The Thermodynamic Binding Constants

The Adair equation is equivalent to the BI written in terms of the thermodynamic binding constants AT,- (see Section 2.3), namely. 

The identity of the hard donor group and how it is incorporated in a molecular structure has a bearing on the affinity of a siderophore for iron(III). An analysis of siderophore structure and its relationship to iron(III) binding affinity as expressed by the thermodynamic stability constant is useful in understanding structure/function relationships and in the design of siderophore mimics for specific applications. 

Solution equilibria for gadolinium imaging agents have been studied with consideration for pharmacokinetic, protein binding, elimination, and safety aspects of the dmgs. The thermodynamic stability constant, Kq defined by equation 7.4 must be large for clinically viable agents. Some Kq l data are listed in Table 7.3. 

The retention factor is related to the thermodynamic equilibrium constant K for solute binding by k = (IK, where f is the phase ratio of the column. The free-energy change for the chromatographic process is expressed by... 

The probabilistic and thermodynamic interpretations of follow directly from the definition. By substituting the various binding constants, one can rewrite the GPF as well as the BI in terms of the conditional constant. Particularly simple are the expressions for the individual Bis. For instance. 

The intrinsic binding constants were calculated from the experimental thermodynamic constants (see Section 2.3) as follows ... 

Thus, k is the intrinsic binding constant for the site a, while kab is the intrinsic binding constant for the pair of sites a and b. When the sites are identical, then one should take care to distinguish between the thermodynamic (sometimes referred to as macroscopic) constant Ky, which is the binding constant to the rsr site, and the intrinsic (sometimes referred to as microscopic) binding constant Ky/2, which refers to a specific single site. In the case of two different sites, the thermodynamic first constant, as measured from the total BI, is simply k + k. ... 

In a second experiment designed to determine thermodynamic binding constants of pyrazines with the protein types, only a 400 mg level of protein was used. This was equivalent to a 16% soy substituted ground beef. The protein was preheated in the microreactor prior to injecting 2 microliters of a standard solution of methyl substituted pyrazines in heptane. Six concentrations from 3mM to 0.03mM were tested at 120° and 145°C. The standard solutions were heated under the same conditions as was the diffusate. Replicate values were averaged and binding parameters were determined from Klotz plots of the results. 

Figure 2 The dependence of O2 binding on Hb concentration. Binding curves are shown (solid black lines) for Hb concentrations of 0.005, 0.04, 0.10, 0.27,1.0, 5.4, and 38 pM (from left to right). Theoretical binding curves (broken red lines) are shown for a pure tetramer solution and a pure dimer solution. The macroscopic, thermodynamic linkage scheme relates the dimer tetramer assembly constants to the O2 binding constants for free dimer and assembled tetramer. The brackets around figurines indicate that the O2 ligand may be bound at any one of the available deoxy hemesites. Thus, the macroscopic constants are average values for multiple microscopic processes.

In another approach Gauthier et. al. (3) devebped a technique based on fluorescence quenching to determine the equilibrium binding constants of polycyclic aromatic hydrocarbons (PAH) with DOC. PAH are eflBcient fluorophores, nonionic, and are usually considered to be insoluble in water. These last two properties thermodynamically drive the PAH from the aqueous phase to the less polar DOC. Also, PAHs are important exan les of hydrophobic organic contaminants in the environment because these properties cause them to accumulate in the l id deposits of higher organisms. 

The apparent binding constants determined for the mass-law adsorption equations are empirical parameters related to thermodynamic constants (so-called intrinsic constants) via activity coefficients of the surface species. 

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