Medicinal Chemistry

and where the fraction of occupied sites υis

2.6.1 Direct Plot

In the direct plot, equation (2.22) is solved for [DR] and its value substituted into
equation (2.23):

KDcan then be obtained from a plot of υagainst [D] if the receptor concentration is con-
stant. This is, of course, the same as the direct plot of enzyme activity shown in every
biochemistry textbook. As with all hyperbolic relationships, there are several draw-
backs to this technique: many data points are needed at the beginning of the curve, at
low [D] values, where accuracy is limited. Also, determination of the maximum effect
is almost impossible, since we are dealing with an asymptotic curve.

2.6.2 Titration Plot

In the titration plot, equation (2.24) is solved for KD:

and, obtaining log 10 of both sides,

where one can use the negative logarithms

and

and arrive at

In acid–base titrations, pD is pH and pKDis pKabecause [D] ≈[H+]. This is the reason
for the name of the curve, well known from analytical chemistry. The drawback of this
plot is that many points are needed in the vicinity of the inflection point.

82 MEDICINAL CHEMISTRY

v=

[DR]

[DR]+[R]

(2.23)

v=

[D]

KD+[D]

(2.24)

KD=[D]

( 1 −v)

v

(2.25)

logKD=log [D]+log

1 −v

v

(2.26)

−log [D]=pD (2.27)

−log KD=pKD (2.28)

pD=pKD+log

(

1 −v

v

)

(2.29)