On the beam propagation through active media

An analytical iterative procedure has been established to determine the amplitude of a laser beam propagating through an active medium. The treatment is valid for both homogeneous and inhomogeneous broadening, and for arbitrary inhomogeneities of the parameters characterizing the active medium, namely, the refractive index, the small-signal gain and the saturation intensity. After a supplementary approximation, a thin-sheet gain approach is derived from the first iteration. The formalism enables us to provide analytical criteria for evaluating both the accuracy of each iteration and the propagation distances for which the thin-sheet solution can be used. This revised version was published online in November 2006 with corrections to the Cover Date.     

Highlights of 20?years of electrochemical measurements of exocytosis at cells and artificial cells

Advances in electrochemical methodology over the past 30?years have allowed chemical measurements to be made with decreasing amounts of analyte and at smaller spatial dimensions. This has allowed the investigation of single cells and single vesicles in cells either during release of chemical transmitter or separately. The cellular event called exocytosis can be measured with amperometry or cyclic voltammetry as discovered by Wightman and first published in 1990. In addition, the measurement of vesicle contents with electrochemistry is a new approach we have termed electrochemical cytometry. This involves isolation of intact vesicles, separation of the vesicles, and then lysing followed by coulometric analysis of the electroactive vesicle content. In this review, we will highlight work done by us and by others to discuss measurements of exocytosis at single cells and measurements at artificial cell models for studying the biophysical properties of vesicle membrane dynamics and lipid nanotubes connecting artificial cells using electrochemical methods.     

Greatly attenuated experimental autoimmune encephalomyelitis in aquaporin-4 knockout mice

Background  

The involvement of astrocyte water channel aquaporin-4 (AQP4) in autoimmune diseases of the central nervous system has been suggested following the identification of AQP4 autoantibodies in neuromyelitis optica, an inflammatory demyelinating disease.     

Spatial characterization of the transversal structure of rotationally symmetric pulsed beams

A simple analytical model is proposed to describe the transversal spatial structure of a tridimensional rotationally symmetric pulsed beam. The spatial behaviour of the pulse amplitude is shown to be linked to its (measurable) second- and higher-order intensity moments, namely, beam width, quality parameter and kurtosis. As an illustrative experimental example, this model has been applied to high-quality TEA CO2 laser pulses. This revised version was published online in November 2006 with corrections to the Cover Date.     

Differences Between Consecutive Primes

Let p_n be the nth prime. Then this paper is concerned with provingthe following result on the distribution of consecutive primes. The exponent of x in this theorem improves on the work of Heath-Brownwho proved (1) with exponent . Under the Riemann hypothesisone can prove (1) with exponent .The proof of the theorem startswith the Heath-Brown–Linnik identity which leads to aformula giving the number of primes in an interval in termsof coefficients of certain Dirichlet series. I then estimatethe coefficients by using, among other things, the informationwhich can be gained from Montgomery's mean value theorem andHuxley's version of the Hal' asz lemma. Furthermore, by usingfamiliar sieve arguments I am able to discard some of the coefficientsallowing us to gain an improvement over the previous resultof Heath-Brown. 1991 Mathematics Subject Classification: 11N05.     

Excited Fluorophores Enhance the Opening of Vesicles at Electrode Surfaces in Vesicle Electrochemical Cytometry

Electrochemical cytometry is a method developed recently to determine the content of an individual cell vesicle. The mechanism of vesicle rupture at the electrode surface involves the formation of a pore at the interface between a vesicle and the electrode through electroporation, which leads to the release and oxidation of the vesicle's chemical cargo. We have manipulated the membrane properties using excited fluorophores conjugated to lipids, which appears to make the membrane more susceptible to electroporation. We propose that by having excited fluorophores in close contact with the membrane, membrane lipids (and perhaps proteins) are oxidized upon production of reactive oxygen species, which then leads to changes in membrane properties and the formation of water defects. This is supported by experiments in which the fluorophores were placed on the lipid tail instead of the headgroup, which leads to a more rapid onset of vesicle opening. Additionally, application of DMSO to the vesicles, which increases the membrane area per lipid, and decreasing the membrane thickness result in the same enhancement in vesicle opening, which confirms the mechanism of vesicle opening with excited fluorophores in the membrane. Light‐induced manipulation of membrane vesicle pore opening might be an attractive means of controlling cell activity and exocytosis. Additionally, our data confirm that in experiments in which cells or vesicle membranes are labeled for fluorescence monitoring, the properties of the excited membrane change substantially.     

Positioning lipid membrane domains in giant vesicles by micro-organization of aqueous cytoplasm mimic

We report localization of lipid membrane microdomains to specific "poles" of asymmetric giant vesicles (GVs) in response to local internal composition. Interior aqueous microdomains were generated in a simple model cytoplasm composed of a poly(ethyleneglycol) (PEG)/dextran aqueous two-phase system (ATPS) encapsulated in the vesicles. The GV membrane composition used here was a modification of a DOPC/DPPC/cholesterol mixture known to form micrometer-scale liquid ordered and liquid disordered domains; we added lipids with PEG 2000 Da-modified headgroups. Osmotically induced budding of the ATPS-containing GVs led to structures where the PEG-rich and dextran-rich interior aqueous phases were in contact with different regions of the vesicle membrane. Liquid ordered (L o) membrane domains rich in PEG-terminated lipids preferentially coated the PEG-rich aqueous phase vesicle "body", while coexisting liquid disordered (L d) membrane domains coated the dextran-rich aqueous phase "bud". Membrane domain positioning resulted from interactions between lipid headgroups and the interior aqueous polymer solutions, e.g., PEGylated headgroups with PEG and dextran polymers. Heating resulted first in patchy membranes where L o and L d domains no longer showed any preference for coating the PEG-rich vs dextran-rich interior aqueous volumes, and eventually complete lipid mixing. Upon cooling lipid domains again coated their preferred interior aqueous microvolume. This work shows that nonspecific interactions between interior aqueous contents and the membrane that encapsulates them can drive local chemical heterogeneity, and offers a primitive experimental model for membrane and cytoplasmic polarity in biological cells.     

Quantum superarrivals and information transfer through a time-varying boundary

The time-dependent Schrödinger equation is solved numerically for the case of a Gaussian wave packet incident on a time-varying potential barrier. The time evolving reflection and transmission probabilities of the wave packet are computed for several different time-dependent boundary conditions obtained by reducing or increasing the height of the potential barrier. We show that in the case when the barrier height is reduced to zero, a time interval is found during which the reflection probability is larger (superarrivals) compared to the unperturbed case. We further show that the transmission probability exhibits superarrivals when the barrier is raised from zero to a finite value of its height. Superarrivals could be understood by ascribing the features of a real physical field to the Schrödinger wave function which acts as a carrier through which a disturbance, resulting from the boundary condition being perturbed, prpagates from the barrier to the detectors measuring reflected and transmitted probabilities. The speed of propagation of this effect depends upon the rate of reducing or raising the barrier height, thus suggesting an application for secure information transfer using superarrivals.     

Analytical tools to monitor exocytosis: a focus on new fluorescent probes and methods

A great deal of research has been focused on unraveling the processes governing the exocytotic pathway and the extent of release during the process. Arguments abound for and against both the occurrence and significance of full release during exocytosis and partial release including kiss-and-run events. Several optical methods to directly observe the exocytosis process have been developed and here we focus on fluorescence methods and probes for this work. Although fluorescence imaging has been used for cell experiments for decades, in the last two decades a plethora of new approaches have arrived on the scene. These include application of new microscopy techniques, like total internal reflectance and stimulated emission depletion that are offering new ways to circumvent the limits of far field microscopy with a diffraction limit of 200 nm, and allow tracking of single synaptic vesicles. For selective imaging of synaptic vesicles the introduction of methods to stain the vesicular compartment has involved developing probes of the vesicular membrane and intravesicular solution, nanoparticle quantum dots that can be observed during exocytosis but not via the fusion pore, and fluorescent false neurotransmitters.     

Cyclobutane-substituted diacetamido sulfides and 2,5-diacylthiophenes

A general and convenient route for the synthesis of 2,5-di[1-methyl-1-arylcyclobutane-3-yl]- thiophenes 4a–c and bis[1-methyl-1-arylcyclobutane-3-yl]-2-(2-oxyethtylamido)thiazole sulfides 7a–c is reported. The characterization of these compounds was obtained by elemental analyses, IR, ¹³C, and ¹H NMR techniques. © 2003 Wiley Periodicals, Inc. 15:26–31, 2004; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/.hc10207