Kinetic experiments

Unlike the saturation and competition binding experiments, kinetic studies provide information about the time-course of the binding. These studies usually comprise two types of experiments (Figure 45):

• Determination of dissociation rate constant: in these experiments the radioligand is incubated with the receptor and the dissociation is initiated either by adding an excess of unlabelled ligand (so that free receptors are immediately occupied and no longer accessible to the radioligand) or by dilution (usually after washing away the free radioligand, so that its free concentration is too low to undergo noticeable re-association). Then, the amount of binding is measured after different periods of time (t). First-order reactions occur when the radioligand-receptor complex is a single bimolecular species (L—R). Binding decreases exponentially and the dissociation rate constant (k— x) can be shown to be related to the time it takes for half of the L—R complexes to dissociate (t1/2) by the equation k—1 = 0.693/t1/2. Dissociation data can easily be calculated by plotting ln(binding at time t/binding at the start of the dissociation experiment) (i.e. ln(Bt/Bt=0)) versus the dissociation time. In the case of a first-order reaction, the plot will be linear and the slope corresponds to the negative value of k_ 1 (usually expressed in min—1).

• Determination of the association rate constant: in these experiments the radioligand is incubated with the receptor and the amount of binding is measured after different periods of time (t). Binding will increase until equilibrium (equilibrium binding Beq) is reached. Under circumstances where [L] is added at concentrations in considerable excess of [R] (as is most often the case), [L] can be assumed not to change throughout the incubation. In contrast, as only [R] decreases, the rate of association may be regarded as being a 'pseudo first-order' reaction. When plotting ln(Beq/ (Beq — B)) versus the association time, the slope of the plot gives the pseudo first-order rate constant (kobs). Since the radioligand also undergoes dissociation from the receptor in this type of experiments, it ensues that kobs reflects both the association and

Tipping Point

Figure 45 Association and dissociation binding of [3H]NPY to the neuropeptide Y receptors of the Yj-type in the human SK-N-MC cells. Reprinted from European Journal of Pharmacology, 346, Van Liefde, I., Vanderheyden, P. M., Fraeyman, N., De Backer, J. P., Vauquelin, G., Human neuropeptide YY1 receptors exert unequal control of the extracellular acidification rate in different cell lines, 87-95. Copyright (1998), with permission from Elsevier.

Figure 45 Association and dissociation binding of [3H]NPY to the neuropeptide Y receptors of the Yj-type in the human SK-N-MC cells. Reprinted from European Journal of Pharmacology, 346, Van Liefde, I., Vanderheyden, P. M., Fraeyman, N., De Backer, J. P., Vauquelin, G., Human neuropeptide YY1 receptors exert unequal control of the extracellular acidification rate in different cell lines, 87-95. Copyright (1998), with permission from Elsevier.

the dissociation of the radioligand. The true, bimolecular association rate constant k1 (usually expressed in M-1 X min-1) can be obtained by the following equation:

Kinetic data allow the discrimination between fast reversible, slowly reversible and irreversible ligands (dissociation kinetics). Both the association and dissociation constants provide an estimation of the equilibrium dissociation constant (KD) independently of saturation binding experiments, i.e.:

When the k^/kj ratio is quite distinct from the KD obtained from saturation binding experiments, the possibility arises that the ligand induces a time-dependent change in receptor conformation that goes along with an increase (or decrease) in receptor affinity. An alternative explanation is that the value is incorrect due to 'rebinding' of dissociated radioligand molecules to the receptors (see below) or to the fact that the unlabelled ligand used to prevent such 'rebinding' interacts with an allosteric site at the receptor (see Section 4.14).

Kinetic data also provide information about the time required for binding of a radioligand reaching equilibrium (association kinetics). This information is crucial for the set-up of saturation and competition binding experiments. Indeed, the KD and Ki values which are derived from such experiments are only meaningful when, at any concentration of radioligand and competitor, binding is at or at least close to equilibrium. When the incubation time is to short, it could:

• Produce a false estimation of Bmax and KD values for saturation binding.

• Produce a false estimation of IC50 and K values for competition binding experiments.

Radioligands that are dissociated from the receptor will accumulate in the medium and, if they are not constantly removed, they may bind to the receptor again. This

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Washout time (min)

Figure 46 Cells expressing ATj receptors were incubated for 30 min at 37 °C with [3H]candesartan, washed and incubated in fresh medium with no or different concentrations of the unlabelled ATj-receptor antagonist losartan. The remaining binding of [3H]candesartan was measured after the time intervals indicated. Reprinted from European Journal of Pharmacology, 367, Fierens, F., Vanderheyden, P. M., De Backer, J. P., Vauquelin, G., Binding of the antagonist [3H]candesartan to angiotensin II ATI receptor-transfected Chinese hamster ovary cells, 413-422. Copyright (1999), with permission from Elsevier.

Washout time (min)

Figure 46 Cells expressing ATj receptors were incubated for 30 min at 37 °C with [3H]candesartan, washed and incubated in fresh medium with no or different concentrations of the unlabelled ATj-receptor antagonist losartan. The remaining binding of [3H]candesartan was measured after the time intervals indicated. Reprinted from European Journal of Pharmacology, 367, Fierens, F., Vanderheyden, P. M., De Backer, J. P., Vauquelin, G., Binding of the antagonist [3H]candesartan to angiotensin II ATI receptor-transfected Chinese hamster ovary cells, 413-422. Copyright (1999), with permission from Elsevier.

'reassociation' or 'rebinding' is particularly prominent when the radioligand displays high affinity for the receptor. Whereas rebinding might take place if the incubation medium is simply replaced by fresh medium, it will be effectively prevented when the same or another unlabelled ligand is present in sufficiently large excess in the fresh medium. This is because the receptors become immediately occupied by the unlabelled ligand as soon as the radioligand dissociates. This effectively prevents the 'rebinding' of the radioligand. It is only in the absence of such rebinding that the dissociation rate/half-life of a radioligand-receptor complex can be correctly measured.

This phenomenon has unequivocally been demonstrated by binding studies with the ATrreceptor antagonist [3H]candesartan (Figure 46). When ATrreceptor expressing cells were incubated with [3H]candesartan and the medium was replaced by fresh medium only, its dissociation was estimated to be half-maximal after 6-8 hours. Yet, when unlabelled candesartan or any other ATrreceptor ligand was present in the replacing medium, they all produced a concentration-wise decrease in the apparent half-life of the [3H]candesartan-receptor complex until a half-life of two hours was attained. This value reflects the actual dissociation of this radioligand.

Another factor that severely affects kinetic measurements is the temperature (Figure 47). In this respect, the association and dissociation of radioligands and their receptors are markedly accelerated upon increasing the temperature.

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dissociation time (min)

Figure 47 Dissociation of [3H]candesartan from human ATj receptors on CHO cells. Cells were incubated for 30 min at 37 °C with [3H]candesartan, washed and incubated in fresh medium (containing losartan) at the temperatures indicated. Remaining binding of [3H]candesartan (B, expressed as a percentage of Bo) was measured after the time intervals indicated. Reprinted from Biochemical Pharmacology, 63, Fierens, F., Vanderheyden, P.M. L., Roggeman, C., Vande Gucht, P., De Backer, J.-P. and Vauquelin, G., Distinct binding properties of the ATI receptor antagonist [3H]candesartan to intact cells and membrane preparations, 1273-1279. Copyright (2002), with permission from Elsevier.

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