On the time to extinction for a two-type version of Bartlett's epidemic model

We are interested in how the addition of type heterogeneities affects the long time behaviour of models for endemic diseases. We do this by analysing a two-type version of a model introduced by Bartlett under the restriction of proportionate mixing. This model is used to describe diseases for which individuals switch states according to susceptible-->infectious-->recovered and immune, where the immunity is life-long. We describe an approximation of the distribution of the time to extinction given that the process is started in the quasi-stationary distribution, and we analyse how the variance and the coefficient of variation of the number of infectious individuals depends on the degree of heterogeneity between the two types of individuals. These are then used to derive an approximation of the time to extinction. From this approximation we conclude that if we increase the difference in infectivity between the two types the expected time to extinction decreases, and if we instead increase the difference in susceptibility the effect on the expected time to extinction depends on which part of the parameter space we are in, and we can also obtain non-monotonic behaviour. These results are supported by simulations.     

Brucellosis, botflies, and brainworms: the impact of edge habitats on pathogen transmission and species extinction

Ecological interactions between species that prefer different habitat types but come into contact in edge regions at the interfaces between habitat types are modeled via reaction-diffusion systems. The primary sort of interaction described by the models is competition mediated by pathogen transmission. The models are somewhat novel because the spatial domains for the variables describing the population densities of the interacting species overlap but do not coincide. Conditions implying coexistence of the two species or the extinction of one species are derived. The conditions involve the principal eigenvalues of elliptic operators arising from linearizations of the model system around equilibria with only one species present. The conditions for persistence or extinction are made explicit in terms of the parameters of the system and the geometry of the underlying spatial domains via estimates of the principal eigenvalues. The implications of the models with respect to conservation and refuge design are discussed. Received: 10 June 1999 / Revised version: 7 July 2000 / Published online: 20 December 2000     

Stochastic epidemics: the probability of extinction of an infectious disease at the end of a major outbreak

 The aim of this study is to derive an asymptotic expression for the probability that an infectious disease will disappear from a population at the end of a major outbreak (‘fade-out’). The study deals with a stochastic SIR-model. Local asymptotic expansions are constructed for the deterministic trajectories of the corresponding deterministic system, in particular for the deterministic trajectory starting in the saddle point. The analytical expression for the probability of extinction is derived by asymptotically solving a boundary value problem based on the Fokker-Planck equation for the stochastic system. The asymptotic results are compared with results obtained by random walk simulations. Received 20 July 1995; received in revised form 6 May 1996     

Impact of myxomatosis in relation to local persistence in wild rabbit populations: the role of waning immunity and the reproductive period

Many diseases are less severe when they are contracted in early life. For highly lethal diseases, such as myxomatosis in rabbits, getting infected early in life can represent the best chance for an individual to survive the disease. For myxomatosis, early infections are attenuated by maternal antibodies. This may lead to the immunisation of the host, preventing the subsequent development of the lethal form of the disease. But early infection of young individuals requires specific demographic and epidemiological contexts, such as a high transmission rate of the pathogen agent. To investigate other factors involved in the impact of such diseases, we have built a stochastic model of a rabbit metapopulation infected by myxomatosis. We show that the impact of the pathogen agent can be reduced by early infections only when the agent has a long local persistence time and/or when the host subpopulations are highly connected. The length of the reproductive period and the duration of acquired immunity are also important factors influencing the persistence of the pathogen and thus, the impact of the disease. Besides confirming the role of classical factors in the persistence of a pathogen agent, such as the size of the subpopulation or the degree of connectivity, our results highlight novel factors that can modulate the impact of diseases whose severity increase with age.     

Blood amino acids concentration during insulin induced hypoglycemia in rats: the role of alanine and glutamine in glucose recovery

Summary. Our purpose was to determine the blood amino acid concentration during insulin induced hypoglycemia (IIH) and examine if the administration of alanine or glutamine could help glycemia recovery in fasted rats. IIH was obtained by an intraperitoneal injection of regular insulin (1.0 U/kg). The blood levels of the majority of amino acids, including alanine and glutamine were decreased (P < 0.05) during IIH and this change correlates well with the duration than the intensity of hypoglycemia. On the other hand, the oral and intraperitoneal administration of alanine (100 mg/kg) or glutamine (100 mg/kg) accelerates glucose recovery. This effect was partly at least consequence of the increased capacity of the livers from IIH group to produce glucose from alanine and glutamine. It was concluded that the blood amino acids availability during IIH, particularly alanine and glutamine, play a pivotal role in recovery from hypoglycemia.     

Kinetics of biomarkers: biological and technical validity of isoprostanes in plasma

Summary. Isoprostanes, non-enzymatic peroxidation products of arachidonic acid, are attractive biomarkers of oxidative stress in research in biology, medicine and nutrition. For the appropriate use of biomarkers it is required that these are both biologically and technically valid. Whereas the biological validity of isoprostanes is well-established, it is technically quite complicated to measure isoprostanes and its metabolites in body fluids, and its rapid disappearance from plasma may hamper practical application. This paper shortly introduces isoprostanes as a biomarker for studies with humans, describes a novel fast and sensitive method for measuring isoprostanes in plasma by high-performance liquid chromatography and tandem mass spectrometry, and provides several examples of the use of the method in studies in humans. By taking care of the biological and technical validity of this biomarker it is possible to establish the antioxidant effects of some food ingredients in studies with human volunteers.     

Programmed cell death: similarities and differences in animals and plants. A flower paradigm

Summary. After an overview of the criteria for the definition of cell death in the animal cell and of its different types of death, a comparative analysis of PCD in the plant cell is reported. The cytological characteristics of the plant cell undergoing PCD are described. The role of plant hormones and growth factors in the regulation of this event is discussed with particular emphasis on PCD activation or prevention by polyamine treatment (doses, timing and developmental stage of the organism) in a Developmental cell death plant model: the Nicotiana tabacum (tobacco) flower corolla. Some of the effects of polyamines might be mediated by transglutaminase catalysis. The activity of this enzyme was examined in different parts of the corolla during its life span showing an acropetal trend parallel to the cell death wave. The location of transglutaminase in some sub-cellular compartments suggests that it exerts different functions in the corolla DCD.     

Adrenomedullin: molecular mechanisms and its role in cardiac disease

Summary. Adrenomedullin (AM) is a potent, long-lasting vasoactive peptide originally isolated from human pheochromocytoma. Since its discovery, serum and tissue AM expression have been shown to be increased in experimental models and in patients with cardiac hypertrophy, myocardial infarction and end-stage heart failure with several beneficial effects. Considerable evidence exists for a wide range of autocrine, paracrine and endocrine mechanisms for AM which include vasodilatory, anti-apoptotic, angiogenic, anti-fibrotic, natriuretic, diuretic and positive inotropic. Thus, through regulation of body fluid or direct cardiac mechanisms, AM has additive and beneficial effects in the context of heart disease. Notable molecular mechanisms of AM include cyclic adenosine monophosphate, guanosine-3′,5′-monophosphate, PI3K/Akt and MAPK-ERK-mediated cascades. Given the endogenous and multifunctional nature of AM, we consider this molecule to have great potential in the treatment of cardiovascular diseases. In agreement, early experimental and preliminary clinical studies suggest that AM is a new and promising therapy for cardiovascular diseases.     

Polyamine contents in current foods: a basis for polyamine reduced diet and a study of its long term observance and tolerance in prostate carcinoma patients

Summary. Our aim was to develop a liquid chromatography and electrospray ionization tandem mass spectrometry (LCMS²) method to measure free amino acid (FAA) and dipeptide (DP) concentrations in biological fluids. We synthesized chloroformate derivatives of FAA and DP, identified the major precursor ions and used LCMS² to obtain the most intense product ions. Using serial dilutions of unlabeled and labeled standards ([²H₃]-L-Dopa, homoarginine, homophenylalanine, [¹⁵N]-Glutamine and [²H₃]-methionine), we observed linear relationships in MS response that we used to calculate the amounts of FAA and DP in biological samples. This method is sensitive with a limit of detection (LOD) for most of the FAAs and DPs tested in the 0.05–1 pmol range and is linear over 3–5 orders of magnitude when many metabolites were measured simultaneously. Reproducibility and between run or daily variations were <10% for most FAAs and DPs. We applied this method to human samples and quantitatively measured 21 FAAs and 2 DPs in 200 μl CSF, 31 FAAs and 6 DPs in 100 μl plasma, and 23 FAAs and 5 DPs in 200 μl urine. These data demonstrate the potential for using LCMS² to discover changes in FAA and DP metabolic pathways that occur during disease pathogenesis.     

Wood formation in poplar: identification, characterization, and seasonal variation of xylem proteins

Proteins that are preferentially produced in developing xylem may play a substantial role in xylogenesis. To reveal the identity of these proteins, comparative two-dimensional polyacrylamide gel electrophoresis was performed on young differentiating xylem, mature xylem, and bark of poplar (Populus trichocarpa Hook. cv. `Trichobel') harvested at different times of the year. The most-abundant xylem proteins were identified by microsequence analysis. For 17 of these proteins a putative function could be assigned based on similarity with previously characterized proteins, and for 15 out of these corresponding expressed sequence tags (ESTs) were found in the poplar EST database. The identified xylem–preferential proteins, defined by comparing the protein patterns from xylem and bark, were all involved in the phenylpropanoid pathway: two caffeoyl-coenzyme A O-methyltransferases (CCoAOMT), one phenylcoumaran benzylic ether reductase (PCBER), one bispecific caffeic acid/5-hydroxyferulic acid O-methyltransferase (COMT), five S-adenosyl-L-methionine synthetases, and one homologue of glycine hydroxymethyltransferase (GHMT). Remarkably, the biological function of the two most-abundant xylem-preferential proteins (PCBER and a GHMT homologue) remains unclear. In addition, several housekeeping enzymes were identified: two enolases, two glutamine synthetases, one 70-kDa heat-shock cognate, one calreticulin, and one α-tubulin. In comparison to the xylem-preferential proteins, the housekeeping proteins were expressed at significant levels in the bark as well. Also, several additional protein spots were detected for CCoAOMT, PCBER, and COMT by immunoblot. Our data show that for the study of xylogenesis, two-dimensional protein gel comparisons combined with systematic protein sequencing may yield information complementary to that from EST sequencing strategies. Received: 28 June 1999 / Accepted: 3 September 1999     

Polyamines: metabolism to systems biology and beyond

Summary. Polyamines and the metabolic and physiopathological processes in which they are involved represent an active field of research that has been continuously growing since the seventies. In the last years, the trends in the focused areas of interest within this field since the 1970s have been confirmed. The impact of “-omics” in polyamine research remains too low in comparison with its deep impact on other biological research areas. These high-throughput approaches, along with systems biology and, in general, more systemic and holistic approaches should contribute to a renewal of this research area in the near future.     

Influence of nitric oxide synthase activity on amino acid concentration in the quinolinate lesioned rat striatum: A microdialysis and histochemical study

Summary. The influence of nitric oxide synthase (NOS) activity on the KCl-evoked amino acid concentrations was investigated by in vivo microdialysis in the striatum in a rat model of excitotoxic lesion. Basal microdialysate levels of amino acids decreased during the quinolinic acid-induced neurodegeneration process, except for glutamine that increased initially and returned to control values 30 days after quinolinic acid exposure. KCl-evoked increase of extracellular amino acid concentration was reduced due to NOS activity in the striatum of both controls and lesioned animals, except for 120 days after quinolinic acid injection. These changes of amino acid concentrations in microdialysates correlated with the known biochemistry of the consecutive domineered cell types during the lesion process as revealed by histochemistry for NOS, NADPH-diaphorase, GFAP and isolectin B4. The present data provide direct evidence that NOS activity can modulate extracellular amino acid concentrations in the striatum not only under physiological conditions, but also during a pharmacologically induced lesion process and, thus, suggests that nitric oxide affects neurodegeneration via this pathway. Received October 20, 1999; Accepted February 25, 2000     

Stochastic multitype epidemics in a community of households: estimation and form of optimal vaccination schemes

This paper treats a stochastic model for an SIR (susceptible-->infective-->removed) multitype household epidemic. The community is assumed to be closed, individuals are of different types and each individual belongs to a household. Previously obtained probabilistic and inferential results for the model are used to derive the optimal vaccination scheme. By this is meant the scheme that vaccinates the fewest among all vaccination schemes that reduce the threshold parameter below 1. This is done for the situation where all model parameters are known and also for the case where parameters are estimated from an outbreak in the community prior to vaccination. It is shown that the algorithm which chooses vaccines sequentially, at each step selecting the individual which reduces the threshold parameter the most, is not in general an optimal scheme. As a consequence, explicit characterisation of the optimal scheme is only possible in certain special cases. Two different types of vaccine responses, leaky and all-or-nothing, are considered and compared for the problems mentioned above. The methods are illustrated with some numerical examples.     

Effects of endogenous glutamate on extracellular concentrations of taurine in striatum and nucleus accumbens of the awake rat: Involvement of NMDA and AMPA/kainate receptors

Summary. Using microdialysis, the effects of endogenous glutamate on extracellular concentrations of taurine in striatum and nucleus accumbens of the awake rat were investigated. The glutamate uptake inhibitor L-trans-pyrrolidine-2,4-dicarboxylic acid (PDC) was used to increase the extracellular concentration of glutamate. PDC (1, 2 and 4 mM) produced a dose-related increase of extracellular concentrations of glutamate and taurine in striatum and nucleus accumbens. Increases of extracellular taurine were significantly correlated with increases of extracellular glutamate, but not with PDC doses, which suggests that endogenous glutamate produced the observed increases of extracellular taurine in striatum and nucleus accumbens. The role of ionotropic glutamate receptors on the increases of taurine was also studied. In striatum, perfusion of the antagonists of NMDA and AMPA/kainate glutamate receptors attenuated the increases of extracellular taurine. AMPA/kainate, but not NMDA receptors, also reduced the increases of extracellular taurine in nucleus accumbens. These results suggest that glutamate-taurine interactions exist in striatum and nucleus accumbens of the awake rat. Received March 5, 1999/Accepted September 22, 1999     

Reactivity and oxidative potential of fructose and glucose in enkephalin-sugar model systems

Summary. The reactions of Leu- and Met-enkephalin (Tyr-Gly-Gly-Phe-Leu/Met) with fructose resulted in the parallel formation of Heyns compounds (N-peptidyl-d-mannosamine and -d-glucosamine) and sugar-peptide generated imidazolidinone diastereomers. Glucose showed higher level of reactivity than fructose with respect to the extent of glycated product formation. The presence of fructose in the incubation mixtures makes Met residue more susceptible to oxidation than glucose. Authors’ address: Dr. Štefica Horvat, Division of Organic Chemistry and Biochemistry, Ruđer Bošković Institute, POB 180, 10002 Zagreb, Croatia     

Abscisic acid and hydraulic conductivity of maize roots: a study using cell- and root-pressure probes

Using root- and cell-pressure probes, the effects of the stress hormone abscisic acid (ABA) on the water-transport properties of maize roots (Zea mays L.) were examined in order to work out dose and time responses for root hydraulic conductivity. Abscisic acid applied at concentrations of 100–1,000 nM increased the hydraulic conductivity of excised maize roots both at the organ (root Lp_r: factor of 3–4) and the root cell level (cell Lp: factor of 7–27). Effects on the root cortical cells were more pronounced than at the organ level. From the results it was concluded that ABA acts at the plasmalemma, presumably by an interaction with water channels. Abscisic acid therefore facilitated the cell-to-cell component of transport of water across the root cylinder. Effects on cell Lp were transient and highly specific for the undissociated (+)-cis-trans-ABA. The stress hormone ABA facilitates water uptake into roots as soils start drying, especially under non-transpiring conditions, when the apoplastic path of water transport is largely excluded. Received: 26 February 2000 / Accepted: 17 August 2000     

Inoculation and nitrate alter phytohormone levels in soybean roots: differences between a supernodulating mutant and the wild type

 The levels of different cytokinins, indole-3-acetic acid (IAA) and abscisic acid (ABA) in roots of Glycine max [L.] Merr. cv. Bragg and its supernodulating mutant nts382 were compared for the first time. Forty-eight hours after inoculation with Bradyrhizobium, quantitative and qualitative differences were found in the root's endogenous hormone status between cultivar Bragg and the mutant nts382. The six quantified cytokinins, ranking similarly in each genotype, were present at higher concentrations (30–196% on average for isopentenyl adenosine and dihydrozeatin riboside, respectively) in mutant roots. By contrast, the ABA content was 2-fold higher in Bragg, while the basal levels of IAA [0.53 μmol (g DW)⁻¹, on average] were similar in both genotypes. In 1 mM NO₃ ⁻-fed Bragg roots 48 h post-inoculation, IAA, ABA and the cytokinins isopentenyl adenine, and isopentenyl adenosine quantitatively increased with respect to uninoculated controls. However, only the two cytokinins increased in the mutant. High NO₃ ⁻ (8 mM) markedly reduced root auxin concentration, and neither genotypic differences nor the inoculation-induced increase in auxin concentration in Bragg was observed under these conditions. Cytokinins and ABA, on the other hand, were little affected by 8 mM NO₃ ⁻. Root IAA/cytokinin and ABA/cytokinin ratios were always higher in Bragg relative to the mutant, and responded to inoculation (mainly in Bragg) and nitrate (both genotypes). The overall results are consistent with the auxin-burst-control hypothesis for the explanation of autoregulation and supernodulation in soybean. However, they are still inconclusive with respect to the inhibitory effect of NO₃ ⁻. Received: 16 April 1999 / Accepted: 13 December 1999     

N-acetyl-L-cysteine as a source of sulfane sulfur in astrocytoma and astrocyte cultures: correlations with cell proliferation

Summary. N-acetyl-L-cysteine (NAC), a precursor of L-cysteine, not only elevates the level of glutathione in both astrocytoma and astrocyte cultures, but also affects the cellular level of sulfane sulfur. Astrocytoma cells were investigated using the stable U373 human cell line. In the U373 cells, N-acetyl-L-cysteine, depending on the concentration in the culture medium and culture duration, either elevated or diminished the level of sulfane sulfur, and this was respectively accompanied by decreased or increased cellular proliferation. In murine astrocytes, in turn, NAC was capable of lowering the level of sulfane sulfur and in this way decreased cellular proliferation. It seems that normal (astrocyte) and transformed (astrocytoma) cells differed in their reaction to NAC in the culture medium. The effect of N-acetyl-L-cysteine on astrocytoma cells was advantageous in that it inhibited their proliferation through the elevation of the level of sulfane sulfur. Authors’ address: Maria Wróbel, Chair of Medical Biochemistry, Jagiellonian University Medical College, Kopernika 7 St., 31-034 Kraków, Poland