A graph-theoretic method for the basic reproduction number in continuous time epidemiological models

In epidemiological models of infectious diseases the basic reproduction number is used as a threshold parameter to determine the threshold between disease extinction and outbreak. A graph-theoretic form of Gaussian elimination using digraph reduction is derived and an algorithm given for calculating the basic reproduction number in continuous time epidemiological models. Examples illustrate how this method can be applied to compartmental models of infectious diseases modelled by a system of ordinary differential equations. We also show with these examples how lower bounds for can be obtained from the digraphs in the reduction process.     

Effects of common soil anions and pH on the uptake and accumulation of perchlorate in lettuce

A mechanistic understanding of perchlorate () entry into plants is important for establishing the human health risk associated with consumption of contaminated produce and for assessing the effectiveness of phytoremediation. To determine whether common soil anions affect uptake and accumulation in higher plants, a series of competition experiments using lettuce (Lactuca sativa L.) were conducted between (50 nM) and (4–12 mM), (1–10 mM), or Cl⁻ (5–15 mM) in hydroponic solution. The effects of (0–5 mM) and pH (5.5–7.5) on uptake were also examined. Increasing in solution significantly reduced the amount of taken up by green leaf, butter head, and crisphead lettuces. Sulfate and Cl⁻ had no significant effects on uptake in lettuce over the concentrations tested. Increasing pH significantly reduced the amount of taken up by crisphead and green leaf lettuces, whereas increasing significantly reduced uptake in butter head lettuce. The inhibition by across all lettuce genotypes suggests that may share an ion carrier with , and the decrease in uptake with increasing pH or provides macroscopic evidence for cotransport across the plasma membrane.     

Photosynthetic limitation by CO<Subscript>2</Subscript> diffusion in drought stressed orange leaves on three rootstocks

Photosynthetic limitations under moderate water deficit were evaluated in ‘Valência’ orange trees grafted on three different rootstocks, in pots. Net CO₂ assimilation rate (A _N), stomatal conductance (g _s), and photosystem II (PS II) operating efficiency ( ) in response to changing intercellular CO₂ partial pressure (C _i) were analyzed under controlled conditions. Drought decreased A _N and g _s, whereas remained unchanged. This resulted in a higher ratio between electron transport rate (ETR) and gross CO₂ assimilation rate (A _G). Since the comparison of A _N–C _i gas exchange curves can lead to incorrect conclusions, a normalization of C _i values () of stressed leaves was applied. Then, the relationship established for irrigated trees between the ETR/A _G ratio and C _i was used to estimate the from ETR/A _G ratios measured under water stress. The response of A _N to suggests that the CO₂ diffusional restriction is the main factor that limits photosynthesis in orange leaves under moderate water deficit.     

Use of isotopic signatures to assess the food web in a tropical shallow marine ecosystem of Southeastern Brazil

A dual isotope approach was used to assess the relative importance of terrestrial vegetation detritus and other primary producers in the trophic web of Flamengo Sound (Ubatuba, SP), SE Brazil, surrounded by the Atlantic Rain Forest. Primary producers showed distinct C signatures and the observed values suggest that little terrestrial or bulk sediment organic matter enter the food web of the sound. Suspended particulate organic matter (POM, supports the bulk of the consumers, with some contribution by macroalgae . Consumers C values ranged from −17.4 to . At least three trophic levels were detectable in the food web. The N value of POM was , while that of sediment and detritus was . The N values of suspension feeding benthic invertebrates were 8.2–, deposit feeders 8.3–, and carnivores 10.7–. Values for fishes were for detritivore, 11.4– for benthic feeders, 12.4– for zooplanktivores, and for piscivores/benthic invertebrate feeders. Squid mean value was . There is a reasonable agreement between feeding habits information from the literature and N values from this study. In the sound, the first and second trophic steps seem to be about 1– higher than those of similar organisms studied in temperate waters and this may reflect an input of allochtonous anthropogenic nitrogen enriched in ¹⁵N from human activities.     

Factors affecting denitrification in agricultural headwater streams in Northeast Ohio,USA

As a result of increased anthropogenic nitrogen (N) loading in surface waters of agricultural watersheds, there is enhanced interest to understand and quantify N removal mechanisms. Denitrification, an important N removal mechanism in aquatic systems, may contribute to reducing N pollution in agricultural headwater streams. However, the key factors controlling this process in lotic systems remain unclear. The objective of our study was to examine the factors regulating rates of denitrification in the sediments of agricultural headwater streams in the mid-western USA. Denitrification rates were variable among streams and treatments (<0.1–28.0 μg N g AFDM⁻¹ h⁻¹) and on average, were higher than those reported for similar headwater streams. Carbon quantity and quality, and pH had no effect on denitrification, while temperature and nitrate ( ) concentrations had a positive effect on rates of denitrification. Specifically, controlled denitrification following Michaelis-Menten kinetics. We calculated a value of k_m (1.0 mg -N L^-1) that was comparable to other studies in aquatic sediments but was well below the median in-stream concentrations (5.2–17.4 mg -N L⁻¹) observed at the study sites. Despite high rates of denitrification, this removal mechanism is most likely saturated in the agricultural headwater streams we examined, suggesting that these systems are not effective at removing in-stream N. Handling editor: D. Ryder     

Determination of the chemical composition of ulvan, a cell wall polysaccharide from Ulva spp. (Ulvales, Chlorophyta) by FT-IR and chemometrics

The water-soluble cell wall polysaccharides from green seaweeds of Ulva spp. (Ulvales, Chlorophyta), referred to as ulvan, demonstrate composition- and structure-related functional properties. Mid-infrared spectroscopy combined with chemometric techniques was investigated as a means to rapidly predict the chemical composition of ulvan extracts. A calibration was realized with 41 ulvan extracts from two Ulva species. The variables studied included the constituent sugars (rhamnose, xylose, glucose, galactose, glucuronic acid, iduronic acid), protein, and sulfate contents. The correlation between Fourier transform infrared and chemical data was developed using partial least squares (PLS) regression with full cross-validation (leave one out). The coefficients of determination in cross-validation () and the standard error in cross-validation were determined for each variable. The PLS model validation resulted in a coefficient of determination () and a standard error in prediction. Good predictions were obtained for rhamnose ( = 0.9244), xylose ( = 0.8758), glucuronic acid ( = 0.9415), and sulfate ( = 0.9218), which are the main ulvan constituents. However, minor components such as proteins, glucose, galactose, and iduronic acid were not correctly predicted. This study showed that mid-infrared spectroscopy combined with PLS regression is a reliable and fast method for the quantification of the main chemical constituents of ulvan extracts.     

Model-consistent estimation of the basic reproduction number from the incidence of an emerging infection

We investigate the merit of deriving an estimate of the basic reproduction number early in an outbreak of an (emerging) infection from estimates of the incidence and generation interval only. We compare such estimates of with estimates incorporating additional model assumptions, and determine the circumstances under which the different estimates are consistent. We show that one has to be careful when using observed exponential growth rates to derive an estimate of , and we quantify the discrepancies that arise.      

Efficient sampling of RNA secondary structures from the Boltzmann ensemble of low-energy

We adapt here a surprising technique, the boustrophedon method, to speed up the sampling of RNA secondary structures from the Boltzmann low-energy ensemble. This technique is simple and its implementation straight-forward, as it only requires a permutation in the order of some operations already performed in the stochastic traceback stage of these algorithms. It nevertheless greatly improves their worst-case complexity from to , for n the size of the original sequence. Moreover the average-case complexity of the generation is shown to be improved from to in an Boltzmann-weighted homopolymer model based on the Nussinov–Jacobson free-energy model. These results are extended to the more realistic Turner free-energy model through experiments performed on both structured (Drosophilia melanogaster mRNA 5S) and hybrid (Staphylococcus aureus RNAIII) RNA sequences, using a boustrophedon modified version of the popular software UnaFold. This improvement allows for the sampling of greater and more significant sets of structures in a given time.      

Survival Chances of Mutants Starting With One Individual

A simple theoretical model of a Darwinian system (a periodic system with a multiplication phase and a selection phase) of entities (initial form of polymer strand, primary mutant and satellite mutants) is given. First case: one mutant is considered. One individual of the mutant appears in the multiplication phase of the first generation. The probabilities to find N individuals of the mutant after the multiplication phase M of the n-th generation (with probability δ of an error in the replication, where all possible errors are fatal errors) and after the following selection phase S (with probability β that one individual survives) are given iteratively. The evolutionary tree is evaluated. Averages from the distributions and the probability of extinction are obtained. Second case: two mutants are considered (primary mutant and new form). One individual of the primary mutant appears in the multiplication phase of the first generation. The probabilities to find N _p individuals of the primary mutant and N _m individuals of the new form after the multiplication phase M of the n-th generation (probability ɛ of an error in the replication of the primary mutant giving the new form) and after the following selection phase S (probabilities β _p and β _m that one individual each of the primary mutant and of the new form survives) are given iteratively. Again the evolutionary tree is evaluated. Averages from the distributions are obtained. The online version of the original article can be found at .     

Probing the interactions of the solvated electron with DNA by molecular dynamics simulations: II. bromodeoxyuridine-thymidine mismatched DNA

The interaction of solvated electrons with DNA results in various types of DNA lesions. The in vitro and in vivo sensitisation of DNA to -induced damage is achieved by incorporation of the electron-affinity radiosensitiser bromodeoxyuridine (BUdR) in place of thymidine. However, in DNA duplexes containing single-stranded regions (bulged BUdR-DNA), the type of lesion is different and the efficiency of damage is enhanced. In particular, DNA interstrand crosslinks (ICL) form at high efficiency in bulged DNA but are not detectable in completely duplex DNA. Knowledge about the processes and interactions leading to these differences is obscure. Previously, we addressed the problem by applying molecular modelling and molecular dynamics (MD) simulations to a system of normal (BUdR·A)-DNA and a hydrated electron, where the excess electron was modelled as a localised eˉ(H₂O)₆ anionic cluster. The goal of the present study was to apply the same MD simulation to a wobble system, containing a pyrimidine–pyrimidine mismatched base pair, BUdR·T. The results show an overall dynamic pattern similar to that of the motion around normal DNA. However, the number of configuration states when was particularly close to DNA is different. Moreover, in the (BUdR·T)-wobble DNA system, the electron frequently approaches the brominated strand, including BUdR, which was not observed with the normal (BUdR·A)-DNA. The structure and exchange of water at the sites of immobilisation near DNA were also characterised. The structural dynamics of the wobble DNA is prone to more extensive perturbations, including frequent formation of cross-strand (cs) interatomic contacts. The structural deviations correlated with approaching DNA from the major groove side, with sodium ions trapped deep in the minor groove. Altogether, the obtained results confirm and/or throw light on dynamic-structure determinants possibly responsible for the enhanced radiation damage of wobble DNA. Figure The structure of the tightly bound single water-layer between the DNA and the electron (Site-8, five H₂O molecules, bold capped sticks); the rest of the “second” shell waters (lines, in atom type colour) surround the ˉ(H₂O)₆ cluster (yellow, space fill). Orange dashed lines H-bonds; only one of the five molecules from the single H₂O layer mediates a single-step H-bond bridge with N7(A8); the other four present a network of two(three)-step H-bond bridges between DNA/ partner atoms     

A bias correction for estimates of effective population size based on linkage disequilibrium at unlinked gene loci*

Analysis of linkage disequilibrium (=mean squared correlation of allele frequencies at different gene loci) provides a means of estimating effective population size (N _e) from a single sample, but this method has seen much less use than the temporal method (which requires at least two samples). It is shown that for realistic numbers of loci and alleles, the linkage disequilibrium method can provide precision comparable to that of the temporal method. However, computer simulations show that estimates of N _e based on for unlinked, diallelic gene loci are sharply biased downwards ( in some cases) if sample size (S) is less than true N _e. The bias is shown to arise from inaccuracies in published formula for when S and/or N _e are small. Empirically derived modifications to for two mating systems (random mating and lifetime monogamy) effectively eliminate the bias (residual bias in % in most cases). The modified method also performs well in estimating N _e in non-ideal populations with skewed sex ratio or non-random variance in reproductive success. Recent population declines are not likely to seriously affect , but if N has recently increased from a bottleneck can be biased downwards for a few generations. These results should facilitate application of the disequilibrium method for estimating contemporary N _e in natural populations. However, a comprehensive assessment of performance of with highly polymorphic markers such as microsatellites is needed.The US Governmentȁ9s right to retain a non-exclusive, royalty-free license in and to any copyright is acknowledged.     

An Analytical Model of Gene Evolution with 9 Mutation Parameters: An Application to the Amino Acids Coded by the Common Circular Code

We develop here an analytical evolutionary model based on a trinucleotide mutation matrix 64× 64 with nine substitution parameters associated with the three types of substitutions in the three trinucleotide sites. It generalizes the previous models based on the nucleotide mutation matrices 4× 4 and the trinucleotide mutation matrix 64× 64 with three and six parameters. It determines at some time t the exact occurrence probabilities of trinucleotides mutating randomly according to these nine substitution parameters. An application of this model allows an evolutionary study of the common circular code of eukaryotes and prokaryotes and its 12 coded amino acids. The main property of this code is the retrieval of the reading frames in genes, both locally, i.e. anywhere in genes and in particular without a start codon, and automatically with a window of a few nucleotides. However, since its identification in 1996, amino acid information coded by has never been studied. Very unexpectedly, this evolutionary model demonstrates that random substitutions in this code and with particular values for the nine substitutions parameters retrieve after a certain time of evolution a frequency distribution of these 12 amino acids very close to the one coded by the actual genes.     

Determination of the average shear rate in a stirred and aerated tank bioreactor

A method for evaluating the average shear rate () in a stirred and aerated tank bioreactor has been proposed for non-Newtonian fluids. The volumetric oxygen transfer coefficient (k _L a) was chosen as the appropriate characteristic parameter to evaluate the average shear rate (). The correlations for the average shear rate as a function of N and rheological properties of the fluid (K and n) were obtained for two airflow rate conditions (ϕ_air). The shear rate values estimated by the proposed methodology lay within the range of the values calculated by classical correlations. The proposed correlations were utilized to predict the during the Streptomyces clavuligerus cultivations carried out at 0.5 vvm and four different rotational impeller speeds. The results show that the values of the average shear rate () varied from 437 to 2,693 s⁻¹ by increasing with N and flow index (n) and decreasing with the fluid consistency index (K).     

Report on non-temperature related variations in CO<Subscript>2</Subscript> efflux rates from young tree stems in the dormant season

Respiration rates are reported to increase exponentially with temperature. Respiration rates of woody tissues are commonly measured as CO₂ efflux rates () from that tissue. However, this paper describes clear variations in stem that were not related to temperature for the case of a young beech (Fagus sylvatica L.) and oak (Quercus robur L.) tree during the dormant season. The CO₂ concentration ([CO₂]) in the xylem of the beech tree showed similar temperature-independent variations. The trees were grown in a growth chamber in which radiation patterns and temperature were kept constant. was measured with an IRGA connected to cuvettes surrounding a stem segment. Xylem [CO₂] was measured in situ using a CO₂ microelectrode. Depressions in and [CO₂] occurred during the light period, despite equal temperatures in the light and dark period. Explanations found in literature for discrepancies in the exponential relationship between temperature and are the influence of (1) sap flow or (2) decreased cell water content. However, (1) the variations were observed in the dormant season, when no sap flow was observed yet, and (2) reduced cell water content was not likely to be apparent as differences in stem transpiration rates between the dark and light period were not significant. Hence, previously formulated theories failed to explain our results. This work therefore provides a new ground for discussion on other possible causes of daytime depressions in . One might be the refixation of respired CO₂ by corticular photosynthesis in the stem parts adjacent to the stem segment enclosed by the cuvette.     

The role of body surfaces and ventilation in gas exchange of the abalone, <Emphasis Type="Italic">Haliotis iris</Emphasis>

The archaeogastropod Haliotis iris possesses paired bipectinate gills and normally four to six shell holes. In still water, endogenous water flow entered the branchial chamber anteriorly to the left of the head and was exhaled primarily from the three most posterior holes. The first or second anterior aperture was occasionally weakly inhalant. Cardiac interaction superimposed an oscillatory component upon ciliary ventilation but did not augment mean flow. At normal endogenous flow rates 49% of oxygen was extracted from the branchial flow, increasing to 71% at lower flows. In still water, normoxic was 0.47 μmol g⁻¹ h⁻¹. Oxyregulation occurred down to with partial oxyregulation down to 45 Torr (P _crit), and oxyconformity below this. The oxyregulatory plateau was absent in artificially ventilated animals but normoxic was higher (0.65 μmol g⁻¹ h⁻¹). Endogenous ventilation was unaffected by hypoxia to 15 Torr. Heart rate decreased by ~20% at 26 Torr before falling more steeply. Oxygen uptake from the branchial ventilation stream fully accounted for normoxic In hypoxia (<30 Torr), no uptake occurred from the head or foot despite extensive eversion of the epipodium. Blood oxygen measurements excluded the right mantle as a significant gas exchange organ. Changes in oxygen uptake caused by changes in the velocity of external water currents support the concept of induced ventilation and suggest that in still water aerobic respiration was ventilation-limited. Although ciliary ventilation appears adequate to support resting aerobic metabolism, induced ventilation may provide increased aerobic scope for activity and repayment of oxygen debt. An erratum to this article can be found at     

Hologram and 3D-quantitative structure toxicity relationship studies of azo dyes

Amino azobenzenes are important dyes in the food and textile industry but their application is limited due to their mutagenicity. Computational modeling techniques were used to help understand the factors responsible for mutagenicity, and several quantitative structure toxicity relationship (QSTR) models have been derived. HQSTR (hologram QSTR) analyses indicated that different substituents at sites on both rings contribute to mutagenicity. Fragment parameters such as bond (B) and connectivity(C), as well as donor-acceptor (DA)-based model provide significant results (q² = 0.59, r² = 0.92, ) explaining these harmful effect. HQSTR results indicated that a bulky group at ring “Y” and small group at ring “X” might help to decrease mutagenicity. 3D-QSTR based on comparative molecular field analyses (CoMFA) and comparative molecular similarity index analyses (CoMSIA) are also in agreement with HQSTR. The 3D QSTR studies reveal that steric and electrostatic field effects have a strong relationship with mutagenicity (for CoMFA: q² = 0.51, r² = 0.95, and for CoMSIA: q² = 0.51, r² = 0.93 and ). In summary, negative groups and steric bulk at ring “Y” and small groups at carbon-3 of ring “X” might be helpful in reducing the mutagenicity of azo dyes.     

Regional Assessment of N Saturation using Foliar and Root \varvec {\delta}^{\bf 15}{\bf N}

N saturation induced by atmospheric N deposition can have serious consequences for forest health in many regions. In order to evaluate whether foliar may be a robust, regional-scale measure of the onset of N saturation in forest ecosystems, we assembled a large dataset on atmospheric N deposition, foliar and root and N concentration, soil C:N, mineralization and nitrification. The dataset included sites in northeastern North America, Colorado, Alaska, southern Chile and Europe. Local drivers of N cycling (net nitrification and mineralization, and forest floor and soil C:N) were more closely coupled with foliar than the regional driver of N deposition. Foliar increased non-linearly with nitrification:mineralization ratio and decreased with forest floor C:N. Foliar was more strongly related to nitrification rates than was foliar N concentration, but concentration was more strongly correlated with N deposition. Root was more tightly coupled to forest floor properties than was foliar . We observed a pattern of decreasing foliar values across the following species: American beech>yellow birch>sugar maple. Other factors that affected foliar included species composition and climate. Relationships between foliar and soil variables were stronger when analyzed on a species by species basis than when many species were lumped. European sites showed distinct patterns of lower foliar , due to the importance of ammonium deposition in this region. Our results suggest that examining values of foliage may improve understanding of how forests respond to the cascading effects of N deposition.     

Radiosterilization of Fluoroquinolones and Cephalosporins: Assessment of Radiation Damage on Antibiotics by Changes in Optical Property and Colorimetric Parameters

A most common problem encountered in radiosterilization of solid drugs is discoloration or yellowing. By pharmacopoeia method, discoloration can be assessed by measuring absorbance of solutions of irradiated solid samples at 450 nm. We propose to evaluate discoloration of solid samples directly by recording their diffuse reflectance spectra. Further, the reflectance spectrum is used to compute various color parameters: CIE XYZ tristimulus value, CIE Lab, (color difference), yellowness index (YI), dominant wavelength, and excitation purity by CIE method. The investigation of difference reflectance spectra and color parameters revealed that for fluoroquinolones, e-beam was more damaging than gamma radiation, whereas for cephalosporins, trend was reversed. The quantum of discoloration with gamma radiation and e-beam is found to be nearly equal when assessed by pharmacopeia method, and it is therefore inadequate to assess small color differences. The color parameters and ΔYI are found to be reliable indicators of discoloration. The tolerance limits proposed in terms of and ΔYI are ±2 and ±10 U, respectively. The dominant wavelength for all compounds has shifted to higher values indicating change in hue but defining color tolerance limit with this parameter requires adjunct excitation purity value.     

Leaching losses of inorganic N and DOC following repeated drying and wetting of a spruce forest soil

Forest soils are frequently subjected to dry–wet cycles, but little is known about the effects of repeated drying and wetting and wetting intensity on fluxes of , and DOC. Here, undisturbed soil columns consisting of organic horizons (O columns) and organic horizons plus mineral soil (O + M columns) from a mature Norway spruce stand at the Fichtelgebirge; Germany, were repeatedly desiccated and subsequently wetted by applying different amounts of water (8, 20 and 50 mm day⁻¹) during the initial wetting phase. The constantly moist controls were not desiccated and received 4 mm day⁻¹ during the entire wetting periods. Cumulative inorganic N fluxes of the control were 12.4 g N m⁻² (O columns) and 11.4 g N m⁻² (O + M columns) over 225 days. Repeated drying and wetting reduced cumulative and fluxes of the O columns by 47–60 and 76–85%, respectively. Increasing (0.6–1.1 g N m⁻²) and decreasing fluxes (7.6–9.6 g N m⁻²) indicate a reduction in net nitrification in the O + M columns. The negative effect of dry–wet cycles was attributed to reduced net N mineralisation during both the desiccation and wetting periods. The soils subjected to dry–wet cycles were considerably drier at the final wetting period, suggesting that hydrophobicity of soil organic matter may persist for weeks or even months. Based on results from this study and from the literature we hypothesise that N mineralisation is mostly constrained by hydrophobicity in spruce forests during the growing season. Wetting intensity did mostly not alter N and DOC concentrations and fluxes. Mean DOC concentrations increased by the treatment from 45 mg l⁻¹ to 61–77 mg l⁻¹ in the O tlsbba columns and from 12 mg l⁻¹ to 21–25 mg l⁻¹ in the O + M columns. Spectroscopic properties of DOC from the O columns markedly differed within each wetting period, pointing to enhanced release of rather easily decomposable substrates in the initial wetting phases and the release of more hardly decomposable substrates in the final wetting phases. Our results suggest a small additional DOC input from organic horizons to the mineral soil owing to drying and wetting.