Association

Association refers to the binding interaction between a free ligand (L) and a free receptor or other target protein (P) to create a complex between the two species (LP):

The rate of association is governed by an association rate constant, referred to here as k_on, but often also as k₁.  The units of k_on for the binding interaction between one ligand molecule and one target protein are M^-1s^-1. The meaning of k_on is not intuitively apparent; the numerical value indicates the number of association events that could occur between a single protein target and a ligand present at a concentration of 1 M, in one second, if the protein was always available to associate with a ligand. This abstract idea is easier to visualise if the reciprocal of the association rate constant is thought of as the time required to complete one association event. For example, if k_on is 1×10⁷ M^-1s^-1, then a single protein target molecule could form a complex with ligand (present at 1 M) 10⁷ times every second, or alternatively, one association event is completed every 10^-7 seconds.

The actual rate of the forward reaction (creating LP) is found by multiplying the concentrations of the two reactants, L and P, by the association rate constant. Thus, rate = k_on[L][P]. The rate calculated in this way indicates the initial rate of increase in concentration of the LP complex. However, as the concentrations of the reactants (in particular, the concentration of the unbound target protein, P) are depleted, the association rate slows (often rapidly), and in the absence of dissociation, a plot of [LP] versus time would be an exponential association curve with a half-life equal to 0.693/k_on.

In reality, association does not occur in the absence of dissociation. Therefore, the exponential association curve apparent on a plot of [LP] versus time, from real data obtained from a transient state kinetics experiment, reaches a plateau when a state of equilibrium binding is achieved, due both to a falling association rate and an increasing dissociation rate. The half-life for the observed hybrid binding process is equal to 0.693/k_obs, where k_obs is the observed rate constant with contributions from both k_on and k_off. The relationship yields an equation for a straight line: k_obs = k_on×[L]+k_off.  Therefore, if k_obs is determined at several ligand concentrations, a plot of k_obs versus [ligand] will yield a straight line with slope k_on and y-intercept k_off.

Popular convention has been that for many biological interactions between small molecule ligands and target proteins, values for k_on lie within an order of magnitude in either direction from 1×10⁷ M^-1s^-1 – in other words, between 1×10⁶ M^-1s^-1 and 1×10⁸ M^-1s^-1. As such, differences between binding affinities of different ligands for a protein target have been considered as due largely to differences in dissociation constants. However, it is now accepted that association rate constants lie across a very wide range and that effects on drug behaviour may be quite profound.

Further details and examples may be found under the manual entry for affinity.