# Methodical Challenges and a Possible Resolution in the Assessment of Receptor Reserve for Adenosine, an Agonist with Short Half-Life

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{3}-[3-(4-(fluorosulfonyl)benzoyloxy)propyl]-N

^{1}-propylxanthine), an irreversible A

_{1}adenosine receptor antagonist, and NBTI (S-(2-hydroxy-5-nitrobenzyl)-6-thioinosine), a nucleoside transport inhibitor, i.e., FSCPX may blunt the effect of NBTI.

## 1. Introduction

_{A}) and half-maximal effect (EC

_{50}): PSR = K

_{A}/EC

_{50}[1]. A more sophisticated index is the percentage receptor reserve (RR

_{%}) that is the difference of effect (E

_{%}) and receptor occupancy (ρ

_{%}), both expressed as a percent of their maximums: RR

_{%}= E

_{%}− ρ

_{%}[12]. RR

_{%}addresses the essence of receptor reserve, i.e., stimulation of a given percent of total receptor population can elicit a higher percent of maximal effect. In other words, the receptor reserve refers to the percent of receptors not required for the production of maximal effect (being “spare receptors”) [4]. As shown, RR

_{%}depends on the particular value of E

_{%}, the latter of which is the asymptotic maximum of RR

_{%}. RR

_{%}is usually computed for arbitrary E

_{%}values, e.g., for the half maximal or (near) maximal effect. For the above-mentioned calculations, at first the K

_{A}values should be determined based on evaluating E/c curves (generated with a given agonist, in a given tissue and with measuring a given effect). A characteristic feature of this procedure is that these E/c curves should be constructed both in the absence and presence of an irreversible antagonist against the investigated receptor (preferably at a concentration that is able to significantly reduce the achievable maximal effect).

^{6}-cyclopentyladenosine) and CHA (N

^{6}-cyclohexyladenosine), three synthetic A

_{1}adenosine receptor (A

_{1}receptor) agonists with long half-lives, in the guinea pig atrium. We plotted RR

_{%}against E

_{%}, thereby characterizing the receptor reserve with a function. RR

_{%}/E

_{%}functions indicated considerably great A

_{1}receptor reserve values for the direct negative inotropic effect [13]. In addition, the shape of these functions showed that the maximal effect, theoretically, can be achieved only at maximal receptor occupancy (that can be produced only by infinitely high agonist concentration). Thus, historical receptor reserve values published for maximal effect should actually apply to some near maximal effect. Indeed, the above-mentioned RR

_{%}/E

_{%}functions reached their maximums (80–92%) at great but not maximal E

_{%}values (90–96%) [13].

_{1}receptor that initiates robust retaliatory effects (limiting energy consumption, such as negative inotropic effect) and adaptive processes (e.g., to ischemia, also reflected by the phenomenon of ischemic preconditioning) [18,19,20,21]. Accordingly, several compounds exhibiting A

_{1}receptor agonist, A

_{1}receptor enhancer or endogenous adenosine level-elevating properties are in the pipeline or in use for numerous indications, as antiarrhythmic, antianginal, antidiabetic and antinociceptive agents [8,9,22,23,24]. For this reason, it is important to explore the exact role of adenosine in the A

_{1}adenosinergic mechanisms throughout the body that requires reliable E/c data.

_{1}receptor-mediated direct negative inotropy in the guinea pig left atrium. Consistent with earlier methods [5,7,13], the essence of this procedure is the construction of adenosine E/c curves before and after a treatment with FSCPX (8-cyclopentyl-N

^{3}-[3-(4-(fluorosulfonyl)benzoyloxy)propyl]-N

^{1}-propylxanthine), an irreversible A

_{1}receptor antagonist, but in the presence of NBTI (S-(2-hydroxy-5-nitrobenzyl)-6-thioinosine), an inhibitor of the equilibrative and NBTI-sensitive nucleoside transporter (ENT1). NBTI, by preventing cellular uptake and consequent intracellular elimination of adenosine, prolongs the half-life of this purine nucleoside in the guinea pig atrium [25]. In addition, it is also obligatory to generate E/c curves with a stable A

_{1}receptor agonist (e.g., CPA) in the absence and presence of NBTI, and to construct an E/c curve with this stable agonist after an FSCPX treatment (but without NBTI), in order to collect data for the correction of the adenosine E/c curves subjected to NBTI (for explanation, see Section 4). The receptor reserve will be indicated by the distance of final parts of the two corrected adenosine E/c curves (constructed without and with FSCPX treatment) because the final sections of these E/c curves show the maximal effect elicited by adenosine upon unaffected and reduced A

_{1}receptor populations (respectively). The closer these final parts are to each other, the greater the A

_{1}receptor reserve for adenosine (and for the given tissue and the measured effect). By means of our method (using FSCPX with the recommended maximal concentration and duration time), we have found that the receptor reserve for adenosine is comparable in extent with that for NECA, CPA and CHA, three synthetic high-efficacy agonists with long half-lives, when measuring the direct negative inotropic effect mediated by the atrial A

_{1}receptor [27,31].

_{1}receptor, i.e., the direct negative inotropic effect [31]. For the sake of clarity, adenosine and CPA were simulated as agonist A and B, respectively, while FSCPX and NBTI were simulated as irreversible antagonist (IA) and transport inhibitor (TI), respectively.

## 2. Results

#### 2.1. Features of the Simple Unbiased E/c Curves of Agonists A and B

#### 2.2. The Effect of a Treatment with TI Alone and a Co-Treatment with IA and TI on the E/c Curve of Agonist A (Biased E/c Curves of Agonist A)

_{1}receptor antagonist appeared to increase the maximal effect of adenosine; Figure 2A), however, was not reproducible in silico under the assumption that TI elicits its action irrespectively of the IA treatment. In contrast, when we introduced an interaction between IA and TI at the level of the transmembrane transport of agonist A, the relative position of the three E/c curves could be made similar to that seen in the biological model (Figure 2B).

#### 2.3. The Effect of a TI Treatment on the E/c Curve of Agonist B (Biased E/c Curve of Agonist B)

^{−7}versus 4 × 10

^{−7}, respectively).

#### 2.4. The Corrected E/c Curves of Agonist A (Derived from the Biased Ones)

_{1}receptor reserve pertaining to the direct negative inotropic effect of adenosine is substantially great in the guinea pig atrium [27,31].

_{x}value (the expected equieffective concentration of agonist B) was used for the quantification of the surplus concentration of agonist A produced by TI. As this c

_{x}was obtained from IA-naïve E/c curves, it informs us about the agonist accumulation under complete agonist transport blockade. Therefore, this c

_{x}could not be used to correct IA-treated E/c curves.

_{x}value for all calculations in our earlier studies [27,31]. Taken the results of the present study into account, this practice has proven to be theoretically objectionable. However, conclusions previously drawn from corrected E/c curves (more precisely, from the final parts of these curves indicating the maximal effect of adenosine) have remained correct. This is indicated by the observation of the present study, i.e., in the range of excessive concentrations of agonist A, a slightly bigger agonist A transport caused by IA treatment (in comparison with the condition upon complete transport inhibition) no longer significantly influences the effect evoked (Figure 4B).

## 3. Discussion

_{1}receptor. Specifically, we reproduced a special set of adenosine E/c curves presented in our prior ex vivo study [31] for determining receptor reserve by means of our recently published method [27]. Then, we evaluated the simulated functions in a manner described for the ex vivo E/c curves [27,31] in order to validate our method and to ensure the best interpretation of its results.

_{1}receptor also cannot be excluded. To clarify the exact mechanism, further investigations are warranted.

_{1}receptor described previously [27,31]. Furthermore, it has validated our method as a reliable tool to assess receptor reserve. In addition, results of this investigation also draw attention to the obligatory precaution concerning possible unexpected effects (e.g., unanticipated interactions) of the chemicals used.

_{1}receptor agonists, proved to have a significant effect only in tissues with great A

_{1}receptor reserve, have been being developed in numerous indications [8,9,22,23,24]. However, as some drugs influence the level and/or distribution of endogenous agonists, receptor reserve data related to these agonists also have therapeutical significance that indicates the raison d’être of our method to assess receptor reserve. Beyond these considerations, our method can be utilized for basic research as well, namely, to investigate the E/c relationship of endogenous agonists upon different conditions. In a prior work, based on results obtained using the correction procedure being a part of our new method (see Section 4), we proposed a new, thyroid hormone-sensitive effect of adenosine deaminase inhibition, i.e., inhibition of adenosine deaminase appeared to increase the signal amplification of the atrial A

_{1}adenosinergic system, an effect that was more pronounced in hyperthyroidism (in this investigation, no irreversible A

_{1}receptor antagonist was administered) [32]. This mechanism may be of practical significance in improving ischemic tolerance of the heart.

_{A}values (marked with K in the present study, see Section 4) needed for computing exact receptor reserve values, especially in the case of the complex G protein-coupled receptors [33,34,35]. This criticism also affects the operational model [36] and Furchgott’s method [5], two procedures that are used to determine K

_{A}values for the quantification of receptor reserve (as an example, see: [13]). Moreover, quantification of affinity and efficacy parameters for an agonist-receptor interaction is always exposed to theoretical pitfalls to some extent [34,37]. However, our method is a qualitative one and is not constrained by premises of the traditional receptor theory, rather it is based on the (quite general) assumptions and requirements of the Hill equation (as receptor function model [38]) supplemented with some limits specific for RRM [28,29]. Our method exploits the phenomenon underlying the concept of receptor reserve, i.e., the extent of decrease in maximal effect in response to a treatment with an irreversible antagonist at a given concentration [27,31]. Taking all together, we feel that tailoring the concept of receptor reserve to the requisites of the post-traditional receptor theory era, including the extension of its definition beyond the receptor per se to a receptor system as a tissue-dependent functional unit (containing the receptor and the postreceptorial signaling pathways involved), the assessment of receptor reserve will have further translational and resultant clinical implications that can be utilized in rational drug development.

_{A}and τ (including K

_{E}) values (see Equation (3) in see Section 4), if the operational model is fitted to E/c curve data [2,39]. In the present work, however, this model was used to generate functions shaping E/c curves, and K

_{A}(herein K) values of this model were not applied to calculate exact receptor reserve values.

## 4. Materials and Methods

#### 4.1. Properties of the Biological Model to Be Simulated

_{max}) to adenosine and to decrease the adenosine concentration needed for the half-maximal response (EC

_{50}), as a result of the decreased elimination of exogenous adenosine. On the other hand, it also tends to decrease E

_{max}and to increase EC

_{50}because the interstitially accumulated endogenous adenosine consumes a significant portion of the response capacity of A

_{1}receptors (importantly, before the construction of the E/c curve with exogenous adenosine). The net effect of these two influences is that NBTI slightly reduces E

_{max}but markedly decreases EC

_{50}of the adenosine E/c curve, at least in terms of the direct negative inotropy mediated by the guinea pig atrial A

_{1}receptor [25,43].

_{max}and increases EC

_{50}, a phenomenon that can be completely explained by the interstitial accumulation of endogenous adenosine in response to ENT1 inhibition that in part uses up the responsiveness of A

_{1}receptors before taking the CPA E/c curve [25,43].

_{1}receptor agonist used to construct the E/c curve, the surplus interstitial endogenous adenosine produced by NBTI tends to cause a characteristic bias (i.e., depression of maximal effect and dextral displacement) on the E/c curve. However, this bias is unmasked only if this effect is the single effect of NBTI, i.e., level of the agonist used for the E/c curve is not affected by NBTI (as is the case for CPA). In general, the mechanism by which this bias develops is that the surplus endogenous agonist concentration and its effect is overlooked during the evaluation of effect values that are assigned to the agonist concentrations administered for the E/c curve. Nevertheless, the extent of this E/c curve modification provides an opportunity to quantify the neglected extra concentration of the endogenous agonist by the equieffective concentration of an agonist (optimally a stable one with a long half-life) used for the E/c curve. This concentration estimating procedure, termed RRM, is based on fitting the biased E/c curves to a specific equation (see Equation (5) below), best-fit value of which yields the equieffective concentration [25,28,43].

#### 4.2. Applied Mathematical Tools

- To generate unbiased E/c curves, the operational model of agonism, a comprehensive receptor function model forming a hybrid between empirical and mechanistic models [39], was applied. Two equations of this model was used, one determining the effect of one agonist [36], and another one described for the co-action of two (different or the same) agonists [44]. In this latter equation, one agonist was present always at a single concentration, while the other one was applied in a range of concentrations. Functions provided by the equation for one agonist’s action represented simple unbiased E/c curves, while those, yielded by the equation for the co-action of two agonists, simulated unbiased E/c curves that could be easily biased by ignoring the agonist concentration used with a single value (see below). This ignored agonist concentration (defined arbitrarily for the simulation) served as a model for the surplus interstitial concentration of endogenous adenosine produced by NBTI, while increasing concentrations of the other agonist simulated the concentrations administered for the E/c curve.
- To geometrically characterize functions via curve fitting or to calculate effect values from concentrations and best-fit values obtained by curve fitting, the Hill equation, the most widely used empirical receptor function model [38], was applied.
- Adenosine and CPA were modelled with an agonist A and B, respectively. Therefore, a continuous extracellular production, intracellular elimination and transmembrane transport of agonist A were considered. Thus, “exogenous” agonist A concentrations (simulating the administration of agonist A for an E/c curve) were manipulated, when calculating their effect, to model the function of nucleoside transporters (see paragraph 5). Furthermore, a surplus “endogenous” agonist A concentration was designated as a response to the inhibition of nucleoside transport (for simplicity, only ENT1, i.e., an inhabitable carrier, was built into the present model). In contrast, agonist B concentrations were considered to be constant after their administration (see paragraph 5).
- NBTI and FSCPX were represented by a so-called transport inhibitor (TI) and irreversible antagonist (IA), respectively.
- Development of agonist concentrations was considered in two compartments. For all agonists, concentration values in the bathing medium were defined to be independent from any kind of simulated treatments. When constructing E/c curves, effect values were always plotted against the bathing medium concentrations (simulating the condition that usually these concentrations are known during ex vivo experiments). However, effect values were always computed from near-receptor concentrations defined as follows (after testing several value combinations). The bathing medium concentration was designated as a concentration at the receptors for agonist B (in all circumstances) and for agonist A under TI treatment and without IA treatment (simulating complete ENT1 inhibition). Furthermore, the bathing medium concentration divided by 400 was designated as near-receptor concentration for agonist A without IA and TI treatment (simulating the presence of intact ENT1). Finally, the bathing medium concentration divided by 3 was designated as near-receptor concentration for agonist A in the presence of TI and after an IA treatment (simulating the incomplete inhibition of ENT1). These simple operations simulated the effect of ENT1 on the concentration of adenosine, but not CPA, in the vicinity of the cell-surface A
_{1}receptors, producing a parallel leftward shift of the treatment-naïve E/c curve of agonist A as compared to that of agonist B. This is in accordance with the fact that adenosine and CPA, two A_{1}receptor agonists, have practically the same E_{max}but very different EC_{50}[25]. - Consistently, the effect of TI was simulated by omitting the division by 400, when computing the near-receptor concentration of the exogenous agonist A from the bathing medium one (see the previous paragraph), and also by taking a surplus near-receptor concentration of endogenous agonist A into account (see paragraphs 3 and 7).
- The effect of IA treatment was simulated with a division of the total receptor concentration ([R
_{0}]) by 5 (see below). Thus, according to our previous results with FSCPX [13], it was assumed that 20% of the A_{1}receptors remained intact after IA treatment. In addition, in the case of IA and TI co-treatment, bathing medium concentrations of exogenous agonist A were divided by 3 to compute its near-receptor levels. Furthermore, a third of the value of surplus near-receptor concentration of endogenous agonist A, which was designated to simulate the treatment with TI alone, was taken into account (see paragraphs 3 and 6). - For the correction of the biased effect values, RRM was applied as described previously [27]. Briefly, the biased E/c curves of agonist B were fitted to the equation of RRM to provide information about the neglected surplus near-receptor concentration of agonist A. Using this information along with Hill parameters of the simple unbiased E/c curves of agonist B, the biased effect values were corrected by means of a rearranged form of the equation used for the biasing transformation (see paragraph 8).

#### 4.3. First Step: Construction and Analysis of Simple Unbiased E/c Curves

_{m}is the possible maximal effect; [R

_{0}] is the total receptor concentration (receptor number); c is the agonist concentration at the receptors; K is the equilibrium dissociation constant of the agonist-receptor complex (a measure for agonist affinity); K

_{E}is a measure of agonist efficacy; and n

_{op}is the operational slope factor.

_{m}= 100, K = 3 × 10

^{−5}, K

_{E}= 5 × 10

^{−14}and n

_{op}= 0.7.

^{−10}to 3.1623 × 10

^{−3}(being logarithm of which −10 and −2.5, respectively). Near-receptor concentrations (c values for Equation (1)) were calculated according to the nature of simulated agonists and treatments (see the previous subsection).

_{0}] equaling 10

^{−10}or 2 × 10

^{−11}to represent atrial samples without or with an FSCPX treatment (i.e., having naïve or reduced A

_{1}receptor population), respectively.

_{max}is the maximal effect that can be elicited by the given agonist in the given system; EC

_{50}is the agonist concentration in the bathing medium that leads to half-maximal effect; n is the Hill slope factor; and c is the agonist concentration in the bathing medium.

#### 4.4. Second Step: Computation of Unbiased Effect Values for a Subsequent Biasing Transformation

_{m}is the possible maximal effect; c

_{bias}is the surplus near-receptor concentration of endogenous agonist A that represents the extra endogenous adenosine concentration accumulated interstitially in response to NBTI; c

_{test}is one of the increasing concentrations of exogenous agonist A or agonist B at the receptors that models the concentration of the agonist administered for the E/c curve; K

_{bias}and K

_{test}are K values (see Equation (1)) for the agonist providing c

_{bias}and c

_{test}, respectively (in the final model: K

_{bias}= K

_{test}= 3 × 10

^{−5}); τ

_{bias}and τ

_{test}are equal to [R

_{0}]/K

_{Ebias}and [R

_{0}]/K

_{Etest}, respectively, where K

_{Ebias}and K

_{Etest}are K

_{E}values (see Equation (1)) for the agonist supplying c

_{bias}and c

_{test}, respectively (in the final model: K

_{Ebias}= K

_{Etest}= 5 × 10

^{−14}).

_{test}values were simulated with agonist A, calculations were carried out with both [R

_{0}] values (10

^{−10}and 2 × 10

^{−11}), and when c

_{test}was agonist B, only [R

_{0}] = 10

^{−10}was considered.

_{bias}value into the simulation, and, on the other hand, by omitting the division of the bathing medium concentration of agonist A by 400 (that provided c

_{test}values). When TI was used together with IA, the influence of IA on the action of TI was taken into account through trisecting the originally defined value of c

_{bias}as well as the bathing medium concentration of agonist A (that resulted in c

_{test}values for this case). In the final model, c

_{bias}was fixed at 4 × 10

^{−7}, when simulating the use of TI alone, while it was computed as (4 × 10

^{−7})/3, when simulating an IA treatment before the administration of TI.

#### 4.5. Third Step: Construction and Analysis of Biased E/c Curves

_{bias}is the effect elicited by c

_{bias}(computed with Equation (3) by setting c

_{test}at zero, with other parameters being the same as for the corresponding E).

_{bias}and its effect (E

_{bias}). Biased effect values yielded by Equation (4) were plotted against the bathing medium concentrations of the given agonist (providing c

_{test}).

_{x}is the concentration of agonist B that is expected to be equieffective with c

_{bias}, the surplus near-receptor concentration of the endogenous agonist A (c

_{x}is the only best-fit value provided by Equation (5)); E

_{max}, logEC

_{50}and n are parameters of Equation (2) fitted to the simple unbiased E/c curve of agonist B generated in the system having a naïve receptor population. Use of fitted data as input for RRM simulated the data collection in biological samples in order to quantify the effect of NBTI on the interstitial concentration of endogenous adenosine.

#### 4.6. Fourth Step: Construction of Corrected E/c Curves from the Biased E/c Curves of Agonist A

_{x}were computed by means of the Hill equation (in the following form identical with Equation (3) in [27]):

_{x}is the effect value elicited by c

_{x}; c

_{x}is the agonist B concentration expected to be equieffective with c

_{bias}(provided by Equation (5)); E

_{max}, EC

_{50}and n are parameters of Equation (2) fitted to the simple unbiased E/c curves of agonist B in both systems (with normal and reduced receptor number, see below). These latter parameters describe the E/c relationship between agonist B and the two systems (in a way that is also achievable for biological samples).

_{x}, computed with Equation (6), simulated the effect evoked solely by the extra concentration of endogenous agonist accumulated by NBTI in the biological model. When E

_{x}was computed for the system with a naïve receptor population, Hill parameters of the simple unbiased E/c curve of agonist B generated in the system with normal receptor number were substituted into Equation (6). In turn, when E

_{x}was calculated for the system with reduced receptor number, Hill parameters of the simple unbiased E/c curve of agonist B constructed in the system with reduced receptor population were used for Equation (6).

_{test}was agonist A) were corrected by means of the rearranged form of Equation (4) as follows (equivalent with Equation (4) in [27]):

_{corr}is the corrected effect value that is expected to equal the corresponding unbiased effect value; E′ is the corresponding biased effect value; and E

_{x}is the effect value solely elicited by c

_{x}(according to Equation (6)).

#### 4.7. Computer Simulation and Data Analysis

_{50}and c

_{x}in the equations used for curve fitting (i.e., Equations (2) and (5)) were expressed as common logarithms [45]. Effect values of Equations (1), (3), (4), (6) and (7), together with E

_{bias}in Equation (4), were computed with Microsoft Excel 2013 (Microsoft Co., Redmond, WA, USA). For curve plotting and fitting, GraphPad Prism 7.03 for Windows (GraphPad Software Inc., La Jolla, CA, USA) was used.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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Sample Availability: Not Available. |

**Figure 1.**Ex vivo biological (panel

**A**) and in silico simulated (panel

**B**) models showing concentration-response (E/c) curves of two agonists with short (square symbols) and long (circle symbols) half-lives, acting in systems with unaffected (filled symbols) and reduced (open symbols) receptor number. The x-axis shows the common logarithm of the molar concentration of agonists (in the bathing medium), and the y-axis indicates the effect. The continuous lines denote the fitted Hill equation. On the panel

**A**, symbols show mean ± SEM. Ado: adenosine (the endogenous A

_{1}adenosine receptor agonist with a short half-life); CPA: N

^{6}-cyclopentyladenosine (a synthetic A

_{1}adenosine receptor agonist with a long half-life); FSCPX: a prior treatment with 8-cyclopentyl-N

^{3}-[3-(4-(fluorosulfonyl)benzoyloxy)propyl]-N

^{1}-propylxanthine (an irreversible A

_{1}adenosine receptor antagonist); A: agonist A (simulating adenosine); B: agonist B (simulating CPA); IA: a prior treatment with an irreversible antagonist (simulating an FSCPX pretreatment); CF: contractile force. Data of panel

**A**are redrawn from [31].

**Figure 2.**Ex vivo biological (panel

**A**) and in silico simulated (panel

**B**) models displaying E/c curves of an agonist with a short half-life, in the absence and presence of an agonist transport inhibitor, acting in systems with unaffected (filled symbols) and reduced (open symbols) receptor number. The real and the simulated agonist used to generate the E/c curves are both identical with the endogenous agonist of the given model that agonist is extensively transported and then eliminated. The x-axis denotes the common logarithm of the molar concentration of agonists (in the bathing medium), and the y-axis indicates the effect. The continuous lines represent the fitted Hill equation. On the panel

**A**, symbols show mean ± SEM. Ado: adenosine; NBTI: a treatment with S-(2-hydroxy-5-nitrobenzyl)-6-thioinosine (an inhibitor of the nucleoside transporter type ENT1); FSCPX: a prior treatment with 8-cyclopentyl-N

^{3}-[3-(4-(fluorosulfonyl)benzoyloxy)propyl]-N

^{1}-propylxanthine (an irreversible A

_{1}adenosine receptor antagonist); A: agonist A (simulating adenosine); TI: a treatment with an inhibitor of agonist A transport (simulating the presence of NBTI); IA: a prior treatment with an irreversible antagonist (simulating an FSCPX pretreatment); CF: contractile force. Data of panel

**A**are redrawn from [31].

**Figure 3.**Ex vivo biological (panel

**A**) and in silico simulated (panel

**B**) models exhibiting E/c curves of a synthetic agonist with a long half-life, in the absence and presence of an agonist transport inhibitor, acting in a system with naïve receptor population. The transport inhibition do not affect the fate of the agonist used for the E/c curves, only the transport of the endogenous agonist (activating the same receptor as the synthetic one) was inhibited in both models. The x-axis indicates the common logarithm of the molar concentration of agonists (in the bathing medium), and the y-axis denotes the effect. The continuous lines represent the fitted Hill equation, while the dotted lines show the fitted equation of RRM (receptorial responsiveness method). On the panel

**A**, symbols show the mean ± SEM. CPA: N

^{6}-cyclopentyladenosine; NBTI: a treatment with S-(2-hydroxy-5-nitrobenzyl)-6-thioinosine; B: agonist B (simulating CPA); TI: a treatment with an inhibitor of the transport of agonist A but not B (simulating the presence of NBTI); CF: contractile force. Data of panel

**A**are redrawn from [31].

**Figure 4.**Ex vivo biological (panel

**A**) and in silico simulated (panel

**B**) models showing corrected E/c curves of an agonist with a short half-life, in the absence and presence of an agonist transport inhibitor, acting in systems with unaffected (filled symbols) and reduced (open symbols) receptor number (while symbols of the built-in in silico control curves labelled as “unbiased” are simply x and asterisk). The x-axis denotes the common logarithm of the molar concentration of agonists (in the bathing medium), and the y-axis indicates the effect. The dotted lines between symbols only connect them, while the dotted lines without symbols represent the Hill equation fitted to data of the control adenosine E/c curve (panel A) and the simple unbiased E/c curve of agonist A generated upon naïve receptor population (panel B). Ado: adenosine; NBTI: a treatment with S-(2-hydroxy-5-nitrobenzyl)-6-thioinosine; FSCPX: a prior treatment with 8-cyclopentyl-N

^{3}-[3-(4-(fluorosulfonyl)benzoyloxy)propyl]-N

^{1}-propylxanthine; A: agonist A (simulating adenosine); TI: a treatment with an inhibitor of agonist A transport (simulating the presence of NBTI); IA: a prior treatment with an irreversible antagonist (simulating an FSCPX pretreatment); unbiased: unbiased E/c curves of agonist A (control functions for the corresponding corrected E/c curves); corrected: E/c curves corrected with our method; CF: contractile force. Data of panel

**A**are redrawn from [31].

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## Share and Cite

**MDPI and ACS Style**

Zsuga, J.; Erdei, T.; Szabó, K.; Lampe, N.; Papp, C.; Pinter, A.; Szentmiklosi, A.J.; Juhasz, B.; Szilvássy, Z.; Gesztelyi, R. Methodical Challenges and a Possible Resolution in the Assessment of Receptor Reserve for Adenosine, an Agonist with Short Half-Life. *Molecules* **2017**, *22*, 839.
https://doi.org/10.3390/molecules22050839

**AMA Style**

Zsuga J, Erdei T, Szabó K, Lampe N, Papp C, Pinter A, Szentmiklosi AJ, Juhasz B, Szilvássy Z, Gesztelyi R. Methodical Challenges and a Possible Resolution in the Assessment of Receptor Reserve for Adenosine, an Agonist with Short Half-Life. *Molecules*. 2017; 22(5):839.
https://doi.org/10.3390/molecules22050839

**Chicago/Turabian Style**

Zsuga, Judit, Tamas Erdei, Katalin Szabó, Nora Lampe, Csaba Papp, Akos Pinter, Andras Jozsef Szentmiklosi, Bela Juhasz, Zoltán Szilvássy, and Rudolf Gesztelyi. 2017. "Methodical Challenges and a Possible Resolution in the Assessment of Receptor Reserve for Adenosine, an Agonist with Short Half-Life" *Molecules* 22, no. 5: 839.
https://doi.org/10.3390/molecules22050839