Equation: Kinetics of competitive binding

Kinetics experiments can determine the dissociation and association rate constants (off-rate and on-rate) of an unlabeled compound. Add labeled and unlabeled ligand together and measure the binding of the labeled ligand over time. Fit to the appropriate model described below, constraining the rate constants of the labeled ligand to constant values determined from other experiments, and fit the rate constants of the unlabeled compound.

Using only a single concentration of labeled and radioligand, it is very hard to determine the rate constants with any reasonable precision. But measure the kinetics at two (or more) concentrations of the unlabeled ligand, and the results are much more precise.

Create an XY data table. Enter time in minutes into X, and specific binding in cpm into Y. Enter the binding for one concentration of of the unlabeled ligand in column A, and another concentration in column B. Enter the concentrations, in nM, into the column titles.

From the table of specific binding, click Analyze, choose nonlinear regression, choose the panel of Kinetics Binding equations, and choose Kinetics of competitive binding.

Constrain k1 and k2 to constant values determined from kinetic binding experiments. k1 is the association rate constant of the hot ligand in M-1 min-1and k2 is its dissociation rate constant in units of min-1.

Also constrain L to be a constant value equal to the concentration of labeled ligand in nM.

I is constrained to be a column constant whose value comes from the column titles.

Bmax is the total number of receptors. Either leave as a variable or set to a constant you know from other experiments. The Bmax is the maximum binding at equilibrium with a very high concentration of radioligand. It is usually much larger than any binding seen in the experiment.

•	This equation does not account for ligand depletion. It assumes that only a small fraction of radioligand binds to receptors, so that the free concentration of radioligand is very close to the added concentration.

•	This method will only give reliable results if you have plenty of data points at early time points.

•	The ratio K4/K3 is the equilibrium dissociation constant of the cold ligand in Molar. You should compare this value (determined via kinetics) with the same value determined by equilibrium competition.

This method was described by Motulsky and Mahan in Molecular Pharmacology 25:1-9, 1984.