Association binding experiments are used to determine the association rate constant. You add radioligand and measure specific binding at various times thereafter.

Binding follows the law of mass action:

At any given time, the rate at which receptor-ligand complexes form is proportional to the radioligand concentration and the number of receptors still unoccupied. The rate of dissociation is proportional to the concentration of receptor-ligand complexes.

Binding increases over time until it plateaus when specific binding equals a value we call Ymax. This is not the same as Bmax. Ymax is the amount of specific binding at equilibrium for a certain concentration of ligand used in an association experiment. Bmax is the maximum amount of binding extrapolated to a very high concentration of ligand. The free concentration of receptors at any time equals Ymax minus the amount of specific binding at that time.

These principles let us define the model mathematically.

Integrate that differential equation to obtain the equation defining the kinetics of association:

The rate at which binding increases is determined by three factors (as well as experimental conditions such as pH and temperature):

	•	The association rate constant, kon or k+1. This is what you are trying to determine.

	•	The concentration of radioligand. If you use more radioligand, the system equilibrates faster.

	•	The dissociation rate constant, koff or k-1. Some people are surprised to see that the observed rate of association depends in part on the dissociation rate constant. During the incubation, radioligand both binds to and dissociates from receptors. The system reaches equilibrium when the two rates are equal. The observed rate of association measures how long it takes to reach equilibrium. If the radioligand dissociates quickly from the receptor, equilibrium will be reached faster (but with less binding).

Analyzing "on rate" experiments with Prism

To analyze association (on-rate) data:

1. Enter the data with X equal to time and Y equal to specific binding. (If you enter total binding, you'll need to use a more complicated equation that accounts for the kinetics of nonspecific binding.)

2. Fit the specific binding data to the one-phase exponential association equation.

3. The variable k in the exponential association equation is the observed rate constant, kob, expressed in units of inverse time. If you entered X values in minutes, then kob is expressed in min-1. This is not the same as the association rate constant, kon.

4. This equation assumes that a small fraction of the radioligand binds to receptors, so the concentration of free radioligand equals the amount you added and does not change over time.

5. To calculate the association rate constant (kon or k1) usually expressed in units of Molar-1 min-1, use this equation: