Substituting [PD] =Ka[D][P] from eqn 2.3 into the fraction and rearranging
the terms yields the expression:
(2.5)
For the ITC measurements, the heat, q, released or absorbed for any given
injection is proportional to the number of moles of the PD complex formed
upon injection, which can be written in terms of the total volume, V, and
concentration [PD]. Making use of the expression for the fraction θallows
the heat to be written in terms of the association constant:
(2.6)
Thus, the heat profiles from the ITC experiments can be used to deter-
mine the binding affinity for the drug to the protein. The proportionality
constant is given by the amount of heat released (or absorbed) for the
binding of each molecule.
This approach has been successfully used to probe drug targets. For
example, in human leukemia, the mixed-lineage leukemia (MLL) gene is
associated with chromosomal translocations and is critical for the regula-
tion of chromatin structure and gene activity (Allen et al. 2006). By using
ITC and other structural measurements, the DNA-binding properties of
the protein expressed by this gene have been characterized, providing
researchers with a platform for developing therapeutics for leukemias that
target the DNA-binding site. ITC has also been used with structural studies
to understand the mechanism of conotoxins, which are a large family of
toxins (Celie et al. 2005). Such toxins are under investigation for neuro-
logical diseases, including epilepsy. Knowledge concerning the binding of
these toxins to receptors in the cell membrane enhances our understanding
of the action of these toxins and the potential for drug design. The deter-
mination by ITC of the energetics of cAMP to a transcriptional activator
termed CAP, for catabolite-activator protein, showed a biphasic isotherm
which pointed to the existence of two nonequivalent binding sites with
different characteristics (Popovych et al. 2006).
Work
In classical mechanics, work is performed when a force, F, is used to move
an object through a distance, Δx, according to the relationship:
w=−FΔx (2.7)
qV V V
Ka
[ ] [] [][]
∝= =
+
PD P P
D
totalθ total 1 KK
a[]D⎛
⎝
⎜⎜
⎞
⎠
⎟⎟
θ
[]
[] [ ]
[][]
[] [ ][]
=
+
=
+
PD
PPD
DP
PDP
K
K
a
a[]
[]
=
+
K
K
a
a