Kinetics of competitive binding

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Kinetics of competitive binding

The standard methods of analyzing competitive binding experiments assume that the incubation has reached equilibrium. These experiments are usually used to learn the dissociation constant of the receptors for the unlabeled compound, the Ki. The law of mass action tells us that the Ki is the ratio of the off-rate to the on-rate of the unlabeled compound. You can determine these values in a kinetics experiment as follows. Add labeled and unlabeled ligand together and measure the binding of the labeled ligand over time. This method was described by Motulsky and Mahan in Molecular Pharmacology 25:1-9, 1984.

KA = K1*L*1E-9 + k2
KB = K3*I*1e-9 + K4
S=SQRT((KA-KB)^2+4*K1*K3*L*I*1e-18)
KF = 0.5 * (Ka + KB + S)
KS = 0.5 * (KA + KB - S)
DIFF=KF - KS
Q=Bmax*K1*L*1e-9/DIFF
Y=Q*(k4*DIFF/(KF*KS)+((K4-Kf)/KF)*exp(-KF*X)-((K4-KS)/KS)*exp(-KS*X))
Select this equation from the Advanced Radioligand Binding equation library.

Variable	Units	Comments
X	Minutes	Time.
Y	cpm	Specific binding.
k1	M-1 min-1	Association rate constant of radioligand. Set to a constant value known from other experiments.
k2	min-1	Dissociation rate constant of radioligand. Set to a constant value known from other experiments.
k3	M-1 min-1	Association rate constant of unlabeled ligand. Variable to be fit. Try 1e8 as an initial value.
k4	min-1	Dissociation rate constant of unlabeled ligand. Variable to be fit. Try 0.01 as an initial value.
L	nM	Concentration of radioligand. Set to a constant value you know from experimental design.
Bmax	Units of Y axis. Usually cpm.	Total number of receptors. Either leave as a variable or set to a constant you know from other experiments. If a variable, set the initial value to 100*Ymax (assumes that it bind to 1% of receptors.
I	nM	Constant set experimentally. Concentration of unlabeled ligand.

Notes:


	•	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.