Isoprenaline: A Potential Contributor in Sick Sinus Syndrome—Insights from a Mathematical Model of the Rabbit Sinoatrial Node

The mechanism of isoprenaline exerting its effects on cardiac pacemaking and driving in sick sinus syndrome is controversial and unresolved. In this paper, mathematical models for rabbit sinoatrial node cells were modified by incorporating equations for the known dose-dependent actions of isoprenaline on various ionic channel currents, the intracellular Ca2+ transient, and i Na changes induced by SCN5A gene mutations; the cell models were also incorporated into an intact SAN-atrium model of the rabbit heart that is based on both heterogeneities of the SAN electrophysiology and histological structure. Our results show that, in both central and peripheral cell models, isoprenaline could not only shorten the action potential duration, but also increase the amplitude of action potential. The mutation impaired the SAN pacemaking. Simulated vagal nerve activity amplified the bradycardic effects of the mutation. However, in tissue case, the pacemaker activity may show temporal, spatial, or even spatiotemporal cessation caused by the mutation. Addition of isoprenaline could significantly diminish the bradycardic effect of the mutation and the SAN could restart pacing and driving the surrounding tissue. Positive effects of isoprenaline may primarily be attributable to an increase in i Na and i Ca,T which were reduced by the mutation.


Introduction
Sick sinus syndrome (SSS) comprises a variety of conditions involving sinus node dysfunction (SND) which occurs as a result of anatomical damage to the sinoatrial node (SAN) of the heart. Abnormalities encompassed in this syndrome include sinus bradycardia, sinus arrest or exit block, combinations of sinoatrial and atrioventricular nodal conduction disturbances, and atrial tachyarrhythmias [1]. Patients may experience syncope, presyncope, palpitations, or dizziness who have to be fitted with an electronic pacemaker [1,2]. While the syndrome can occur in elderly and pediatric patients, it can also occur in healthy people without any evident structural heart disease but with genetic defects. Recent studies have shown that familial SSS is linked to loss-offunction mutations of the SCN5A gene [3], which result in decreased inward Na + current [4,5].
Currently, no medications are routinely used to treat symptomatic SND. However, acute treatment with the anticholinergic agent atropine and the adrenergic agonist isoprenaline (Iso) may be warranted. Studies have shown thatadrenergic stimulation could increase the heart rate through accelerating the spontaneous activity of the pacemaker of the heart [6]. It is also believed that this occurs through -adrenoceptor mediated modulation of ionic currents that contribute to pacemaker activity [7]. Iso is a sympathomimetic -adrenergic agonist medication and known to accelerate the sinus node and enhance AV nodal conduction [8]. Experiments have shown that Iso increases the L-type calcium current [9][10][11] and the delayed rectifier potassium current [10,11] and shifts voltage-dependent activation curve to more positive potentials [12][13][14][15]. Furthermore, a number of clinical studies have shown that Iso exerts positive inotropic and chronotropic effects on the heart.    Whereas, to our knowledge, many researchers have investigated the effect of Iso mainly at the cellular level, its effect on the abnormal activity at the tissue level has been rarely studied before, particularly for the abnormal activity associated with sick sinus syndrome. Thus, an intriguing problem is whether patients with SSS could recover with the help of Iso and do not need cardiac pacing. In this study, we modified models of SAN to investigate theoretically the effect of Iso on the SSS and discussed the inherent mechanism between them.

Model Description.
In order to address the above issues, mathematical model of the rabbit central and peripheral SAN cells proposed by Kurata et al. [16] was used in this paper. The action potentials generated by using the models of a central cell and a peripheral cell were shown in Figure 1(c). Besides, a 2D anatomic model of the intact SAN-atrium tissue developed by Butters et al. [17] was also used to study the effects of Iso on SAN pacemaking and driving. This 2D intact SAN-atrium tissue model was based on histologically reconstructed geometry of a single slice of the rabbit right atrium, which was cut through the atrial muscle of the crista terminalis (CT) and the intercaval region with central and peripheral SAN areas. And an experimentally observed [18,19] nonconductive region (block zone) next to the SAN toward the atrial septum was also incorporated in this model (see Figure 1(a)). Figure 1 The mechanism underlying the genesis of SND (clinically known as SSS) is believed to be associated with changes in the intrinsic properties of the SAN with age [20]. Intercellular electrical coupling strength ( ) is considered to reflect the changes in the intrinsic properties of the SAN. To incorporate the effects of SCN5A mutation and acetylcholine (Ach) into the models, (i) parameters of the Na + current were changed according to the study of Butters et al. [17] and (ii) an Ach-activated K + current ( K,Ach ), the inhibited L-type Ca 2+ current ( Ca, ), and the shift in hyperpolarization-activated current ( ) activation curve were introduced.
The model equations used for the cells, 2D tissue, modified Na + channel current, and the channel currents relative to Ach are presented in Table 1. A detailed description of parameters of these models are listed in Table 3 and can be found in [16,[19][20][21].

Effects of Iso on Ionic Currents.
In order to simulate the chronotropic effect of Iso on the pacemaker activity, Zhang et al. have incorporated a set of equations of the known Table 1: Model equations of the SAN single cell, 2D tissue, and some channel currents.

Single cell model of SAN
Changes of sodium current induced by mutation Effects of Ach on currents K,Ach = K,Ach,max actions of Iso on related ion channels into two established action potential models of rabbit SAN recently [22]. According to the study of Zhang et al., we modified the models mentioned above as follows.
(1) Based on the voltage clamp experimental data on the kinetics of ionic channels and regional differences in the ionic current densities, we incorporated equations for concentration-dependent actions of Iso on the macroscopic conductance of Ca, , K, , st , and K, and to describe changes in the kinetics of and K, by the same amount as observed experimentally [23][24][25].
(2) Because Iso was also found to increase the amplitude and minimal diastolic level of [Ca 2+ ] in mammalian [26,27] pacemaker cells and to alter SR Ca 2+ uptake and release by stimulation of calmodulin kinase II [26,28], in our simulations, we adopted the approach of Kharche et al. [29] to modify the Ca 2+ handling equations to increase the amplitude and minimal diastolic level of [Ca 2+ ] , as observed in experimental studies [30,31] by increasing the maximal SR Ca 2+ release (by 20%) and reducing the SR Ca 2+ release (by 20%) fluxes.
A general remodeling of these ionic channels is given in Table 2. Using the models, the simulated effects of Iso are shown in Figure 2, in which the percentage of decrease of pacemaking cycle length (CL) is plotted against Iso concentration. The simulated data (solid line) from the central (Figure 2(a)) and the peripheral (Figure 2(b)) cell models were compared with the experimental data obtained from rabbit isolated SAN cells by Zaza et al. [23] (open circle) and Lei et al. [24,25] (open diamond).  The Scientific World Journal  And then, we introduced the effect of Ach into the modified models. Application of Ach slowed down pacemaking rates in both central and peripheral SAN cells, with larger effect on the central cells [32]. Simulating effects of 0.01 M/L Ach resulted in the CL increasing from 406 ms to 660 ms for the central SAN cell (Figure 3 It has been shown that the mutations slowed down pacemaking rate in peripheral, but not in central, SAN cells that control the heart rhythm [17]. Thus, we simulated the effect of Iso on pacemaking action potentials with the DelF1617 mutant channel for the peripheral SAN cells, and the results are shown in Figures 3(c)(i) and 3(c)(ii). One notices that, when only the effects of the DelF1617 mutation were introduced into the peripheral cells, the CL increased from 280 ms to 344 ms (Figure 3

Iso Effects on Two-Dimensional Tissues.
We investigated further the functional influences of Iso on action potential conduction across the intact SAN-atrium under control and other conditions associated with the symptoms of SSS (i.e., DelF1617 mutation; [Ach] = 0.03 M/L; = 0.1 mm 2 /ms). Results are shown in Figure 4, which presents the spatial and temporal profiles of action potentials recorded from representative cells across the SAN-atrium in the model (Figure 1(a)). And the conduction in the normal tissue (with the wild type channel, = 1.0 mm 2 /ms, no Iso and no Ach) is presented in Figure 1(d). Figure 3(a) shows the action potential profile with the DelF1617 mutation. The CL was increased by 25.8% compared with the normal tissue, and the ability of the SAN to drive atrium was not impaired. However, with Ach The Scientific World Journal 7   (Figure 4(c)) and produced a conduction block in the direction toward the atrial septum; the action potential conduction in the direction toward the CT was sustained. As we know, electrotonic interaction between the SAN and the surrounding tissues played an important role in determining the SAN pacing and driving. When the coupling strength was fixed to be small (i.e., = 0.1 mm 2 /ms), the SAN was able to generate spontaneous activity but failed to drive the surrounding atrium; conduction exit block occurred in both directions (Figure 4(d)).
When Iso addition was simulated at tissue level, three noteworthy results can be addressed. First, pacemaking rate with the DelF1617 mutation was significantly increased. The measured CL was decreased from 472.5 ms (Figure 4(a)) to 414.2 ms (Figure 4(b)) in the presence of 0.5 M/L Iso. Second, the spatial cessation of pacemaker activity in the direction toward the atrial septum cannot be recovered by addition of Iso (Figure 4(c)). Third, a conduction block in the direction toward the CT can be avoided. Through the application of 0.5 M/L Iso, the action potential was initiated in the center and propagated toward the CT, but not continually (Figure 4(e)); however, with the Iso concentration increasing to 2.0 M/L, the spatial cessation of pacemaker activity can be recovered completely (Figure 4(f)).
To characterize the effects of Iso, a series of simulations were performed with [Iso] changing systematically from 0.0001 M/L to 10 M/L. The results are represented in Figure 5(a), in which the computed CL was plotted against 3.3. Role of Na and Ca, . Due to the functional role of several major ionic currents, it is necessary to study the corresponding deterministic kinetics of these channel currents. Figure 6 presents the time series of the ionic currents, in which some useful clues can be found to infer the mechanism responsible for the positive effect of Iso on the pacemaker activity. Figures 6(a)(i), (6(b)(i)), 6(a)(ii), and (6(b)(ii)) show the time series of Na ( Ca, ) under normal condition and with the DelF1617 mutation. Compared with Figures 6(a)(i) and (6(b)(i)), Na ( Ca, ) was reduced or even zero in Figures  6(a)(ii) and (6(b)(ii)). Besides, other major underlying currents (such as Ca, and K, ) were not greatly affected (data are not shown). Thus, we can conclude that the slowing of the pacemaking was primarily attributable to the mutation-induced decrease in Na and Ca, (Figures 6(a)(ii) and 6(b)(ii)).
However, in this case, through the application of Iso (i.e., [Iso] = 0.1 M/L), Na was significantly increased as well as Ca, (Figures 6(a)(iii) and 6(b)(iii)), and both of the currents can be even increased to a normal level. This means that proper concentration of Iso can increase Na and Ca, which were reduced by the mutation. As a result of changes in the two currents, such abnormal pacemaking behavior could be eliminated.

Conclusions
In this study, by using a 2D anatomical model of the intact SAN-atrium, we have investigated the effects of Iso and the DelF1617 mutation on initiation and conduction of the pacemaker activity. The main findings of this study are as follows. (1) Iso could accelerate the pacemaking rate and affect the shape of action potentials in both the central and peripheral SAN cells, which are consistent with experimental observations [23,24]. (2) The DelF1617 mutation slowed down pacemaking rate. Simulated addition of Ach amplified the bradycardic effect of the mutation and compromised the ability of the SAN to pace and drive the atrial septum. (3) When combined effects of Ach and the changes in the intrinsic properties of the SAN with the mutation were considered, conduction block can occur in both directions toward the atrium and CT, leading to a higher probability of SAN exit block and sinus arrest than with the mutation or Ach alone. This finding agrees with that of Smits et al. [34] and may provide further insight into the mechanism underlying high risk of cardiac arrest in SSS patients at night, when Ach concentration is high [35,36]. (4) Abnormal pacemaking or even cessation state can be eliminated by proper concentration of Iso. Functional effects of Iso on the other mutations were similar (i.e., T220I, P1298L, and E161 K). What is more, Iso would be also useful for the treatment of bradycardia and improve atrial mechanical function [37]. It can be seen that these results are in good accordance with the clinical findings reported by Rokseth and Hatle [27], who provided the results of a 4-year prospective study regarding the occurrence, clinical pattern, and treatment of sinus arrest in patients with acute myocardial infarction. Taken together, we conclude that Iso could improve the pacemaking ability of the SAN cells as one of the fundamental medicines for SSS.