Mechanism-Based Pharmacodynamic Modeling ofS(–)-Atenolol: Estimation of in Vivo Affinity for the β₁-Adrenoceptor with an Agonist-Antagonist Interaction Model

Abstract

The aim of this study was the development of an agonistantagonist interaction model to estimate the in vivo affinity of S(Ϫ)-atenolol for the ␤ 1 -adrenoreceptor. Male Wistar-Kyoto (WKY) rats were used to characterize the interaction between the model drugs isoprenaline (to induce tachycardia) and S(Ϫ)-atenolol. Blood samples were taken to determine plasma pharmacokinetics. Reduction of isoprenaline-induced tachycardia was used as a pharmacodynamic endpoint. The pharmacokinetic-pharmacodynamic relationship of isoprenaline was first characterized with the operational model of agonism using the literature value for the affinity (K A ) of isoprenaline (3.2 ϫ 10 Ϫ8 M; left atria WKY rats). Resulting estimates for baseline (E 0 ), maximal effect (E max ), and efficacy () were 374 (1.9%), 130 (5.9%), and 247 (33%) beats per minute, respectively. In addition, the interaction between isoprenaline and S(Ϫ)-atenolol was characterized using a pharmacodynamic interaction model based on the operational model of agonism that describes the heart rate response based on the affinity of the agonist (K A ), the affinity of the antagonist (K B ), the efficacy (), the maximal effect (E max ), the Hill coefficient (n H ), the concentrations of isoprenaline and atenolol, and the displacement of the endogenous agonist adrenaline. The estimated in vivo affinity (K B ) of S(Ϫ)-atenolol for the ␤ 1 -receptor was 4.6 ϫ 10 Ϫ8 M. The obtained estimate for in vivo affinity of S(Ϫ)-atenolol (4.6 ϫ 10 Ϫ8 M) is comparable to literature values for the in vitro affinity in functional assays. In conclusion, a meaningful estimate of in vivo affinity for S(Ϫ)-atenolol could be obtained using a mechanismbased pharmacodynamic modeling approach.The concentration-effect relationships of agonists depend on a combination of the binding to the target (affinity) and the efficiency in activating the target (intrinsic efficacy). In contrast, the activity of a pure antagonist depends solely on binding because it results from the displacement of the (endogenous) agonist from the target (Hardman et al., 2001). Although in theory the mechanism of action of antagonists is less complex than that of agonists, the characterization and quantification of the pharmacological effect of antagonists in vivo is challenging; it requires not only information on concentration of the antagonist but also on the concentration and the intrinsic efficacy of the agonist(s) to be replaced from the target (Kenakin, 1993).In drug development, in vitro binding studies are typically performed to characterize the association between the new chemical entity and receptor by its ability to displace the radioligand at various concentrations (Sweetnam et al., 1993). Quantitative analysis of the displacement curve yields estimates of the affinity of the drug, which is usually represented as the equilibrium dissociation constant (K D ) (Copeland et al., 2006). In functional studies, the affinity of an antagonist can be obtained from a functional assay (i.e., cAMP accumulation) using the d...

Influence of Plasma Protein Binding on Pharmacodynamics: Estimation of In Vivo Receptor Affinities of β Blockers Using a New Mechanism-Based PK–PD Modelling Approach

“…15 For the b-blockers, the PK and the PD interaction with isoprenaline were quantified using nonlinear mixed-effects modelling as implemented in NONMEM software version V, level 1.1. 19 This approach takes into account structural effects, as well as both intraand interanimal variability.…”

“…For all b-blockers, blood samples of 100 mL were taken and one sample was obtained before the start of the infusion (predose). For S(À)-propranolol, a total of 14 samples were taken at 5,10,14,15,18,20,30,36,58,66,100,134,198,240 and 360 min after the start of the infusion. For S(À)-metoprolol, a total of 14 samples were obtained at 5, 10, 15, 17.5, 20, 25, 31, 36, 40, 45, 70, 90, 120 and 180 min after the start of the infusion.…”

“…14,15 For the other compounds, the rats were randomly divided into four groups. The rats in the treatment groups received S(À)-propranolol at doses of 1 (n ¼ 7) or 5 mg/kg (n ¼ 7), S(À)-metoprolol at a dose of 2.5 mg/kg (n ¼ 11), or timolol at a dose of 5 mg/kg (n ¼ 12), all under isoprenaline-induced tachycardia.…”

“…A mechanism-based model was applied to the concentration-effect relationship of isoprenaline under the assumption that the maximal obtainable effect in the system equals the maximal effect of isoprenaline. 7,15 An estimate for the in vitro affinity of isoprenaline was obtained from literature. 21 The efficacy (t) of isoprenaline was estimated using Eq.…”

“…The advantage of a mechanismbased approach is that an estimate of in vivo receptor affinity (K B,vivo ) can be obtained for the b-blockers, which can be compared to the in vitro affinity (K B,vitro ) from a functional assay. 15 Comparison of the in vitro-in vivo correlation for receptor affinity on the basis of free (unbound) drug and total drug will provide insight on whether the free or total drug concentration is the main determinant for the pharmacological response for the b-blockers.…”