This review addresses the 100-year-old Hill equation (published in January 22, 1910), the first formula relating the result of a reversible association (e.g., concentration of a complex, magnitude of an effect) to the variable concentration of one of the associating substances (the other being present in a constant and relatively low concentration). In addition, the Hill equation was the first (and is the simplest) quantitative receptor model in pharmacology. Although the Hill equation is an empirical receptor model (its parameters have only physico-chemical meaning for a simple ligand binding reaction), it requires only minor a priori knowledge about the mechanism of action for the investigated agonist to reliably fit concentration-response curve data and to yield useful results (in contrast to most of the advanced receptor models). Thus, the Hill equation has remained an important tool for physiological and pharmacological investigations including drug discovery, moreover it serves as a theoretical basis for the development of new pharmacological models.

Although the A1 adenosine receptor (A1 receptor), the main adenosine receptor type in cardiac muscle, is involved in powerful cardioprotective processes such as ischemic preconditioning, the atrial A1 receptor reserve has not yet been quantified for the direct negative inotropic effect of adenosine. In the present study, adenosine concentration-effect (E/c) curves were constructed before and after pretreatment with FSCPX (8-cyclopentyl-N3-[3-(4-(fluorosulfonyl)benzoyloxy)propyl]-N1-propylxanthine), an irreversible A1 receptor antagonist, in isolated guinea pig atria. To prevent the intracellular elimination of the administered adenosine, NBTI (S-(2-hydroxy-5-nitrobenzyl)-6-thioinosine), a nucleoside transport inhibitor, was used. As expected, NBTI alone and FSCPX-pretreatment alone shifted the adenosine E/c curve to the left and right, respectively. However, in the presence of NBTI, FSCPX-pretreatment appeared to increase the maximal response to adenosine. By means of the receptorial responsiveness method (RRM), our recently developed procedure, adenosine E/c curves generated in the presence of NBTI were corrected for the bias caused by the endogenous adenosine accumulated by NBTI. The corrected curves indicate a substantial A1 receptor reserve for the direct negative inotropy evoked by adenosine. In addition, our results suggest that accumulation of an endogenous agonist may bias the E/c curve constructed with the same or similar agonist that can lead to seemingly paradoxical results.

We created a simple method based on curve fitting in order to assess the concentration of pharmacological agonists or antagonists in the microenvironment of the receptors. We tested our method in electrically driven guinea pig left atria by estimating the concentration of N6-cyclopentyladenosine (CPA; A1 adenosine receptor agonist), acetyl-beta-methylcholine (muscarinic receptor agonist) and verapamil (L-type Ca2+ channel inhibitor) added previously to the atria in known amounts. Our results validated the fitness of the model under specified conditions. In addition, our data suggest a relatively slow elimination of CPA in isolated, practically bloodless guinea pig atrial myocardium.

Several accepted methods are available to estimate the adenosine (Ado) concentration of interstitial fluid ([Ado]ISF) in functioning heart, providing results spanning over nano- to micromolar concentrations. This extremely large range points to the necessity of novel approaches for estimating [Ado]ISF or at least the alteration from basal [Ado]ISF. In the present study, the change in [Ado]ISF was characterized following nucleoside transport (NT) blockade elicited by 10 micromol/L dipyridamole or 10 micromol/L nitrobenzylthioinosine in isolated guinea pig atria, by means of our novel procedure referred to as receptorial responsiveness method (RRM). The RRM provided an index of the change in [Ado]ISF under NT blockade, namely the concentration of N-cyclopentyladenosine (CPA; a relatively stable A1 Ado receptor agonist), which is equieffective with the change in [Ado]ISF regarding the contractility. Our results show that dipyridamole or nitrobenzylthioinosine produced an elevation in [Ado]ISF at the cardiomyocyte A1 Ado receptors equivalent to about 16 or 20 nmol/l CPA, respectively. In addition, nitrobenzylthioinosine was found more appropriate for selective NT blockade than dipyridamole.

Based on in silico results, recently we have assumed that FSCPX, an irreversible A1 adenosine receptor antagonist, inhibits the action of NBTI that is apparent on E/c curves of adenosine receptor agonists. As a mechanism for this unexpected effect, we hypothesized that FSCPX might modify the equilibrative and NBTI-sensitive nucleoside transporter (ENT1) in a way that allows ENT1 to transport adenosine but impedes NBTI to inhibit this transport. This assumption implies that our method developed to estimate receptor reserve for agonists with short half-life such as adenosine, in its original form, overestimates the receptor reserve. In this study, therefore, our goals were to experimentally test our assumption on this effect of FSCPX, to improve our receptor reserve-estimating method and then to compare the original and improved forms of this method. Thus, we improved our method and assessed the receptor reserve for the direct negative inotropic effect of adenosine with both forms of this method in guinea pig atria. We have found that FSCPX inhibits the effects of NBTI that are mediated by increasing the interstitial concentration of adenosine of endogenous (but not exogenous) origin. As a mechanism for this action of FSCPX, inhibition of enzymes participating in the interstitial adenosine production can be hypothesized, while modification of ENT1 can be excluded. Furthermore, we have shown that, in comparison with the improved form, the original version of our method overestimates receptor reserve but only to a small extent. Nevertheless, use of the improved form is recommended in the future.