Binding constant Formation constant

The association constant (the synonymous expressions binding constant, stability constant, or complex constant can be found in the literature) K for complex formation of guest molecules with host CyD can be determined from NMR titration experiments. Assuming a given stoichiometry of the complex ... 

It was established that Ab to Klebsiella pneumoniae didn t demonstrate the cross-reactivity to antigens of the relative bacterial species so, it could be considered that antibodies investigated was highly specific only to the own antigen. The physical-chemical characteristics of the immunological interaction such as constants of formation of Ag-Ab complex were obtained. The binding constants of immune complex were Ka =(9.7 l.l)-10 and Ka,=(1.7+0.3)T0 (mg/ml)f... 

Table 4-3. Binding Constants and Rate Constants for Complex Formation between a-Cyclodextrin and Azo Dyes ...

In aqueous solutions at pH 7, there is little evidence of complex formation between [MesSnflV)] and Gly. Potentiometric determination of the formation constants for L-Cys, DL-Ala, and L-His with the same cation indicates that L-Cys binds more strongly than other two amino acids (pKi ca. 10,6, or 5, respectively). Equilibrium and spectroscopic studies on L-Cys and its derivatives (S-methyl-cystein (S-Me-Cys), N-Ac-Cys) and the [Et2Sn(IV)] system showed that these ligands coordinate the metal ion via carboxylic O and the thiolic 5 donor atoms in acidic media. In the case of S-Me-Cys, the formation of a protonated complex MLH was also detected, due to the stabilizing effect of additional thioether coordination. ... 

Fig. 15-5 Comparative adsorption of several metals onto amorphous iron oxyhydroxide systems containing 10 M Fej and 0.1 m NaNOs. (a) Effect of solution pH on sorption of uncomplexed metals, (b) Comparison of binding constants for formation of soluble Me-OH complexes and formation of surface Me-O-Si complexes i.e. sorption onto Si02 particles, (c) Effect of solution pH on sorption of oxyanionic metals. (Figures (a), (c) reprinted with permission from Manzione, M. A. and Merrill, D. T. (1989). "Trace Metal Removal by Iron Coprecipitation Field Evaluation," EPRI report GS-6438, Electric Power Research Institute, California. Figure (b) reprinted with permission from Balistrieri, L. et al. (1981). Scavenging residence times of trace metals and surface chemistry of sinking particles in the deep ocean, Deep-Sea Res. 28A 101-121, Pergamon Press.)...

Thermodynamic control (Figure 1, right) is based on adsorption of substances until quasi-equilibrium stage. In this case, the surface ratio of the adsorbed species is defined by the ratio of products of their concentration and binding constant. This deposition is much less influenced by poorly controllable fluctuations of external conditions and provides much better reproducibility. The total coverage can be almost 100%. Because of these reasons, the thermodynamic control is advantageous for preparation of mixed nanostructured monolayers for electrochemical applications including a formation of spreader-bar structures for their application as molecular templates for synthesis of nanoparticles. 

However, an application of thermodynamic control may be complicated by too large difference in binding constant of adsorbed species. The highest concentration of an adsorbate in deposition solution cannot exceed its solubility. The lowest concentration should provide enough high amounts of molecules for formation of a monomolecular layer. For most of compounds and... 

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).

Mammalian metallothioneins typically bind seven metal ions in cluster structures, with bridging sulfur groups, as seen in the x-ray structure of the Cd5Zn2MT complex (86). It is therefore difficult to develop a simple formation-constant description for the binding of metal ions to MT (87), considering that protonation-deprotonation equilibria of the free protein itself should also be taken into account. However, the usefulness of Table VIII as a guide to the affinity of metal ions for mercapto donor ligands is seen in that the ability of metal ions to... 

The formation constants of simple ligands such as F , Cl , and OH with the O-BISTREN complex (92) with two Cu(II) ions in it can be compared with the situation where these ligands bind to the free Cu2+ ion. 

The complex Cu(II)2(0-BISTREN) is much more acidic than the free Cu2+ ion, by a factor of more than three log units. This is primarily due to the presence of two Cu(II) ions, because the formation constant of the Cu2(OH)+ complex is not much less than that for the Cu2(0-BISTREN) complex with hydroxide. This is not a good indication of how well two free Cu2+ ions would bind hydroxide compared to the Cu2(0-BISTREN) complex, however, since one must take into account the dilution effect operative in the chelate effect to make the comparison more realistic (90). Thus, the formation constant for the Cu2OH+ complex above applies for the standard reference state of 1 M Cu2 +. In contrast, in 10 6 M Cu2+, for example, the pH at which Cu2(OH) + would form is raised from pH 5.6 to 11.6, ignoring the fact that Cu(OH)2(s) would precipitate out long before this pH as reached. By comparison, the acidity of the Cu2(0-BISTREN) complex is not affected by dilution and would still form the hydroxide complex at pH 3.9 if present at a 10"6 M concentration. 

Higuchi and Lachman [122] pioneered the approach of improving drug stability by complexation. They showed that aromatic esters can be stabilized in aqueous solutions in the presence of xanthines such as caffeine. Thus, the half-lives of benzocaine, procaine hydrochloride, and tetracaine are increased by approximately two- to fivefold in the presence of 2.5% caffeine. This increase in stability is attributed to the formation of a less reactive complex between caffeine and the aromatic ester. Professor K. A. Connors has written a comprehensive textbook that describes methods for the measurement of binding constants for complex formation in solution—along with discussions of pertinent thermodynamics, modeling statistics,... 

C NMR studies suggest that 1,4,7,10-tetra-azacyclododecane-l,7-diacetic acid binds to zinc in a cis octahedral geometry—the two carboxylate oxygens are cis and the remaining four donors from the cyclen macrocycle. The formation constant was determined for the complex.733... 

Such internal thermodynamic equilibria where A is a protein are found for non-metal components, including free coenzymes and substrates where B is a small molecule, or where free M is an ion of either a non-metal, e.g. Cl" or HCOj, or a metal, e.g. K+ or Mg2+, or is H+, and they are involved in, even necessary for, catalysis, pumping and cooperative controls of many metabolic paths. All such combinations reach equilibrium, as long as exchange is fast, where a fast rate can be taken as, say, 10-3 s for dissociation in cells. Note that equilibria with defined binding constants for AB or AM formation in any system reduce the number of variables and hence AB and AM concentrations are defined by those of free A, B and M, leaving two independent variables for each equilibrium. In some cases, the... 

Each value listed in Tables 8.12 and 8.13 is the logarithm of the overall formation constant for the cumulative binding of a ligand L to the central metal cation M, viz. ... 

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