Conditional equilibrium constants in multicomponent heterogeneous adsorption: The conditional affinity spectrum

The concept of conditional stability constant is extended to the competitive binding of small molecules to heterogeneous surfaces or macromolecules via the introduction of the conditional affinity spectrum (CAS). The CAS describes the distribution of effective binding energies experienced by one complexing agent at a fixed concentration of the rest. We show that, when the multicomponent system can be described in terms of an underlying affinity spectrum [integral equation (IE) approach], the system can always be characterized by means of a CAS. The thermodynamic properties of the CAS and its dependence on the concentration of the rest of components are discussed. In the context of metal/proton competition, analytical expressions for the mean (conditional average affinity) and the variance (conditional heterogeneity) of the CAS as functions of pH are reported and their physical interpretation discussed. Furthermore, we show that the dependence of the CAS variance on pH allows for the analytical determination of the correlation coefficient between the binding energies of the metal and the proton. Nonideal competitive adsorption isotherm and Frumkin isotherms are used to illustrate the results of this work. Finally, the possibility of using CAS when the IE approach does not apply (for instance, when multidentate binding is present) is explored. © 2006 American Institute of Physics.

Solvatochromism in Binary Mixtures: First Report on a Solvation Free Energy Relationship between Solvent Exchange Equilibrium Constants and the Properties of the Medium

We have employed UV-vis spectroscopy in order to investigate details of the solvation of six solvatochromic indicators, hereafter designated as ""probes"", namely, 2,6-diphenyl-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (RB); 4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePM; 1-methylquinolinium-8-olate, QB; 2-bromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr, 2,6-dichloro-4-(2,4,6-triphenylpyridinium-1-yl) phenolate (WB); and 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr,, respectively. These can be divided into three pairs, each includes two probes of similar pK(a) in water and different lipophilicity. Solvation has been studied in binary mixtures, BMs, of water, W, with 12 protic organic solvents, S, including mono- and bifunctional alcohols (2-alkoxyethanoles, unsaturated and chlorinated alcohols). Each medium was treated as a mixture of S, W, and a complex solvent, S-W, formed by hydrogen bonding. Values of lambda(max) (of the probe intramolecular charge transfer) were converted into empirical polarity scales, E(T)(probe) in kcal/mol, whose values were correlated with the effective mole fraction of water in the medium, chi w(effective). This correlation furnished three equilibrium constants for the exchange of solvents in the probe solvation shell; phi(W/S) (W substitutes S): phi(S-W/W) (S-W substitutes W), and phi(S-W/S) (S-W substitutes S), respectively. The values of these constants depend on the physicochemical properties of the probe and the medium. We tested, for the first time, the applicability of a new solvation free energy relationship: phi = constant + a alpha(BM) + b beta(BM) + s(pi*(BM) + d delta) + p log P(BM), where a, b, s, and p are regression coefficients alpha(BM), beta(BM), and pi*(BM) are solvatochromic parameters of the BM, delta is a correction term for pi*, and log P is an empirical scale of lipophilicity. Correlations were carried out with two-, three-, and four-medium descriptors. In all cases, three descriptors gave satisfactory correlations; use of four parameters gave only a marginal increase of the goodness of fit. For phi(W/S), the most important descriptor was found to be the lipophilicity of the medium; for phi(S-W/W) and phi(S-W/S), solvent basicity is either statistically relevant or is the most important descriptor. These responses are different from those of E(T)(probe) of many solvatochromic indicators in pure solvents, where the importance of solvent basicity is usually marginal, and can be neglected.

A Contribution to the Estimation of Binary Halide and Pseudo-Halide Equilibrium Constants using a Linear Extrapolation Methodology

The molar single ion activity coefficient (y(F)) of fluoride ions was determined at 25 degrees C and ionic strengths between 0.100 and 3.00 mol L(-1) NaClO(4) using an ion-selective electrode. The activity coefficient dependency on ionic strength was determined to be Phi(F) = log y(F) = 0.2315I-0.041I(2). The function Phi(F)(I), combined with functions obtained in previous work for copper (Phi(Cu)) and hydrogen (Phi(H)), allowed us to make the estimation of the stoichiometric and thermodynamic protonation constants of some halides and pseudo-halides as well as the formation constants of some pseudo-halides and fluoride 1:1 bivalent cation complexes. The calculation procedure proposed in this paper is consistent with critically-selected experimental data. It was demonstrated that it is possible to use Phi(F)(I) for predicting the thermodynamic equilibrium parameters independently of Pearson's hardness of acids and bases.

Environmental coordination chemistry: Binary systems comprising some bivalent cations and monocarboxylates in aqueous solution. Ionic medium effects on equilibrium constants

The molar single activity coefficients associated with propionate ion (Pr) have been determined at 25 degrees C and ionic strengths comprised between 0.300 and 3.00 M, adjusted with NaClO4, as background electrolyte. The investigation was carried out potentiometrically by using a second class Hg/Hg2Pr2 electrode. It was found that the dependence of propionate activity coefficients as a function of ionic strength (I) can be assessed through the following empirical equation: log y(Pr) = -0.185 I-3/2 + 0.104 I-2. Next, simple equations relating stoichiometric protonation constants of several monocarboxylates and formation constants associated with 1:1 complexes involving some bivalent cations and selected monocarboxylates, in aqueous solution, at 25 degrees C, as a function of ionic strength were derived, allowing the interconversion of parameters from one ionic strength to another, up to I = 3.00 M. In addition, thermodynamic formation constants as well as parameters associated with activity coefficients of the complex species in the equilibria are estimated. The body of results shows that the proposed calculation procedure is very consistent with critically selected experimental data.

Ionic medium effects on equilibrium constants .2. Binary systems comprising some bivalent cations and monocarboxylates in aqueous solution

Simple equations were derived relating stoichiometric protonation constants of several monocarboxylates and formation constants associated with 1:1 complexes involving some bivalent cations and selected monocarboxylates, in aqueous sodium perchlorate media, at 25 degrees C, as a function of ionic strength (I), allowing the interconversion of parameters from one ionic strength to another, up to I = 3.00 M. In addition, thermodynamic formation constants as well as activity coefficients of the species involved in the equilibria were estimated. The results show that the proposed calculation procedure is very consistent with critically selected experimental data.

Ionic medium effects on equilibrium constants .1. Proton, copper(II), cadmium(II), lead(II) and acetate activity coefficients in aqueous solution

The molar single ion activity coefficients associated with hydrogen, copper(II), cadmium(II) and lead(II) ions were determined at 25 degrees C and ionic strengths between 0.100 and 3.00 M (NaClO4), whereas for acetate the ionic strengths were fixed between 0.300 and 2.00 M, held with the same inert electrolyte. The investigation was carried out potentiometrically by using proton-sensitive glass, copper, cadmium and lead ion-selective electrodes and a second-class Hg\Hg-2(CH3COO)(2) electrode. It was found that the activity coefficients of these ions (y(i)) can be assessed through the following empirical equations:log y(H) = -0.542I(0.5) + 0.451I; log y(Cu) = -1.249I(0.5) + 0.912I; log y(Cd) = -0.829I(0.5) + 0.448I(1.5);log y(Pb) = -0.404I(0.5) + 0.117I(2); and log y(Ac) = 0.0370I .

Equilibrium constants and free energies in unfolding of proteins in urea solutions

A novel thermodynamic approach to the reversible unfolding of proteins in aqueous urea solutions has been developed based on the premise that urea ligands are bound cooperatively to the macromolecule. When successive stoichiometric binding constants have values larger than expected from statistical effects, an equation for moles of bound urea can be derived that contains imaginary terms. For a very steep unfolding curve, one can then show that the fraction of protein unfolded, B̄, depends on the square of the urea concentration, U, and is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{equation*}\bar {B}=\frac{{\mathit{A}}^{{\mathit{2}}}_{{\mathit{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}n\bar {B}}{\mathit{U}}^{{\mathit{2}}}}{{\mathrm{1\hspace{.167em}+\hspace{.167em}}}{\mathit{A}}^{{\mathrm{2}}}_{{\mathrm{1}}}{\mathit{e}}^{{\mathrm{{\lambda}}}\bar {B}}{\mathit{U}}^{{\mathrm{2}}}}{\mathrm{.}}\end{equation*}\end{document} A12 is the binding constant as B̄→ 0, and λ is a parameter that reflects the augmentation in affinities of protein for urea as the moles bound increases to the saturation number, n. This equation provides an analytic expression that reproduces the unfolding curve with good precision, suggests a simple linear graphical procedure for evaluating A12 and λ, and leads to the appropriate standard free energy changes. The calculated ΔG° values reflect the coupling of urea binding with unfolding of the protein. Some possible implications of this analysis to protein folding in vivo are described.

Exact theory of sedimentation equilibrium made useful

The exact description of the thermodynamics of solutions has been used to describe, without approximation, the distribution of all the components of an incompressible solution in a centrifuge cell at sedimentation equilibrium. Thermodynamic parameters describing the interactions between solute components of known molar mass can be obtained by direct analysis of the experimental data. Interpretation of the measured thermodynamic parameters in terms of molecular interactions requires that an arbitrary distinction be made between nonassociative forces, like hard-sphere volume-exclusion and mean-field electrostatic repulsion or attraction, and specific short-range forces of association that give rise to the formation of molecular aggregates. Provided the former can be accounted for adequately, the effects of the latter can be elucidated in the form of good estimates of the equilibrium constants for the reactions of aggregation.

Equilibrium, Thermoanalytical and Spectroscopic Studies to Characterize Phytic Acid Complexes with Mn(II) and Co(II)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Thermochemical equilibrium modeling of biomass downdraft gasifier: Stoichiometric models

The aim of this work is to develop stoichiometric equilibrium models that permit the study of parameters effect in the gasification process of a particular feedstock. In total four models were tested in order to determine the syngas composition. One of these four models, called M2, was based on the theoretical equilibrium constants modified by two correction factors determined using published experimental data. The other two models, M3 and M4 were based in correlations, while model M4 was based in correlations to determine the equilibrium constants, model M3 was based in correlations that relate the H-2, CO and CO2 content on the synthesis gas. Model M2 proved to be the more accurate and versatile among these four models, and also showed better results than some previously published models. Also a case study for the gasification of a blend of hardwood chips and glycerol at 80% and 20% respectively, was performed considering equivalence ratios form 0.3 to 0.5, moisture contents from 0%-20% and oxygen percentages in the gasification agent of 100%, 60% and 21%. (C) 2013 Elsevier Ltd. All rights reserved.

Determination of binding constants by affinity chromatography

This review summarizes developments in the use of affinity chromatography to characterize biospecific interactions in terms of reaction stoichiometry and equilibrium constant. In that regard, the biospecificity incorporated into the design of the experiment ensures applicability of the method regardless of the sizes of the reacting solutes. By the adoption of different experimental strategies (column chromatography, simple partition equilibrium, solid-phase immunoassay and biosensor technology protocols) quantitatiative affinity chromatography can be used to characterize interactions governed by an extremely broad range of binding affinities. In addition, the link between ligand-binding studies and quantitative affinity chromatography is illustrated by means of partition equilibrium studies of glycolytic enzyme interactions with muscle myofibrils. an exercise which emphasizes that the same theoretical expressions apply to naturally occurring examples of affinity chromatography in the cellular environment. (C) 2004 Elsevier B.V. All rights reserved.

Thermo-solvatochromism in binary mixtures of water and ionic liquids: on the relative importance of solvophobic interactions

The thermo-solvatochromism of 2,6-dibromo-4-[(E)-2-(1-methylpyridinium-4-yl)ethenyl] phenolate, MePMBr(2), has been studied in mixtures of water, W, with ionic liquids, ILs, in the temperature range of 10 to 60 degrees C, where feasible. The objectives of the study were to test the applicability of a recently introduced solvation model, and to assess the relative importance of solute-solvent solvophobic interactions. The ILs were 1-allyl-3-alkylimidazolium chlorides, where the alkyl groups are methyl, 1-butyl, and 1-hexyl, respectively. The equilibrium constants for the interaction of W and the ILs were calculated from density data; they were found to be linearly dependent on N(C), the number of carbon atoms of the alkyl group; van't Hoff equation (log K versus 1/T) applied satisfactorily. Plots of the empirical solvent polarities, E(T) (MePMBr(2)) in kcal mol(-1), versus the mole fraction of water in the binary mixture, chi(w), showed non-linear, i.e., non-ideal behavior. The dependence of E(T) (MePMBr(2)) on chi(w), has been conveniently quantified in terms of solvation by W, IL, and the ""complex"" solvent IL-W. The non-ideal behavior is due to preferential solvation by the IL and, more efficiently, by IL-W. The deviation from linearity increases as a function of increasing N(C) of the IL, and is stronger than that observed for solvation of MePMBr(2) by aqueous 1-propanol, a solvent whose lipophilicity is 12.8 to 52.1 times larger than those of the ILs investigated. The dependence on N(C) is attributed to solute-solvent solvophobic interactions, whose relative contribution to solvation are presumably greater than that in mixtures of water and 1-propanol.

On the solubility of proteins as a function of pH: Mathematical development and application

Thermodynamic relations between the solubility of a protein and the solution pH are presented in this work. The hypotheses behind the development are that the protein chemical potential in liquid phase can be described by Henry`s law and that the solid-liquid equilibrium is established only between neutral molecules. The mathematical development results in an analytical expression of the solubility curve, as a function of the ionization equilibrium constants, the pH and the solubility at the isoelectric point. It is shown that the same equation can be obtained either by directly calculating the fraction of neutral protein molecules or by integrating the curve of the protein average charge. The methodology was successfully applied to the description of the solubility of porcine insulin as a function of pH at three different temperatures and of bovine beta-lactoglobulin at four different ionic strengths. (C) 2011 Elsevier B.V. All rights reserved.

Real-time monitoring and kinetic parameter estimation of the affinity interaction of jArtinM and rArtinM with peroxidase glycoprotein by the electrogravimetric technique

ArtinM is a D-mannose binding lectin that has been arousing increasing interest because of its biomedical properties, especially those involving the stimulation of Th1 immune response, which confers protection against intracellular pathogens The potential pharmaceutical applications of ArtinM have motivated the production of its recombinant form (rArtinM) so that it is important to compare the sugar-binding properties of jArtinM and rArtinM in order to take better advantage of the potential applications of the recombinant lectin. In this work, a biosensor framework based on a Quartz Crystal Microbalance was established with the purpose of making a comparative study of the activity of native and recombinant ArtinM protein The QCM transducer was strategically functionalized to use a simple model of protein binding kinetics. This approach allowed for the determination of the binding/dissociation kinetics rate and affinity equilibrium constant of both forms of ArtinM with horseradish peroxidase glycoprotein (HRP), a N-glycosylated protein that contains the trimannoside Man alpha 1-3[Man alpha 1-6]Man, which is a known ligand for jArtinM (Jeyaprakash et al, 2004). Monitoring of the real-time binding of rArtinM shows that it was able to bind HRP, leading to an analytical curve similar to that of jArtinM, with statistically equivalent kinetic rates and affinity equilibrium constants for both forms of ArtinM The lower reactivity of rArtinM with HRP than jArtinM was considered to be due to a difference in the number of Carbohydrate Recognition Domains (CRDs) per molecule of each lectin form rather than to a difference in the energy of binding per CRD of each lectin form. (C) 2010 Elsevier B V. All rights reserved

Quantitative affinity chromatography

The objective of this review is to summarize developments in the use of quantitative affinity chromatography to determine equilibrium constants for solute interactions of biological interest. Affinity chromatography is an extremely versatile method for characterizing interactions between dissimilar reactants because the biospecificity incorporated into the design of the affinity matrix ensures applicability of the method regardless of the relative sizes of the two reacting solutes. Adoption of different experimental strategies, such as column chromatography, simple partition equilibrium experiments, solid-phase immunoassay, and biosensor technology, has led to a situation whereby affinity chromatography affords a means of characterizing interactions governed by an extremely broad range of binding affinities-relatively weak interactions (binding constants below 10(3) M-1) through to interactions with binding constants in excess of 10(9) M-1. In addition to its important role in solute separation and purification, affinity chromatography thus also possesses considerable potential for investigating the functional roles of the reactants thereby purified. (C) 2001 Elsevier Science B.V. All rights reserved.