Quantifying chaos for ecological stoichiometry

The theory of ecological stoichiometry considers ecological interactions among species with different chemical compositions. Both experimental and theoretical investigations have shown the importance of species composition in the outcome of the population dynamics. A recent study of a theoretical three-species food chain model considering stoichiometry [B. Deng and I. Loladze, Chaos 17, 033108 (2007)] shows that coexistence between two consumers predating on the same prey is possible via chaos. In this work we study the topological and dynamical measures of the chaotic attractors found in such a model under ecological relevant parameters. By using the theory of symbolic dynamics, we first compute the topological entropy associated with unimodal Poincareacute return maps obtained by Deng and Loladze from a dimension reduction. With this measure we numerically prove chaotic competitive coexistence, which is characterized by positive topological entropy and positive Lyapunov exponents, achieved when the first predator reduces its maximum growth rate, as happens at increasing delta(1). However, for higher values of delta(1) the dynamics become again stable due to an asymmetric bubble-like bifurcation scenario. We also show that a decrease in the efficiency of the predator sensitive to prey's quality (increasing parameter zeta) stabilizes the dynamics. Finally, we estimate the fractal dimension of the chaotic attractors for the stoichiometric ecological model.

Studies in stoichiometry with compositional data

Geochemical data that is derived from the whole or partial analysis of various geologic materialsrepresent a composition of mineralogies or solute species. Minerals are composed of structuredrelationships between cations and anions which, through atomic and molecular forces, keep the elementsbound in specific configurations. The chemical compositions of minerals have specific relationships thatare governed by these molecular controls. In the case of olivine, there is a well-defined relationshipbetween Mn-Fe-Mg with Si. Balances between the principal elements defining olivine composition andother significant constituents in the composition (Al, Ti) have been defined, resulting in a near-linearrelationship between the logarithmic relative proportion of Si versus (MgMnFe) and Mg versus (MnFe),which is typically described but poorly illustrated in the simplex.The present contribution corresponds to ongoing research, which attempts to relate stoichiometry andgeochemical data using compositional geometry. We describe here the approach by which stoichiometricrelationships based on mineralogical constraints can be accounted for in the space of simplicialcoordinates using olivines as an example. Further examples for other mineral types (plagioclases andmore complex minerals such as clays) are needed. Issues that remain to be dealt with include thereduction of a bulk chemical composition of a rock comprised of several minerals from which appropriatebalances can be used to describe the composition in a realistic mineralogical framework. The overallobjective of our research is to answer the question: In the cases where the mineralogy is unknown, arethere suitable proxies that can be substituted?Kew words: Aitchison geometry, balances, mineral composition, oxides

Comparison of H/Al stoichiometry of mineral and organic soils in Brazil

Exchangeable Al has been used as a criterion for the calculation of lime requirement in several Brazilian States. However, the laboratory method with extraction by a 1 mol L-1 KCl solution followed by indirect alkaline titration is not accurate for some Brazilian soils, mainly in the case of soils with high organic matter content. The objective of this study was therefore to evaluate the stoichiometry of H+/Al3+ in KCl soil extracts. The results suggested that organically complexed Al is the main contributor to exchangeable acidity in soils enriched with organic matter. Liming recommendations for organic soils based exclusively on exchangeable Al determined by the NaOH titration method should therefore be revised.

Stoichiometry of Heteromeric BAFF and APRIL Cytokines Dictates Their Receptor Binding and Signaling Properties.

The closely related TNF family ligands B cell activation factor (BAFF) and a proliferation-inducing ligand (APRIL) serve in the generation and maintenance of mature B-lymphocytes. Both BAFF and APRIL assemble as homotrimers that bind and activate several receptors that they partially share. However, heteromers of BAFF and APRIL that occur in patients with autoimmune diseases are incompletely characterized. The N and C termini of adjacent BAFF or APRIL monomers are spatially close and can be linked to create single-chain homo- or hetero-ligands of defined stoichiometry. Similar to APRIL, heteromers consisting of one BAFF and two APRILs (BAA) bind to the receptors B cell maturation antigen (BCMA), transmembrane activator and CAML interactor (TACI) but not to the BAFF receptor (BAFFR). Heteromers consisting of one APRIL and two BAFF (ABB) bind to TACI and BCMA and weakly to BAFFR in accordance with the analysis of the receptor interaction sites in the crystallographic structure of ABB. Receptor binding correlated with activity in reporter cell line assays specific for BAFFR, TACI, or BCMA. Single-chain BAFF (BBB) and to a lesser extent single-chain ABB, but not APRIL or single-chain BAA, rescued BAFFR-dependent B cell maturation in BAFF-deficient mice. In conclusion, BAFF-APRIL heteromers of different stoichiometries have distinct receptor-binding properties and activities. Based on the observation that heteromers are less active than BAFF, we speculate that their physiological role might be to down-regulate BAFF activity.

The determination of the stoichiometry of the mixed complex of vanadium with hydrogen peroxide and with 4-(2-Pyridilazo) Resorcinol

The present study reports details of the stoichiometric characterization of the mixed complex system, V(H2O2)PAR, formed when vanadium adequately reacts with hydrogen peroxide and with 4-(2-Pyridilazo)Resorcinol. Also the presence of polynuclear species was investigated in order to elucidate about unambiguous assignment of the molar absorptivity, stability constant and composition of the complex. Two mathematical treatments methods of the experimental results were employed. From the results it can be concluded that this system corresponds to a mononuclear complex with 1:1:1 stoichiometry.

Consequences of warming and resource quality on the stoichiometry and nutrient cycling of a stream shredder

As a result of climate change, streams are warming and their runoff has been decreasing in most temperate areas. These changes can affect consumers directly by increasing their metabolic rates and modifying their physiology and indirectly by changing the quality of the resources on which organisms depend. In this study, a common stream detritivore (Echinogammarus berilloni Catta) was reared at two temperatures (15 and 20°C) and fed Populus nigra L. leaves that had been conditioned either in an intermittent or permanent reach to evaluate the effects of resource quality and increased temperatures on detritivore performance, stoichiometry and nutrient cycling. The lower quality (i.e., lower protein, soluble carbohydrates and higher C:P and N:P ratios) of leaves conditioned in pools resulted in compensatory feeding and lower nutrient retention capacity by E. berilloni. This effect was especially marked for phosphorus, which was unexpected based on predictions of ecological stoichiometry. When individuals were fed pool-conditioned leaves at warmer temperatures, their growth rates were higher, but consumers exhibited less efficient assimilation and higher mortality. Furthermore, the shifts to lower C:P ratios and higher lipid concentrations in shredder body tissues suggest that structural molecules such as phospholipids are preserved over other energetic C-rich macromolecules such as carbohydrates. These effects on consumer physiology and metabolism were further translated into feces and excreta nutrient ratios. Overall, our results show that the effects of reduced leaf quality on detritivore nutrient retention were more severe at higher temperatures because the shredders were not able to offset their increased metabolism with increased consumption or more efficient digestion when fed pool-conditioned leaves. Consequently, the synergistic effects of impaired food quality and increased temperatures might not only affect the physiology and survival of detritivores but also extend to other trophic compartments through detritivore-mediated nutrient cycling.

Studies in stoichiometry with compositional data

Geochemical data that is derived from the whole or partial analysis of various geologic materials represent a composition of mineralogies or solute species. Minerals are composed of structured relationships between cations and anions which, through atomic and molecular forces, keep the elements bound in specific configurations. The chemical compositions of minerals have specific relationships that are governed by these molecular controls. In the case of olivine, there is a well-defined relationship between Mn-Fe-Mg with Si. Balances between the principal elements defining olivine composition and other significant constituents in the composition (Al, Ti) have been defined, resulting in a near-linear relationship between the logarithmic relative proportion of Si versus (MgMnFe) and Mg versus (MnFe), which is typically described but poorly illustrated in the simplex. The present contribution corresponds to ongoing research, which attempts to relate stoichiometry and geochemical data using compositional geometry. We describe here the approach by which stoichiometric relationships based on mineralogical constraints can be accounted for in the space of simplicial coordinates using olivines as an example. Further examples for other mineral types (plagioclases and more complex minerals such as clays) are needed. Issues that remain to be dealt with include the reduction of a bulk chemical composition of a rock comprised of several minerals from which appropriate balances can be used to describe the composition in a realistic mineralogical framework. The overall objective of our research is to answer the question: In the cases where the mineralogy is unknown, are there suitable proxies that can be substituted? Kew words: Aitchison geometry, balances, mineral composition, oxides

Estimation of the stoichiometry of volatile fatty acid production in the rumen of lactating cows

The purpose of this study was to improve the prediction of the quantity and type of Volatile Fatty Acids (VFA) produced from fermented substrate in the rumen of lactating cows. A model was formulated that describes the conversion of substrate (soluble carbohydrates, starch, hemi-cellulose, cellulose, and protein) into VFA (acetate, propionate, butyrate, and other VFA). Inputs to the model were observed rates of true rumen digestion of substrates, whereas outputs were observed molar proportions of VFA in rumen fluid. A literature survey generated data of 182 diets (96 roughage and 86 concentrate diets). Coefficient values that define the conversion of a specific substrate into VFA were estimated meta-analytically by regression of the model against observed VFA molar proportions using non-linear regression techniques. Coefficient estimates significantly differed for acetate and propionate production in particular, between different types of substrate and between roughage and concentrate diets. Deviations of fitted from observed VFA molar proportions could be attributed to random error for 100%. In addition to regression against observed data, simulation studies were performed to investigate the potential of the estimation method. Fitted coefficient estimates from simulated data sets appeared accurate, as well as fitted rates of VFA production, although the model accounted for only a small fraction (maximally 45%) of the variation in VFA molar proportions. The simulation results showed that the latter result was merely a consequence of the statistical analysis chosen and should not be interpreted as an indication of inaccuracy of coefficient estimates. Deviations between fitted and observed values corresponded to those obtained in simulations. (c) 2005 Elsevier Ltd. All rights reserved.

Control of framework stoichiometry in MeGaPO laumontites using 1-methylimidazole as structure-directing agent

A series of heterometal substituted gallium phosphates, (N2C4H7)(0.5+x)[Me0.5+xGa2.5-x(PO4)(3)] (Me = Mn, Fe, Co and Zn, x approximate to 0.25), has been synthesised under solvothermal conditions at 433 K in ethylene glycol using I-methylimidazole as a templating agent and their structures determined at 150 K using single-crystal X-ray diffraction. The compounds are isostructural, crystallising in the monoclinic space group C 2/c, with lattice parameters ca. 15 x 13 x 15 angstrom and beta = 112 degrees, and adopt the laumontite framework type (LAU). The incorporation of 1-methylimidazole cations into the one-dimensional pore systems of these materials is about three quarters the uptake value obtained previously for the less-bulky amine cations of imidazole and pyridine in other MeGaPO laumontites, which have the formula (TH)[MeGa2(PO4)(3)] (Me = Mn, Fe, Co and Zn; T = C5H5N and C3N2H4). The size, shape and charge of the amine clearly influence both the metal-phosphate framework stoichiometry (i.e. Me2+:Ga3+ ratio) and the framework charge. (C) 2007 Elsevier Inc. All rights reserved.

Modelling the interdependence between the stoichiometry of receptor oligomerization and ligand binding for a coexisting dimer/tetramer receptor system

Many G protein-coupled receptors have been shown to exist as oligomers, but the oligomerization state and the effects of this on receptor function are unclear. For some G protein-coupled receptors, in ligand binding assays, different radioligands provide different maximal binding capacities. Here we have developed mathematical models for co-expressed dimeric and tetrameric species of receptors. We have considered models where the dimers and tetramers are in equilibrium and where they do not interconvert and we have also considered the potential influence of the ligands on the degree of oligomerization. By analogy with agonist efficacy, we have considered ligands that promote, inhibit or have no effect on oligomerization. Cell surface receptor expression and the intrinsic capacity of receptors to oligomerize are quantitative parameters of the equations. The models can account for differences in the maximal binding capacities of radioligands in different preparations of receptors and provide a conceptual framework for simulation and data fitting in complex oligomeric receptor situations.

Stoichiometry and thermodynamics of the interaction between the C-terminus of human 90 kDa heat shock protein Hsp90 and the mitochondrial translocase of outer membrane Tom70

A large majority of the 1000-1500 proteins in the mitochondria are encoded by the nuclear genome, and therefore, they are translated in the cytosol in the form and contain signals to enable the import of proteins into the organelle. The TOM complex is the major translocase of the outer membrane responsible for preprotein translocation. It consists of a general import pore complex and two membrane import receptors, Tom20 and Tom70. Tom70 contains a characteristic TPR domain, which is a docking site for the Hsp70 and Hsp90 chaperones. These chaperones are involved in protecting cytosolic preproteins from aggregation and then in delivering them to the TOM complex. Although highly significant, many aspects of the interaction between Tom70 and Hsp90 are still uncertain. Thus, we used biophysical tools to study the interaction between the C-terminal domain of Hsp90 (C-Hsp90), which contains the EEVD motif that binds to TPR domains, and the cytosolic fragment of Tom70. The results indicate a stoichiometry of binding of one monomer of Tom70 per dimer of C-Hsp90 with a K(D) of 360 30 nM, and the stoichiometry and thermodynamic parameters obtained suggested that Tom70 presents a different mechanism of interaction with Hsp90 when compared with other TPR proteins investigated. (C) 2011 Elsevier Inc. All rights reserved.

Influence of chronic alcoholism and oestrogen deficiency on the variation of stoichiometry of hydroxyapatite within alveolar bone crest of rats

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