#
Accuracy and Precision of the Receptorial Responsiveness Method (RRM) in the Quantification of A_{1} Adenosine Receptor Agonists

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## Abstract

**:**

_{x}). The model of RRM describes the co-action of two agonists that consume the same response capacity (due to the use of the same postreceptorial signaling in a biological system). While using RRM, uniquely, an acute increase in the concentration of an agonist (near the receptors) can be quantified (as c

_{x}), via evaluating E/c curves that were constructed with the same or another agonist in the same system. As this measurement is sensitive to the implementation of the curve fitting, the goal of the present study was to test RRM by combining different ways and setting options, namely: individual vs. global fitting, ordinary vs. robust fitting, and three weighting options (no weighting vs. weighting by 1/Y

^{2}vs. weighting by 1/SD

^{2}). During the testing, RRM was used to estimate the known concentrations of stable synthetic A

_{1}adenosine receptor agonists in isolated, paced guinea pig left atria. The estimates were then compared to the known agonist concentrations (to assess the accuracy of RRM); furthermore, the 95% confidence limits of the best-fit values were also considered (to evaluate the precision of RRM). It was found that, although the global fitting offered the most convenient way to perform RRM, the best estimates were provided by the individual fitting without any weighting, almost irrespective of the fact whether ordinary or robust fitting was chosen.

## 1. Introduction

_{x}, for more detail, see below). Under certain circumstances, RRM can be used to estimate an acute increase in the level of an agonist (as c

_{x}) in the vicinity of its receptors in a biological system [11]. Technically, it is of great impact to possess reliable input data and ensure the most appropriate implementation of the fitting of the model of RRM.

_{x}) [11]. The fitting of this model requires two sets of concentration-effect (E/c) curves to be generated. E/c curves that are suitable for RRM are XY graphs where X is the (logarithm of the) concentration of a pharmacological agonist, while Y is a response of a biological system that is evoked by the given agonist concentration (indicated by the corresponding X value) alone (first set of curves) or together with a single extra concentration (c

_{x}) of the same or another agonist, which was administered to the system before the generation of the E/c curve (second set of curves). Quantifying this extra agonist concentration as a c

_{x}value is the goal of RRM [11,12,13].

_{x}, is a concentration of the agonist used for the E/c curve that is equieffective with the agonist added in a single extra dose. If the two agonists in question are the same, c

_{x}is a real concentration, and, if not, c

_{x}is a surrogate parameter of the single extra concentration of the other agonist [14,15]. The application of RRM might be useful when the concentration of this extra agonist is unknown and difficult to determine in any other manners [12,13]. As the single extra agonist concentration distorts (biases) the E/c curve in the second set as compared to the corresponding E/c curve in the first set (generated the same way except for the administration of the single extra agonist concentration), it will be referred to as “biasing” concentration.

_{1}adenosine receptor is uniquely suitable for this method, due to its slow and incomplete desensitization in the presence of even a full agonist [16,17].

^{2}(relative weighting) and 1/|Y| (Poisson weighting). The relative weighting and, to a lesser extent, the Poisson weighting reduce the influence of the higher Y values on the best-fit values and the regression curve. In addition, the Poisson weighting (performed with ordinary regression) can serve as an inferior alternative of the Poisson regression. A rarely used, although theoretically meaningful, choice is weighting by 1/SD

^{2}(the inverse of the variance of Y values related to the same X value), which is expected to reduce the undue impact of Y replicates with bigger scatter [18,19].

_{1}adenosine receptor stimulation. Adenosine is particularly suitable for this purpose, because it is quickly eliminated without yielding confounding byproducts [21]. For the second E/c curve, one of three widespread, relatively stable, synthetic A

_{1}adenosine receptor agonists (CPA, NECA, and CHA) was used, in the absence or presence of a “biasing” concentration of the same agonist. The accuracy and precision of RRM was investigated via assessing this known “biasing” concentration in a well-established isolated and paced guinea pig left atrium model. Accordingly, c

_{x}, estimate yielded by RRM, has been expected to directly provide the “biasing” concentration.

_{1}adenosine receptor agonists was determined as an effect. In the ventricular myocardium of most mammalian species, adenosine receptor agonists fail to directly evoke a negative inotropic effect, i.e., without a previous increase of the cellular cAMP level [22]. In the mammalian atrium, however, stimulation of the A

_{1}adenosine receptor can considerably reduce even the resting contractile force, exerting a significant direct negative inotropic effect [23,24]. As, for this study, paced left atria were used, the negative tropic effects that were mediated by the A

_{1}adenosine receptor can manifest themselves only in a decrease of the resting contractile force. This feature has made our results more reliable and easier to interpret, as the direct negative inotropy is sensitive to any change in the frequency of contractions [25].

## 2. Results

#### 2.1. Response to Adenosine

#### 2.2. Responses to Synthetic A_{1} Adenosine Receptor Agonists

_{50}(but not E

_{max}and n) parameter (Table 2). In accordance with the fact that CPA, NECA, and CHA are worse substrates for adenosine-handling enzymes and carriers than adenosine [16,26], the EC

_{50}values of the synthetic agonists were considerably smaller (by about two–three orders of magnitude) than EC

_{50}of adenosine, with similar E

_{max}values for all four agonists (cf. Figure 1 and Figure 2a).

_{50}value) produced a substantial depression of the maximal response and a considerable dextral displacement of the E/c curve of the same agonist, when added before its construction (Figure 2b–d).

#### 2.3. Curve Fitting to the Biased Responses Given to Synthetic A_{1} Adenosine Receptor Agonists

_{x}, the best-fit value (indicated by the nearness of its antilog (c

_{x}) to the corresponding “biasing” concentration) and by the precision of the curve fitting (as indicated by the 95% confidence interval (95% CI) of the best-fit value).

_{x}values proved to be acceptable estimates of the “biasing” concentrations in all cases when RRM was carried out without any weighting. In contrast, weighting by 1/SD

^{2}and, especially, by 1/Y

^{2}, dramatically worsened the accuracy of estimates; moreover, in some cases, it hindered the curve fitting (Table 3). Narrow 95% CIs could be obtained when using ordinary regression (capable of yielding 95% confidence limits for the best-fit values) without weighting, if Equation (2) was individually fitted (i.e., separately to the E/c curves averaged within the groups; more precisely, separately to each set of replicate E/c curves forming one group). If not (namely, in case of global regression), the curve fitting provided wide 95% CIs (Table 3).

_{x}values, yielded less accurate estimates than the conventional individual fitting (Table 3). Consistent with this, the global regression increased (rather than decreased) the uncertainty of the curve fitting, which produced wide 95% CIs (Table 3).

#### 2.4. Curve Fitting to the Intact Responses Given to Synthetic A_{1} Adenosine Receptor Agonists

_{x}values for the corresponding “Intact” and “Biased” E/c curves at once. All the curve fittings used for internal control (that did not fail) yielded very small best-fit values (antilogs of which were near zero in most cases), as expected (Table 3).

^{2}in the Intact NECA group) appears to be a chance rather than a regular behavior (Table 3).

## 3. Discussion

_{1}adenosine receptor, as any alteration in its responsiveness might modify vital protective and regenerative processes throughout the body [16,28]. Probably in strong association with this fact, the desensitization of the A

_{1}adenosine receptor is slower than that of other receptors [16,17]. Owing to this, the A

_{1}adenosine receptor (with its cellular environment) forms a biological system, in which RRM, which is a time-consuming (≈40 min.) procedure, can be successfully performed. Accordingly, although adenosine has a short half-life (seconds) in living tissues [26], RRM was first applied to estimate the interstitial accumulation of endogenous adenosine in the presence of a nucleoside transport inhibitor (dipyridamole or nitrobenzylthioinosine) in atria isolated from eu- and hyperthyroid guinea pigs. CPA equivalents of these surplus adenosine concentrations were, in fact, determined, as CPA was used to generate the necessary E/c curves [12,13,29,30,31].

_{1}adenosine receptor signaling in the hyperthyroid guinea pig atrium under adenosine deaminase inhibition by pentostatin [32]. On the other hand, data provided by RRM can be applied to correct the E/c curves that are biased by an unknown (and thereby usually neglected) concentration of an agonist that has previously been accumulated in the system. The corrected adenosine E/c curves (constructed in the presence of nitrobenzylthioinosine) enabled us to qualitatively assess the receptor reserve for the negative inotropic effect of adenosine in eu- and hyperthyroid guinea pig atria in another earlier investigation [29,30]. It should be noted that the traditional methods to determine receptor reserve have not proved to be useful for adenosine due to the short half-life of adenosine [33], although receptor reserve values in the cardiac adenosinergic system seem to be of importance, even in terms of diagnostic aspects [34]. Finally, of course, data that were obtained with RRM can serve as input data for in silico investigations dealing with the RRM itself [14,15], and with the adenosinergic mechanisms in the atrial myocardium [35,36].

_{1}and A

_{2}adenosine receptors, while CPA and CHA are highly selective for the A

_{1}adenosine receptor [16,27], the predominant adenosine receptor type of the myocardium [16,24]. These synthetic compounds are less sensitive to adenosine-handling enzymes and carriers than adenosine, the endogenous agonist of the adenosine receptor family [16,26], so E/c curves of these synthetic agonists are more suitable for quantitative evaluation than those of adenosine.

_{x}), because the expected estimate (c

_{x}) is zero, the logarithm of which is not defined. This problem does not occur when RRM is done with individual regression, because the “intact” E/c curve is fitted to the Hill equation (Equation (1)) that can yield reliable best-fit values (which ones will be then substituted into Equation (2) before the fitting of the “biased” E/c curve). Thus, the individual fitting is the appropriate choice for RRM.

## 4. Materials and Methods

#### 4.1. Materials

_{2}∙2H

_{2}O: 3.7 (147.02); NaH

_{2}PO

_{4}: 1.56 (137.99); MgCl

_{2}∙6H

_{2}O: 2.7 (203.3); NaHCO

_{3}: 21 (84.01); glucose∙H

_{2}O: 22 (198.18); l-ascorbic acid: 0.1 (176.12); and, dissolved in 10 L of redistilled water.

_{1}adenosine receptor agonists, adenosine, N

^{6}-cyclopentyladenosine (CPA), 5′-(N-ethylcarboxamido)adenosine (NECA), and N

^{6}-cyclohexyladenosine (CHA), all being purchased from Sigma (St. Louis, MO, USA), were used. Adenosine was dissolved in 36 °C Krebs solution. CPA, NECA, and CHA were dissolved in ethanol:water (1:4) solution (v/v). All of the stock solutions were adjusted to a concentration of 10 mM. Stock solutions were diluted with Krebs solution.

#### 4.2. Animals, Preparations and Protocols

_{2}and 5% CO

_{2}(36 °C; pH = 7.4). Atria were electrically paced by platinum electrodes (3 Hz, 1 ms, twice the threshold voltage) by means of a programmable stimulator (type: Experimetria ST-02; manufacturer: Experimetria Kft, Budapest, Hungary) and power amplifier (type: Experimetria PST-02; manufacturer: Experimetria Kft, Budapest, Hungary). The amplitude of the isometric twitches (contractile force) was measured by means of a transducer (type: Experimetria SD-01; manufacturer: Experimetria Kft, Budapest, Hungary) and strain gauge (type: Experimetria SG-01D; manufacturer: Experimetria Kft, Budapest, Hungary), and recorded by a polygraph (type: Medicor R-61 6CH Recorder; manufacturer: Medicor Művek, Budapest, Hungary).

#### 4.3. Empirical Characterization of the E/c Curves

_{max}: the maximal effect; EC

_{50}: the agonist concentration producing half-maximal effect (sometimes called as median-effective agonist concentration); and, n: the Hill coefficient (slope factor).

#### 4.4. Assessment of the “Biasing” Concentration

_{x}, see below), which was calculated from the raw data in a conventional manner (i.e., regardless of whether a “biasing” concentration was present); E

_{max}, EC

_{50}, n: empirical parameters of the intact E/c relationship according to the Hill model (Equation (1)); c: the concentration of the agonist administered during the construction of the E/c curve; and, c

_{x}: the “biasing” concentration (the estimate provided by RRM).

_{max}, EC

_{50}, and n).

_{x}values for both the ”Intact” and “Biased” E/c curves at once).

#### 4.5. Fitting Settings

^{2}vs. weighting by 1/SD

^{2}. The different ways and setting options were combined with one another in all possible manners (Table 1).

^{2}, where the mean of Y replicates could only be considered). For every other setting, the default option was used [19].

#### 4.6. Data Analysis

_{50}, and c

_{x}) in the equations used for curve fitting were expressed as common logarithms (logc, logEC

_{50}, and logc

_{x}), as recommended [18,19]. Statistical analysis and curve fitting were performed with GraphPad Prism 8.2.1 for Windows (GraphPad Software Inc., La Jolla, CA, USA), while other calculations were made by means of Microsoft Excel 2016 (Microsoft Co., Redmond, WA, USA).

## Author Contributions

## Funding

## Conflicts of Interest

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**Figure 1.**The direct negative inotropic response of isolated guinea pig left atria to adenosine, in the six groups. The x-axis denotes the common logarithm of the molar concentration of adenosine (administered during the construction of the E/c curve). The y-axis shows the effect (percentage decrease in the initial contractile force). The terms “Intact” (filled symbols) and “Biased” (open symbols) in the group names refer to a subsequent (and not the current) condition. The responses to adenosine were averaged within the groups and indicated by the symbols (±SEM). The curves illustrate the Equation (1) (Hill model) fitted to the averaged responses. CPA: N

^{6}-cyclopentyladenosine; NECA: 5′-(N-ethylcarboxamido)adenosine; CHA: N

^{6}-cyclohexyladenosine.

**Figure 2.**The direct negative inotropic response of isolated guinea pig left atria to three synthetic A

_{1}adenosine receptor agonists, in the six groups. The x-axis denotes the common logarithm of the molar concentration of the given agonist (administered during the construction of the E/c curve). The y-axis shows the effect (percentage decrease in the initial contractile force). Atria in the “Intact” groups (filled symbols) underwent a conventional concentration-effect (E/c) curve construction, while atria in the “Biased” groups (open symbols) received a surplus dose (of the agonist indicated below the x-axis) before the generation of the E/c curve. All “Intact” groups are presented in the panel (

**a**), while E/c curves of CPA, NECA and CHA are separately shown in panels (

**b**–

**d**), respectively. The symbols indicate the responses to the agonists averaged within the groups (±SEM). The continuous lines show the fitted Equation (1) (Hill model). The thin dotted lines denote the individually fitted Equation (2) (the model of RRM), while the thick dotted lines illustrate the globally fitted Equation (2). Settings for Equation (2) for both ways of fitting were robust regression with no weighting (providing, in general, the most accurate estimates). CPA: N

^{6}-cyclopentyladenosine; NECA: 5′-(N-ethylcarboxamido)adenosine; CHA: N

^{6}-cyclohexyladenosine.

**Table 1.**Combination of two fitting ways with two setting options addressing the data distribution and with three further setting options addressing the data homo- or heteroscedasticity (reflecting the properties of our curve fitting software, i.e., the lack of weighting during robust fitting [19]).

Ordinary Fit | Robust Fit | |
---|---|---|

No weighting | Individual fit | Individual fit |

Global fit | Global fit | |

Weighting by 1/Y^{2} | Individual fit | |

Global fit | ||

Weighting by 1/SD^{2} | Individual fit | |

Global fit |

**Table 2.**Empirical data (mean ± SEM) of the concentration-effect curves in the “Intact” groups (seen in the Figure 2a).

Intact CPA (n = 6) | Intact NECA (n = 7) | Intact CHA (n = 6) | |
---|---|---|---|

E_{max} (%) | 97.4 ± 0.8 | 97.5 ± 0.5 ns | 94.8 ± 1.7 ns, ns |

logEC_{50} | −8.1 ± 0.09 | −7.66 ± 0.05 ** | −7.33 ± 0.11 ###, + |

n | 1.02 ± 0.05 | 1.14 ± 0.07 ns | 0.98 ± 0.03 ns, ns |

**+**: NECA vs. CHA). The number of marks refers to the level of statistical significance (one mark: p < 0.05; two marks: p < 0.01; three marks: p < 0.001). CPA: N

^{6}-cyclopentyladenosine; NECA: 5′-(N-ethylcarboxamido)adenosine; CHA: N

^{6}-cyclohexyladenosine; ns: non-significant.

**Table 3.**Best-fit values (logc

_{x}) with their 95% confidence intervals (95% CI) and antilog values (c

_{x}) in all the six groups.

Individual, Ordinary, ø | Biased CPA | Intact CPA | Biased NECA | Intact NECA | Biased CHA | Intact CHA |

logc_{x} | −6.88 | −19,107 | −6.87 | −8.92 | −6.45 | −52,574 |

95% CI | −6.93 to −6.83 | very wide | −6.92 to −6.83 | ? to −8.32 | −6.55 to −6.36 | very wide |

c_{x} (nM) | 131.4 | 0 | 133.6 | 1.2 | 352.7 | 0 |

Individual, Robust, ø | Biased CPA | Intact CPA | Biased NECA | Intact NECA | Biased CHA | Intact CHA |

logc_{x} | −6.9 | −19,107 | −6.88 | −8.64 | −6.47 | −5257 |

c_{x} (nM) | 125.9 | 0 | 131.4 | 2.3 | 335.8 | 0 |

Global, Ordinary, ø | Biased CPA | Intact CPA | Biased NECA | Intact NECA | Biased CHA | Intact CHA |

logc_{x} | −6.84 | −7201 | −6.77 | −35,907 | −6.39 | −9,892,707,770 |

95% CI | very wide | very wide | very wide | very wide | very wide | very wide |

c_{x} (nM) | 145.9 | 0 | 170 | 0 | 403.7 | 0 |

Global, Robust, ø | Biased CPA | Intact CPA | Biased NECA | Intact NECA | Biased CHA | Intact CHA |

logc_{x} | −6.85 | −7201 | −6.82 | −35,907 | −6.36 | −9,892,707,770 |

c_{x} (nM) | 142.6 | 0 | 153.3 | 0 | 439 | 0 |

Individual, Ordinary, 1/Y^{2} | Biased CPA | Intact CPA | Biased NECA | Intact NECA | Biased CHA | Intact CHA |

logc_{x} | −8.21 | −19107 | −6.36 | −8.51 | −317,820,174,071 | −52,574 |

95% CI | ? to −8.163 | very wide | ? to −6.34 | −8.89 to −8.2 | very wide | very wide |

c_{x} (nM) | 6.2 | 0 | 438.5 | 3.1 | 0 | 0 |

Global, Ordinary, 1/Y^{2} | Biased CPA | Intact CPA | Biased NECA | Intact NECA | Biased CHA | Intact CHA |

logc_{x} | −366.5 | −7201 | −6.146 | −35,907 | - | - |

95% CI | very wide | very wide | very wide | very wide | ||

c_{x} (nM) | 0 | 0 | 714.8 | 0 | ||

Individual, Ordinary, 1/SD^{2} | Biased CPA | Intact CPA | Biased NECA | Intact NECA | Biased CHA | Intact CHA |

logc_{x} | −6.9 | −42,781 | - | −8.66 | −6.5 | −56,039 |

95% CI | −6.99 to −6.82 | very wide | ? to −7.96 | −6.77 to −6.26 | very wide | |

c_{x} (nM) | 125.7 | 0 | 2.2 | 318.6 | 0 | |

Global, Ordinary, 1/SD^{2} | Biased CPA | Intact CPA | Biased NECA | Intact NECA | Biased CHA | Intact CHA |

logc_{x} | −6.87 | −1353 | - | - | −8.26 | −22.51 |

95% CI | very wide | very wide | very wide | very wide | ||

c_{x} (nM) | 136.5 | 0 | 554.1 | 3.11 × 10^{−14} |

^{6}-cyclopentyladenosine; NECA: 5′-(N-ethylcarboxamido)adenosine; CHA: N

^{6}-cyclohexyladenosine. In some cases, no results could be obtained.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Szabo, A.M.; Viczjan, G.; Erdei, T.; Simon, I.; Kiss, R.; Szentmiklosi, A.J.; Juhasz, B.; Papp, C.; Zsuga, J.; Pinter, A.;
et al. Accuracy and Precision of the Receptorial Responsiveness Method (RRM) in the Quantification of A_{1} Adenosine Receptor Agonists. *Int. J. Mol. Sci.* **2019**, *20*, 6264.
https://doi.org/10.3390/ijms20246264

**AMA Style**

Szabo AM, Viczjan G, Erdei T, Simon I, Kiss R, Szentmiklosi AJ, Juhasz B, Papp C, Zsuga J, Pinter A,
et al. Accuracy and Precision of the Receptorial Responsiveness Method (RRM) in the Quantification of A_{1} Adenosine Receptor Agonists. *International Journal of Molecular Sciences*. 2019; 20(24):6264.
https://doi.org/10.3390/ijms20246264

**Chicago/Turabian Style**

Szabo, Adrienn Monika, Gabor Viczjan, Tamas Erdei, Ildiko Simon, Rita Kiss, Andras Jozsef Szentmiklosi, Bela Juhasz, Csaba Papp, Judit Zsuga, Akos Pinter,
and et al. 2019. "Accuracy and Precision of the Receptorial Responsiveness Method (RRM) in the Quantification of A_{1} Adenosine Receptor Agonists" *International Journal of Molecular Sciences* 20, no. 24: 6264.
https://doi.org/10.3390/ijms20246264