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