HIV spread in the San Francisco cohort: Scaling of the effective logistic rate for seropositivity

A simple scaling (semigroup) property is manifest in the functional form of the effective logistic rate for the increase in the HIV seropositive fraction in the San Francisco (City Clinic) cohort. Witht _i=4.5 years, this scaling property—r→λ^-2r undert→[λt+(λ−1)t _i] for all parameter values λ≧1—encapsulates the effects of relevant biological and sociological changes in the key epidemiological variables during the 8-year seropositive rise period, 1978–1985 inclusive.     

Four-urn catenary model for excretion

A chain-like arrangement of four urns (a catenary system) into which different color balls (white, corresponding to radio atoms, and black, corresponding to stable atoms) are being transferred is used to simulate the transport of atoms down the GI tract of man and animals. Into the first urn (stomach) are placedw _o white balls andr black balls while in the 2nd (small intestines) and 3rd (large intestines) urn, onlyr blacks are put in, with no whites. A sample of sizer is transferred from the 1st, 2nd and 3rd urns to the 2nd, 3rd and 4th (infinite universe) urns. From the random variable difference equations the first and second moments for the distribution of the number of radio atoms present in each urn are obtained. The variance of the contents of radioatoms in the excretion urn is Research sponsored by the Office of Health and Environmental Research, U.S. Department of Energy under contract W-7405-eng-26 with the Union Carbide Corporation.     

Fecundity,reproductive rate,longevity, and intrinsic rate of increase of an aphidiid parasitoidLysiphlebia mirzai

A life-table was constructed for a little known aphidiid waspLysiphlebia mirzai, a parasitoid of cereal aphid,Rhopalosiphum maidis. The female parasitoid survived 6.4 ± 1.17 (SD) days and oviposited intensively 4.0 ± 0.47 days. The total fecundity rate, R_t, was 169.2 ± 6.94 mummies/female and net reproductive rate, R_o, was 92.70 female offspring/female. The intrinsic total fecundity rate, r_t, and intrinsic rate of natural increase, r_m, the finite rate of total fecundity, λ^t, and finite rate of increase, λ^m, was 0.27048, 0.24155, 1.31059 and 1.27322 respectively. The mean generation time (18.75 days) and doubling time of the population (2.87 days) was slightly higher than other aphidiids studied so far. The proportion of female progenies decreased significantly on the successive oviposition days.      

Species abundance distributions in neutral models with immigration or mutation and general lifetimes

We consider a general, neutral, dynamical model of biodiversity. Individuals have i.i.d. lifetime durations, which are not necessarily exponentially distributed, and each individual gives birth independently at constant rate λ. Thus, the population size is a homogeneous, binary Crump–Mode–Jagers process (which is not necessarily a Markov process). We assume that types are clonally inherited. We consider two classes of speciation models in this setting. In the immigration model, new individuals of an entirely new species singly enter the population at constant rate μ (e.g., from the mainland into the island). In the mutation model, each individual independently experiences point mutations in its germ line, at constant rate θ. We are interested in the species abundance distribution, i.e., in the numbers, denoted I _n (k) in the immigration model and A _n (k) in the mutation model, of species represented by k individuals, k = 1, 2, . . . , n, when there are n individuals in the total population. In the immigration model, we prove that the numbers (I _t (k); k ≥ 1) of species represented by k individuals at time t, are independent Poisson variables with parameters as in Fisher’s log-series. When conditioning on the total size of the population to equal n, this results in species abundance distributions given by Ewens’ sampling formula. In particular, I _n (k) converges as n → ∞ to a Poisson r.v. with mean γ/k, where γ : = μ/λ. In the mutation model, as n → ∞, we obtain the almost sure convergence of n ⁻¹ A _n (k) to a nonrandom explicit constant. In the case of a critical, linear birth–death process, this constant is given by Fisher’s log-series, namely n ⁻¹ A _n (k) converges to α ^k /k, where α : = λ/(λ + θ). In both models, the abundances of the most abundant species are briefly discussed.     

Note on a combinatorial problem

In the first part of this paper we have assembled some properties of the quantitiesR _m ⁿ , whereR _m ⁿ denotes the number of distributions ofn different objects intom indifferent parcels, with no empty parcels allowed. We then discuss the following problem (N. Rashevsky, 1954, 1955 a,b, 1956): to find the total number,G _n , of graphs that can be obtained from the biotopological transformation (T ⁽¹⁾ X) for a given value of the parametern. This is related to the distribution ofn indifferent objects intom different boxes. A formula forG _n is given which, however, is not very convenient for practical computations because it involves a summation over certain “admissible partitions” of the numbermn (m is a second parameter of the transformation). Some theorems are derived; with their help we can simplify the calculation ofG _n to a small extent. The numbersG _n are calculated forn≤9 and estimated forn=10. It is found thatG ₇≈5.4×10⁴,G ₈≈8.3×10⁵,G ₉≈1.4×10⁷, andG ₁₀≈3×10⁸. These values ofn are those which might be used in connection with N. Rashevsky’s work (cf. Rashevsky, 1956).     

Radial theory of the ion current onto a probe in a low-pressure plasma with allowance for volume ionization and collisions with neutrals

The ion current onto a spherical or cylindrical probe is analyzed in the cold-ion approximation with allowance for ionization and collisions with neutrals. An expression for the ion density that takes into account both ionization and collision in the finite-size perturbed region is derived. The current-voltage characteristics for the dimensionless parameters r _p/λ _D = 0.0001−10, λ _i /λ _D = 0.01 − ∞, and zλ _D/(kT _e /M)^1/2 = 0−5 are determined by numerically solving Poisson’s equation, and the corresponding approximate expressions are obtained.     

The gas washout determination under a symmetry assumption

In an open circuit gas washout determination the output of test substance is shown to be of the form ∑ _i=0 ^∞ A _i λ _i ^k on thekth expiration whereA _i >0,i=1,2,... and 1 > λ₁ ≥ λ₂...≥ 0 provided the transition from inspiration to expiration has certain symmetry properties with the transition from expiration to inspiration. In general, no direct physical interpretation such as volume for theA _t ’s or fraction of retained gas on expiration for the λ _i is justified.     

λ-Glutamylcysteine synthetase in higher plants: catalytic properties and subcellular localization

λ-Glutamylcysteine synthetase activity (EC 6.3.2.2) was analysed in Sephacryl S-200 eluents of extracts from cell suspension cultures ofNicotiana tabacum L. cv. Samsun by determination of λ-glutamylcysteine as its monobromobimane derivative. The enzyme has a relative molecular mass (M_r) of 60000 and exhibits maximal activity at pH 8 (50% at pH 7.0 and pH9.0) and an absolute requirement for Mg²⁺. With 0.2mM Cd²⁺ or Zn²⁺, enzyme activity was reduced by 35% and 19%, respectively. Treatment with 5 mM dithioerythritol led to a heavy loss of activity and to dissociation into subunits (M_r 34000). Buthionine sulfoximine andl-methionine-sulfoximine, known as potent inhibitors of λ-glutamylcysteine synthetase from mammalian cells, were found to be effective inhibitors of the plant enzyme too. The apparent K_m values forl-glutamate,l-cysteine, and α-aminobutyrate were, respectively, 10.4mM, 0.19 mM, and 6.36 mM. The enzyme was completely inhibited by glutathione (K_i=0.42 mM). The data indicate that the rate of glutathione synthesis in vivo may be influenced substantially by the concentration of cysteine and glutamate and may be further regulated by feedback inhibition of λ-glutamylcysteine synthetase by glutathione itself. λ-Glutamylcysteine synthetase is, like glutathione synthetase, localized in chloroplasts as well as in the cytoplasm. Chloroplasts fromPisum sativum L. isolated on a Percoll gradient contained about 72% of the λ-glutamylcysteine synthetase activity in leaf cells and 48% of the total glutathione synthetase activity. In chloroplasts ofSpinacia oleracea L. about 61% of the total λ-glutamylcysteine synthetase activity of the cells were found and 58% of the total glutathione synthetase activity. These results indicate that glutathione synthesis can take place in at least two compartments of the plant cell. Dedicated to Professor A. Prison on the occasion of his 80th birthday     

A re-examination of the age and growth of sand tiger sharks, Carcharias taurus, in the western North Atlantic: the importance of ageing protocols and use of multiple back-calculation techniques

Age and growth estimates for sand tiger sharks, Carcharias taurus, in the western North Atlantic were derived from 96 vertebral centra collected from sharks ranging from 94 to 277 cm total length (TL), and compared to previously published age and growth data. The oldest female and male sand tiger sharks aged in this study were 17 and 15 years of age, respectively. von Bertalanffy growth parameters derived from vertebral length-at-age data are L _∞ = 295.8 cm TL, k = 0.11 year⁻¹, and t ₀ = −4.2 years for females, and L _∞ = 249.5 cm TL, k = 0.16 year⁻¹, and t ₀ = −3.4 years for males. Sexual maturity is estimated to be 9–10 years for females and 6–7 years for males. Weight-to-length relationships determined for female and male sand tiger sharks in the western North Atlantic are; W = 1.3 × 10⁻⁴ × L ^2.4 (r ² = 0.84, n = 55) and W = 9.0 × 10⁻⁵ × L ^2.5 (r ² = 0.84, n = 47), respectively, and 7.9 × 10⁻⁵ × L ^2.5 (r ² = 0.84) for the sexes combined. Our results show sand tigers possess a slower rate of growth than previously thought. This information is crucial for accurately assessing this population’s ability to recover, and further justifies the need for this species to be fully protected.     

Ecological Characterisation of the Colonic Microbiota in Arctic and Sub-Arctic Seals

Dominant colonic bacteria in wild hooded (n = 9), harbour (n = 1) and grey (n = 1) seals were identified using 16S rRNA gene clone libraries (313 clones), revealing 52.7% Bacteroidetes, 41.5% Firmicutes, 4.5% Proteobacteria and 1.0% Fusobacteria. Thirty (77%) of the 39 phylotypes identified were novel, showing <97% sequence similarity to their nearest cultivated relatives. Mean colonic bacterial cell density, determined by real-time PCR, was high (12.8 log₁₀ cells/g wet wt) for the hooded seals, while the number of methanogenic Archea was low (4.0 log₁₀ cells/g wet wt). The level of ampicillin (amp^r) and tetracycline-resistant (tet^r) isolates was investigated by cultivation. Aerobic amp^r isolates were only detected in colon contents from four hooded seals, whereas aerobic tet^r isolates were found in seven of the nine hooded seals. These data provide novel insight to the gut microbiota of Arctic and sub-Arctic seals living in the wild.     

On the distribution of the time required to remove white balls from an URN

Balls are removed one-at-a-time at equal time intervals from an urn initially containingw ₀ white balls and a large number b of black balls and each black or white ball is immediately replaced by a black ball. The distribution of the number of white balls remaining aftert iterations (under certain limiting operations) is taken from the literature. The problem is to use this result to find the time required to remove a fixed number of white ballsw ₁ from the urn. We then find the mean and variance of this distribution and also look at the special case whenw ₁ =w ₀.     

Inhibition by light of CO2 evolution from dark respiration: Comparison of two gas exchange methods

Two approaches to determine the fraction (μ) of mitochondrial respiration sustained during illumination by measuring CO₂ gas exchange are compared. In single leaves, the respiration rate in the light (`day respiration' rate R<sub>d</sub>) is determined as the ordinate of the intersection point of A–c<sub>i</sub> curves at various photon flux densities and compared with the CO<sub>2</sub> evolution rate in darkness (`night respiration' rate R_n). Alternatively, using leaves with varying values of CO₂ compensation concentration (Γ), intracellular resistance (r_i) and R_n, an average number for μ can be derived from the linear regression between Γ and the product r_iċR_n. Both methods also result in a number c* for that intercellular CO₂ concentration at which net CO₂ uptake rate is equal to –R_d. c* is an approximate value of the photocompensation point Γ* (Γ in the absence of mitochondrial respiration), which is related to the CO₂/O₂ specificity factor of Rubisco S_c/o. The presuppositions and limitations for application of both approaches are discussed. In leaves of Nicotiana tabacum, at 22 °C, single leaf measurements resulted in mean values of μ = 0.71 and c_* = 34 μmol mol⁻¹. At the photosynthetically active photon flux density of 960 μmol quanta m⁻² s⁻¹, nearly the same numbers were derived from the linear relationship between Γ and r_iċR_n. c* and R_d determined by single leaf measurements varied between 31 and 41 μmol mol⁻¹ and between 0.37 and 1.22 μmol m⁻² s⁻¹, respectively. A highly significant negative correlation between c* and R_d was found. From the regression equation we obtained estimates for Γ* (39 μmol mol⁻¹), S_c/o (96.5 mol mol⁻¹) and the mesophyll CO₂ transfer resistance (7.0 mol⁻¹ m² s). This revised version was published online in June 2006 with corrections to the Cover Date.     

Effects of root diameter and root nitrogen concentration on in situ root respiration among different seasons and tree species

Knowledge of root respiration is a prerequisite for a better understanding of ecosystem carbon budget and carbon allocation. However, there are not many relevant data in the literature on direct measurements of in situ root respiration by root chamber method. Furthermore, few studies have been focused on the effects of root diameter (D _r) and root nitrogen concentration (N _r) on in situ root respiration among different seasons and tree species. To address these goals, we used a simplified root-chamber system to measure in situ root respiration rates of Acacia crassicarpa and Eucalyptus urophylla in subtropical plantations of south China. We found that the species and season variation in root respiration were affected by D _r and N _r. Also, the root respiration per unit dry mass (R _r, nmol CO₂ g⁻¹ s⁻¹) and root respiration per unit N (R _n, nmol CO₂ g N⁻¹ s⁻¹) were affected by D _r and N _r. The R _r, R _n, N _r and soil temperature sensitivity (Q ₁₀) of R _r for the two species significantly decreased with an increase of D _r. The R _r of the two species showed significant an inter-seasonal and diurnal pattern, and this trend decreased with increasing D _r. Both the R _r and Q ₁₀ of the two species increased with increasing N _r. The D _r and N _r explained 54 and 52% of the observed variation in R _r for A. crassicarpa, and 65 and 70% for E. urophylla. The R _r, N _r, and Q ₁₀ of A. crassicarpa were significantly higher than those of E. urophylla. Our results indicated that root respiration was dependent on D _r and N _r, and this dependence varied with season and plant species.     

Development of a colorimetric assay for rapid quantitative measurement of clavulanic acid in microbial samples

We developed a colorimetric assay to quantify clavulanic acid (CA) in culture broth of Streptomyces clavuligerus, to facilitate screening of a large number of S. clavuligerus mutants. The assay is based on a β-lactamase-catalyzed reaction, in which the yellow substrate nitrocefin (λ _max=390 nm) is converted to a red product (λ _max=486 nm). Since CA can irreversibly inhibit β-lactamase activity, the level of CA in a sample can be measured as a function of the A ₃₉₀/A ₄₈₆ ratio in the assay mixture. The sensitivity and detection window of the assay were determined to be 50 μg L⁻¹ and 50 μg L⁻¹ to 10 mg L⁻¹, respectively. The reliability of the assay was confirmed by comparing assay results with those obtained by HPLC. The assay was used to screen a pool of 65 S. clavuligerus mutants and was reliable for identifying CA over-producing mutants. Therefore, the assay saves time and labor in large-scale mutant screening and evaluation tasks. The detection window and the reliability of this assay are markedly better than those of previously reported CA assays. This assay method is suitable for high throughput screening of microbial samples and allows direct visual observation of CA levels on agar plates.     

Comparison of biological and demographic parameters forMononychellus progresivus andOligonychus gossypii on cassava: influence of temperature

The effect of five constant temperatures (16, 22, 26, 31 and 36°C) on biological (survival and duration of developmental stages, fecundity and longevity of females, sex-ratio) and demographic parameters (R _o , G, r _m and λ) of the two main phytophagous mites that attack cassava in Africa,Mononychellus progresivus Doreste andOligonychus gossypii (Zacher), was studied in the laboratory. Experiments were performed simultaneously on the two mite species reared on the same cassava variety (1M20) under controlled conditions: 70±10% r.h. and 12L∶12D. The lower thermal threshold was 13°C forM. progresivus and 11°C forO. gossypii. Both species developed in the range from 22 to 36°C. The shortest development time was obtained at 31°C for both species; it was 7.2 days forM. progresivus and 8.2 days forO. gossypii. Maximum fecundity of both species was recorded at 26°C with 42.1 eggs forM. progresivus and 36.3 eggs forO. gossypii The highest intrinsic rate of increase (r _m ) was obtained at 31°C for both species with 0.289 and 0.214 forM. progresivus andO. gossypii, respectively.     

Total Relaxivities of Material Content in Various Cysts and Ameloblastoma: Implications for Discriminating Different Fluids

Nuclear magnetic resonance T ₁ and T ₂ relaxivities (r ₁ and r ₂) exhibit efficiency of a material to alter the relaxation rates (1/T ₁ and 1/T ₂), and they are being used for diagnostic purposes. The determination of total relaxivities (r _1t and r _2t) of cystic fluid content and ameloblastoma may therefore be useful for discriminative purposes. In order to determine what makes total relaxivities of hemorrhagic cysts, four sets of tubes containing pooled cyst were doped with increasing concentrations of iron, copper, albumin, and γ-globulins. These sets were replaced in a phantom together with six individual cysts and one ameloblastoma. The relaxation times were measured by magnetic resonance imaging operating at 1.5 T. The relaxivities of individual ions and proteins were determined from the slope of the relation between relaxation rates and concentration, while total relaxivities were determined by using the increases in relaxation rates and material content of cystic fluid (MC). Iron, copper, albumin, and γ-globulins were found to be the sources of r _1t and r _2t. Each of r _1t, r _2t, r _1tMC, r _2tMC, and r _2t/r _1t are distinctive parameters for each cystic category and ameloblastoma. Except for MC, the parameters measured for ameloblastoma are significantly smaller than those of cysts. The similarity of the present results to those used in clinical applications suggests that each of r _1t, r _2t, r _1tMC, r _2tMC, and r _2t/r _1t has an ability to discriminate various fluids and masses. The present work also suggests that r _1tMC, r _2tMC, and r _2t/r _1t can be determined in vivo.     

Electroporative deformation of salt filled lipid vesicles

Membrane electroporation, vesicle shape deformation and aggregation of small, NaCl-filled lipid vesicles (of radius a = 50 nm) in DC electric fields was characterized using conductometric and turbidimetrical data. At pulse durations t_E≤ 55 ± 5 ms the increase in the conductivity of the vesicle suspension is due to the field-induced efflux of electrolyte through membrane electropores. Membrane electroporation and Maxwell stress on the vesicle membrane lead to vesicle elongation concomitant with small volume reduction (up to 0.6% in an electric field of E = 1 MV m^–1). At t_E > 55 ± 5 ms, further increases in the conductivity and the optical density suggest electroaggregation and electrofusion of vesicles. The conductivity changes after the electric pulse termination reflect salt ion efflux through slowly resealing electropores. The analysis of the volume reduction kinetics yields the bending rigidity κ = (4.1 ± 0.3) ⋅ 10^–20 J of the vesicle membrane. If the flow of Na⁺ and Cl^– ions from the vesicle interior is treated in terms of Hagen-Poiseuille's equation, the number of permeable electropores is N = 39 per vesicle with mean pore radius r_p = 0.85 ± 0.05 nm at E = 1 MVm^–1 and t_E≤ 55 ± 5 ms. The turbidimetric and conductometric data suggest that small lipid vesicles (a ≤ 50 nm) are not associated with extensive membrane thermal undulations or superstructures. In particular with respect to membrane curvature, the vesicle results are suggestive for the design and optimization of electroporative delivery of drugs and genes to cell tissue at small field strengths (≤1 MVm^–1) and large pulse durations (≤100 ms). Received: 8 July 1997 / Accepted: 15 September 1997     

Estimation of Noise-Free Variance to Measure Heterogeneity

Variance is a statistical parameter used to characterize heterogeneity or variability in data sets. However, measurements commonly include noise, as random errors superimposed to the actual value, which may substantially increase the variance compared to a noise-free data set. Our aim was to develop and validate a method to estimate noise-free spatial heterogeneity of pulmonary perfusion using dynamic positron emission tomography (PET) scans. On theoretical grounds, we demonstrate a linear relationship between the total variance of a data set derived from averages of n multiple measurements, and the reciprocal of n. Using multiple measurements with varying n yields estimates of the linear relationship including the noise-free variance as the constant parameter. In PET images, n is proportional to the number of registered decay events, and the variance of the image is typically normalized by the square of its mean value yielding a coefficient of variation squared (CV ²). The method was evaluated with a Jaszczak phantom as reference spatial heterogeneity (CV_r ²) for comparison with our estimate of noise-free or ‘true’ heterogeneity (CV _t ²). We found that CV _t ² was only 5.4% higher than CV _r ². Additional evaluations were conducted on 38 PET scans of pulmonary perfusion using ¹³NN-saline injection. The mean CV _t ² was 0.10 (range: 0.03–0.30), while the mean CV ² including noise was 0.24 (range: 0.10–0.59). CV _t ² was in average 41.5% of the CV ² measured including noise (range: 17.8–71.2%). The reproducibility of CV _t ² was evaluated using three repeated PET scans from five subjects. Individual CV _t ² were within 16% of each subject''s mean and paired t-tests revealed no difference among the results from the three consecutive PET scans. In conclusion, our method provides reliable noise-free estimates of CV _t ² in PET scans, and may be useful for similar statistical problems in experimental data.     

Bounds on the total particle number for species governed by reaction-diffusion equations in the infinite spatial domain

Differential inequality methods are developed for establishing upper and lower bounds on the total particle numberN(t)=∫θ(x,t) d³ x associated with solutions to nonlinear reaction-diffusion equations of the form ∂θ/∂t=D∇²θ+fθ-gθ ⁿ⁺¹ , whereD(>0),n(>0),f andg are constant parameters. If finite in a neighborhood oft=0,N(t) is bounded below for allt≥0 by a certain derived function oft for equations withg≥0. An upper bound onN(t) is obtained for equations withn=1,f<0 andg<0. These results provide general preservation and extinction criteria for the total particle number.     

The convergence in distribution of some simple epidemics

A group of n susceptible individuals exposed to a contagious disease isconsidered. It is assumed that at each point in time one or more susceptible individuals can contract the disease. The progress of this simple batch epidemic is modeled by a stochastic process X_n(t), t[0, ∞), representing the number of infectiveindividuals at time t. In this paper our analysis is restricted to simple batch epidemics with transition rates given by [α²X_n(t){n −X_n(t) +X_n(0)}]^1/2, t[0, ∞), α(0, ∞). This class of simple batch epidemics generalizes a model used and motivated by McNeil (1972) to describe simple epidemic situations. It is shown for this class of simple batch epidemics, that X_n(t), with suitable standardization, converges in distribution as n→∞ to a normal random variable for all t(0, t₀), and t₀ is evaluated.