Equilibrium binding isotherm

Equation (8.2.5) establishes the connection between the rate of the enzymatic reaction within the steady-state approximation, and the equilibrium binding isotherm. 

Quantitative determination of equilibrium binding isotherms for multiple ligand-macromolecule interactions using spectroscopic methods... 

The experimental results obtained by measuring ions activity after equilibration with pectins are plotted as binding isotherms [Me +Jb/Cp vs [Me +Jt/Cp where [Me2+]b is the bound cation concentration at equilibrium (equiv.l-i) calculated from measured activity using previously calculated activity coefficients. 

The mode of binding was characterised by replotting experimental data obtained from binding isotherms in terms of the Scatchard representation, [Me +Jb / (Cp.[Me2+]f) vs [Me2+]b/Cp where [Me2+]f corresponds to the final ion concentration at equilibrium. Metal ion concentrations were here expressed in molarity and Cp in number of chain.l l (using the weight-average molecular weights M,). 

The ultrasonic absorption spectrum for a series of inorganic salts with /i-CD showed one relaxation process.166 No absorption was observed for solutions only containing /i-CD. The equilibrium constants determined from competitive binding isotherms were relatively low (2-30 M-1). The relaxation frequency (/, ) was related to the observed relaxation rate constant, which is equal to the sum of the association and dissociation processes. The association rate constants for all salts with the exception of perchlorate were similar and this result was interpreted to mean that... 

The second property is that each term of the PF is proportional to the probability of occurrence of the particular state it represents when the system is at equilibrium. We shall use mainly the second property of the PF. The next section is devoted to this aspect of the theory. Once we have the probabilities of all possible events we can compute average quantities pertaining to the system at equilibrium. Of these, the average occupation number, or the binding isotherm, will be the central quantity to be examined and analyzed in this book. 

While there are several books that deal with the subject matter of this volume, the only one that develops the statistical mechanical approach is T. L. Hill s monograph (1985), which includes equilibrium as well as nonequilibrium aspects of cooperativity. Its style is quite condensed, formal, and not always easy to read. The emphasis is on the effect of cooperativity on the form of the PF and on the derived binding isotherm (BI). Less attention is paid to the sources of cooperativity and to the mechanism of communication between ligands, which is the main subject of the present volume. 

Furthermore, in 3.3 we turn to reactive binary ion-exchange. An equilibrium binding reaction (adsorption) with a Langmuir-type isotherm is considered. Formation of sharp propagating concentration fronts is studied via an unconventional asymptotic procedure [1]. 

In the binding isotherm model [55], a polyion labeled P has N fixed charges. The poly ion is divided into sections [55]. There is no section of the polyion that has more than one binding site. Let the counterion valence be zc. Let. 1 denote a specific configuration of the nc counterions. In this configuration, the counterions bind to the poly ion and form the complex Dj(nc), and are described by the equilibrium [55]... 

This equations expresses the dependence of a bound reagent [AB] (once again, in the case of 1 1 binding it is equal to the amount of complex in equilibrium) versus free reagent [B], Plotting [AB] versus [B] results in a typical binding isotherm with hyperbolic shape. The double-reciprocal form of the binding isotherm,... 

The binding equilibrium is expressed in the form of a binding isotherm in many cases, 0 is plotted against log [A]. 

XH NMR experiments show that the viologen residue interacts effectively with the CB7 host [53], Voltammetric and mass spectrometric data are also consistent with the formation of inclusion complexes between the dendronized viologens and CB7. As was the case with methylviologen, complexation by CB7 depresses the molar absorptivity coefficient for the viologen UV absorption band and this effect can be conveniently utilized to fit the absorbance data in titration experiments to 1 1 binding isotherms. From the optimization of these fittings we obtained the corresponding equilibrium association constants (Table 3). 

FIG. 14 Binding isotherm of a short C18-modified polyacrylic acid to bovine serum albumin obtained from equilibrium dialysis against polymer solutions in 20 mM borate buffer, pH 9. Polymer Mw 5,000 in its acid form grafting rate 3 mol%. (Reprinted with permission from Ref. 33. Copyright 1998 American Chemical Society.)... 

Fig. 3 Set of sensorgrams (model) suitable for equilibrium analysis (left) and binding isotherm with indicated equilibrimn sensorgram results (right). Model of pseudo first-order reaction. Parameters ft = I nM cm, K = 10 M fca = 4.5 x 10 M s ...

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