In silico study of the effects of anti-arrhythmic drug treatment on sinoatrial node function for patients with atrial fibrillation

Sinus node dysfunction (SND) is often associated with atrial fibrillation (AF). Amiodarone is the most frequently used agent for maintaining sinus rhythm in patients with AF, but it impairs the sinoatrial node (SAN) function in one-third of AF patients. This study aims to gain mechanistic insights into the effects of the antiarrhythmic agents in the setting of AF-induced SND. We have adapted a human SAN model to characterize the SND conditions by incorporating experimental data on AF-induced electrical remodelling, and then integrated actions of drugs into the modified model to assess their efficacy. Reductions in pacing rate upon the implementation of AF-induced electrical remodelling associated with SND agreed with the clinical observations. And the simulated results showed the reduced funny current (If) in these remodelled targets mainly contributed to the heart rate reduction. Computational drug treatment simulations predicted a further reduction in heart rate during amiodarone administration, indicating that the reduction was the result of actions of amiodarone on INa, IKur, ICaL, ICaT, If and beta-adrenergic receptors. However, the heart rate was increased in the presence of disopyramide. We concluded that disopyramide may be a desirable choice in reversing the AF-induced SND phenotype.


Methods
This work was conducted based on a mathematical model and didn't involve any experimental animals or human participants.
Modelling AF-induced electrical remodelling underlying SND. The human SAN cell model developed by Fabbri et al. 27 was used as the base model for single-cell simulations in this study since the model was based on and validated using electrophysiological data from isolated human SAN pacemaker cells. In the cellular model, an ordinary differential equation was used to describe the transmembrane potential V: where t is the time, C m (57 pF) is the capacitance across the cell membrane, and I ion is the total ionic current across the membrane.
= + + + + + + + + + +  I  I  I  I  I  I  I  I  I  I  I  I (2) The precise behavior of the individual channels was based on a wide range of human cell electrophysiological data, and details can be found in the study conducted by Fabbri et al. 27 Under the SND conditions, AF-induced electrical remodelling included voltage clock-associated ionic currents and calcium clock-associated calcium handling. The ionic current formulations were modified based on data from Yeh et al., who investigated the voltage clock of single SAN cells from dogs that underwent atrial tachypacing and measured SAN transcript expressions for I f -associated subunits, I K -related subunits and I Ca subunits 6 . Alterations in calcium handling properties were derived from experimental data of Joung et al., who evaluated the calcium clock of single SAN cells in pacing-induced AF dogs, and determined expression of RyR, SERCA and phospholamban (PLB) 9 . In the Fabbri et al. model, I f , I CaL , I CaT , I Ks , J rel and J up were decreased to 50%, 90%, 92%, 65%, 33% and 71%, respectively, for describing the AF-induced SND condition (Fig. 1A

Modelling effects of drugs on SND.
In the present study, we focused on investigating the effects of amiodarone on SAN automaticity. The effects of amiodarone were incorporated into the cellular model by modifying ionic currents, involving beta-adrenergic receptor and membrane targets. For the block effects of amiodarone on the beta-adrenergic receptor, we decreased the effects of ISO stimulation by 15.2% 28 . For the effects of amiodarone on membrane targets, we integrated the block effects of amiodarone on funny current (I f ) 29 , sodium currents (I Na ) 30  , and sodium/potassium pump current I NaK . 37 Block of ionic currents provoked by amiodarone was simulated by including the fraction of unblocked channels in their formulations, estimated using the standard sigmoid dose-response curve parametrized using the half-maximal inhibitory concentration (IC 50 ) and Hill coefficient (nH) 26 . Within the framework of pore block theory, the maximal conductance g i of an ionic current type i was modified in a concentration-dependent manner, such that where g control,i represents the maximal conductance of the i current channel in drug-free conditions and D is the drug concentration. According to clinical data, the therapeutic concentration range of amiodarone, disopyramide, quinidine and digoxin, respectively, was 0.77~3.88 μM [38][39][40][41][42][43] , 6~15 µM 44 , 4~17 μM 45 and 0.64~2.56 nM 46 . Therefore, D for amiodarone, disopyramide, quinidine and digoxin was set to be 1.55 μM, 10 µM, 4 μM and 1 nM, respectively. In addition, the concentration-dependent effects of drugs were also investigated at the low, middle, and high concentrations (Supplementary Table 2). The IC 50 and nH values describing the effects of drugs on ionic currents were listed in the Supplementary Tables 3-6. www.nature.com/scientificreports www.nature.com/scientificreports/ Autonomic modulation. According to the method of Fabbri et al. 27 , autonomic regulation of SAN cells was studied by simulating the effects of acetylcholine (ACh, 10 nM) and isoprenaline (ISO, 1.0 μM) stimulations. Changes in I f , I CaL , I Ks , I KACh , I NaK and J up due to ACh and ISO stimulations were listed in the Supplementary  Table 7.

Multicellular 1D simulations.
A 1D SAN-atrial model, which consists of 30 SAN cells and 60 atrial cells, was developed to simulate electrical waves under the AF-induced SND condition in the presence of drugs. In the 1D cable model, the mathematical model of the human atrial myocyte developed in our previous study [47][48][49][50][51][52] was used, and AF was simulated by introducing electrical remodelling based on experimental data [53][54][55][56][57][58][59][60][61][62] (listed in the  Supplementary Table 8). The membrane potential is described by: where V(i) is the membrane potential of the i th cell, t is time, I ion is the sum of the transmembrane ionic currents, C m is the total membrane capacitance and G gap is the gap-junction coupling, which is given by: The heterogeneity of the SAN was implemented in the model following the strategies of Zhang et al. 63 and Garny et al. 37 The method uses the parameters of the central and the peripheral cell to determine the characteristics of transitional cells. A scaling factor F cell is calculated by:

Simulation protocol and data analysis.
To quantitatively assess the sensitivity of action potential (AP) and calcium features to parameters affected by electrical remodelling/drug actions, we changed values of parameters associated with each target between 100% to x%. x was set to be the minimal value to generate AP. Maximum diastolic potential (MDP), diastolic depolarization rate (DDR 100 ), maximum voltage of AP (OS), maximum rate of rise of membrane potential (dV/dt) max , maximum value of intracellular calcium concentration (Cai max ), minimum value of intracellular calcium concentration (Cai min ) and heart rate were used to quantify electrophysiological characteristics of SAN myocytes. And electrophysiological features of atrial cells were quantified by measuring MDP, OS, (dV/dt) max , Cai max , Cai min and AP duration at 90% repolarization (APD 90 ). An explicit Euler method for solving the ordinary differential Eq. (4) with a time step of 0.00001 s was used. Simulations were run until steady-state was reached after 100 s (~10000000 times). For 1D simulations, it took about 5 h using the Intel Core I5-4210m Processor (3 M Cache, up to 3.20 GHz) to compute 100 s.

Effects of AF-induced electrical remodeling on electrophysiological properties in SND.
Singlecell simulations were performed under normal and SND conditions and effects of AF-induced electrical remodeling on AP were investigated (Fig. 2). Note that due to AF-induced electrical remodelling, the SND AP had a decrease in OS from 26.4 mV to 24.9 mV, a more gradual transition from phase 4 to phase 0 (DDR 100 , from 56.7 mV/s to 46.4 mV/s) ( Fig. 2A) and a small (dV/dt) max (Fig. 2B). Compared with the normal condition, the heart rate in the SND case decreased from 74 to 60 beats/min (Fig. 2C), which was consistent with clinical findings 17,64-68 (Fig. 2D).  (Fig. 3H) of remodeled SAN cells were compared with AP features in normal cells. A more detailed analysis of the AP features reveals that changes in MDP and Cai min were almost negligible for all remodelled conditions. DDR 100 and Cai max showed a substantial decrease for the SND I f condition, whereas OS, (dV/dt) max and Cai max showed a reduction for the SND I CaL condition. Of note, a significant reduction in heart rate (from 74 to 65.8 beats/min) was only observed in the SND I f condition, but not under other remodeled conditions. www.nature.com/scientificreports www.nature.com/scientificreports/ Effects of amiodarone on ionic currents/fluxes of the human sinus node. To investigate the effects of amiodarone on SAN function in patients with AF, we simulated APs (Fig. 4A) and computed heart rate using the SND model by including the actions of amiodarone on ionic currents. In the presence of amiodarone, MDP was increased from -58.99 mV for the SND condition to -56.50 mV (Fig. 4B), DDR 100 , OS and (dV/dt) max were reduced (Fig. 4C-E), and Cai max and Cai min were slightly increased (Fig. 4F,G). The model also predicted a decrease in the heart rate (Fig. 4H).
To quantitatively assess the sensitivity of pacing rate to each target (I CaL , I CaT , I f , I Na , I Kur , I Ks , I Kr , I to , I NaK , I NCX , J rel or J up ) of AF-induced remodelling and amiodarone actions, we carried out experiments by reducing each ionic current/flux from 100% to x % (the minimal value to generate AP). As is shown in Fig. 5A, a reduction in heart rate in blocking I CaL , I CaT , I f , I Na , I Kur , or J rel condition, an increase in heart rate in the case of inhibiting I Kr , I to , I NaK , I NCX or J up, and no significant changes (i.e., changes in heart rate are no more than one beat) in heart rate under www.nature.com/scientificreports www.nature.com/scientificreports/ blocking I Ks condition are observed (Supplementary Table 9). Based on the role of each ionic current/flux modulated by amiodarone in regulating heart rate, ionic currents were grouped into three categories: #1 (I CaL , I CaT , I f , I Na , I Kur and J rel ), #2 (I Ks ) and #3 (I Kr , I to , I NaK , I NCX and J up ). Figure 5B showed changes in heart rate when each ionic current/flux was blocked only in the presence of 1.55 µM amiodarone. The combined effect of amiodarone on AP was further investigated in each of the groups (Fig. 5C), and the respective heart rate was 0, 60.63 and 78.81 beats/ min, respectively (Fig. 5D). Thus, opposing effects were present. However, the combined actions of targets in the #1 far outweighed the effects of amiodarone on membrane targets in the #3.
Effects of amiodarone on autonomic modulation of the human sinus node. To investigate the effects of amiodarone on the autonomic modulation of human SAN in patients with AF, we simulated APs of SAN cells with ACh and ISO stimulation under the normal without amiodarone (Normal/Wout), SND/Wout and SND with amiodarone (SND/Ami) conditions. After the administration of ACh, the heart rate for Normal/ Wout and SND/Wout cells was 58.40 and 45.03 beats/min, respectively. The amiodarone actions further reduced the heart rate and caused heart arrest under the SND/Ami condition (Fig. 6A,B). After the administration of ISO, the heart rate for Normal/Wout and SND/Wout cells was 112.72 and 94.23 beats/min, respectively. With the addition of amiodarone on top of ISO, the heart rate was reduced to 47.47 beats/min under the SND/Ami condition (Fig. 6C,D). www.nature.com/scientificreports www.nature.com/scientificreports/ Effects of disopyramide, quinidine and digoxin on the human sinus node. To examine whether there are antiarrhythmic drugs that have efficacy for the treatment of AF-induced SND, we investigated the effects of amiodarone (Ami), digoxin (Digo), disopyramide (Diso) and quinidine (Quin) on SAN function (Fig. 7). Compared with the drug-free SND condition (SND/Wout), there was an increase in cycle length in the presence of amiodarone, but a reduction in cycle length was observed in the presence of digoxin, quinidine and disopyramide (Fig. 7A). In the presence of disopyramide (SND/Diso), MDP, OS, Cai max and Cai min were slightly increased, whereas (dV/dt) max had almost no changes and DDR 100 was slightly reduced. In the presence of quinidine (SND/Quin), MDP, DDR 100 and Cai min were increased, whereas OS, (dV/dt) max and Cai max were significantly reduced. In the presence of digoxin (SND/Digo), all biomarkers had almost no changes (Fig. 7B-G). The heart rate was reduced from 60.62 to 45.94 beats/min in the presence of amiodarone, whereas the heart rate was increased from 60.62 to 61.79, 98.60 and 116.03 beats/min, respectively, in the presence of digoxin, disopyramide and quinidine (Fig. 7H).
The concentration-dependent effects of these drugs were also investigated at the low, middle, and high concentrations. Compared with the drug-free SND condition (SND/Wout), heart arrest was observed in the presence of amiodarone (SND/Ami(High)) or quinidine (SND/Quin(High)) at the high concentration, an increase in heart rate was predicted in the presence of disopyramide, and no significant changes in heart rate were shown in the presence of digoxin (Supplementary Fig. 1).
Further simulations were conducted to examine whether these antiarrhythmic drugs have efficacy for improving the SAN function using a 1D SAN-atrial model. Compared with the normal condition (Supplementary Fig. 2A), the number of electrical waves within 5 s reduced from 7 to 5 beats under the SND condition without any drugs (Supplementary Fig. 2B). In the presence of drugs, the number of electrical waves under the SND condition showed an increase in the presence of disopyramide ( Supplementary Fig. 2C), no significant changes in the presence of digoxin ( Supplementary Fig. 2D), a reduction in the presence of amiodarone (Supplementary Fig. 2E) and SAN arrest in the presence of quinidine (Supplementary Fig. 2F).

Discussion
In the present study, we formulated a human AP model of AF-induced SND and investigated the impact of amiodarone on human SAN function. We further assessed whether other drugs (i.e., disopyramide, quinidine and digoxin) could reverse the AF-induced SND phenotype. The major findings of this study are as follows: (1) the AF-induced SND can be mainly attributed to down-regulation of I f ; (2) the effects of amiodarone lead to a lower DDR 100 and more prolonged diastolic depolarization phase, resulting in a slower pacemaking rate and contributing to the impact of amiodarone on human SAN function; (3) the bradycardiac effects of amiodarone are likely to be amplified by vagal nerve activity (simulated addition of ACh to the SND cells with amiodarone causes SAN arrest); and (4) our model predicted an increase in pacemaking rate in the presence of disopyramide. Together, these data point to voltage-clock dysfunction underlying SND and provide evidence substantiating the impact of amiodarone on the function of the SAN. The leading causes of bradycardia under the AF-induced SND are electrophysiological remodelling related to the voltage clock of the human SAN. Previous experiments on canine SAN cells have demonstrated that AF-induced remodelling of ion channels, particularly for the "pacemaker" subunit I f , may contribute to the clinically significant association between SND and AF 6 . Our simulated effects of remodelled I f are concordant with this experimental findings 33 . In additional to remodelled I f , changes in I Ks , I CaL and I CaT were observed in SAN cells of the pacing-induced AF canine model 69 . We assumed that a similar ionic remodelling may also occur in human AF-induced SND. The combined effect of the electrical remodelling slowed down the heart rate significantly. The reduction in heart rate was mainly the result of a lower DDR 100 arising from the downregulation of inward currents (including I f , I CaL and I CaT ). And remodelled I Ks has a negligible effect on DDR 100 and the pacemaking rate. These findings agree with previous work showing the strong contributions of I f , I CaL and I CaT to DDR 100 and the pacing rate 27 . The sensitivity analysis highlighted the strong impact of I CaL on heart rate. 52% block of I CaL is able to lead to heart arrest, whereas 95% block of I CaT results in hart arrest and a slow heart rate is obtained with 100% block of I f (Fig. 5A). The illustrative investigation of the effects of changes in maximal conductances of ionic current suggests that I CaL plays a role in pacemaking, which is consistent with the sensitivity analysis by Fabbri et al. 27 . Under the SND condition, I CaL , I CaT and I f were decreased to 90%, 92% and 50%, respectively (Fig. 1B). Remodelled I CaL and I CaT caused a reduction in heart rate from 74 to 70.7 and 71.2 beats/min, respectively, whereas remodelled I f led to a slower heart rate from 74 to 65.8 beats/min. Therefore, the reduced I f under the SND condition mainly contributed to the heart rate reduction.
Previous experiments have shown that AF-induced SND is also associated with calcium handling abnormalities. Here, we also investigated the effects of calcium handling properties on SAN automaticity. AF-induced changes in calcium handling (the downregulation of J rel and J up ) in our human SAN model are similar to experimental data from a canine model of pacing-induced AF 9 . Downregulation of J rel could decrease the pacemaking rate (from 73.7 to 72.1 beats/min) which is consistent with experimental observations 9 , whereas remodelled J up could increase heart rate (from 73.7 to 74.2 beats/min) which is a good agreement with previous modelling study 27 . However, changes in the pacemaking rate due to calcium handling abnormalities were almost negligible. Altogether, our simulation results indicate that voltage-clock malfunction might be the mechanism underlying AF-induced SND (Fig. 8A) and our SND mathematical model for human SAN cells can be useful in the design of experiments and the development of drugs.
Amiodarone is the most frequently used agent to reverse AP shortening ( Supplementary Fig. 3) in patients with AF, which is partly resulted from electrical remodelling 70 (Supplementary Table 10). However, computational drug treatment simulations predicted a dramatical reduction in the pacemaking rate, indicating the impact of amiodarone on the SAN function. These findings agree with the previous work showing amiodarone-induced bradycardia in AF patients 71 . These changes in the pacemaking rate may be attributable to the effects of amiodarone on multiple ion channels and beta-adrenergic receptors. Inhibition of I Na , I Kur , I CaL , I CaT , I f , J rel and beta-adrenergic receptors leads to a slower heart rate, whereas the block of I Kr , I to , I KACh , I NaK , I NCX and J up causes a higher heart rate. Thus, opposing effects were present. However, deceleration effects of amiodarone far outweighed its acceleration effects, leading to a slow pacemaking rate. In addition, the slow heart rate since the actions of amiodarone on I CaL in the current study in accordance with the work of Nattel et al. 72 , suggesting that changes in SAN function can be attributable to amiodarone's calcium channel-blocking properties and account for the adverse consequence of amiodarone.
Our study substantiates the notion that beta-adrenergic blocking effects of amiodarone may explain the unresponsiveness of SAN to sympathetic stimulation in AF patients 17 . Reports of AF patients suggest that amiodarone causes SND, which results in reduced P-wave amplitude at baseline and during ISO infusion. The anti-adrenergic effects of amiodarone showed a reduction of receptor density in the cellular membrane, suggesting that amiodarone leads to the unresponsiveness of SAN to ISO stimulation 73 . Moreover, the overall pacing rate acceleration because of the administration of 1 µM ISO was the result of a balance between opposing contributors. Previous modelling studies have demonstrated that in five targets (I f , I CaL , I NaK , I Ks and J up ) ISO-induced changes occur in I f and I CaL , leading to a faster heart rate 27 . However, amiodarone has block effects on both I f and I CaL . And our simulated results show that the SAN pacing rate decreases in the presence of amiodarone. These studies and our results suggest that amiodarone causes bradycardia by partly inhibiting I f , I CaL and beta-adrenergic receptors in the human SAN. Thus, our results suggest that amiodarone cannot be used safely in patients that have SND associated with AF. We further investigated effects of quinidine, disopyramide and digoxin on the function of the SAN under the AF-induced SND condition and simulated results demonstrated that disopyramide was necessary to considerably increase the heart rate (Fig. 8B).
Several limitations specific to this study are addressed here. Firstly, the electrophysiological representation of AF-induced remodelling in the human SND model is based on data from previous canine models of AF 6,9 , however, because of the lack of experimental data on humans. Special attention must be paid to the differences between canine and human sinoatrial node 74 . Secondly, the blocking effects of drugs on ionic currents were modelled using the total plasma concentrations of drugs, nH and IC 50 in the present study. However, drug efficacy needs to be related to free drug concentrations, not the total plasma concentrations 75 . Special attention should be paid to explain our simulated results, and free drug concentrations of drugs in plasma should be used to further assess the efficacy of drugs in the treatment of AF-induced SND. In addition, the large variability in IC 50 was observed for most of the drugs, including amiodarone 76 . In a previous study, differential responses of ventricular and atrial ion channels to antiarrhythmic drugs were observed 77 . In the present study, IC 50 values are chosen based on experimental data from atrial cells (where data are available) and large ventricular cells (where atrial data are not available). Thirdly, the uncertainty analysis is important for a more precise evaluation of the safety of antiarrhythmic drugs 25,78 . Therefore, our models and methodology should be improved, and statistics and treatment of uncertainties should be considered [78][79][80] and further investigated. Fourthly, the block effects of amiodarone on beta-adrenergic receptors were modelled with the same percentage decrease in the effects of Scientific RepoRtS | (2020) 10:305 | https://doi.org/10.1038/s41598-019-57246-5 www.nature.com/scientificreports www.nature.com/scientificreports/ beta-adrenergic receptor stimulation on targets. The strict linearity is unlikely and the modelling approach should be improved based on experimental data. Fifthly, simulated results demonstrated that inhibition of I Kr increases heart rate, but experimental studies showed that dofetilide (an I Kr blocker) depolarized the maximum diastolic potentials, reduced the slope of the pacemaker potential and then abolished spontaneously firing action potentials in the nodal cells, suggesting I Kr blockers slowed spontaneous activity 81,82 . The I Kr model of Fabbri et al. model should be modified and verified based on these experimental data. Finally, the coupling between calcium clock and voltage clock is limited in the Fabbri et al. model, but the coupled-clock mechanism was established in two mathematical models by Kharche et al. 83 , and Maltsev and Lakatta 84 . Therefore, the Fabbri et al. model should be improved and calcium clock under the AF-induced SND condition should be further investigated. in combination may be responsible for the diastolic depolarization, the so-called "voltage clock". Diastolic spontaneous calcium release via RyR increases the calcium concentration ([Ca 2+ ] i ) and activates sodium-calcium exchanger. The inward I NCX contributes to the diastolic depolarization, the so-called "calcium clock". Therefore, AF-induced electrical remodelling impairs both the voltage clock and the calcium clock, resulting in the heart rate reduction and SND. (B) Under the AF-induced SND condition, the action of amiodarone impairs sinoatrial node function, leading to a reduction in the sinus rate, whereas disopyramide may improve sinoatrial node function and increase the sinus rate.