202
Chapter 6
In 1910 Hill proposed an empirical expression for the uptake of oxygen by the protein
hemoglobin. He found that the rate of oxygen uptake when pictured against the oxygen partial
pressure had a sigmoidal shape, and the data could be fitted to
r
=
s" + K"
(6.17)
The maximum uptake rate /•„,„ and the denominator constant
K
(typical unit mg substrate/mg
enzyme) are similar to the two parameters of the Michaelis Menten kinetics, and r/rmax = 0.5
when
s = K.
The new parameter
n
is greater than one when the substrate is cooperatively bound
to the enzyme.
Eq (6.17) has the property that
dr/ds
is zero for 5 = 0 whenever
n
is greater than one, and
r/r„,„
increases rapidly from about zero to nearly one in a rather narrow 5-interval around
K.
To be more
specific:
The point
P
of inflexion of
r{s)
is at
ft-
1
/1
+
1
K
(6.18)
The value of
r!rmm
is ( « - ! ) / (2
n)
at s = ,vlIin„
(6.19)
Figure 6.5
T h e H ill equation (6.17) for
n = 4
and
K =
0.1 and 0.2 (arbitrary units).
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