Affinity Chromatography - Department of Molecular and Cellular ...

Appendix 7
Kinetics in affinity chromatography
The binding (adsorption) and elution (desorption) of a target protein (T) to and from an
affinity ligand (L) can be considered in terms of the binding equilibria involved and the
kinetics of adsorption and desorption.
Binding equilibria: Non-selective elution by changing K D
L
+ T
LT
The standard definition of the equilibrium dissociation constant K D is shown below. Free
ligand is the ligand that is not bound to a target protein and free target is the target which
is not bound to a ligand.
At equilibrium
K D = [L][T]
[LT]
K D is the equilibrium dissociation constant
[L] is the concentration of free ligand
[T] is the concentration of free target
[LT] is the concentration of the ligand/target complex
Standard definition of the equilibrium constant.
Graves and Wu in Methods in Enzymology 34, 140–163 (1974) have shown that:
Bound target
Total target
L 0
~
K D + L 0
K D is the equilibrium dissociation constant
L 0 is the concentration of ligand, usually 10 -4 - 10 -2 M
There are many assumptions and simplifications behind the derivation of this equation,
but, although it is not an exact description, it does give a reasonable qualitative description.
The ratio of bound to total target should be close to 1 during binding, i.e. almost all the
target binds to the ligand. K D should be small compared to the ligand concentration, i.e. K D
is 10 -6 - 10 -4 M when L 0 is 10 -4 - 10 -2 M, to achieve efficient binding.
Since K D can be changed by altering pH, temperature, ionic strength and other parameters,
these parameters can be modified to cause elution in affinity chromatography. If the
conditions are changed the binding equilibrium changes and to get a reasonable elution the
dissociation constant must be increased by quite a large factor (Figure 77).
During binding K D 10 -6 - 10 -4 M
L + T
LT
During elution K D 10 -1 - 10 -2 M
LT
L + T
Fig. 77. Changes in binding and elution alter K D
.
146