Binding isotherms

The intrinsic enantioselectivity of the micelles has been established based on single-component binding isotherms [73], resulting in a remarkably high value of 7.7. 

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. 

Figure 2. Influence of the ionic strength and the polymer concentration on the binding isotherms of Pb2+ by sugar-beet pectins in water (empty symbols) and in 0.1 M NaNOs (full symbols) at 25°C ( ) 2 mequiv. COO. l-, ( ) 8 mequiv. COO-.l-i (—) total binding of added Pbz+.

Figure 3. Influence the metal ion type on the binding isotherms of sugar-beet (A) and citrus (B) pectins at 2 mequiv. COO-.l- in 0.1 M NaNOs and at 25 °C. Symbols as in figure 1.

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,). 

Binding isotherms presented the same characterisitics for sugar-beet and citrus pectins according to the pectin concentration and the conditions of ionic strength. The single case of... 

By comparing the level of the binding isotherms (figure 3) for both metals and pectins, it became possible to set up an affinity order of pectins, whatever their origin, for the five metal ions Cu2+ Pb + Zn2+ Ni2+ > Ca2+. This scale, already found by pH-measurements, confirmed that Cu2+ and Pb2+ were more strongly bound than the other thi cations with no difference between pectins. 

Usually non-cooperative and non-Unear binding isotherms were observed in alkaloid-B-DNA complexation and the data were fitted to a theoretical curve drawn according to the excluded site model [126] developed by McGhee and von Hippel [127] for a non-Unear non-cooperative ligand binding system using the following equation ... 

Figure 5 also shows the effect of the ionophore concentration of the Langmuir type binding isotherm. The slope of the isotherm fora membrane with 10 mM of ionophore 1 was roughly three times larger than that with 30 mM of the same ionophore. The binding constant, K, which is inversely proportional to the slope [Eq. (3)], was estimated to be 4.2 and 11.5M for the membranes with 10 mM and 30 mM ionophore 1, respectively. This result supports the validity of the present Langmuir analysis because the binding constant, K, should reflect the availability of the surface sites, the number of which should be proportional to the ionophore concentration, if the ionophore is not surface active itself In addition, the intercept of the isotherm for a membrane with 10 mM of ionophore 1 was nearly equal to that of a membrane with 30 mM ionophore 1 (see Fig. 5). This suggests the formation of a closest-packed surface molecular layer of the SHG active Li -ionophore 1 cation complex, whose surface concentration is nearly equal at both ionophore concentrations. On the other hand, a totally different intercept and very small slope of the isotherm was obtained for a membrane containing only 3 mM of ionophore 1. This indicates an incomplete formation of the closest-packed surface layer of the cation complexes due to a lack of free ionophores at the membrane surface, leading to a kinetic limitation. In this case, the potentiometric response of the membrane toward Li+ was also found to be very weak vide infra).

Fractional velocity as a function of inhibitor concentration, as illustrated in Figure 5.2, can be fit to a simple binding isotherm equation (see Appendix 2) ... 

Derivation of the Enzyme-Ligand Binding Isotherm Equation... 

Note that Equations (A2.14) and (A2.18) do not take into account any influence of substrate concentration on the apparent value of Kd. As described in Chapter 5, this can be accounted for most generally by replacing the term Kd in these equations with the observed value of Kfp or IC50. Making this substitution in Equation (A2.18), we obtain the binding isotherm equation that has been used throughout this book ... 

Both Reynolds and Karim worked at neutral pH, with denatured proteins, and with reduced disulfide bonds. Under these conditions, proteins are in a random coil conformation (Mattice et al., 1976), so that their hydrodynamic radius is monotoni-cally related to their molar mass. Takagi et al. (1975) reported that the binding isotherm of SDS to proteins strongly depends upon the method of denaturing disulfide bonds. Presumably, protein-SDS complexes are not fully unfolded when disulfide bonds are left intact, which breaks the relationship between molar mass and hydrodynamic... 

Takagi, T., Tsujii, K., Shirahama, K. (1975). Binding isotherms of sodium dodecyl sulfate to protein polypeptides with special reference to SDS-polyacrylamide gel electrophoresis. J. Biochem. (Tokyo) 77, 939-947. 

When DsPheno1 Dsmlcelle, significant binding of phenol to micelles occurs, )Pheno1 is largely reduced. From the binding isotherm, an estimation of phenol molecules per surfactant molecule can be obtained. 

The experimentally observed pseudo-first order rate constant k is increased in the presence of DNA (18,19). This enhanced reactivity is a result of the formation of physical BaPDE-DNA complexes the dependence of k on DNA concentration coincides with the binding isotherm for the formation of site I physical intercalative complexes (20). Typically, over 90% of the BaPDE molecules are converted to tetraols, while only a minor fraction bind covalently to the DNA bases (18,21-23). The dependence of k on temperature (21,24), pH (21,23-25), salt concentration (16,20,21,25), and concentration of different buffers (23) has been investigated. In 5 mM sodium cacodylate buffer solutions the formation of tetraols and covalent adducts appear to be parallel pseudo-first order reactions characterized by the same rate constant k, but different ratios of products (21,24). Similar results are obtained with other buffers (23). The formation of carbonium ions by specific and general acid catalysis has been assumed to be the rate-determining step for both tetraol and covalent adduct formation (21,24). 

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... 

Figure 13.10 Calorimetric titration response showing the exothermic raw (downward-projecting peaks, upper panel) heats of the binding reaction over a series of injections titrating 0.061 mM RNase A (sample) with 2.13 mM 2CMP at 30°C. Bottom panel shows the binding isotherm obtained by plotting the areas under the peaks in the upper panel against the molar ratio of titrant added. The thermodynamic parameters were estimated (shown in the inlay of the upper panel) from a fit of the binding isotherm.

The calorimetric binding isotherms of the carbamoylated quinine and quinidine selectors clearly reveal that the heats released upon binding are strongly different for 5- and R-enantiomers of DNB-Leu, which is commensurate with the remarkable enantioselective molecular recognition capability of these selectors (Figure 1.14a,b). As can be seen from Table 1.4, the binding constants for R- and 5-enantiomers differ by about one order of magnitude in case of the carbamate-type selectors. Furthermore,... 

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