User`s manual
54 Chapter 5: Software Description
Calorimetry Sciences Corp.
CSC 5300 N-ITC III 55
User’s Manual
Cooperative Binding Model
This model assumes at least two binding sites
on the macromolecule as well as interaction
between the two ligand molecules (Figure
5-28). For two binding sites the variables
that dene the cooperative binding are 2 sets
of ∆H and β. The rst set denes interac-
tion between the macromolecule and the rst
ligand molecule. The second set determines
the interaction between the macromolecule
and second ligand molecule. The third one
denes the interaction between the two ligand
molecules.
In cases when the number of binding sites is equal to three, number of sets will be equal
to six, etc., BindWorks includes implementations for the cooperative model with two and
three binding sites as a separate models Cooperative (2 sites) and Cooperative (3 sites).
The general Partition function for the cooperative model:
Where β is Adair’s equilibrium constants and x is the free ligand concentration. The de-
gree of saturation can be expressed as:
The total amount of ligand:
Figure 5-28: Cooperative Binding.
Ligand 2
Ligand 1
Macromolecule
Equation 5-4
∑
+=
n
i
i
xßZ 1
Equation 5-6
X X X
t b
= +
Equation 5-5
∑
=
∂
∂
=
n
i
i
xiß
ZX
Z
Y
1
ln
ln