Local Osmosis and Isotonic Transport

Osmotically driven water flow, u (cm/s), between two solutions of identical osmolarity, c_o (300 mM in mammals), has a theoretical isotonic maximum given by u = j/c_o, where j (moles/cm²/s) is the rate of salt transport. In many experimental studies, transport was found to be indistinguishable from isotonic. The purpose of this work is to investigate the conditions for u to approach isotonic. A necessary condition is that the membrane salt/water permeability ratio, ε, must be small: typical physiological values are ε = 10⁻³ to 10⁻⁵, so ε is generally small but this is not sufficient to guarantee near-isotonic transport. If we consider the simplest model of two series membranes, which secrete a tear or drop of sweat (i.e., there are no externally-imposed boundary conditions on the secretion), diffusion is negligible and the predicted osmolarities are: basal = c_o, intracellular ≈ (1 + ε)c_o, secretion ≈ (1 + 2ε)c_o, and u ≈ (1 − 2ε)j/c_o. Note that this model is also appropriate when the transported solution is experimentally collected. Thus, in the absence of external boundary conditions, transport is experimentally indistinguishable from isotonic. However, if external boundary conditions set salt concentrations to c_o on both sides of the epithelium, then fluid transport depends on distributed osmotic gradients in lateral spaces. If lateral spaces are too short and wide, diffusion dominates convection, reduces osmotic gradients and fluid flow is significantly less than isotonic. Moreover, because apical and basolateral membrane water fluxes are linked by the intracellular osmolarity, water flow is maximum when the total water permeability of basolateral membranes equals that of apical membranes. In the context of the renal proximal tubule, data suggest it is transporting at near optimal conditions. Nevertheless, typical physiological values suggest the newly filtered fluid is reabsorbed at a rate u ≈ 0.86 j/c_o, so a hypertonic solution is being reabsorbed. The osmolarity of the filtrate c_F (M) will therefore diminish with distance from the site of filtration (the glomerulus) until the solution being transported is isotonic with the filtrate, u = j/c_F.With this steady-state condition, the distributed model becomes approximately equivalent to two membranes in series. The osmolarities are now: c_F ≈ (1 − 2ε)j/c_o, intracellular ≈ (1 − ε)c_o, lateral spaces ≈ c_o, and u ≈(1 + 2ε)j/c_o. The change in c_F is predicted to occur with a length constant of about 0.3 cm. Thus, membrane transport tends to adjust transmembrane osmotic gradients toward εc_o, which induces water flow that is isotonic to within order ε. These findings provide a plausible hypothesis on how the proximal tubule or other epithelia appear to transport an isotonic solution.     

Exponential growth of “snow molds” at sub-zero temperatures: an explanation for high beneath-snow respiration rates and Q 10 values

Numerous studies have demonstrated exceptionally high temperature sensitivity of the beneath-snow respiratory flux in cold-winter ecosystems. The most common, but still untested, explanation for this high sensitivity is a physical one based on the observation that water availability in soils increases exponentially as soils warm from −3 to 0°C. Here, we present evidence for a biological hypothesis to explain exponential kinetics and high Q ₁₀ values as beneath-snow soils warm from −3 to 0°C during the early spring in a high-elevation subalpine forest. First, we show that some of the dominant organisms of the beneath-snow microbial community, “snow molds”, exhibit robust exponential growth at temperatures from −3 to −0.3°C. Second, Q ₁₀ values based on growth rates across the temperature range of −2 to −0.3°C for these snow molds vary from 22 to 330. Third, we derive an analytical equation that combines the relative contributions of microbial growth and microbial metabolism to the temperature sensitivity of respiration. Finally, we use this equation to show that with only moderate snow mold growth (several generations), the combined sensitivities of growth and metabolism to small changes in beneath-snow soil temperature, create a double exponential in the Q ₁₀ function that may explain the extremely high (~1 × 10⁶) Q ₁₀ values observed in past studies. Our biological explanation for high Q ₁₀ levels is supported by several independent studies that have demonstrated build up of microbial biomass under the snow as temperatures warm from −2 to 0°C.     

Mathematical biology of social behavior: III

A society composed of individuals each of whom can perform one of two mutually exclusive activitiesR ₁ andR ₂ is considered. The tendency toward the performance of those activities is measured by the intensities ε₁ and ε₂ of excitation of two corresponding neural centers, which cross-inhibit each other. It follows from the theory developed by H. D. Landahl that an individual with ε₁ − ε₂ = 0, that is one who has no preference for either one of the two activities, will on the average performR ₁ andR ₂ with equal probability. As ε₁ − ε₂ increases, the probabilityP ₁ ofR ₁ increases, tending to 1. As ε₂ − ε₁ increases, the probabilityP ₂ ofR ₂ increases, tending to 1. We haveP ₁+P ₂=1. The effect of imitation is now studied. The total number of individuals in the society which exhibits an activityR ₁ at a given time is considered as constituting a stimulus which increases ε₁. Similarly, the total number of individuals which exhibits activityR ₂ at a given time constitutes a stimulus which increases ε₂. Using the standard equations of the mathematical biophysics of the central nervous system, equations are established which govern the behavior of such a society and the following conclusions are reached. It the quantity ε₁ − ε₂ is distributed in the society in such a way that the distribution function is symmetric with respect to ε₁ − ε₂ = 0, then on the average one-half of the population exhibitsR ₁, the other halfR ₂. This social configuration may, however, be unstable. The slightest accidental excess of individuals exhibiting, for example,R ₁, may bring it into a stable configuration, in which most individuals exhibitR ₁, and only a smaller fraction exhibitR ₂. A slight initial deviation in favor ofR ₂ brings it into a stable configuration, in which most individuals exhibitR ₂. Thus in this case there may be two stable configurations. If the population is in one of those stable configurations, and the distribution function of ε₁ − ε₂ is made asymmetric, favoring the other activity, the population will pass into a stable configuration, in which that other activity is predominant, if the asymmetry of the distribution exceeds a threshold value. By making some drastic simplifications the equations derived here may be reduced to a form which waspostulated by the author previously in his mathematical theory of human relations.     

Boron nitride cages from B12N12 to B36N36: square–hexagon alternants vs boron nitride tubes

The structures and stabilities of square–hexagon alternant boron nitrides (B _x N _x , x=12–36) vs their tube isomers containing octagons, decagons and dodecagons have been computed at the B3LYP density functional level of theory with the correlation-consistent cc-pVDZ basis set of Dunning. It is found that octagonal B₂₀N₂₀ and B₂₄N₂₄ tube structures are more stable than their square–hexagon alternants by 18.6 and 2.4 kcal mol⁻¹, respectively, while the square–hexagon alternants of other cages are more stable. Trends in stability as a function of cluster size are discussed.Figure The octagonal B₂₀N₂₀ and B₂₄N₂₄ tube structures are more stable than their square-hexagon alternant cagesDedicated to Professor Dr. Paul von Ragué Schleyer on the occasion of his 75th birthday     

Apparent carboxylation efficiency and relative stomatal and mesophyll limitations of photosynthesis in an evergreen cerrado species during water stress

Miconia albicans, a common evergreen cerrado species, was studied under field conditions. Leaf gas exchange and pre-dawn leaf water potential (Ψ_pd) were determined during wet and dry seasons. The potential photosynthetic capacity (P _Npmax) and the apparent carboxylation efficiency (ε) dropped in the dry season to 28.0 and 0.7 %, respectively, of the maximum values in the wet season. The relative mesophyll (L_m) and stomatal (L_s) limitations of photosynthesis increased, respectively, from 24 and 44 % in the wet season to 79 and 57 % at the peak of the dry season when mean Ψ_pd reached −5.2 MPa. After first rains, the P _Npmax, ε, and L_m recovered reaching the wet season values, but L_s was maintained high (63 %). The shallow root system growing on stonemason limited by lateral concrete wall to a depth of 0.33 m explained why extreme Ψ_pd was brought about. Thus M. albicans is able to overcome quickly the strains imposed by severe water stress.     

Investigation of exchange couplings in [Fe3S4]+ clusters by electron spin-lattice relaxation

3 S₄]⁺, S=1/2, composed of three, antiferromagnetically coupled high-spin ferric ions) by continuous wave (CW) and pulsed EPR techniques: Azotobacter vinelandii ferredoxin I, Desulfovibrio gigas ferredoxin II, and the 3Fe forms of Pyrococcus furiosus ferredoxin and aconitase. The 35 GHz (Q-band) CW EPR signals are simulated to yield experimental g tensors, which either had not been reported, or had been reported only at X-band microwave frequency. Pulsed X- and Q-band EPR techniques are used to determine electron spin-lattice (T ₁, longitudinal) relaxation times at several positions on the samples' EPR envelope over the temperature range 2–4.2 K. The T ₁ values vary sharply across the EPR envelope, a reflection of the fact that the envelope results from a distribution in cluster properties, as seen earlier as a distribution in g ₃ values and in ⁵⁷ Fe hyperfine interactions, as detected by electron nuclear double resonance spectroscopy. The temperature dependence of 1/T ₁ is analyzed in terms of the Orbach mechanism, with relaxation dominated by resonant two-phonon transitions to a doublet excited state at ∼20 cm⁻¹ above the doublet ground state for all four of these 3Fe proteins. The experimental EPR data are combined with previously reported ⁵⁷Fe hyperfine data to determine electronic spin exchange-coupling within the clusters, following the model of Kent et al. Their model defines the coupling parameters as follows: J ₁₃=J, J ₁₂=J(1+ε′), J ₂₃=J(1+ε), where J _ij is the isotropic exchange coupling between ferric ions i and j, and ε and ε′ are measures of coupling inequivalence. We have extended their theory to include the effects of ε′≠0 and thus derived an exact expression for the energy of the doublet excited state for any ε, ε′. This excited state energy corresponds roughly to ε J and is in the range 5–10 cm⁻¹ for each of these four 3Fe proteins. This magnitude of the product ε J, determined by our time-domain relaxation studies in the temperature range 2–4 K, is the same as that obtained from three other distinct types of study: CW EPR studies of spin relaxation in the range 5.5–50 K, NMR studies in the range 293–303 K, and static susceptibility measurements in the range 1.8–200 K. We suggest that an apparent disagreement as to the individual values of J and ε be resolved in favor of the values obtained by susceptibility and NMR (J≳200 cm⁻¹ and ε≳0.02 cm⁻¹ ), as opposed to a smaller J and larger ε as suggested in CW EPR studies. However, we note that this resolution casts doubt on the accepted theoretical model for describing the distribution in magnetic properties of 3Fe clusters. Received: 23 December 1999 / Accepted: 8 March 2000     

High vapour pressure deficit exacerbates xylem cavitation and photoinhibition in shade-grown Piper auritum H.B. & K. during prolonged sunflecks

Water relations dynamics during simulated sunflecks at high (36°C) and medium (27°C) temperatures and high and low vapour pressure deficits beween leaf and air (VPD) were studied on shade-grown Piper auritum H.B. & K. plants, a pioneer tree, common in gaps and clearings of tropical rain forests. The leaves of P. auritum wilt rapidly when exposed to high light. Exposure to high VPD and high light caused substantial and rapid dehydration of leaves. Dehydration could be prevented under high humidity irrespective of temperature. Water stored in leaf cells served as initial source for transpiration upon high light exposure. This effect increased with increasing VPD and temperature. The pronounced decrease in leaf water content over time in high light caused a rapid decrease in leaf water potential (Ψ_l) and a concomitant increase in water potential gradient (ΔΨ/Δx) between trunk and leaf, yet the high leaf elasticity (small bulk elastic modulus, ε) allowed turgor maintenance under most conditions. Under high VPD and high temperature, stomata remained open and ΔΨ/Δx frequently exceeded 0.95 MPa · m⁻¹, the cavitation-inducing threshold (ΔΨ/Δx _cav) causing high rates of acoustic emissions from stems and leaf petioles and leading to concomitant losses in hydraulic conductance per leaf area (k _l). At medium temperature (high VPD), stomatal closure contained xylem embolism by keeping ΔΨ/Δx at or below this threshold. We argue that wilting substantially contributes to creating a sufficient driving force for water uptake from the soil, and reducing the VPD (through a decrease in radiation load and thus leaf temperature) to avoid excessive dehydration. Received: 3 March 1996 / Accepted: 10 November 1996     

Magnetic Surface Polariton in a Planar Biaxial Metamaterial with Dual Negative Magnetic Permeabilities

The magnetic surface polaritons (MSPs) mode rarely exists in natural materials, mainly due to their limited magnetic response. In order to understand the relationship between the MSPs mode and the limited magnetic response, we theoretically derive a general dispersion equation of the MSPs mode for two kinds of biaxial anisotropic media. The dispersion equation suggests the requirements of μ _x  < 0 < ε _z , μ _x μ _y  > 1, and momentum conservation need to be satisfied, which guides us to design a planar biaxial magnetic metamaterials (PBMM) with two orthogonal negative permeabilities (i.e., μ _x  < 0 and μ _y  < 0). In addition, the results of the retrieval magnetic permeability and electric permittivity indeed point out that our PBMM satisfies the aforementioned requirements. Meanwhile, we investigate the mechanism of the magnetic field by a consideration of an induced current loop, and subsequently we demonstrate the artificial MSPs mode under transverse electric excitation by numerical simulation. After a numerical fit of simulation results, we find that the field of the MSPs mode is in good agreement with the analytical calculation of Maxwell’s equations. Moreover, we also simulate three unsatisfied aforementioned requirements as control conditions to verify the general dispersion equation of the MSPs mode.     

Incorporating diffuse photosynthetically active radiation in a single-leaf model of canopy photosynthesis for a 56-year-old Douglas-fir forest

A simple top-down model of canopy photosynthesis (P) was developed and tested in this study. The model (referred to as the Q_e-MM model) is P = αQ _e P _max/(αQ _e + P _max), α and P _max are quantum-use efficiency and potential P, respectively. Q _e is given by Q _{d 0} + kQ _{b 0}, where Q _{d 0} and Q _{b 0} are the diffuse and direct photosynthetically active radiation (PAR) incident on the canopy, respectively. Q _e can be considered to be the effective incident PAR contributing to P and k is a measure of the contribution of Q _{b 0} to Q _e. When k = 1, the Q_e-MM model becomes the regular Michaelis-Menten type model of P (referred to as the MM model). A major objective of this study was to determine how well the Q_e-MM model could estimate P of a 56-year-old coastal Douglas-fir stand. To this end, we parameterized the Q_e-MM model using five and half years of eddy-covariance measurements of CO₂ flux above the Douglas-fir stand. The Q_e-MM model, with the incorporation of a function of air temperature, accounted for 74% of the variance in over 34,000 half-hourly P measurements. P estimated using the Q_e-MM model had no systematic errors with respect to Q _{d 0}. Although the Q_e-MM model has only one more parameter than the MM model, it accounted for 30% more variance in P than the latter when total incident PAR exceeded 900 μmol m⁻² s⁻¹. On average, k was found to be 0.22. We show that this small value of k reflects the significant effect of the scattering of the solar beam and the fraction of light-limited sunlit leaves. We also show that the success of the Q_e-MM model was due to the fact that a large fraction of the sunlit leaves were light-limited as a result of their orientation to the solar beam.     

Basis of the 1:1 stoichiometry of the high affinity receptor FcεRI-IgE complex

A soluble fragment of the high-affinity IgE receptor FcεRI α-chain (sFcεRIα) binds to the Fc fragment of IgE (IgE-Fc) as a 1:1 complex. IgE-Fc consists of a dimer of the Cε2, Cε3 and Cε4 domains of the ε-heavy chain of IgE. This region of IgE has been modelled on the crystal structure of the Fc region of IgG₁, which exhibits twofold rotational symmetry. This implies that IgE should be divalent with respect to its ligands. X-ray scattering studies reveal however that the twofold rotational symmetry of IgE-Fc is perturbed by a bend in the linker region between the Cε2 and Cε3 domains. The 1:1 stoichiometry could then arise from the conformational asymmetry or from steric occlusion of one of the sites by the overhanging Cε2 domains. To test this hypothesis we have expressed a recombinant ε-chain fragment containing Cε3 and Cε4. This product, Fcε3–4, is secreted from cells as a disulphide linked dimer and binds with higher affinity than either IgE or IgE-Fc to cell surface FcεRI. Titration experiments, together with molecular mass measurements of the Fcε3–4/sFcεRIα complex, reveal that Fcε3–4 binds only a single receptor molecule. This excludes the possibility that steric hindrance by Cε2 accounts for the unexpected stoichiometry. Received: 31 July 1996 / Accepted: 1 December 1996     

Water potential and gas exchange did not reflect performance of Pinus radiata D. Don in an agroforestry system under conditions of soil-water deficit in a temperate environment

In order to understand how radiata pines respond to declining supply of soil-water in agroforestry systems, we monitored water potential in xylem (ψ _x ), osmotic potential (ψ) and relative water content (q) for fascicles at pre-dawn and at mid-day for 3-year-old trees that were raised from either seedlings (Seedling) or from tissue culture (TC3 and TC4), and grown either alone (Control) or over lucerne (Medicago sativa) pasture (Lucerne). Water relations at dawn were mostly similar for all the pines, except late in the season when ψ was lower, bulk turgor pressure (P), deduced as the difference between ψ _x and ψ, was higher, for TC3 than for the other two pines. At mid-day, Seedling often had higher ψ _x and ψ, but because of its poor osmotic adjustment (OA) had lower P, than either TC3 or TC4. The cell walls were more elastic in Seedling with modulus of elasticity (e) of 6.5 MPa compared with 8.1 MPa for both TC3 and TC4, while loss of turgor was estimated to occur at ψ _x of −1.45 MPa for Seedling, −1.38 MPa for TC3 and −1.35 MPa for TC4. All trees irrespective of their origin had higher ψ _x , P, CO₂ assimilation (A), and stomatal conductance (g _s ), but lower ψ, in Control than in Lucerne in which the soil profile was consistently drier. The trends in ψ _x , ψ, q and A did not reflect the known differences in dry weight of trees, P was in the order TC3 > TC4 > Seedling, consistent with previously reported tree weights. Both TC3 and TC4 had higher P, due to their larger OA, than Seedling, although the latter had higher A. Thus ψ _x and A that are routinely measured may not always adequately explain differences in growth amongst pines; it is advisable that ψ be determined to allow deductions of P be made when using water relations to analyse plant growth.     

Variability in Light-Use Efficiency for Gross Primary Productivity on Great Plains Grasslands

Gross primary productivity (GPP) often is estimated at regional and global scales by multiplying the amount of photosynthetically active radiation (PAR) absorbed by the plant canopy (PARa) by light-use efficiency (ε _g ; GPP/PARa). Mass flux techniques are being used to calculate ε _g . Flux-based estimates of ε _g depend partly on how PAR absorption by plants is modeled as a function of leaf area index (LAI). We used CO₂ flux measurements from three native grasslands in the Great Plains of USA to determine how varying the value of the radiation extinction coefficient (k) that is used to calculate PARa from LAI affected variability in estimates of ε _g for each week. The slope of linear GPP–PARa regression, an index of ε _g , differed significantly among the 18 site-years of data, indicating that inter-annual differences in ε _g contributed to the overall variability in ε _g values. GPP–PARa slopes differed among years and sites regardless of whether k was assigned a fixed value or varied as an exponential function of LAI. Permitting k to change with LAI reduced overall variability in ε _g , reduced the slope of a negative linear regression between seasonal means of ε _g and potential evapotranspiration (PET), and clarified the contribution of inter-annual differences in precipitation to variation in ε _g . Our results imply that greater attention be given to defining dynamics of the k coefficient for ecosystems with low LAI and that PET and precipitation be used to constrain the ε _g values employed in light-use efficiency algorithms to calculate GPP for Great Plains grasslands.     

Highly polar environments catalyze the unfolding of PrPC helix 1

The first α-helix (H1) likely plays an important role in the conversion of the cellular prion protein (PrP^C) into its pathogenic isoform (PrP^Sc). In this conversion, H1 may either have to unfold or may represent a site of intermolecular contact. A recent molecular dynamics simulation suggested that H1 can unfold if it is detached from the protein core (Hirschberger et al. in Biophys J 90:3908, 2006). It has been hypothesized that the high dielectric constant ε _S of the bulk water environment facilitates the unfolding of H1. To check this hypothesis, we performed a number of replica exchange molecular dynamics simulations of an H1 peptide in solvents of different ε _S . We found that the equilibrium helix fraction in water is less than 40%, in agreement with previous experimental findings, and that the helix unfolds much faster in water than in less polar solvents. The kinetically stabilizing effect of the organic solvents is largely unspecific and correlates well with their dielectric constant ε _S .     

Temperature effect on maintenance and growth respiration coefficients of young, field-grown hinoki cypress (Chamaecyparis obtusa)

Respiration measurements were made on the entire aboveground parts of young, field-grown hinoki cypress (Chamaecyparis obtusa) trees at monthly intervals over a 5-year period, to examine the effect of temperature on maintenance and growth respiration coefficients. The respiration rate of the trees was grouped on a monthly basis and then partitioned into maintenance and growth components. The maintenance respiration coefficient increased exponentially with air temperature. The maintenance respiration coefficient at a temperature of 0°C and itsQ ₁₀ value were 0.205 mmol CO₂ g⁻¹ d.w. month⁻¹ and 1.81, respectively. The growth respiration coefficient, which was virtually independent of temperature, had a mean value of 38.06±1.95 (SE) mmol CO₂g⁻¹ d.w. The growth rate increased exponentially with increasing temperature up to a peak at around 18°C, and thereafter declined, thereby resulting in the growth respiration rate being increasingly less sensitive to increasing air temperature. The reported decreases in theQ ₁₀ value of total respiration with increasing air temperature is due to the way in which the growth component of respiration responds to temperature.     

A model of photosystem II for the analysis of fast fluorescence rise in plant leaves

The polyphasic patterns of fluorescence induction rise in pea leaves in vivo and after the treatment with ionophores have been studied using a Plant Efficiency Analyzer. To analyze in detail photosystem II (PS II) electron transfer processes, an extended PS II model was applied, which included the sums of exponential functions to specify explicitly the light-driven formation of the transmembrane electric potential (ΔΨ(t)) as well as pH in the lumen (pH_L(t)) and stroma (pH_S(t)). PS II model parameters and numerical coefficients in ΔΨ(t), pH_L(t), and pH_S(t) were evaluated to fit fluorescence induction data for different experimental conditions: leaf in vivo or after ionophore treatment at low or high light intensity. The model imitated changes in the pattern of fluorescence induction rise due to the elimination of transmembrane potential in the presence of ionophores, when ΔΨ = 0 and pH_L(t), pH_S(t) changed to small extent relative to control values in vivo, with maximum ΔΨ(t) ∼ 90 mV and ΔΨ(t) ∼ 40 mV for the stationary state at ΔpH ≅ 1.8. As the light intensity was increased from 300 to 1200 μmol m⁻² s⁻¹, the heat dissipation rate constants increased threefold for nonradiative recombination of P680⁺Phe⁻ and by ∼30% for P680⁺Q_A⁻. The parameters ΔΨ, pH_S and pH_L were analyzed as factors of PS II redox state populations and fluorescence yield. The kinetic mechanism of fluorescence quenching is discussed, which is related with light-induced lumen acidification, when ⁺Q_A⁻ and P680⁺ recombination probability increases to regulate the Q_A reduction.     

Theoretical studies on 2-diazo-4,6-dinitrophenol derivatives aimed at finding superior propellants

In an attempt to find superior propellants, 2-diazo-4,6-dinitrophenol (DDNP) and its –NO₂, –NH₂, –CN, –NC, –ONO₂, and –NF₂ derivatives were studied at the B3LYP/6-311++G^** level of density functional theory (DFT). Sensitivity was evaluated using bond dissociation enthalpies (BDEs) and molecular surface electrostatic potentials. The C–NO₂ bond appears to be the trigger bond during the thermolysis process for these compounds, except for the –ONO₂ and –NF₂ derivatives. Electrostatic potential results show that electron-withdrawing substituents make the charge imbalance more anomalous, which may change the strength of the bond, especially the weakest trigger bond. Most of the DDNP derivatives have the impact sensitivities that are higher than that of DDNP, making them favorable for use as solid propellants in micro-rockets. The theoretical densities (ρ), heats of formation (HOFs), detonation energies (Q), detonation pressures (P), and detonation velocities (D) of the compounds were estimated. The effects of various substituent groups on ρ, HOF, Q, D, and P were investigated. Some derivatives exhibit perfect detonation properties. The calculated relative specific impulses (I _r,sp) of all compounds except for –NH₂ derivatives were higher than that of DDNP, and also meet the requirements of propellants.     

Approximation of the Basic Reproduction Number <Emphasis Type="Italic">R</Emphasis><Subscript>0</Subscript> for Vector-Borne Diseases with a Periodic Vector Population

The main purpose of this paper is to give an approximate formula involving two terms for the basic reproduction number R ₀ of a vector-borne disease when the vector population has small seasonal fluctuations of the form p(t) = p ₀ (1+ε cos (ωt − φ)) with ε ≪ 1. The first term is similar to the case of a constant vector population p but with p replaced by the average vector population p ₀. The maximum correction due to the second term is (ε²/8)% and always tends to decrease R ₀. The basic reproduction number R ₀ is defined through the spectral radius of a linear integral operator. Four numerical methods for the computation of R ₀ are compared using as example a model for the 2005/2006 chikungunya epidemic in La Réunion. The approximate formula and the numerical methods can be used for many other epidemic models with seasonality. MSC 92D30 ⋅ 45C05 ⋅ 47A55     

Vapor Phase Deposition, Structure, and Plasmonic Properties of Polymer-Based Composites Containing Ag–Cu Bimetallic Nanoparticles

Nanocomposite (NC) thin films with noble metal nanoparticles embedded in a dielectric material show very attractive plasmonic properties due to dielectric and quantum confinement effects. For single component nanoparticles (NPs), the plasmon resonance frequency can only be tuned in a narrow range. Much interest aroused in bimetallic nanoparticles (BNPs), however many wet chemical approaches do not allow large variation of the NP alloy composition and filling factor. Here, we report a vapor phase co-deposition method to produce polymer–metal NCs with embedded Ag_1 − x Cu _x alloy particles. The method allows production of NPs with controlled alloy composition (x), metal filling (f) and nanostructure in a protecting Teflon AF matrix. The nanostructure size and shape were characterized by transmission electron microscope. Energy dispersive X-ray spectroscopy was used to determine x and f. The optical properties and the position of surface plasmon resonances were studied by UV–Vis spectroscopy. The plasmon resonances can be tuned over a large range of the visible spectrum associated with the change in x, f, and nanostructure. For low filling factors and small particle sizes, only one resonance peak was observed. This is attributed to enhanced miscibility at the nanoscale. Double plasmon resonances were seen for larger particle sizes in accord with phase separation expected from the bulk phase diagram and were explained in terms of the formation of core-shell structures with Cu core and Ag shell. Changes upon annealing at 200 °C are also reported.     

A note on abstract relational biologies

It is shown that the class of abstract block diagrams of (M, ℜ)-systems which can be constructed out of the objects and mappings of a particular subcategoryG ₀ of the categoryG of all sets depends heavily on the structure ofG ₀, and in particular on the number of sets of mappingsH(A, B) which are empty inG ₀. In the context ofG ₀-systems, there-fore, each particular categoryG ₀ gives rise to a different “abstract biology” in the sense of Rashevsky. A number of theorems illustrating the relation between the structure of a categoryG ₀ and the embeddability of an arbitrary mapping αεG ₀ into an (M, ℜ)-system are proved, and their biological implication is discussed. This research was supported by the United States Air Force through the Air Force Office of Scientific Reserch of the Air Research and Development Command, under Contract No. AF 49(638)-917.     

Characterization of excitation beam on second-harmonic generation in fibrillous type I collagen

Following our established theoretical model to deal with the second-harmonic generation (SHG) excited by a linearly polarized focused beam in type I collagen, in this paper, we further quantitatively characterize the differences between SHG emissions in type I collagen excited by collimated and focused beams. The effects of the linear polarization angle (α) and the fibril polarity characterized by the hyperpolarizability ratio ρ on SHG emission has been compared under collimated and focused beam excitation, respectively. In particular, SHG emission components along the i axis ( I_2w,i )\left( {I_{2\omega {,}i} } \right) (i = x,y,z), the induced SHG emission deviation angle γ _ij , and the detected SHG signals (I _2ω,ij ) in the ij plane by rotating the applied polarizer angle φ _ij have been investigated (i = x, x, y; j = y, z, z). Results show that under our simulation model, SHG emission in the xy plane, such as I _2ω,x ,I _2ω,y ,γ _xy and I _2ω,xy varying as polarization angle (α) under collimated and focused light, presents no significant difference. The reverse of the fibril polarity has induced great impact on I _2ω,x ,γ _xy and I _2ω,xy in both collimated and focused light. I _2ω,x and γ _xy show similarity, but I _2ω,xy at α = 30° demonstrates a slight difference in focused light to that in collimated light. Under focused light, the reverse of fibril polarity causes obvious changes of the collected SHG intensity I _2ω,xz and I _2ω,yz at a special polarization angle α = 60° and γ _xz , γ _yz along α.