Secondary Equilibria Research Articles

Mathematical evaluation of the role of cross immunity and nonlinear incidence rate on the transmission dynamics of two dengue serotypes

Dengue fever is a common disease which can cause shock, internal bleeding, and death in patients if a second infection is involved. In this paper, a multi-serotype dengue model with nonlinear incidence rate is formulated to study the transmission of two dengue serotypes. The dynamical behaviors of the proposed model depend on the threshold value R_{{0}}^{{n}} known as the reproductive number which depends on the associated reproductive numbers with serotype-1 and serotype-2. The value of R_{{0}}^{{n}} is used to reflect whether the disease dies out or becomes endemic. It is found that the proposed model has a globally stable disease-free equilibrium if R_{{0}}^{{n}}leq 1, which indicates that if public health measures that make (and keep) the threshold to a value less than unity are carried out, the strategy in disease control is effective in the sense that the number of infected human and mosquito populations in the community will be brought to zero irrespective of the initial sizes of sub-populations. When R_{{0}}^{{n}}>1, the endemic equilibria called the co-existence primary and secondary infection equilibria are locally asymptotically stable. The effects of cross immunity and nonlinear incidence rate are explored using data from Thailand to determine the effective strategy in controlling and preventing dengue transmission and reinfection.

A spectroscopic study of a cyclodextrin-based polymer and the “molecular accordion” effect

The formation of host–guest complexes was studied for two hosts: β-cyclodextrin (β-CD) and a cross-linked polymer containing an equimolar ratio of β-CD and hexamethylene diisocyanate (HDI), denoted as HDI-1. The thermodynamics of host–guest binding were studied with 1-anilinonaphthalene-8-sulfonic acid (1,8-ANS) using steady-state fluorescence spectroscopy in aqueous solution at variable temperature and ambient pH. The association of 1,8-ANS with β-CD and HDI-1 showed a fluorescence enhancement of ∼4 and 12 units, respectively. Greater fluorescence enhancement for the polymer/dye system indicates the presence of multiple binding sites (inclusion and interstitial). By contrast, the β-CD/dye system adopts trends that indicate the formation of well-defined inclusion complexes. HDI-1 has inclusion sites (β-CD) and interstitial domains (HDI) that afford dual binding with variable binding affinity. Simplified binding models employed herein address the role of inclusion binding without an explicit account for higher order or secondary binding equilibria. The approximate 1:1 binding constant (K1:1) for CD/1,8-ANS is about two-fold greater over the HDI-1/1,8-ANS system. HDI-1 displays cooperative effects among the polymer subunits, according to changes in relative fluorescence intensity due to structural transitions and binding site loci. The relative fluorescence intensities of the HDI-1/1,8-ANS system relate to a reversible temperature-driven structural transition (globular ⇌ extended) of the polymer between 5 °C and 60 °C, in contrast to the β-CD/1,8-ANS complex. The temperature- and guest-driven structural transition, described as the “molecular accordion” effect, is supported by new insight provided by complementary fluorescence and1H NMR spectral results in aqueous solution.

Effect of Secondary Equilibria on the Adsorption of Ibuprofen Enantiomers on a Chiral Stationary Phase with a Grafted Antibiotic Eremomycin

The chromatographic separation of ibuprofen enantiomers on a Nautilus-E chiral stationary phase with a grafted eremomycin antibiotic at high column loading is accompanied by distortion of the shape of chromatographic peaks. A model is proposed to explain this phenomenon. A number of factors are considered in the model: the ionization of ibuprofen in the mobile phase, the pH change in the mass transfer zone caused by ionization, and competitive adsorption involving buffer components. Simulations performed using this model within the theory of nonequilibrium chromatography allow the shape of chromatograms for large amounts of S- and R-ibuprofen samples to be predicted. The adsorption mechanism is found to be mainly ion-exchange. The contribution from the molecular adsorption of ibuprofen to the total retention is shown to be several percent.

Quantification of circulating steroids in individual zebrafish using stacking to achieve nanomolar detection limits with capillary electrophoresis and UV-visible absorbance detection.

Capillary electrophoresis and UV-visible absorbance detection are used with sample stacking to achieve detection limits ranging from 0.2 to 2 ng/mL (0.8 to 6 nM) for steroids. Stacking is accomplished using negatively charged cyclodextrin steroid-carrier molecules at a discrete pH interface between the reconstituted sample and the separation electrolyte. Steroids are then separated in under 5 min using capillary electrophoresis that incorporates secondary equilibria via sodium dodecyl sulfate and cyclodextrin. The effectiveness of the method for measurements of multiple steroids in limited sample volumes is demonstrated in individual female fish with total circulating blood volumes of 5 μL or less. Steroid recoveries from plasma following a sample processing method developed with commercial extraction cartridges range from 81 to 109 % for 17α,20β-dihydroxy-pregn-4-en-3-one, testosterone, 11-ketotestosterone, estrone, 17β-estradiol, and 17α-ethinyl estradiol. When applied to reproductively active female zebrafish, changes were detected in the levels of circulating steroids as a result of exposure to different solvents and 17β-estradiol.Graphical abstractSteroids are measured in individual zebrafish subject to chemical exposureElectronic supplementary materialThe online version of this article (doi:10.1007/s00216-015-8785-0) contains supplementary material, which is available to authorized users.

α-flips and T-points in the Lorenz system

We consider the Lorenz system near the classic parameter regime and study the phenomenon we call an α-flip. An α-flip is a transition where the one-dimensional stable manifolds Ws(p±) of two secondary equilibria p± undergo a sudden transition in terms of the direction from which they approach p±. This is a bifurcation at infinity and does not involve an invariant object in phase space. This fact was discovered by Sparrow in the 1980s but the stages of the transition could not be calculated and the phenomenon was not well understood (Sparrow 1982 The Lorenz equations (New York: Springer)). Here we employ a boundary value problem set-up and use pseudo-arclength continuation in AUTO to follow this sudden transition of Ws(p±) as a continuous family of orbit segments. In this way, we geometrically characterize and determine the moment of the actual α-flip. We also investigate how the α-flip takes place relative to the two-dimensional stable manifold of the origin, which shows no apparent topological change before or after the α-flip. Our approach allows for easy detection and subsequent two-parameter continuation of the first and further α-flips. We illustrate this for the first 25 α-flips and find that they end at terminal points, or T-points, where there is a heteroclinic connection from the secondary equilibria to the origin. It turns out that α-flips must occur naturally near T-points. We find scaling relations for the α-flips and T-points that allow us to predict further such bifurcations and to improve the efficiency of our computations.

Secondary Equilibria Control of Cromoglycate Ion Flux Through Polyamide Membrane

Secondary Equilibria Control of Cromoglycate Ion Flux Through Polyamide Membrane

5-Fluoro pyrimidines: labels to probe DNA and RNA secondary structures by 1D 19 F NMR spectroscopy

19F NMR spectroscopy has proved to be a valuable tool to monitor functionally important conformational transitions of nucleic acids. Here, we present a systematic investigation on the application of 5-fluoro pyrimidines to probe DNA and RNA secondary structures. Oligonucleotides with the propensity to adapt secondary structure equilibria were chosen as model systems and analyzed by 1D 19F and 1H NMR spectroscopy. A comparison with the unmodified analogs revealed that the equilibrium characteristics of the bistable DNA and RNA oligonucleotides were hardly affected upon fluorine substitution at C5 of pyrimidines. This observation was in accordance with UV spectroscopic melting experiments which demonstrated that single 5-fluoro substitutions in double helices lead to comparable thermodynamic stabilities. Thus, 5-fluoro pyrimidine labeling of DNA and RNA can be reliably applied for NMR based nucleic acid secondary structure evaluation. Furthermore, we developed a facile synthetic route towards 5-fluoro cytidine phosphoramidites that enables their convenient site-specific incorporation into oligonucleotides by solid-phase synthesis.

19F NMR Spectroscopy for the Analysis of RNA Secondary Structure Populations

Labeling of RNA with site-specific fluorine atoms has become straightforward in recent years and in particular has become an integrated part of engineered functional RNA with therapeutic potential, e.g. for siRNA technologies. Here, we demonstrate that temperature-dependent one-dimensional (19)F NMR spectroscopy of oligoribonucleotides is a powerful tool to obtain direct information on the conformational behavior. The approach is particularly useful for the quantification of monomolecular vs bimolecular secondary structure equilibria.

On-column electrochemical redox derivatization for enhancement of separation selectivity of liquid chromatography: Use of redox reaction as secondary chemical equilibrium

An on-column electrochemical redox derivatization for enhancement of high-performance liquid chromatography (HPLC) separation selectivity is presented using electrochemically modulated liquid chromatography (EMLC) and porous graphitic carbon (PGC) as the packing material. PGC therefore serves two purposes: it acts both as a chromatographic stationary phase and as a working electrode. The capability of on-column electrochemical redox derivatization was evaluated using hydroquinone and catechol as model compounds. By manipulation of the applied potential, hydroquinone and catechol will migrate as equilibrium mixtures, hydroquinone and p-benzoquinone and catechol and o-benzoquinone in the potential region of 25–125 mV and 150–200 mV (vs. Ag/AgCl), respectively. These redox reactions can be used as secondary chemical equilibria so that the corresponding equilibrium mixtures elute as single peaks and their retention times can be controlled by alterations in the potential applied to the PGC stationary phase. Homogeneity of the redox activity of the PGC stationary phase applied potential was also demonstrated.

06/01348 Secondary mineral-fluid equilibria in the Krafla and Námafjall geothermal systems, Iceland: Gudmundsson, B. T. and Arnórsson, S. Applied Geochemistry, 2005, 20, (9), 1607–1625

06/01348 Secondary mineral-fluid equilibria in the Krafla and Námafjall geothermal systems, Iceland: Gudmundsson, B. T. and Arnórsson, S. Applied Geochemistry, 2005, 20, (9), 1607–1625

Complexometric determination: Part I - EDTA and complex formation with the Cu2+ ion

Compounds forming very stable complexes - chelates, have a wide field of application in analytical chemistry. The most famous group of these compounds are complexons. Complexons represent organic polyaminocarbonic acids as for example ethylenediaminetetraacetic acid (EDTA) and its salts. The EDTA molecule has six coordinative sites. It is a hexadentate ligands i.e. it has two binding nitrogen atoms and four oxygen atoms from carboxyl groups and it forms complexes with almost all metal ions. EDTA as a tetraprotonic acid, H4Y disociates through four steps, yielding the ions HsY-, H2Y2-, HY3- and Y4-. Which of the EDTA forms will be encountered in a solution, depends on the pH. Due to the poor solubility of EDTA in pure water, as well as in most organic solvents, the disodium salt of EDTA Na2H2Y-2H2O, under the commercial name complexon III, is utilized for analytical determinations. In water, EDTA forms soluble, stabile chelate complexes with all cations, at the molar ratio 1:1, regardless of the charge of the metal ion. In contrast to other equilibria, which are mainly defined by Le Chatellier's principle, equilibria related to metal-EDTA complex formation are also dependent on the influence of the secondary equilibria of EDTA complex formation. Complexing reactions, which are equilibrium reactions, are simultaneously influenced by the following factors: solution pH and the presence of complexing agents which may also form a stabile complex with metal ions. The secondary reaction influence may be viewed and monitored through conditional stability constants. In the first part of the paper, the reaction of the formation of the Cu2+-ion complex with EDTA is analyzed beginning from the main reaction through various influences of secondary reactions on the complex Cu2+-EDTA: pH effect, complexation effect and hydrolysis effect. The equations are given for conditional stability constants, which include equilibrium reactions under actual conditions.

Comparison of the Binding Constant of Decanesulfonate with β-Cyclodextrin as Determined by Liquid Chromatography with a Water Mobile Phase and Flow Injection Analysis Coupled with Dynamic Surface Tension Detection

This paper compares two independent methods for the determination of the inclusion complex binding constant between β-cyclodextrin (β-CD) and decanesulfonate. First, reverse-phase liquid chromatography (RP-LC) separations of four surfactants are examined under two conditions for the binding constant determination. The first separation relies on RP-LC using a 100% water mobile phase and a cyanopropyl stationary phase. Hexanesulfonate, octyl sulfate, and decanesulfonate were separated in under 10 min. With the addition of only 1 mM β-CD to the water mobile phase, the same three surfactants, in addition to dodecyl sulfate, were separated in 6 min. Limits of detection were in the parts-per-billion range using conductivity detection but did not require a mobile phase conductivity suppressor. The binding constant for decanesulfonate with β-CD using RP-LC with a water mobile phase was found to be (3.13 ± 0.38) × 103M−1. Second, flow injection analysis (FIA) is coupled with dynamic surface tension detection (DSTD) to provide an independent method to determine the binding constant of β-CD with decanesulfonate. Using FIA with DSTD, a decanesulfonate binding constant with β-CD of (4.75 ± 1.25) × 103M−1was obtained. The two binding constant values were in close agreement, suggesting that secondary equilibria were minimal in RP-LC with a water mobile phase. The combination of FIA with DSTD is shown to be an excellent method to help study reverse-phase retention mechanisms involving complexation equilibria.

Secondary chemical equilibria in high-performance liquid chromatography: influence of ionic strength and pH on retention of peptides

In this work a model describing the effect of pH on retention in LC is established and tested for two series of peptides using an octadecylsilica column. The suggested model uses the pH value measured in the acetonitrile–water mixture instead of the pH value in water and takes into account the effect of the activity coefficients. The proposed equations permit the prediction of the pH optimum using a minimum number of measurements and can be combined with the previously derived equations, that relate the retention with the solvent composition of the mobile phase, to establish a general model that relates the elution behaviour of the solute with the significant mobile phase properties: composition, pH and ionic strength.

Concentration Effects in Field-Flow Fractionation with Secondary Chemical Equilibria

In field-flow fractionation with secondary chemical equilibria (SCE-FFF), small solutes can be separated according to their distribution coefficient between a carrier additive species affected by the applied field and the bulk carrier. Due to its interaction with the applied field, the average additive concentration within the FFF channel is generally significantly larger than in the carrier reservoir and becomes so high that additive-additive interactions cannot be neglected. A recent retention model of FFF at finite concentrations is applied to SCE-FFF. In contradistinction with previous theories in which additiveadditive interactions were not accounted for, it is found that the retention time of a given solute goes to a maximum when the additive concentration in the carrier increases. Published SCE-FFF experimental data are examined in light of this model. The potential of this FFF operating mode and guidelines for optimizing the separation are discussed

Modification of the Electrophoretic Mobility of Neutral and Charged Polysaccharides

Suitable buffer additives can either induce or reduce the electrophoretic mobility of certain polysaccharides during capillary electrophoresis. With water-soluble cellulose derivatives, adsorption of detergents on the analyte molecules governs the migration rates. Different types of adsorption sites, including multilayer formation, were found to be present on the cellulose-derived polymers. For highly charged polysaccharides (heparins), the electrophoretic mobility can be controlled by the use of ion-pairing reagents. The concentration and number of cationic charges appear useful in optimizing the separation selectivity. Migration models based on secondary thermodynamic equilibria are presented and evaluated for different polysaccharides.

Retention in field-flow fractionation with secondary chemical equilibria

The application range of field-flow fractionation (FFF) can be extended to low molecular weight solutes, as demonstrated a few years ago by Berthod et al., by taking profit of secondary chemical equilibria (SCE) occurring between the bulk carrier and a retained carrier component. The theory of solute retention in this SCE-FFF method is developed for any value of the solute distribution coefficient and of the retention ratio of the retained carrier component, provided that the Brownian mode of retention applies for this component and that the flow velocity profile is parabolic. This removes some of the limitations of the model previously developed by Berthod and Armstrong and sheds light on the potentialities of the SCE-FFF method for physico-chemical studies about secondary chemical equilibria in colloidal systems. Remaining assumptions in the model are discussed.

Secondary equilibria and their interaction with chromatographic transport

The existence of “eigenpeaks” and the possibility of indirect detection in high-performance liquid chromatography and capillary zone electrophoresis can be understood with the same mathematical treatment. The coupled transport equations, when suitably linearized for small disturbances, can be treated as a linear eigenvalue problem. The solution predicts, in accordance with earlier results obtained by other workers, the existence of N eigenpeaks in a chromatographic or electrophoretic system, where N is the number of degrees of freedom in the description of the composition of the solution involved. Each eigenpeak corresponds to a capacity factor or mobility and is associated with an eigenvector that describes the relative intensities of the disturbances in all compounds that occur in the solution. An important experimental facility offered by these phenomena is indirect detection. A few general conclusions pertaining to this technique, invented before these phenomena were fully understood, are drawn.

Theoretical aspects of an equilibrium study in the non-dissociating molecular solvent acetic acid

The bromide complexes of copper(II) were studied spectrophotometrically in acetic acid. This non-dissociating solvent presents secondary equilibria such as perchlorate ⇌ acetate and in the case of copper acetate in acetic acid, monomer ⇌ dimer. A matrix rank treatment of the optical densities identified four mononuclear bromo complexes which are formulated as Cu(OAc)Br, CuBr 2, LiCuBr 3 and Li 2 CuBr 4. The overall stability constants of these species are log β 1 = 3.2, log β 2 = 6.5, log β 3 = 7.7 and log β 4 = 7.7. The electronic spectra of the individual species, in this solvent, are reported for the first time. The d-d transition band of the tetrabromocuprate is calculated to be at 1120 nm and confirms the structure of a flattened tetrahedron.

Retention modification of nucleic acid constituents in reversed-phase high-performance liquid chromatography

Secondary equilibria in reversed-phase liquid chromatography have been investigated as a means of enhancing selectivity and optimizing separations of nucleic acid constituents. The retention behavior of various nucleotides, nucleosides and modified compounds has been examined as a function of five different metal ion additives in the mobile phase: K +, Mg 2+, Mn 2+, Ni 2+ and Zn 2+. Complexation of the solute molecules with the metal ions changes the electronic structure and alters solute-solvent interactions. Alkali and alkaline earth metals bind primarily to phosphate groups while transition metals also interact with the N 7 of purine bases. All nucleotides were found to be eluted very close to the void volume of the high-performance liquid chromatographic column without any metal additive, but retention increased as the concentration of a given cation increased. The transition metals were found to have the greatest effect, with affinities for nucteotide monophosphates on the order of 100 times greater than potassium, and 10 times that of magnesium. Differences in affinity based upon phosphate structure ( i.e., cyclic vs. linear), phosphate position ( e.g., 2′- vs. 3′-monophosphates), and base modification were also noted. The retention of most nucleosides, unlike the charged compounds, remained relatively constant as the ionic strength or type of cation was varied. Also, improvements were obtained in the resolution of some oligonucleotides with the addition of divalent ions to a potassium buffer mobile phase.

Prediction of retention behaviour on modification of the mobile phase in high-performance liquid chromatography using metal ions: 2-aminophenol as a model system

A model has been developed for predicting the effect of transition metals as components of the mobile phase in high-performance liquid chromatography on the retention of an analyte containing a chelating group. It takes into account the secondary chemical equilibria in solution, including the formation constants of the complexes, the pH of the mobile phase and the concentration of the metal ions. The model was tested by comparison with data determined for the retention of 2-aminophenol on a porous polystyrene-divinylbenzene polymer column in the presence of metal ions.