4.2. Simulation of the Adenosine Homeostasis and A1 Adenosinergic Control of Contractility in the Guinea Pig Atrial Myocardium

Broadly, the simulation was performed as it was described in our recent computer simulation study [13]. Some details were modified, as described in this subsection. To generate E/c curves simulating the effect of A₁ adenosine receptor agonists on the contractile force of the isolated, paced guinea pig left atrium, the operational model of agonism was applied, both for the action of one agonist (Equation (1)) [21] and the co-action of two agonists (Equation (2)) [28]. The operational model provides a general, (fully) quantitative description of the relationship between the concentration of bioactive agents and the effect mediated by a receptor specific for the given agents. Moreover, this model contains the appropriate parameters, by means of which the effects of FSCPX (concentration of the operable receptors) and NBTI (parameters for two different agonists) can be considered [21,26,28].

To address the different impact of adenosine of endogenous and exogenous origins, a procedure, developed from RRM [19,20] and first described in [13], was applied (see: Equation (3) below). By means of this procedure, the neglect of one agonist from two co-acting agonists was simulated. The overlooked agonist concentration modelled the extra interstitial concentration of endogenous adenosine accumulated by NBTI, which came into being before the construction of an E/c curve with (exogenous) adenosine or CPA (agonists for the same receptor).

Using different input data (Table 3) and assumptions, four models and two additional model variants of Model 4 were defined that resulted in six sets of E/c curves, each set containing eight curves, four ones belonging to agonists C and four ones belonging to agonists A (Figure 2, Figure 3 and Figure 4). To characterize and illustrate the simulated E/c curves, the Hill equation (Equation (4)) was fitted to them.

Parameters of the operational model of agonism defining four in silico models.

Co: no simulated (pre)treatment; X: simulated pretreatment with agent X; NB: simulated treatment with agent NB; X + NB: simulated pretreatment with agent X followed by a treatment with agent NB (briefly, X + NB co-treatment). For an explanation of abbreviations in the first column, see Equation (1) and (2) below.

Adenosine, the physiological agonist for the A₁ adenosine receptor, the major adenosine receptor type of the supraventricular myocardium [3,4], was modelled with an agonist A. Based on its location, two agonist A concentrations were considered, one “in the organ bath” (a “bathing medium concentration”), and another one “at the receptors” (a “near-receptor” concentration). Based on its origin, an “exogenous” (administered to generate an E/c curve) and an “endogenous” (produced in the atrial tissue) agonist A were distinguished.

The inward transport of adenosine was simulated differently for the exogenous and endogenous agonist A. In the absence of a transport inhibitor, the concentration “in the organ bath” designated for the exogenous agonist A was divided by 400, when computing its effect. This maneuver simulated the fact that, in vivo or ex vivo, the concentration of an intensively transported agonist is lower at its receptors (in the interstitial fluid) than in the blood plasma or bathing medium. In the presence of a transport inhibitor, the concentration of the exogenous agonist A in the organ bath was not divided, or it was but by a number much less than 400 (6 or 14.8952), during the calculation of its effect. In turn, the surplus concentration of the endogenous adenosine, accumulated by a transport inhibitor, was considered as a c_bias value of agonist A, using arbitrary values or values measured in the most recent ex vivo study [14], when calculating its effect (Table 3). All E/c curves generated with the consideration of c_bias (i.e., all E/c curves reflecting the effect of a transport inhibitor) were regarded as “biased”. This is because it was simulated that c_bias and its effect were neglected during the evaluation of the raw E/c data. (Indeed, this is the case during a conventional evaluation of E/c data measured in the presence of a transport inhibitor that accumulates an unknown amount of the endogenous agonist for the given receptor.)

CPA, a synthetic agonist of the A₁ adenosine receptor, was modelled with an agonist C. As CPA is eliminated by adenosine-handling enzymes to a much lesser extent than adenosine, the “bathing medium concentration” and “near-receptor concentration” of agonist C were considered to be equal. Accordingly, when calculated its effect, the “bathing medium concentration” of agonist C was never divided throughout the simulation.

FSCPX, an irreversible A₁ adenosine receptor antagonist, was modelled with an agent X. The effect of a pretreatment with agent X was considered with a division of the total receptor concentration ([R₀]) by ≈5.556 (Table 3), simulating that 18% of the A₁ adenosine receptors remained intact (in agreement with our previous results [10]). In Model 4 and its variants, if a transport inhibitor was present, the agent X pretreatment was considered with a second procedure as well, by introducing a further c_bias value (see: next paragraph and Table 3). Moreover, in Model 4-v2 (one of the variants), if a transport inhibitor was present, the agent X pretreatment was considered with a third procedure as well, through an additional division by 14.8952, when computing the “near-receptor” concentration of agonist A (see Section 4.6).

NBTI, a nucleoside transport inhibitor, was modelled by an agent NB. Its effect was taken into account by omitting the division of the exogenous agonist A concentration “in the organ bath” by 400, or by dividing it using a smaller number (as anticipated above,), and, in addition, by considering a surplus endogenous agonist A concentration (c_bias), when computing an effect. The earlier models contained only one c_bias (Models 1–3), whereas the final one (Model 4) and its two variants possessed two c_bias values: one for a mere NB treatment, and the other one for an X + NB co-treatment. In Models 1 and 2, c_bias was an arbitrary value, while in Models 3 and 4, c_bias values equaled the surplus interstitial adenosine concentrations determined in the most recent ex vivo study [14] (Table 3). As mentioned at the end of the previous paragraph, in Model 4 and its variants, an interaction between agent X pretreatment and agent NB treatment was also taken into account.

Effect values of the simulated E/c curves were plotted against the “bathing medium concentrations” of the given exogenous agonist, as usually these concentrations are only known during the in vivo and ex vivo experiments.