Adair constants

Here, the equalities in parentheses are strictly valid whenever the sites are identical in the strict sense. Otherwise, one should interpret these intrinsic binding constants as average quantities, as discussed in Appendix J. Since Eq. (6.8.5) has the correct functional form of 8(P), it is easy to obtain a good fit of the experimental data with the four Adair constants A, t = 1,2, 3,4. 

The thermodynamic association (or dissociation) constants used in the Adair equation for a ligand binding at sites in a multisite protein. The term Adair constants originally referred only to the four constants for the reversible binding of dioxygen to hemoglobin. See Adair Equation... 

PEPTIDYL TRANSFERASE ADAIR CONSTANTS ADAIR EQUATION ALLOSTERISM COOPERATIVITY... 

The fractional saturation of tetramer YT and the fractional saturation of dimer YD are functions only of [02] at specified T, P, pH, etc., as shown by equations 7.1-18 and 7.3-6. However, since the tetramer form is partially dissociated into dimers, the fractional saturation of heme Y is a function of both [02] and [heme]. Ackers and Halvorson (1974) derived an expression for the function Y([02], [heme]). When Legendre transforms are used, a simpler form of this function is obtained, and it can be used to derive limiting forms at high and low [heme]. These limiting forms are of interest because they show that if data can be obtained in regions where Y is linear in some function of [heme], extrapolations can be made to obtain YT and YD. These fractional saturations can be analyzed separately to obtain the Adair constants for the tetramer and the dimmer (Alberty, 1997a). 

From an analysis of the population of various Hb species and the intensities of the three hfs proton resonances as a function of oxygenation, the four Adair constants for the oxygenation of Hb A in the presence of IHP can be calculated directly (Ho et al., 1982b). Table III gives a comparison of the Adair constants obtained by Tyuma et al. (1973) with our H NMR data. It is clear that the K and K4 values are essentially identical in both sets of data. However, the Ki and K3 values obtained by the NMR method are about twice those obtained by Tyuma et al. (1973). It is possible that the K2 and Ki values obtained by NMR may be more reliable than those reported by Tyuma et al. (1973), because the NMR method may give a more direct estimate of the partially oxygenated species (Ho et al., 1982b). 

Adair Constants for Oxygenation of Human Normal Adult Hemoglobin in the Presence of... 

Adair constant Results of Tyuma etal. (1973) (mm-1) NMR results (mm-1)... 

The binding constants K. (Adair constants) are related to the parameters in the following way ... 

Imai, K.,ahd Yonetani, T., 1975, pH dependence of the Adair constants of human hemoglobin, J. Biol. Chem., 250 2227. 

The four corresponding equilibrium constants, are known as the Adair constants. The sigmoid oxygen equilibrium curve indicates that Ki, the equilibrium constant for uptake of the first oxygen molecule, is less than K4, the constant for uptake of the last oxygen molecule. This means that the ligation state of one haem in a molecule affects the affinity of the other haems in the molecule. The energy of haem-haem interaction is defined as... 

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

S. Adair, H. S. Sinuns, K. Linderstrom-Lang, and, especially, J. Wyman. These treatments, however, were empirical or thermodynamic in content, that is, expressed from the outset in terms of thermodynamic equilibrium constants. The advantage of the explicit use of the actual grand partition function is that it is more general it includes everything in the empirical or thermodynamic approach, plus providing, when needed, the background molecular theory (as statistical mechanics always does). 

If the microscopic dissociation constants are not equal, then the Adair equation predicts a nonhyperbolic (i.e., cooperative) curve. Values for and 24 can be obtained by studying ligand binding at very low and very high ligand concentrations. Values for / 2 and 23 can be ob-... 

The general Adair equation for the binding of a ligand X to a multisite protein where K represents the thermodynamic macroscopic association constant for the fth site and where n is the total number of sites is... 

Note that the Adair equation does not provide a reason for why identical sites would have different dissociation (or association) constants. See Allosterism Cooperativ-ity, Koshland-Nemethy-Filmer Model... 

While Eq. 7-12, known as the Adair equation,11 might seem to provide a complete description of the binding process, it usually does not. In many cases, there is more than one kind of binding site on a macromolecule and Eq. 7-12 tells us nothing about the distribution of the ligand X among different sites in complex PX. To consider this problem we must examine the microscopic binding constants. 

Oxygenation curves of hemoglobin are often fitted with the Adair equation (Eq. 7-12). Thus, at pH 7.4 under the conditions given in Table 7-2, Imai125 found for the successive formation constants Kj = 0.004, K2 = 0.009, K3 = 0.002 and fQ = 0.95 in units of mm Hg 1. From the definition of a formation constant the oxygen... 

Using these assumptions, it is possible to describe the binding of oxygen by four successive binding constants. This is formally equivalent to the Adair equation the KNF model may be considered as a molecular interpretation of that equation. In general, the number of constants required is equal to the number of binding sites, unlike the situation in the MWC model, which always uses three. 

Calculate the fractional saturation YT of the tetramer of human hemoglobin with molecular oxygen using the equilibrium constants determined by Mills, Johnson, and Akers (1976) at 21.5 °C, 1 bar, pH 7.4, [Cl"] = 0.2 M and 0.2 M ionic strength. Make the calculation with the Adair equation and also by using the binding polymomial YT. 

An advantage to assessing ligand binding data with the Adair equation is that this derivation does make assumptions about the type or presence of cooperativity. Instead, cooperativity is evaluated using T n the macroscopic or apparent dissociation constants, and the statistically related microscopic or intrinsic dissociation constants which describe... 

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