116
chapter 7
Enzymes II: Regulation
FIGURE 7-8
The remarkable similarity in the conformations of myoglobin and of the /3-chain of hemoglobin. [Reproduced with
permission from A. Fersht,
E n zym e S tru ctu re a n d M ech a n ism .
(W. H. Freeman, New York, 1977.]
Substituting Equation (7.2) into Equation (7.3), we obtain
[Oz]
[02] +
Kd
(7.4)
Because
(> 2
is a gas, it is convenient to express [0
2
] in terms
of its partial pressure in units of Torr (or mm Hg; multiply by
0.133 to obtain kilopascals). Therefore,
Y =
P(h
P
02
+
Kd
(7.5)
Now we can substitute for
Kd
the term P
5 0
, which is de-
fined as the partial pressure of oxygen at which 50% of the
sites are occupied (i.e., when
Y =
0.5), because this situation
is analogous to the Michaelis-Menten treatment of enzyme
kinetics.
Y =
Po2
P02
+
P
50
(7.6)
A plot of
Y
versus
Po2
yields an oxygen saturation profile
that is a rectangular hyperbola (Figure 7-9), indicating that
the binding of oxygen to myoglobin is noncooperative. Equa-
tion (7.6) can be rearranged to yield a linear plot as follows:
Equation (7.8) is known as the
Hill equation.
A plot of
log (K/1
—
Y)
versus log
Po2
yields a straight line with a
slope of 1
(the Hill coefficient) (Figure 7-10). Thus, a value
Y
= P
02
1
- Y
P50
(7.7)
Taking the logarithms of both sides of Equation (7.7) yields
log
= log
PCh
log
P 5 0
(7.8)
FIGURE 7-9
Profiles of fractional saturation of myoglobin and of hemoglobin with
oxygen as a function of partial pressure of oxygen. Under physiological
conditions, P
50
for myoglobin is only
1
or
2
torr, whereas for hemoglobin it
is 26 torr, indicating that oxygen is bound much more tightly to myoglobin
than to hemoglobin. The loading and unloading to oxygen are cooperative
in the case of hemoglobin but not cooperative in the case of myoglobin.
