Elusive equilibrium: the challenge of interpreting receptor pharmacology using calcium assays

Abstract

Calcium is a key intracellular signal that controls manifold cellular processes over a wide temporal range. The development of calcium-sensitive fluorescent dyes and proteins revolutionized our ability to visualize this important second messenger and its complex signalling characteristics. The subsequent advent of high throughput plate-based fluorescence readers has resulted in the calcium assay becoming the most widely utilized assay system for the characterization of novel receptor ligands. In this review we discuss common approaches to calcium assays, paying particular attention to the potential issues associated with interpretation of receptor pharmacology using this system. Topics covered include dye saturation and forced-coupling of receptors to the calcium pathway, but special consideration is given to the influence of non-equilibrium conditions in this rapid signalling system. Modelling the calcium transient in a kinetic mode allows the influence of ligand kinetics, receptor reserve and read time to be explored. This demonstrates that observed ligand pharmacology at very early time points can be quite different to that determined after longer incubations, even resulting in reversal of agonist potency orders that may be misinterpreted as agonist biased signalling. It also shows that estimates of antagonist affinity, whether by Schild analysis or inhibition curves, are similarly affected by hemi-equilibrium conditions. Finally we end with a discussion on practical approaches to accurately estimate the affinity of insurmountable antagonists using calcium assays.

Linked articles: This article is part of a themed section on Analytical Receptor Pharmacology in Drug Discovery. To view the other articles in this section visit http://dx.doi.org/10.1111/bph.2010.161.issue-6.

Figure 1

(A) Methacholine-induced intracellular calcium responses in CHO cells expressing the recombinant M₃ muscarinic receptor (data re-drawn from Sykes et al., 2009). (B) Concentration-response curves generated from the data in panel A using either peak calcium or area under the curve as the measure of response. (C) Simulated calcium signals (in % of maximal response of the system) generated by increasing concentrations of an agonist (with k₁= 1 10⁷ M⁻¹·min⁻¹ and k₂= 1 min⁻¹) as a function of the post-agonist administration time in a system with low cellular amplification (τ= 0.1) and k₃= 2 min⁻¹. (D) Simulated agonist concentration-response curves obtained by simulating calcium signal peak levels (in % of maximal response of the system) and area under the curve values (AUC, in % of total plot area) in a system with high cellular amplification (τ= 10). Rate constants are the same as in panel C. Parameters of the curves are given in Table 1. AUC, area under the curve; CHO cells, Chinese hamster ovary cells.

Scheme 1

(A) Description of transient calcium response kinetics by a dynamic model adapted from that described by Christopoulos et al. (1999). In this model, binding of the agonist molecules (A) to free receptors (R) proceeds according to a reversible bimolecular reaction so that the amount of occupied receptors [AR] obeys the law of mass-action. The corresponding association and dissociation rate constants are referred to as k₁ and k₂ respectively. Agonist binding generates/favours an active receptor conformation that serves as the ‘stimulus’ for initiating a cascade of intracellular events leading to the response of interest. While the stimulus-response relationship could be linear in certain cases, this only seldom so (especially in recombinant receptor over-expressing cell systems; Brink et al., 2000) because of the limited capacity of some intervening cellular processes to cope with the upstream ‘demand’. Therefore, receptor occupancy-response relationships are commonly described by a logistic rectangular hyperbolic function where K_E (=[R]_total/τ) is an efficacy term (Black and Leff, 1983). Finally, to deal with the transient nature of the calcium response, K_E is set to increase time-wise with the first-order rate constant k₃. (B) Binding of competitive antagonist molecules (I) to free receptors also proceeds according to a reversible bimolecular reaction with association and dissociation rate constants denoted as k₅ and k₆ respectively.

Figure 2

(A) Simulated receptor occupancy as a function of time at 10 nM, 100 nM and 1 µM of a ligand (with k₁= 10⁷ M⁻¹·min⁻¹ and k₂= 1 min⁻¹). Half-maximal binding is attained at 0.63, 0.35 and 0.16 min respectively. (B) Simulated receptor occupancy at different concentrations of the same ligand when measured after 0.1, 0.2, 0.4, 0.8 and 1.6 min. p(BC₅₀) values are 6.17, 6.44, 6.68, 6.86 and 6.96 and slope factors (nH) of the curves are 1.38, 1.35, 1.27, 1.16 and 1.06 respectively.

Figure 3

Simulated agonist concentration-response curves: (A) Effect of τ on agonist-mediated responses recorded after a brief, fixed-time incubations (0.1 and 0.4 min) and at equilibrium. Agonist kinetic parameters are: k₁= 10⁷ M⁻¹·min⁻¹ and k₂= 1 min⁻¹. (B) Effect of τ on calcium signal peak values for the same agonist and k₃= 2 min⁻¹. Time dependencies of the calcium signal at selected agonist concentrations are shown in Figure 1C for τ= 0.1. Parameters of the curves are given in Table 1.

Figure 4

Simulated concentration-response curves for two agonists (with kinetic properties specified in the figure) measured in the following experimenal systems. (A) [³⁵S]GTPγS binding assay in a system with low cellular amplification (τ= 1). Membranes are pretreated for 60 min with increasing concentrations of the agonists. Then [³⁵S]GTPγS is added and its binding is measured after an additional 60 min incubation. (B) Calcium signal peak values for the same agonists in a cellular readout system with very high amplification (τ= 100) and with k₃= 2 min⁻¹. Response values are expressed in per cent of the maximal response produced by each agonist in question.

Figure 5

Simulated agonist concentration- calcium peak response curves in a system with τ= 0.1 (A) or 10 (B) without pretreatment (control, red curve) or after pretreating the cells with a fast, medium- or slow dissociating antagonist (rates specified in the figure and k₅= 10⁸ M⁻¹·min⁻¹ for all). Pretreatment lasts until equilibrium binding (91% receptor occupancy for [I]= 10.K_d) is reached. Then different concentrations of agonist (with k₁= 10⁷ M⁻¹·min⁻¹ and k₂= 1 min⁻¹) are added and calcium peak levels are recorded. Other parameters are: k₃= 2 min⁻¹. Insert of panel A. Same conditions as for the main panel except that τ remains steady (k₃= 0 min⁻¹) and that the response is only measured after a fixed, 10 min incubation with the agonist.

Figure 6

Antagonist pIC₅₀ values from simulated inhibition curves when calcium responses are measured at different agonist concentrations (abscissa) in a system with τ= 0.1 (A) or 10 (B). In the simulations, receptors were pretreated for 30 min with medium alone or with different concentrations of a fast, medium- or slow dissociating antagonist (specified in the figure and k₅= 1 10⁸ M⁻¹·min⁻¹ for all) and then challenged with agonist (with k₁= 10⁷ M⁻¹·min⁻¹ and k₂= 1 min⁻¹). Other parameters are: k₃= 2 min⁻¹. The antagonist IC₅₀ values (expressed as pIC₅₀) are calculated by analysing the so-obtained inhibition curves (not shown) according to a variable-slope one-site competition model.

Figure 7

Simulated inhibition curves of a fast- (panel A: dissociation t_1/2= 0.69 min) and slow dissociating antagonist (panel B: dissociation t_1/2= 69 min) by measuring distinct responses by the same agonist. Receptors are pretreated for 30 min with different concentrations of both antagonists. Then a high concentration (100 µM) of agonist (with k₁= 10⁷ M⁻¹.min⁻¹ and k₂= 1 min⁻¹) is added and calcium peak levels are recorded in a system with high cellular amplification (τ= 10) and k₃= 2 min⁻¹. Alternatively, responses are recorded after 10 min incubation in a system with low and steady cellular amplification (τ= 0.1 and k₃= 0 min⁻¹). Other parameters are: k₅= 10⁸ M⁻¹·min⁻¹.

Figure 8

Illustration of the optimal agonist response levels at which to determine the dose ratio (DR) of an insurmountable antagonist. Data are reproduced from Figure 5A for the most slowly dissociating antagonist (t_1/2= 69 min). Red and green arrows illustrate the DR at 40% and 10% response respectively.