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Bone remodeling theory applied to the study of n unit-elements model.

The aim of this paper is to illustrate the application of mathematical tools for the analysis of non-linear dynamical systems to the study of global stability of one kind of bone remodeling scheme applied to n unit-elements model. The particular aspects analyzed here are the stationary states related to this theory and a condition of their stability. The non-linear equations governing the remodeling process are solved by finite-difference method and the well-known results on the heterogeneous spatial organizations have been retrieved and confirm the analytical study. This kind of remodeling theory is useful for investigating the effects of physiological parameters on the development, maintenance, and adaptation of bone under mechanical loading.

Bone Remodeling↗

Effects of macroalgal mats on intertidal sandflats: an experimental study.

The growth of green macroalgal mats is becoming increasingly common in many marine intertidal habitats. While the ecological effects of such growth has previously been experimentally investigated on mudflats, such experiments have rarely been performed on intertidal sandflats. This study investigated the ecological effects of macroalgal cover on a moderately exposed intertidal sandflat, Drum Sands, Firth of Forth, Scotland. Artificially implanted Enteromorpha prolifera (Müller) caused marked changes in the macrobenthos, together with significant changes in all the measured sediment variables. After 6 weeks, the weed significantly increased the macrofaunal diversity. The numbers of Pygospio elegans (Claparède) were significantly reduced under weed mats, while those of Capitella capitata (Fabricius), oligochaetes and gammarids increased. Percent water, organics and silt/clay contents, medium phi and sorting coefficient significantly increased in the sediments under weed mats which also became significantly more reduced between 1 and 8 cm depth. After 20 weeks, a macrofaunal community numerically dominated by C. capitata, with a significantly reduced diversity, was present under weed mats, while sediment variables were no longer significantly different from controls. The negative effect of E. prolifera on P. elegans was mainly due to larval filtering, suggesting that weed is likely to have detrimental effects on population maintenance of most species which rely on planktonic larval recruitment. These results are broadly similar to those obtained from algal manipulation experiments performed in much more sheltered, muddier environments. We suggest that a predictable deterioration in environmental quality results from the growth of macroalgal mats in soft-bottom habitats. However, the longer term effects of such algal growth are less predictable and depend upon the spatial distributions of the most abundant infaunal species and the spatial heterogeneity of weed mat establishment.

Journal Article↗

Disease propagation in connected host populations with density-dependent dynamics: the case of the Feline Leukemia Virus.

Spatial heterogeneity is a strong determinant of host-parasite relationships, however local-scale mechanisms are often not elucidated. Generally speaking, in many circumstances dispersal is expected to increase disease persistence. We consider the case when host populations show density-dependent dynamics and are connected through the dispersal of individuals. Taking the domestic cats (Felis catus)--Feline Leukemia Virus (FeLV) as a toy model of host-microparasite system, we predict the disease dynamics when two host populations with distinct or similar structures are connected together and to the surrounding environment by dispersal. Our model brings qualitatively different predictions from one-population models. First, as expected, biologically realistic rates of dispersal may allow FeLV to persist in sets of populations where the virus would have gone extinct otherwise, but a reverse outcome is also possible: eradication of FeLV from a small population by connexion to a larger population where it is not persistent. Second, overall prevalence as well as depression of host population size due to infection are both enhanced by dispersal, even at low dispersal rates when disease persistence is not achieved in the two populations. This unexpected prediction is probably due to the combination of dispersal with density-dependent population dynamics. Third, the dispersal of non-infectious cats has more influence on virus prevalence than the dispersal of infectious. Finally, prevalence and depression of host population size are both related to the rate of dispersion, to the health status of individuals dispersing and to the dynamics of host populations.

Animals↗

A dynamical model for phase transitions of lipids induced by calcium ions.

Lipid membranes exist essentially in two different phases. A phase transition can be triggered off either by changing the temperature or, isothermally, by varying an external factor such as ionic concentration, pH, organic solvents, etc. Since the isothermal transition may be induced at physiological temperature, it may play an important regulatory role in diverse cellular functions. Based on the Landau-Ginsburg theory, the thermotropic transitions of lipids has been described by a number of models. In the present work a dynamical model for an isothermal phase transition of phospholipids induced by ionic binding is proposed. The properties of the model show that by ionic binding, phospholipids may form spatial heterogeneous distributions of lipids in fluid and crystalline phases. This heterogeneity possibly being the cause of membrane instabilities, which favour enhanced vesicle fusions observed in the presence of Ca2+.

Calcium↗

On the coexistence of three microbial populations competing for two complementary substrates in configurations of interconnected chemostats.

We examine the question of coexistence of three microbial populations competing for two complementary rate-limiting substrates in configurations of interconnected chemostats. It is known that coexistence of two populations competing for two rate-limiting substrates is possible in a single chemostat, but coexistence is not possible when three populations are involved. We examine whether coexistence of three populations becomes possible by considering configurations of two or three interconnected chemostats, thus allowing for effects of spatial heterogeneity. Computational analysis of the model equations indicates that in the case of two chemostats coexistence is possible only for specific discrete parameter values where the system is structurally unstable and therefore the coexistence state is not practically attainable, whereas in the case of three chemostats coexistence is possible for a whole range of parameter values where the system is structurally stable and therefore the coexistence state can be realized in practice.

Bacteria↗

Competing populations in flows with chaotic mixing.

We investigate the effects of spatial heterogeneity on the coexistence of competing species in the case when the heterogeneity is dynamically generated by environmental flows with chaotic mixing properties. We show that one effect of chaotic advection on the passively advected species (such as phytoplankton, or self-replicating macro-molecules) is the possibility of coexistence of more species than that limited by the number of niches they occupy. We derive a novel set of dynamical equations for competing populations.

Competitive Behavior↗

Quasicycles revisited: apparent sensitivity to initial conditions.

Environmental noise is known to sustain cycles by perturbing a deterministic approach to equilibrium that is itself oscillatory. Quasicycles produced in this way display a regular period but varied amplitude. They were proposed by Nisbet and Gurney (Nature 263 (1976) 319) as one possible explanation for population fluctuations in nature. Here, we revisit quasicyclic dynamics from the perspective of nonlinear time series analysis. Time series are generated with a predator-prey model whose prey's growth rate is driven by environmental noise. A method for the analysis of short and noisy data provides evidence for sensitivity to initial conditions, with a global Lyapunov exponent often close to zero characteristic of populations 'at the edge of chaos'. Results with methods restricted to long time series are consistent with a finite-dimensional attractor on which dynamics are sensitive to initial conditions. These results are compared with those previously obtained for quasicycles in an individual-based model with heterogeneous spatial distributions. Patterns of sensitivity to initial conditions are shown to differentiate phase-forgetting from phase-remembering quasicycles involving a periodic driver. The previously reported mode at zero of Lyapunov exponents in field and laboratory populations may reflect, in part, quasicyclic dynamics.

Algorithms↗

Competition and stoichiometry: coexistence of two predators on one prey.

The competitive exclusion principle (CEP) states that no equilibrium is possible if n species exploit fewer than n resources. This principle does not appear to hold in nature, where high biodiversity is commonly observed, even in seemingly homogenous habitats. Although various mechanisms, such as spatial heterogeneity or chaotic fluctuations, have been proposed to explain this coexistence, none of them invalidates this principle. Here we evaluate whether principles of ecological stoichiometry can contribute to the stable maintenance of biodiverse communities. Stoichiometric analysis recognizes that each organism is a mixture of multiple chemical elements such as carbon (C), nitrogen (N), and phosphorus (P) that are present in various proportions in organisms. We incorporate these principles into a standard predator-prey model to analyze competition between two predators on one autotrophic prey. The model tracks two essential elements, C and P, in each species. We show that a stable equilibrium is possible with two predators on this single prey. At this equilibrium both predators can be limited by the P content of the prey. The analysis suggests that chemical heterogeneity within and among species provides new mechanisms that can support species coexistence and that may be important in maintaining biodiversity.

Animals↗

Effect of mass transfer on concentration wave propagation during anaerobic digestion of solid waste.

A distributed model of anaerobic digestion of solid waste was developed to study effects of mass transfer on the rate of propagation of initiation methanogenic area. The diffusion and advection of volatile fatty acids (VFA) and methanogenic biomass were taken into account in the model of a one-dimensional (ID) reactor. It was considered that VFA inhibits both polymer hydrolysis and acetoclastic methanogenesis. This approach allows to view the bioreactor as an active medium that provokes concentration waves from some area of methanogenic initiation (local VFA depression) to the total reactor volume. The model shows that mass transfer-based acceleration of methane production in the reactor is possible when the intensity of VFA utilization in the methanogenic area is sufficient for a complete digestion of the incoming VFA. Otherwise, initiation methanogenic area will be suppressed by increasing concentration of VFA. The obtained results emphasize the importance of considering spatial heterogeneity of the reaction for the analysis of solid anaerobic digestion in bioreactors and landfills. The digestion of solid waste can be optimized by setting the low rate of mass transfer (mixing or leachate recirculation) during lag-phase of the reaction with subsequent increase in the mass transfer rate in parallel with the propagation of methanogenic population. In this case, the rate of concentration waves substantially increases.

Biomass↗

Effects of particulate explosives on estimating contamination at a historical explosives testing area.

A historical explosives testing area harbored contamination as unevenly distributed solid particles within a contaminant-stained soil matrix. Particles larger than 3 mm diameter accounted for 96.4% of the explosives contamination. Independent sampling and analysis methods showed significant differences in contaminant estimations due to particulate explosives. We present a solvent-based sample averaging method designed to solve spatial heterogeneity problems resulting from the presence of contaminant particles.

Chromatography, High Pressure Liquid↗

Arsenic solubility and distribution in poultry waste and long-term amended soil.

The purpose of this study was to quantify the solubility and distribution of As among solid-phase components in poultry wastes and soils receiving long-term poultry waste applications. Arsenic in the water-soluble, NaOCl-extractable (organically bound), NH(2)OH x HCl-extractable (oxide bound) and residual fractions were quantified in an Upper Coastal Plain soil (Neshoba County, MS) that received annual waste applications. After 25 years, As in the amended soil had a mean of 8.4 mg kg(-1) compared to 2.68 mg kg(-1) for a non-amended soil. Arsenic in the amended soil was mainly in the residual fraction (72% of total), which is generally considered the least bioavailable fraction. Arsenic in poultry waste samples was primarily water-soluble (5.3-25.1 mg kg(-1)), representing 36-75% of the total As. To assess the extent of spatial heterogeneity, total As in a 0.5-ha area within the long-term waste-amended field was quantified. Soil surface samples were taken on 10-m grid points and results for total As appeared negatively skewed and approximated a bimodal distribution. Total As in the amended soil was strongly correlated with Fe oxides, clay and hydroxy interlayered vermiculite concentrations, and negatively correlated with Mehlich III-P, mica and quartz contents.

Animal Feed↗

Sedimentation rates measurements in former channels of the upper Rhône river using Chernobyl 137Cs and 134Cs as tracers.

Former river channels are aquatic ecosystems with a different geomorphology generated by fluvial dynamics more or less linked to the main channel. They present different ecological successions to become terrestrial ecosystems and are thus supposed to have different sedimentation rates. The aim of this paper is to assess this sedimentation rate using radioactive tracer methodology commonly used in lake studies. Chernobyl impacts, expressed in 137Cs concentration and 137Cs/134Cs ratio, were determined in sediment cores. Sites (21) were sampled in the alluvial plain of the Upper Rhône River from 1989 to 1994. The contamination presented a high spatial heterogeneity. The maximum values encountered by site ranged between 34 and 541 Bq/kg of dry matter. The method generally gave good core profiles. Sedimentation rate ranged between 0.14 and 0.70 cm/year for the former meanders and between 0.14 and 2.86 cm/year for the braided channels. The sediment accumulation rates ranged from 0.03 to 0.25 g/cm2 per year and 0.03 to 2.26 g/cm2 per year, respectively. These values are similar to those found for Lake Geneva. The importance of the former channels in relation to the main channel is enhanced by the higher contamination and radionuclides retention. The sediment accumulation rate is related to the organic carbon content in the sediment. A comparison between two former channels with different productivity showed that the the allogenous driven system presents a high organic sediment accumulation rate with a low organic content in the sediment and inversely, a low organic sediment accumulation rate with a high organic carbon content was found for the autogenous drive system.

Carbon↗

Differential effects of stretch and compression on membrane currents and [Na+]c in ventricular myocytes.

Mechano-electrical feedback was studied in the single ventricular myocytes. A small fraction (approximately 10%) of the cell surface could be stretched or compressed by a glass stylus. Stretch depolarised, shortened the action potential and induced extra systoles. Stretch activated non-selective cation currents (I(ns)) showed a linear voltage dependence, a reversal potential of 0 mV, a pure cation selectivity, and were blocked by 8 microM Gd(3+) or 30 microM streptomycin. Stretch reduced Ca(2+) and K(+) (I(K)) currents. Local compression of broadwise attached cells activated I(K) but not I(ns). Cytochalasin D or colchicin, thought to disrupt the cytoskeleton, suppressed the mechanosensitivity of I(ns) and I(K). During stretch, the cytosolic sodium concentration increased with spatial heterogeneities, local hotspots with [Na(+)](c)>24 mM appeared close to surface membrane and t-tubules (pseudoratiometric imaging using Sodium Green fluorescence). Electronprobe microanalysis confirmed this result and indicated that stretch increased total sodium [Na] in cell compartments such as mitochondria, nuclear envelope and nucleus. Our results obtained by local stretch differ from those obtained by end-to-end stretch (literature). We speculate that channels may be activated not only by axial but also by shear stress, and, that stretch can activate channels outside the deformed sarcomeres via second messenger.

Action Potentials↗

Modelling of signalling via G-protein coupled receptors: pathway-dependent agonist potency and efficacy.

A mathematical model is constructed to study promiscuous coupling of receptors to G-proteins and to simulate events leading to the activation of multiple effector pathways within a cell. The model is directed at a better understanding of the factors that determine the efficacy and potency of a drug. Assuming that the receptors can exist in multiple conformational states, and allowing for agonist specific conformation, a system of ordinary differential equations is constructed and subsequently pathway-dependent agonist efficacy and potency order is predicted. A simple case of the compartmentalization of receptors and G-proteins is also given, using the current model to illustrate the effects of spatial heterogeneity on the predicted response.

GTP-Binding Proteins↗

Expression of alpha 7 neuronal nicotinic receptors during postnatal development of the rate cerebellum.

Several lines of evidence suggest that alpha-bungarotoxin-sensitive neuronal nicotinic acetylcholine receptors may play a developmental role by modulating plasticity in neuronal circuits. The alpha 7 subunit, a main component of these receptors, is expressed in most regions of the brain, including the cerebellum, where it is present almost exclusively in Purkinje cells and deep cerebellar nuclei. Purkinje cells constitute the only efferent pathway of the cerebellum and their development involves complex interactions, which have been extensively studied. They therefore provide a potentially useful model for analysis of development plasticity which could be influenced by alpha 7 neuronal nicotinic receptors. In the present study a previously characterized monoclonal antibody (mAb 307) has been used to determine the temporal pattern of expression of the alpha 7 subunit in the developing rat cerebellum. No detectable alpha 7 immunoreactivity is found between P0 and P2. Between P3 and P5, however, the Purkinje cell layer shows moderate immunolabeling. alpha 7 expression in this layer increases rapidly between P8 and P15. This increase in alpha 7 staining, which overlaps in time with important developmental and synaptogenic events, is not uniform throughout the cerebellar cortex. Thus, between P3 and P5 all Purkinje cells are weakly labeled, while at later stages (P8-P15) immunolabeling becomes more intense, but at the same time, disappears from Purkinje cells in rostral lobules. In addition, a very well defined pattern for discontinuous or columnar labeling is detected in regions of the Purkinje cell layer where alpha 7 subunits were being expressed. Finally, at P20, alpha 7 subunit labeling is found again in all Purkinje cells, although with lower intensity. These results suggest that alpha 7 receptor expression is developmentally regulated, with a time course that parallels the final differentiation of Purkinje cells. In addition, the heterogeneous spatial distribution of alpha 7-containing nicotinic receptors indicates that, during cerebellar maturation, these cells may receive different signals that modulate receptor gene expression in a very specific way.

Animals↗

Is hepatic cytochrome P4501A1 expression predictive of hepatic burdens of dioxins, furans, and PCBs in Atlantic tomcod from the Hudson River estuary?

Hepatic cytochrome P4501A1 (CYP1A1) expression in fishes is frequently used to evaluate bioavailable aromatic hydrocarbon contamination of aquatic ecosystems. In controlled laboratory experiments, CYP1A1 expression in naïve fishes is usually dose-responsive to aromatic hydrocarbons and in field studies levels of gene expression in natural populations often correspond with known levels of sediment-borne contaminants. We quantified CYP1A1 mRNA levels in juvenile Atlantic tomcod Microgadus tomcod from 42 sites in the Hudson River estuary to evaluate the correspondence between hepatic CYP1A1 expression and hepatic concentrations of persistent halogenated aromatic hydrocarbons and to determine the utility of CYP1A1 expression as a biomarker in evaluating the microgeographic distribution of bioavailable contaminants within a large aquatic ecosystem. We found significant spatial heterogeneity in CYP1A1 mRNA levels among collection sites with levels of gene expression differing in some cases by 23-34 folds. CYP1A1 mRNA expression was highest in tomcod from the Newark Bay complex and lowest in tomcod from the most upriver collection sites in the main stem of the Hudson River. Although levels of PCDDs, PCDFs, and PCBs expressed as TCDD TEQs and CYP1A1 mRNA were highest in tomcod from the Newark Bay complex, there was no relationship between hepatic halogenated aromatic hydrocarbon levels and hepatic CYP1A1 mRNA in tomcod from sites in the main stem of the Hudson River. These results suggest that levels of CYP1A1 expression in fish from sites highly polluted with mixtures of halogenated aromatic hydrocarbons and other xenobiotics may not always be reflective of levels of bioavailable aromatic hydrocarbon contaminants. Based on these results and earlier controlled laboratory experiments, we hypothesize that elevated levels of CYP1A1 expression in tomcod from the Hudson River may be due primarily to PAHs or other contaminants not measured in this study.

Animals↗

Effects of progestin-estrogen replacement therapy on QT-dispersion in postmenopausal women.

Female gender is considered to be a risk factor for ventricular arrhythmias. Furthermore, experimental studies have shown that estrogen has an impact on the electrophysiological properties of the heart. Thus, the effects of estrogen- (ERT) and progestin-estrogen- (PERT) replacement therapy on QT-interval length and dipersion as indicators of ventricular repolarisation have been examined in the present study. Twenty-two postmenopausal women without hormone replacement therapy and 16 postmenopausal women on ERT and 22 on PERT (age 48-71 years) were included. QT intervals were measured in five subsequent cycles of at least 10 leads of standard ECG. QT-dispersion was calculated as the difference between maximal and minimal QT-interval. QT-intervals and -dispersions were rate (QT(c)) and linear (QT(lc)) corrected. PERT significantly reduced ventricular QT-dispersion (QT-, QT(c)- and QT(lc)-dispersion) compared to the control group (QT(c)-dispersion (ms): 32+/-13 vs. 48+/-14; P<0.05), while ERT significantly prolonged QT-intervals (QT(c) mean (ms): 423+/-28 vs. 398+/-31; P<0.05) without affecting QT-dispersion. These findings support the hypothesis that sex hormones may directly modulate ventricular repolarisation in vivo. Above all, the progestin component of replacement therapy is suggested to homogenize spatial heterogeneity of ventricular repolarisation.

Aged↗

A global livestock production and health atlas (GLiPHA) for interactive presentation, integration and analysis of livestock data.

An interactive electronic atlas has been developed with the purpose of providing a scaleable overview of spatial and temporal variation in animal production and health-related information for decision and policy makers in national and international institutions. The information contained in the atlas is currently managed and presented using the Key Indicators Mapping System (KIMS), and will also be integrated using the Key Indicators Database System (KIDS). Both systems were developed by the World Agricultural Information Centre of the FAO (FAO-WAICENT), the former as a stand-alone application and the latter for access via the Internet. Components of the atlas include vector maps, livestock disease and production databases, rules for country-level disease risk classification and 'disease cards' containing basic background information on diseases included in the atlas. The disease data is currently based primarily on Office International des Epizooties (OIE) disease reports, and the livestock production data on the FAO-WAICENT database. The atlas is highly interactive and allows visual presentation of information using maps, tables and charts. It also contains links to relevant resource information on the Internet. Diseases covered in the animal health layer include most OIE List A diseases and a subset of OIE List B diseases. Extensive analyses have been conducted to develop a set of qualitative and semi-quantitative criteria that allow improved disease status classifications based on 5-years cumulative OIE disease reports, and official disease control declarations. Classification rules were determined depending on the epidemiological features of each disease and considering spatial heterogeneity of disease presence in local regions.

Animal Diseases↗