Hemoglobin Hill coefficient

Where equals the number of sites determined by some other biophysical procedure, we say that the system shows infinite cooperativity. No such behavior has been rigorously demonstrated for an enzyme or receptor. In the case of hemoglobin oxygenation (Fig. 2) under physiologic conditions, the Hill coefficient has a value of about 2.8. Of course, from X-ray structural information, we know that hemoglobin has four sites. Thus, we... 

Fig. 2. Hill plot for oxygenation of human hemoglobin A as a function of the partial pressure (PO2) of molecular oxygen. The diagram at the right shows that the Hill coefficient will reach a limiting value of one at both extremes of ligand concentration. For this reason this cooperativity index is best measured at ligand concentrations near half-maximal saturation.

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. 

As the stability of the tense structure is reduced by the loss of this interaction in the two sliding contacts ai,p2. and a2,pj, less energy is required for oxygen to bind to Hb Mp y. Thus, HbKEMPsEY has a higher oxygen affinity (p50 = 15 torr) and a lower Hill coefficient (see Chap. 9 and Prob. 5.21). Individuals with this hemoglobin compensate by producing more red blood cells. 

Figure 8 Cooperative and noncooperative binding of O2. (a) Binding curves of myoglobin and hemoglobin, (b) Hill plot of binding curves. The Hill coefficient munber is determined from the first derivative (slope) of the HiU plots...

A plot of log(T/l — Y) versus log P02 yields a straight line with a slope of n, the Hill coefficient. For hemoglobin, n = 2.8 (Figure 7-10), which signifies that the binding of oxygen to hemoglobin exhibits positive cooperativity. 

Figure 7.29 Oxygen-binding curves for several Hill coefficients. The curve labeled n = 2,8 closely resembles the curve for hemoglobin.

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. 

Figure 1.3. A Hill plot of the set of designed elastic-contractile model proteins shown in Figure 1.2 with Hill coefficients, n, ranging from 1.5 to 8.0. B Hill plot of myoglobin (n = 1) and hemoglobin (n = 2.8). It is shown that the vaunted hemoglobin positive cooperativity is relatively small compared with that of designed elastic protein-based polymers and, in particular, of designed Model protein v.

---