Dissociation of HIV-1 from follicular dendritic cells during HAART: Mathematical analysis

Follicular dendritic cells (FDC) provide a reservoir for HIV type 1 (HIV-1) that may reignite infection if highly active antiretroviral therapy (HAART) is withdrawn before virus on FDC is cleared. To estimate the treatment time required to eliminate HIV-1 on FDC, we develop deterministic and stochastic models for the reversible binding of HIV-1 to FDC via ligand–receptor interactions and examine the consequences of reducing the virus available for binding to FDC. Analysis of these models shows that the rate at which HIV-1 dissociates from FDC during HAART is biphasic, with an initial period of rapid decay followed by a period of slower exponential decay. The speed of the slower second stage of dissociation and the treatment time required to eradicate the FDC reservoir of HIV-1 are insensitive to the number of virions bound and their degree of attachment to FDC before treatment. In contrast, the expected time required for dissociation of an individual virion from FDC varies sensitively with the number of ligands attached to the virion that are available to interact with receptors on FDC. Although most virions may dissociate from FDC on the time scale of days to weeks, virions coupled to a higher-than-average number of ligands may persist on FDC for years. This result suggests that HAART may not be able to clear all HIV-1 trapped on FDC and that, even if clearance is possible, years of treatment will be required.

Fluorescence correlation spectroscopy reveals fast optical excitation-driven intramolecular dynamics of yellow fluorescent proteins

Fast excitation-driven fluctuations in the fluorescence emission of yellow-shifted green fluorescent protein mutants T203Y and T203F, with S65G/S72A, are discovered in the 10−6–10−3-s time range, by using fluorescence correlation spectroscopy at 10−8 M. This intensity-dependent flickering is conspicuous at high pH, with rate constants independent of pH and viscosity with a minor temperature effect. The mean flicker rate increases linearly with excitation intensity for at least three decades, but the mean dark fraction of the molecules undergoing these dynamics is independent of illumination intensity over ≈6 × 102 to 5 × 106 W/cm2. These results suggest that optical excitation establishes an equilibration between two molecular states of different spectroscopic properties that are coupled only via the excited state as a gateway. This reversible excitation-driven transition has a quantum efficiency of ≈10−3. Dynamics of external protonation, reversibly quenching the fluorescence, are also observed at low pH in the 10- to 100-μs time range. The independence of these two bright–dark flicker processes implies the existence of at least two separate dark states of these green fluorescent protein mutants. Time-resolved fluorescence measurements reveal a single exponential decay of the excited state population with 3.8-ns lifetime, after 500-nm excitation, that is pH independent. Our fluorescence correlation spectroscopy results are discussed in terms of recent theoretical studies that invoke isomerization of the chromophore as a nonradiative channel of the excited state relaxation.

Polarity and permeation profiles in lipid membranes

The isotropic 14N-hyperfine coupling constant, a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\end{document}, of nitroxide spin labels is dependent on the local environmental polarity. The dependence of a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\end{document} in fluid phospholipid bilayer membranes on the C-atom position, n, of the nitroxide in the sn-2 chain of a spin-labeled diacyl glycerophospholipid therefore determines the transmembrane polarity profile. The polarity variation in phospholipid membranes, with and without equimolar cholesterol, is characterized by a sigmoidal, trough-like profile of the form {1 + exp [(n − no)/λ]}−1, where n = no is the point of maximum gradient, or polarity midpoint, beyond which the free energy of permeation decreases linearly with n, on a characteristic length-scale, λ. Integration over this profile yields a corresponding expression for the permeability barrier to polar solutes. For fluid membranes without cholesterol, no ≈ 8 and λ ≈ 0.5–1 CH2 units, and the permeability barrier introduces an additional diffusive resistance that is equivalent to increasing the effective membrane thickness by 35–80%, depending on the lipid. For membranes containing equimolar cholesterol, no ≈ 9–10, and the total change in polarity is greater than for membranes without cholesterol, increasing the permeability barrier by a factor of 2, whereas the decay length remains similar. The permeation of oxygen into fluid lipid membranes (determined by spin-label relaxation enhancements) displays a profile similar to that of the transmembrane polarity but of opposite sense. For fluid membranes without cholesterol no ≈ 8 and λ ≈ 1 CH2 units, also for oxygen. The permeation profile for polar paramagnetic ion complexes is closer to a single exponential decay, i.e., no lies outside the acyl-chain region of the membrane. These results are relevant not only to the permeation of water and polar solutes into membranes and their permeabilities, but also to depth determinations of site-specifically spin-labeled protein residues by using paramagnetic relaxation agents.

Computational mechanics of molecular systems:quantifying high-dimensional dynamics by distribution of Poincaré recurrence times

A framework that connects computational mechanics and molecular dynamics has been developed and described. As the key parts of the framework, the problem of symbolising molecular trajectory and the associated interrelation between microscopic phase space variables and macroscopic observables of the molecular system are considered. Following Shalizi and Moore, it is shown that causal states, the constituent parts of the main construct of computational mechanics, the e-machine, define areas of the phase space that are optimal in the sense of transferring information from the micro-variables to the macro-observables. We have demonstrated that, based on the decay of their Poincare´ return times, these areas can be divided into two classes that characterise the separation of the phase space into resonant and chaotic areas. The first class is characterised by predominantly short time returns, typical to quasi-periodic or periodic trajectories. This class includes a countable number of areas corresponding to resonances. The second class includes trajectories with chaotic behaviour characterised by the exponential decay of return times in accordance with the Poincare´ theorem.

Accurate WKB Approximation for a 1D Problem with Low Regularity

2000 Mathematics Subject Classification: 34L40, 65L10, 65Z05, 81Q20.

Molecular alignment relaxation in polymer optical fibers for sensing applications

A systematic study of annealing behavior of drawn PMMA fibers was performed. Annealing dynamics were investigated under different environmental conditions by fiber longitudinal shrinkage monitoring. The shrinkage process was found to follow a stretched exponential decay function revealing the heterogeneous nature of the underlying molecular dynamics. The complex dependence of the fiber shrinkage on initial degree of molecular alignment in the fiber, annealing time and temperature was investigated and interpreted. Moreover, humidity was shown to have a profound effect on the annealing process, which was not recognized previously. Annealing was also shown to have considerable effect on the fiber mechanical properties associated with the relaxation of molecular alignment in the fiber. The consequences of fiber annealing for the climatic stability of certain polymer optical fiber-based sensors are discussed, emphasizing the importance of fiber controlled pre-annealing with respect to the foreseeable operating conditions.

Quantitative and Qualitative Aspects of Dissolved Organic Carbon Leached from Senescent Plants in an Oligotrophic Wetland

We conducted a series of experiments whereby dissolved organic matter (DOM) was leached from various wetland and estuarine plants, namely sawgrass (Cladium jamaicense), spikerush (Eleocharis cellulosa), red mangrove (Rhizophora mangle), cattail (Typha domingensis), periphyton (dry and wet mat), and a seagrass (turtle grass; Thalassia testudinum). All are abundant in the Florida Coastal Everglades (FCE) except for cattail, but this species has a potential to proliferate in this environment. Senescent plant samples were immersed into ultrapure water with and without addition of 0.1% NaN3 (w/ and w/o NaN3, respectively) for 36 days. We replaced the water every 3 days. The amount of dissolved organic carbon (DOC), sugars, and phenols in the leachates were analyzed. The contribution of plant leachates to the ultrafiltered high molecular weight fraction of DOM (>1 kDa; UDOM) in natural waters in the FCE was also investigated. UDOM in plant leachates was obtained by tangential flow ultrafiltration and its carbon and phenolic compound compositions were analyzed using solid state 13C cross-polarization magic angle spinning nuclear magnetic resonance (13C CPMAS NMR) spectroscopy and thermochemolysis in the presence of tetramethylammonium hydroxide (TMAH thermochemolysis), respectively. The maximum yield of DOC leached from plants over the 36-day incubations ranged from 13.0 to 55.2 g C kg−1 dry weight. This amount was lower in w/o NaN3 treatments (more DOC was consumed by microbes than produced) except for periphyton. During the first 2 weeks of the 5 week incubation period, 60–85% of the total amount of DOC was leached, and exponential decay models fit the leaching rates except for periphyton w/o NaN3. Leached DOC (w/ NaN3) contained different concentrations of sugars and phenols depending on the plant types (1.09–7.22 and 0.38–12.4 g C kg−1 dry weight, respectively), and those biomolecules comprised 8–34% and 4–28% of the total DOC, respectively. This result shows that polyphenols that readily leach from senescent plants can be an important source of chromophoric DOM (CDOM) in wetland environments. The O-alkyl C was found to be the major C form (55±9%) of UDOM in plant leachates as determined by 13C CPMAS NMR. The relative abundance of alkyl C and carbonyl C was consistently lower in plant-leached UDOM than that in natural water UDOM in the FCE, which suggests that these constituents increase in relative abundance during diagenetic processing. TMAH thermochemolysis analysis revealed that the phenolic composition was different among the UDOM leached from different plants, and was expected to serve as a source indicator of UDOM in natural water. Polyphenols are, however, very reactive and photosensitive in aquatic environments, and thus may loose their plant-specific molecular characteristics shortly. Our study suggests that variations in vegetative cover across a wetland landscape will affect the quantity and quality of DOM leached into the water, and such differences in DOM characteristics may affect other biogeochemical processes.

La metrica di Agmon ed il decadimento esponenziale delle soluzioni di equazioni alle derivate parziali

The aim of this master thesis is to study the exponential decay of solutions of elliptic partial equations. This work is based on the results obtained by Agmon. To this purpose, first, we define the Agmon metric, that plays an important role in the study of exponential decay, because it is related to the rate of decay. Under some assumptions on the growth of the function and on the positivity of the quadratic form associated to the operator, a first result of exponential decay is presented. This result is then applied to show the exponential decay of eigenfunctions with eigenvalues whose real part lies below the bottom of the essential spectrum. Finally, three examples are given: the harmonic oscillator, the hydrogen atom and a Schrödinger operator with purely discrete spectrum.

New biomass derived carbon catalysts for biomass valorization

Due to diminishing petroleum reserves, unsteady market situation and the environmental concerns associated with utilization of fossil resources, the utilization of renewables for production of energy and chemicals (biorefining) has gained considerable attention. Biomass is the only sustainable source of organic compounds that has been proposed as petroleum equivalent for the production of fuels, chemicals and materials. In fact, it would not be wrong to say that the only viable answer to sustainably convene our future energy and material requirements remain with a bio-based economy with biomass based industries and products. This has prompted biomass valorization (biorefining) to become an important area of industrial research. While many disciplines of science are involved in the realization of this effort, catalysis and knowledge of chemical technology are considered to be particularly important to eventually render this dream to come true. Traditionally, the catalyst research for biomass conversion has been focused primarily on commercially available catalysts like zeolites, silica and various metals (Pt, Pd, Au, Ni) supported on zeolites, silica etc. Nevertheless, the main drawbacks of these catalysts are coupled with high material cost, low activity, limited reusability etc. – all facts that render them less attractive in industrial scale applications (poor activity for the price). Thus, there is a particular need to develop active, robust and cost efficient catalytic systems capable of converting complex biomass molecules. Saccharification, esterification, transesterification and acetylation are important chemical processes in the valorization chain of biomasses (and several biomass components) for production of platform chemicals, transportation fuels, food additives and materials. In the current work, various novel acidic carbons were synthesized from wastes generated from biodiesel and allied industries, and employed as catalysts in the aforementioned reactions. The structure and surface properties of the novel materials were investigated by XRD, XPS, elemental analysis, SEM, TEM, TPD and N2-physisorption techniques. The agro-industrial waste derived sulfonic acid functionalized novel carbons exhibit excellent catalytic activity in the aforementioned reactions and easily outperformed liquid H2SO4 and conventional solid acids (zeolites, ion-exchange resins etc). The experimental results indicated strong influence of catalyst pore-structure (pore size, pore-volume), concentration of –SO3H groups and surface properties in terms of the activity and selectivity of these catalysts. Here, a large pore catalyst with high –SO3H density exhibited the highest esterification and transesterification activity, and was successfully employed in biodiesel production from fatty acids and low grade acidic oils. Also, a catalyst decay model was proposed upon biodiesel production and could explain that the catalyst loses its activity mainly due to active site blocking by adsorption of impurities and by-products. The large pore sulfonated catalyst also exhibited good catalytic performance in the selective synthesis of triacetin via acetylation of glycerol with acetic anhydride and out-performed the best zeolite H-Y with respect to reusability. It also demonstrated equally good activity in acetylation of cellulose to soluble cellulose acetates, with the possibility to control cellulose acetate yield and quality (degree of substitution, DS) by a simple adjustment of reaction time and acetic anhydride concentration. In contrast, the small pore and highly functionalized catalysts obtained by hydrothermal method and from protein rich waste (Jatropha de-oiled waste cake, DOWC), were active and selective in the esterification of glycerol with fatty acids to monoglycerides and saccharification of cellulosic materials, respectively. The operational stability and reusability of the catalyst was found to depend on the stability of –SO3H function (leaching) as well as active site blocking due to adsorption of impurities during the reaction. Thus, our results corroborate the potential of DOWC derived sulfated mesoporous active carbons as efficient integrated solid acid catalysts for valorization of biomass to platform chemicals, biofuel, bio-additive, surfactants and celluloseesters.

Unravelling the nanostructure of strawberry fruit pectins by atomic force microscopy

Atomic force microscopy (AFM) allows the analysis of individual polymers at nanostructural level with a minimal sample preparation. This technique has been used to analyse the pectin disassembly process during the ripening and postharvest storage of several fleshy fruits. In general, pectins analysed by AFM are usually visualized as isolated chains, unbranched or with a low number of branchs and, occasionally, as large aggregates. However, the exact nature of these structures is unknown. It has been suggested that pectin aggregates represent a mixture of rhamnonogalacturonan I and homogalacturonan, while isolated chains and their branches are mainly composed by polygalacturonic acid. In order to gain insight into the nature of these structures, sodium carbonate soluble pectins from ripe strawberry (Fragaria x ananassa, Duch.) fruits were subjected to enzymatic digestion with endo-Polygalacturonase M2 from Aspergillus aculeatus, and the samples visualized by AFM at different time intervals. Pectins isolated from control, non-transformed plants, and two transgenic genotypes with low level of expression of ripening-induced pectinase genes encoding a polygalacturonase (APG) or a pectate lyase (APEL) were also included in this study. Before digestion, isolated pectin chains from control were shorter than those from transgenic fruits, showing number-average (LN) contour length values of 73.2 nm vs. 95.9 nm and 91.4 nm in APG and APEL, respectively. The percentage of branched polymers was significantly higher in APG polyuronides than in the remaining genotypes, 33% in APG vs. 6% in control and APEL. As a result of the endo-PG treatment, a gradual decrease in the main backbone length of isolated chains was observed in the three samples. The minimum LN value was reached after 8 h of digestion, being similar in the three genotypes, 22 nm. By contrast, the branches were not visible after 1.5-2 h of digestion. LN values were plotted against digestion time and the data fitted to a first-order exponential decay curve, obtaining R2 values higher than 0.9. The half digestion time calculated with these equations were similar for control and APG pectins, 1.7 h, but significantly higher in APEL, 2.5 h, indicating that these polymer chains were more resistant to endo-PG digestion. Regarding the pectin aggregates, their volumes were estimated and used to calculate LN molecular weights. Before digestion, control and APEL samples showed complexes of similar molecular weights, 1722 kDa, and slightly higher than those observed in APG samples. After endo-PG digestion, size of complexes diminished significantly, reaching similar values in the three pectin samples, around 650 kDa. These results suggest that isolated polymer chains visualized by AFM are formed by a HG domain linked to a shorter polymer resistant to endo-PG digestion, maybe xylogalacturonan or RG-I. The silencing of the pectate lyase gene slightly modified the structure and/or chemical composition of polymer chains making these polyuronides more resistant to enzymatic degradation. Similarly, polygalacturonic acid is one of the main component of the aggregates.

Search for the bb¯ decay of the Standard Model Higgs boson in associated (W/Z)H production with the ATLAS detector

A search for the bb¯ decay of the Standard Model Higgs boson is performed with the ATLAS experiment using the full dataset recorded at the LHC in Run 1. The integrated luminosities used from pp collisions at s√=7 and 8 TeV are 4.7 and 20.3 fb−1, respectively. The processes considered are associated (W/Z)H production, where W→eν/μν, Z→ee/μμ and Z→νν. The observed (expected) deviation from the background-only hypothesis corresponds to a significance of 1.4 (2.6) standard deviations and the ratio of the measured signal yield to the Standard Model expectation is found to be μ=0.52±0.32(stat.)±0.24(syst.) for a Higgs boson mass of 125.36 GeV. The analysis procedure is validated by a measurement of the yield of (W/Z)Z production with Z→bb¯ in the same final states as for the Higgs boson search, from which the ratio of the observed signal yield to the Standard Model expectation is found to be 0.74±0.09(stat.)±0.14(syst.).

Double-Exponential Model of a Photovoltaic Cell with Temperature Dependence

The purpose of the research is the creation of mathematical models in MATLAB based on the double exponential model of the photovoltaic cell. The developed model allows for different physical and environmental parameters. An equivalent circuit of the model includes a photocurrent source, two diodes, and a series and parallel resistance. The paper presents the simulation results for each parameter. The simulation data are displayed graphically and numerical results are saved in a file.

Model of single-electron decay from a strongly isolated quantum dot

Recent measurements of electron escape from a nonequilibrium charged quantum dot are interpreted within a two-dimensional (2D) separable model. The confining potential is derived from 3D self-consistent Poisson-Thomas-Fermi calculations. It is found that the sequence of decay lifetimes provides a sensitive test of the confining potential and its dependence on electron occupation

Model of single-electron decay from a strongly isolated quantum dot

Recent measurements of electron escape from a nonequilibrium charged quantum dot are interpreted within a two-dimensional (2D) separable model. The confining potential is derived from 3D self-consistent Poisson-Thomas-Fermi calculations. It is found that the sequence of decay lifetimes provides a sensitive test of the confining potential and its dependence on electron occupation