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The sinoatrial node (SAN) is the natural pacemaker of the mammalian heart. It has been the subject of several mathematical studies, aimed at reproducing its electrical response under normal sinus rhythms, as well as under various conditions. Such studies were traditionally done using data from rabbit SAN cells. More recently, human SAN cell data have become available, resulting in the publication of a human SAN cell model (Fabbri et al., 2017), along with its CellML version. Here, we used the CellML file provided by the model authors, together with some SED-ML files and Python scripts that we created to reproduce the main results of the aforementioned modeling study. EDITOR'S NOTE (v2): this article and its OMEX archive are republished with technical changes made to the corresponding Python scripts to remove a run-time error message displayed when executing each simulation.

Current in vitro assays typically poorly predict cardiac liability as they focus on single ion channels overexpressed in cell lines. Human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs), on the other hand, provide a unique opportunity for drug testing on human cardiomyocytes using high-throughput systems. However, these cells can differ from adult cardiomyocytes in their ion channel expression and, therefore, electrophysiologic properties. One of the main challenges of hiPSC-CMs is the physiologic expression of ion channels such as the inward rectifiers (e.g., Kir2.1-2.3), which conduct the cardiac inward rectifier potassium current (I

Human-induced pluripotent stem cells derived cardiomyocytes (hiPSC-CMs) are a virtually endless source of human cardiomyocytes that may become a great tool for safety pharmacology; however, their electrical phenotype is immature: they show spontaneous action potentials (APs) and an unstable and depolarized resting membrane potential (RMP) because of lack of IK1. Such immaturity hampers their application in assessing drug safety. The electronic overexpression of IK1 (e.g., through the dynamic clamp (DC) technique) is an option to overcome this deficit. In this computational study, we aim to estimate how much IK1 is needed to bring hiPSC-CMs to a stable and hyperpolarized RMP and which mathematical description of IK1 is most suitable for DC experiments. We compared five mature IK1 formulations (Bett, Dhamoon, Ishihara, O'Hara-Rudy, and ten Tusscher) with the native one (Paci), evaluating the main properties (outward peak, degree of rectification), and we quantified their effects on AP features (RMP, V˙max, APD50, APD90 (AP duration at 50 and 90% of repolarization), and APD50/APD90) after including them in the hiPSC-CM mathematical model by Paci. Then, we automatically identified the critical conductance for IK1 ( GK1, critical), the minimally required amount of IK1 suppressing spontaneous activity. Preconditioning the cell model with depolarizing/hyperpolarizing prepulses allowed us to highlight time dependency of the IK1 formulations. Simulations showed that inclusion of mature IK1 formulations resulted in hyperpolarized RMP and higher V˙max, and observed GK1, critical and the effect on AP duration strongly depended on IK1 formulation. Finally, the Ishihara IK1 led to shorter (-16.3%) and prolonged (+6.5%) APD90 in response to hyperpolarizing and depolarizing prepulses, respectively, whereas other models showed negligible effects. Fine-tuning of GK1 is an important step in DC experiments. Our computational work proposes a procedure to automatically identify how much IK1 current is required to inject to stop the spontaneous activity and suggests the use of the Ishihara IK1 model to perform DC experiments in hiPSC-CMs.

Key points We constructed a comprehensive mathematical model of the spontaneous electrical activity of a human sinoatrial node (SAN) pacemaker cell, starting from the recent Severi–DiFrancesco model of rabbit SAN cells. Our model is based on electrophysiological data from isolated human SAN pacemaker cells and closely matches the action potentials and calcium transient that were recorded experimentally. Simulated ion channelopathies explain the clinically observed changes in heart rate in corresponding mutation carriers, providing an independent qualitative validation of the model. The model shows that the modulatory role of the ‘funny current’ (If) in the pacing rate of human SAN pacemaker cells is highly similar to that of rabbit SAN cells, despite its considerably lower amplitude. The model may prove useful in the design of experiments and the development of heart-rate modulating drugs. Abstract The sinoatrial node (SAN) is the normal pacemaker of the mammalian heart. Over several decades, a large amount of data on the ionic mechanisms underlying the spontaneous electrical activity of SAN pacemaker cells has been obtained, mostly in experiments on single cells isolated from rabbit SAN. This wealth of data has allowed the development of mathematical models of the electrical activity of rabbit SAN pacemaker cells. The present study aimed to construct a comprehensive model of the electrical activity of a human SAN pacemaker cell using recently obtained electrophysiological data from human SAN pacemaker cells. We based our model on the recent Severi–DiFrancesco model of a rabbit SAN pacemaker cell. The action potential and calcium transient of the resulting model are close to the experimentally recorded values. The model has a much smaller ‘funny current’ (If) than do rabbit cells, although its modulatory role is highly similar. Changes in pacing rate upon the implementation of mutations associated with sinus node dysfunction agree with the clinical observations. This agreement holds for both loss-of-function and gain-of-function mutations in the HCN4, SCN5A and KCNQ1 genes, underlying ion channelopathies in If, fast sodium current and slow delayed rectifier potassium current, respectively. We conclude that our human SAN cell model can be a useful tool in the design of experiments and the development of drugs that aim to modulate heart rate.

Each heartbeat is initiated by cyclic spontaneous depolarization of cardiomyocytes in the sinus node forming the primary natural pacemaker. In patients with end-stage renal disease undergoing hemodialysis, it was recently shown that the heart rate drops to very low values before they suffer from sudden cardiac death with an unexplained high incidence. We hypothesize that the electrolyte changes commonly occurring in these patients affect sinus node beating rate and could be responsible for severe bradycardia. To test this hypothesis, we extended the Fabbri et al. computational model of human sinus node cells to account for the dynamic intracellular balance of ion concentrations. Using this model, we systematically tested the effect of altered extracellular potassium, calcium, and sodium concentrations. Although sodium changes had negligible (0.15 bpm/mM) and potassium changes mild effects (8 bpm/mM), calcium changes markedly affected the beating rate (46 bpm/mM ionized calcium without autonomic control). This pronounced bradycardic effect of hypocalcemia was mediated primarily by I(CaL) attenuation due to reduced driving force, particularly during late depolarization. This, in turn, caused secondary reduction of calcium concentration in the intracellular compartments and subsequent attenuation of inward I(NaCa) and reduction of intracellular sodium. Our in silico findings are complemented and substantiated by an empirical database study comprising 22,501 pairs of blood samples and in vivo heart rate measurements in hemodialysis patients and healthy individuals. A reduction of extracellular calcium was correlated with a decrease of heartrate by 9.9 bpm/mM total serum calcium (p < 0.001) with intact autonomic control in the cross-sectional population. In conclusion, we present mechanistic in silico and empirical in vivo data supporting the so far neglected but experimentally testable and potentially important mechanism of hypocalcemia-induced bradycardia and asystole, potentially responsible for the highly increased and so far unexplained risk of sudden cardiac death in the hemodialysis patient population.

The description of the underlying phenomena that modulate the heart rate is crucial to better understand arrhythmias. Computational models are powerful tools to investigate the contribution of ion currents to the changes of membrane potential. Among them, the calcium-activated small conductance K+ current (I SK ) is able to modulate the action potential (AP) duration and rate. The aim of this work was to assess how the inclusion of I SK affected the AP and calcium transient features of the human sinoatrial node model we recently developed. The formulation of I SK was adopted according to Kennedy et al. and a sensitivity analysis on g SK (g SK = 0, 4, 10, 41.70 μS/μF) was carried out. The main effects of I SK were an overall reduction of cycle length (CL) (from 814 ms in CTRL to 764, 668 and 439 ms for g SK = 4, 10, 41.70 μS/μF, respectively) due to a decrease of the AP duration at 90% of repolarization (APD 90 ) (from 161 ms in CTRL to 155.0, 143.0 and 96.0 ms) and an increase of the diastolic depolarization rate in the first 100 ms (DDR 100 ) (from 48.1 mV/s to 52.9, 60.6 and87.2 mV/s). The reduction of CL due to the shortening of APD 90 was predictable, since I SK is an outward current. The increase of DDR 100 led to the shortening of the DD phase. This was an unexpected effect of the inclusion of I SK : the latter reduced the contribution of the rapid delayed rectifier K+ current (I Kr ), which compensated and even overcame the outward contribution of I SK .

HCN4 channels are expressed in the human sinoatrial node (SAN) and conduct the hyperpolarization-activated ‘funny current’, If, also known as ‘pacemaker current’. Several loss-of-function mutations in the HCN4 gene have been associated with human sinus bradycardia. Clinical observations suggest that bradycardic effects are present at all levels of autonomic tone. We assessed the effects of three different mutations in HCN4 on human SAN pacemaker activity at different levels of autonomic tone by incorporating experimentally identified mutation-induced changes in If into the recently developed Fabbri et al. model of a single human SAN cell. Different levels of autonomic tone were obtained through simulated administration of specific levels of acetylcholine (ACh) or isoprenaline (Iso). The G480R, A485V, and 695X mutations in HCN4 lowered the control beating rate from 74 to 62, 59, and 65 bpm, the ACh beating rate from 49 to 40, 37, and 45 bpm, and the Iso beating rate from 140 to 115, 100, and 109 bpm, respectively, all in accordance with the clinical observations. We conclude that experimentally observed changes in the expression and kinetics of If channels can explain the clinically observed bradycardic effects of loss-of-function mutations in HCN4 at different levels of autonomic tone.

The sinoatrial node (SAN) is the natural pacemaker of our heart. How this small tissue is able to drive a remarkably larger number of intrinsically quiescent atrial cells is still debated; a computational investigation of the underlying mechanisms can help to better understand the SAN's ability to pace-and-drive the surrounding atrium. Aim of this work is to elucidate how the human SAN action potential can successfully be captured by and propagate into the surrounding atrial tissue. The Fabbri et al. and the Courtemanche et al. models were used to describe the human SAN and atrial cells, respectively. The behaviour of two coupled regions was investigated varying the interregional conductivity (σ) and relative size. Simulations showed that it requires at least an isopotential SAN region 2.85 times wider than the atrial one. A 1D strand of homogeneously coupled SAN and atrial elements was used to identify an interval for σ showing pace-and-drive behaviour (100 SAN vs 100 atrial elements) and to investigate the source-sink interplay (10, 50 or 100 SAN elements vs 100 atrial elements). The 1D strand showed pace-and-drive behaviour for σ = [0.08 — 36] S/m; a stronger source, with a higher number of SAN elements, led to a wider σ range that allowed pace-and-drive behaviour, whereas a stronger sink did not affect the behaviour of the tissue. This preliminary work shows the ability of a small human SAN region to pace-and-drive the surrounding atrial tissue. Further investigations are needed to explore different conductivity configurations, including spatial gradients.

Aim of this work is the formulation of a human sinoatrial node (SAN) action potential (AP) in silico model able to reproduce the available experimental data and to explore a pacemaking aspect through the effects of funny current (If) block on cycle length (CL).The Severi-DiFrancesco rabbit SAN model was the starting point. The quantification of current, pump and exchanger parameters was driven by experimental data from electrophysiology, gene expression and by parameters tuning to reproduce the experimental traces (AP morphology and calcium transient). In order to quantitatively assess the model performances, AP features (action potential duration at 90% of repolarization (APD90), diastolic depolarization rate for the first 100 ms (DDR100)) and intracellular Ca2+ transient features (minimum and maximum Ca2+ concentration (Cai min, Cai max)) were computed. The effects of If modulation on CL were also evaluated by simulating the administration of Cs+ (a If blocker), its progressive block (30, 70, 90, 100%), and shifting the range of activation.The model predictions and experimental traces are in good accordance. Both AP and Cai transient features are in agreement with the experimental values (predicted: CL=825 ms APD90=145.0 ms, DDR100=56.9 mV/s Cai,min=97 nM, Cai, max=195 nM; experimental CL=828±15 ms, APD90=143.5±34.9 ms, DDR100=48.9±18 mV/s Cai,min=110 nM, Cai,max=220 nM). Simulation of If block by Cs+ leads to +27% CL prolongation as in experiments (+26%). Full If block shows a CL increase of +54% (CL=1275 ms, HR=47 bpm). Shifts of If activation in the range ±10 mV shows the capability to continuosly regulate CL in a range about ±25%.This model is a first step to a reliable human SAN model strongly based on the few available data from human SAN.

This work aims to assess: I) the effects of the 1479V/A485E HCN4 channel double mutation (DM), II) the role of cellular coupling (p) and III) the role of cellular heterogeneity (σ) on systems of increasing complexity: ionic channel, single cell, 1D fibre and 2D tissue of the human SAN. The Fabbri et al. model was used to describe the human SAN cell and to build the 1D and 2D models, which are constituted of 100 and 2500 (50×50) cells, respectively. σ = 0.05, 0.1, 0.1873, 0.3, 0.4 and p = 10, 100, 1000, 10000 and ∞ MΩ. m were simulated, in order to test their effect on the heart rate (HR). The reduction of I f current due to the heterozygous condition (gj(WT0.5 + DM) = 45% of gf(WT)) leads to an increase of the cycle length of the simulated action potential of a single cell (924 vs 814 ms; + 14%). This WT0.5+DM bradycardic effect is confirmed also by the 1D model (802 vs 690 ms; +14%) as well as by the 2D one (908 vs 794 ms; +14%). These results were obtained forσ = 0.1873 and p = 100 MΩ· m (50 MΩ. m in 1D). Other combinations of σ and p can provide changes in HR greater than 50%, highlighting the importance of these two parameters in the establishment of a physiologic pacing in the human SAN.