Hemoglobin Hill equation

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... 

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,... 

To adapt the Hill equation to the binding of oxygen to hemoglobin we must again substitute p02 for [L] and Pso for Kd ... 

Heme—chemical models 307 Hemoglobin 289, 304-307 allosteric interactions 289-292, 302 Henderson-Hasselbalch equation 170 Heterotropic 290 Hexokinase 23, 51, 364 Hill constant 299, 300-302, 304 Hill equation 297 - 300 Hinge motions 48 HIV protease 486 Holoe nzyme 458 Homology 8, 9 Homology modeling 537 Homotropic 290 Hpr (histidine-containing... 

Equation (8) is an approximation because it ignores intermediate species that have some, but not all, of the binding sites occupied. Even so, the Hill coefficient provides a useful measure of cooperativity. The binding of 02 to hemoglobin is described well by the Hill equation with n 2.8. In the case of phosphofructokinase, which has four subunits, the dependence of the rate on the fructose-6-phos-phate concentration at a fixed, relatively high concentration of ATP is described well with n 3.8. 

It was noted earlier that Michaelis-Menten kinetics and its linear transformations are not valid for allosteric enzymes. Instead, the Hill equation, an equation originally empirically developed to describe the cooperative binding of Oz to hemoglobin (Chapter 7), is used. The expression describing such a straight-line plot is... 

Most hemoglobins, however, do not obey the simple mass action equation (Equation 7.2) and instead obey the empirical Hill equation ... 

Figure 7.11 shows the oxygen dissociation curve of one such hemoglobin, Hb Rainier, where it is seen that this hemoglobin is still 50% saturated with oxygen at a p02 of about 12 mm Hg compared to 27 mm Hg in normal hemoglobin. The value of n in the Hill equation is 1.5 for this hemoglobin. 

The oxygen contents and partial pressures are related by the hemoglobin dissociation curves for maternal and fetal bloods. We used a modified Hill equation (17, 18) ... 

With hemoglobin, one can see that if the experimental binding data are analyzed in terms of the Hill equation, the calculated value of n is less than the actual number of binding sites the value of n cannot be higher than the number of binding sites, and it is almost always lower. Thus, the value of n does not determine the number of binding sites, but it is just a model-independent fitting parameter. 

In some of his earliest work, published in 1910, A. V. Hill examined how the binding of oxygen to hemoglobin varied with the oxygen partial pressure. He found that the relationship between the two could be fitted by the following equation ... 

Early this century, A.V. Hill derived a useful equation that describes the oxygen dissociation curve of hemoglobin fairly accurately. It is... 

In 1910 Archibald Hill (4) derived an equation similar to Equation 9.4 to describe the hemoglobin 0, sigmoidal curve of Y versus [L] plots. Hill assumed that a protein has n... 

For hemoglobin, successive binding sites have different equilibrium constants and so the above equation has to be modified. It is found that the Hill plot for hemoglobin has a maximum slope of 2.8, giving a Hill coefficient of 2.8 (Fig. 6.8). A Hill coefficient greater than 1.0 indicates positive cooperativity. 

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