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' (I ) 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 I , 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.

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 I K1 . Such immaturity hampers their application in assessing drug safety. The electronic overexpression of I K1 (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 I K1 is needed to bring hiPSC-CMs to a stable and hyperpolarized RMP and which mathematical description of I K1 is most suitable for DC experiments. We compared five mature I K1 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 , APD 50 , APD 90 (AP duration at 50 and 90% of repolarization), and APD 50 /APD 90 ) after including them in the hiPSC-CM mathematical model by Paci. Then, we automatically identified the critical conductance for I K1 ( G K1, critical ), the minimally required amount of I K1 suppressing spontaneous activity. Preconditioning the cell model with depolarizing/hyperpolarizing prepulses allowed us to highlight time dependency of the I K1 formulations. Simulations showed that inclusion of mature I K1 formulations resulted in hyperpolarized RMP and higher _ V max , and observed G K1, critical and the effect on AP duration strongly depended on I K1 formulation. Finally, the Ishihara I K1 led to shorter (À16.3%) and prolonged (þ6.5%) APD 90 in response to hyperpolarizing and depolarizing prepulses, respectively, whereas other models showed negligible effects. Fine-tuning of G K1 is an important step in DC experiments. Our computational work proposes a procedure to automatically identify how much I K1 current is required to inject to stop the spontaneous activity and suggests the use of the Ishihara I K1 model to perform DC experiments in hiPSC-CMs. SIGNIFICANCE In this work, we aim to contribute a method that will facilitate automated dynamic clamp (DC) experiments in which I K1 is injected in induced pluripotent stem-cell-derived cardiomyocytes (iPSC-CMs). By introducing G K1, critical (minimal I K1 conductance needed to stop automaticity of iPSC-CMs), we are proposing a different approach to setting up DC experiments. These are usually based on the injection of a fixed current density. In contrast, G K1, critical is a parameter that depends on the cell under investigation. Our in silico approach analyzed analogies and differences between I K1 formulations without the confounding factor that can be brought by the variability of iPSC-CMs. It highlighted how much the employed mathematical formulation of I K1 can affect G K1, critical and the action potential waveform in DC experiments.

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.