Adair equation

Adair (1925) introduced the stepwise binding model which, for Hb, produces the so-called Adair equation (see Section 2.3). This has the form... 

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

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... 

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... 

Linked-function mechanisms for cooperative binding interaction of metabolites and/or drugs, based on the presence of two or more different conformational states of the protein or receptor. See Adair Equation Cooperative Ligand Binding Hemoglobin Hill Equation Plot Koshland-Nemethy-Filmer Model Monod-Wyman-Changeux Model Negative Cooperativity Positive Cooperativity... 

The chief limitation of this plotting method is that, unlike the Adair Equation, the plot requires that the system obey all of the conditions required by the MWC model. This assumption will often prove to be incorrect ... 

This expression is called a linked function and indicates how the binding of ligands at nearby sites can influence each other. See also Basic Regulatory Kinetics Cooper-ativity Allosterism Feedback Effectors Bohr Effect Hemoglobin Le Chatelier s Principle Adair Equation... 

PEPTIDYL TRANSFERASE ADAIR CONSTANTS ADAIR EQUATION ALLOSTERISM COOPERATIVITY... 

ADAIR EQUATION COOPERATIVE LIGAND BINDING HILL EQUATION PLOT KOSHLAND-NEMETHY-EILMER MODEL MONOD-WYMAN-CHANCEUX MODEL NEGATIVE COOPERATIVITY POSITIVE COOPERATIVITY HEMOGLOBIN ALLOTOPIC EFFECT Allowed electronic transitions,... 

LINKED EUNCTIONS HEMOGLOBIN ADAIR EQUATION BOLTZMANN DISTRIBUTION LAW CRYOENZYMOLOGY BOLUS... 

ADAIR EQUATION FRACTIONATION FACTOR Fraction of active enzyme,... 

COOPERATIVITY ALLOSTERISM INDUCED FIT MODEL MONOD-WYMAN-CHANGEUX MODEL INDEPENDENT BINDING LINKED FUNCTIONS ADAIR EQUATION POSITIVE COOPERATIVITY NEGATIVE COOPERATIVITY KOSMOTROPES CHAOTROPIC AGENTS HOFMEISTER SERIES Kp, Kq, K .. . ... 

BASIC REGULATORY KINETICS BOHR EFFECT COOPERATIVITY FEEDBACK EFFECTORS LE CHATELIER S PRINCIPLE HEMOGLOBIN ADAIR EQUATION LINOLEATE ISOMERASE Linoleoyl ester,... 

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. 

This is often referred to as the Adair equation. A plot of the fractional saturation for tetramer, which shows the cooperative effect, is given in Fig. 7.1. 

The fractional saturation of dimer TD is given by the Adair equation (see equation 7.1-18)... 

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. 

Make the calculation with the Adair equation and also by using the binding polymomial YT. 

Show that if Kt = X2 = X3 = X4, the four-site Adair equation becomes that of a rectangular hyperbola. Note that the statistical factors in the numerator and denominator of the four-site Adair equation, and in fact in the general n-site equation, are the coefficients of the binomial expansion, i.e., the coefficients of the expansion of (1 — jr)". In the present case with n = 4, Eq. (9.50) applies and... 

The shape of the saturation curve defined by Eq. (9.59) depends on the values of L and c. If L = 0, then the T form of the protein does not exist and Y = XR[X]/(1 + XR[X]). This defines a hyperbolic binding function. Similarly if L = Y = XT[X]/(1 + XT[X]). Thus, deviations from hyperbolic binding occur only if both R and T forms exist otherwise the situation described for the Adair equation in Example 9.13 applies since binding is independent and identical at each site. 

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