of membrane-bound melittin. Our results show that the dansyl group in Dns-melittin exhibits red edge excitation shift in vesicles of 1,2-dioleoyl-sn-glycero-3-phosphocholine, implying its localization in a motionally restricted region of the membrane. This is further supported by wavelength-dependent anisotropy and lifetime changes and time-resolved emission spectra characterized by dynamic Stokes shift, which indicates relatively slow solvent relaxation in the excited state. Membrane penetration depth analysis using the parallax method shows that the dansyl group is localized at a depth of approximately 18 A from the center of the bilayer in membrane-bound Dns-melittin. Further analysis of dansyl and tryptophan depths in Dns-melittin shows that the tilt angle between the helix axis of membrane-bound melittin and the bilayer normal is approximately 70 degrees. Our results therefore suggest that melittin adopts a pseudoparallel orientation in DOPC membranes at low concentration.     

Electrophoretic migration of proteins in semidilute polymer solutions

We present a systematic study of the electrophoretic migration of 10-200 kDa protein fragments in dilute-polymer solutions using microfluidic chips. The electrophoretic mobility and dispersion of protein samples were measured in a series of monodisperse polydimethylacrylamide (PDMA) polymers of different molecular masses (243, 443, and 764 kDa, polydispersivity index <2) of varying concentration. The polymer solutions were characterized using rheometry. Prior to loading onto the microchip, the polymer solution was mixed with known concentrations of SDS (SDS) surfactant and a staining dye. SDS-denatured protein samples were electrokinetically injected, separated, and detected in the microchip using electric fields ranging from 100 to 300 V/cm. Our results show that the electrophoretic mobility of protein fragments decreases exponentially with the concentration c of the polymer solution. The mobility was found to decrease logarithmically with the molecular weight of the protein fragment. In addition, the mobility was found to be independent of the electric field in the separation channel. The dispersion is relatively independent of polymer concentration and it first increases with protein size and then decreases with a maximum at about 45 kDa. The resolution power of the device decreases with concentration of the PDMA solution but it is always better than 10% of the protein size. The protein migration does not seem to correspond to the Ogston or the reptation models. A semiempirical expression for mobility given by van Winkle fits the data very well.     

High-performance liquid chromatography and LC-ESI-MS method for the identification and quantification of two biologically active isomeric coumarinolignoids cleomiscosin A and cleomiscosin B in different extracts of Cleome viscosa

A rapid, sensitive and simple reverse-phase high-performance liquid chromatographic-electrospray ionization-mass spectrometry method for simultaneous determination of cleomiscosin A and cleomiscosin B has been developed and validated. The isomeric coumarinolignoids cleomiscosin A (1) and cleomiscosin B (2) were separated on a Waters symmetry C(18) column with a solvent system composed of acetonitrile-methanol (1:2) and acetic acid-water (0.5:99.5) in a gradient elution mode. The absorption at 326 nm was chosen as the measuring wavelength in which resolution and baseline separation of compounds 1 and 2 could be obtained. The identity of the two isomeric compounds 1 and 2 in the samples were determined on a triple quadrupole mass spectrometer with ESI interface operating in the positive mode. Calibration curves were linear (r(2) > 0.993) over the concentration range 20-200 microg/mL for cleomiscosin A and 10-200 microg/mL for cleomiscosin B with acceptable accuracy and precision, respectively. The intra-day and inter-day precision were 1.13 and 0.82% for cleomiscosin A and 1.78 and 1.28% for cleomiscosin B, respectively. The validated method was successfully applied for the analysis of the above two compounds in different extracts of Cleome viscosa.     

Micellar shape transition under dilute salt-free conditions: promotion and self-fluorescence monitoring of stimuli-responsive viscoelasticity by 1- and 2-naphthols

Effect of 1 and 2-naphthols on the shape transition of cetyl trimethylammonium bromide (CTAB) and cetylpyridinium bromide (CPB) micelles are studied. Stimuli-responsive viscoelastic gels of long wormlike micelles are formed at low surfactant concentrations in the presence of neutral naphthols, where H-bonding plays a key role in micellar shape transition in the absence of any charge screening. Micelle-embedded naphthols also act as novel self-fluorescence probes for monitoring viscoelasticity of the system as a function of applied shear. 1H NMR study shows that the solubilization sites of naphthols in the micelle are located near the surface. While UV absorption and Fourier transform infrared studies confirm the presence of intermolecular H-bonds in micelle embedded naphthols, transmission electron micrographs of vacuum-dried samples at room temperature demonstrate the transition in shape from sphere to rodlike micelles.     

Exploring the organization and dynamics of hippocampal membranes utilizing pyrene fluorescence

The organization and dynamics of cellular membranes in the nervous system are crucial for the function of neuronal membrane receptors and signal transduction. Previous work from our laboratory has established hippocampal membranes as a convenient natural source for studying neuronal receptors. In this paper, we have monitored the organization and dynamics of hippocampal membranes and their modulation by cholesterol using pyrene fluorescence. The apparent dielectric constant experienced by pyrene in hippocampal membranes turns out to be approximately 20+/-3, depending on the experimental condition. Our results show that the polarity of the hippocampal membrane is increased upon cholesterol depletion, as monitored by changes in the ratio of pyrene vibronic peak intensities (I1/I3). This is accompanied by an increase in lateral diffusion, measured as an increase in the pyrene excimer/monomer ratio. These results are relevant in understanding the complex organization and dynamics of hippocampal membranes and could have implications in neuronal diseases characterized by defective cholesterol metabolism.     

Nanoneedle method for high-sensitivity low-background monitoring of protein activity

We describe a new method for measuring the activity of protein in miniscule quantities using a carbon nanotube nanoneedle. The unique features of this new method are (a) the immobilization of a few molecules; (b) subsequent translocation and isolation of them near the tip of a position-actuated nanoneedle; and (c) a fixed, defined, and unhindered molecular position to allow rapid real-time sensing and monitoring. The kinetic bioactivity of immobilized alkaline phosphatase (AP) molecules was measured as test model. Results show no decrease in enzymatic activity compared to that of the solution-phase enzyme reaction, suggesting that the immobilization provided unhindered access for ligand binding and minimal conformational modulation caused by undesired surface interactions.