9.6. Allostery[[Student version, January 17, 2003]] 329
00.20.40.60.8105. 10 -6 1. 10 -5 1.5. 10 -5 2. 10 -5 2.5. 10 -5fractional oxygenationYconcentration of O 2 , Mmyoglobinhemoglobinimaginary carriertissue lungsFigure 9.9:(Experimental data with fits.) Fractional degree of oxygen binding as a function of oxygen concentra-
tion.Solid circles:Data for myoglobin, an oxygen-binding molecule with a single binding site. The curve through the
points shows the formula in Your Turn 9m with a suitable choice ofKeq.Open circles:Data for human hemoglobin,
which has four oxygen-binding sites. The curve shows the formula in Your Turn 9n(a) withn=3.1.Dashed curve:
Oxygen binding for an imaginary, noncooperative carrier (n=1), with the value ofKeqadjusted to agree with
hemoglobin at the low oxygen concentration of body tissue(left arrow).The saturation at high oxygen levels(right
arrow)is then much worse for the imaginary carrier than in real hemoglobin. [Data from Mills et al., 1976 and
Rossi-Fanelli & Antonini, 1958.]
- Hemoglobin has a site where an O 2 molecule can bind.
- In an oxygen-rich environment, the binding site is more likely to be occupied, by Le Chˆatelier’s
Principle (Section 8.2.2 on page 265). - In an oxygen-poor environment, the binding site is less likely to be occupied. Thus when
hemoglobin in a red blood cell moves from lungs to tissue, it first binds, then releases oxygen
as desired.
The problem with this tidy little scenario shows up when we try to model oxygen binding to
hemoglobin quantitatively, using the Mass Action rule (Equation 8.16 on page 267) for the reaction
Hb+O 2 HbO 2 .(The symbol “Hb” represents the whole hemoglobin molecule.) Let us represent
the fractional degree of oxygenation byY≡[HbO 2 ]/([Hb] + [HbO 2 ]).
Your Turn 9m
Show that according to the model above,Y=[O 2 ]/([O 2 ]+K−eq^1 ), whereKeqis the equilibrium
constant of the binding reaction. (The equilibrium constant is defined in Equation 8.16 on page
267.)In a set of careful measurements, C. Bohr (father of the physicist Niels Bohr) showed in 1904 that
the curve of oxygen binding versus oxygen concentration in solution (or pressure in the surrounding
air) has a sigmoid, or S-shaped, form (open circles in Figure 9.9). The key feature of the sigmoid
is its inflection point, the place where the graph switches from concave-up to concave-down. The
data show such a point aroundcO 2 =8· 10 −^6 M.The formula you found in Your Turn 9m never
gives such behavior, no matter what value we take forKeq.Interestingly, though, the corresponding
binding curve formyoglobin,arelated oxygen-binding molecule, does have the form expected from