After each injection, any heat absorbed or released in the sample cell
compared to a reference cell is measured. A feedback circuit continuously
supplies thermal power to maintain a constant temperature in both the
sample and reference cells, with any release or absorption of heat in the
sample cell compensated for by a change in the thermal power. As more
of the drug is injected, the number of proteins available for binding
decreases systematically, and so the heat release subsequently decreases
until the sites are saturated and no additional molecules of the drug can
bind to the protein.
The resulting heat profile can be characterized in terms of a traditional
binding curve, yielding the number of drug molecules bound to each pro-
tein as well as the binding constants. The presence of both the drug D and
the protein P in the same chamber will result in binding and formation
of a protein–drug complex, PD. For reversible binding in equilibrium,
the relative amounts of the unbound states and the complex will be deter-
mined by the concentration of the free protein [P], the concentration of
the free drug [D], the concentration of the drug–protein complex [PD],
and the association constant Kaaccording to:
(2.2)
The association constant provides a measure for the binding affinity of the
drug to the protein and has units of M−^1 , with higher values correspond-
ing to higher affinities. The binding constant can be used to determine the
amount of bound drug at a specified concentration of the drug and protein.
A rearrangement of eqn 2.2 shows that the ratio of the drug–protein com-
plex to free protein, [PD]/[P], is directly proportional to the concentration
of the free drug:
(2.3)
Notice that when the protein sites are half occupied, and [PD] =[P], then
the value of Kacan be written simply as 1/[D]. Thus, the concentration of
the drug at which half of the binding sites are occupied corresponds to
1/Ka. Consider a new term, θ, the fraction of binding sites occupied by the
drug compared to the total number of binding sites. This fraction is given
by the relative number of binding sites occupied to the total number of
binding sites, which is the sum of the proteins with and without the drug
bound. This ratio can be expressed in terms of the concentrations of the
protein without drug bound, [P], the concentration of the total protein,
[P]total, and the concentration of protein with the drug bound, [PD]:
θ= (2.4)
Binding sites occupied
Total binding sitees
[PD]
P
[PD]
[]total [] [ ]PPD
==
+
Ka[]
[]
[]
D
PD
P
=
PD PD
PD
PD
[]
[][ ]
+←→⎯=
K
a
a K
28 PARTI THERMODYNAMICS AND KINETICS
