Biomedical Engineering Reference
In-Depth Information
The driving force of each mole of each reactant acts independently of any
other (binding does not alter the ligand or receptor).
These interactions are reversible and at chemical equilibrium, the total driving
force(s) of the reactant(s) is equal to the total driving force(s) of the product(s).
k
on
RLRL
+
⋅
k
off
This type of interaction is commonly referred as a
noncooperative interaction.
The rate of association is:
Number of binding events per unit of time
=
k
on
[Ligand][Receptor]
The probability of dissociation is the same at every instant of time. The recep-
tor does not know how long it has been bound to the ligand. The rate of dissocia-
tion is:
Number of dissociation events per unit of time
=
k
off
[ligand
•
receptor]
After dissociation, the ligand and receptor are the same as at they were before
binding. If either the ligand or receptor is chemically modified, then the binding
does not follow the law of mass action. The time rate of change of the ligand/recep-
tor complexes
dR L
[
d
⋅
]
(7.1)
=
kRL k RL
[ []
−
[
⋅
]
on
off
From this expression, a time-dependent analytical solution can be obtained
if rate constants are available. When equilibrium is reached, that is, the rate at
which new ligand
•
receptor complexes are formed equals the rate at which the
ligand
•
receptor complexes dissociate, then,
dR L
[
d
⋅
]
(7.2)
=
0
Rearrange (7.1) to define the equilibrium dissociation constant
K
D
.
[ []
[
k
RL
off
K
==
⋅
]
D
k
RL
on
The
K
D
has a meaning that is easy to understand. From the
K
D
value, free en-
ergy in the ligand/receptor binding can be calculated using
