Binding constant

The binding constant is a special case of the equilibrium constant K. It is associated with the binding and unbinding reaction of receptor (R) and ligand (L) molecules, which is formalized as:

${\rm R} + {\rm L}\rightleftharpoons {\rm RL}$.

The reaction is characterized by the on-rate constant k_on and the off-rate constant k_off, which have units of 1/(concentration time) and 1/time, respectively. In equilibrium, the forward binding transition ${\rm R} + {\rm L} \to {\rm RL}$ should be balanced by the backward unbinding transition ${\rm RL} \to {\rm R} + {\rm L}$. That is,

$k_{\rm on}\,[{\rm R}]\,[{\rm L}] = k_{\rm off}\,[{\rm RL}]$,

where [R], [L] and [RL] represent the concentration of unbound free receptors, the concentration of unbound free ligand and the concentration of receptor-ligand complexes. The binding constant, or the association constant K_a is defined by

$K_{\rm a} = {k_{\rm on} \over k_{\rm off}} = {[{\rm RL}] \over {[{\rm R}]\,[{\rm L}]}}$.

An often considered quantity is the dissociation constant $K_{\rm d} \equiv 1/K_{\rm a}$, which has the unit of concentration. For the binding of receptor and ligand molecules in solution, the molar Gibbs free energy ΔG, or the binding affinity is related to the dissociation constant K_d via

$\Delta G = -R T\ln{{K_{\rm d} \over c^{\ominus}}}$,

in which R is the ideal gas constant, T temperature and the standard reference concentration $c^{\ominus}$ = 1 mol / L.