Letter to the Editor

Considerations on the size of currents required for pacemaking

Since its discovery, the sinoatrial node (SAN) has represented a fascinating and complex matter of research. Despite over a century of discoveries, a full comprehension of pacemaking has still to be achieved. Experiments often produced conflicting evidence that was used either in support or against alternative theories, originating intense debates. In this context, mathematical descriptions of the phenomena underlying the heartbeat have grown in importance in the last decades since they helped in gaining insights where experimental evaluation could not reach. This review presents the most updated SAN computational models and discusses their contribution to our understanding of cardiac pacemaking. Electrophysiological, structural and pathological aspects – as well as the autonomic control over the SAN - are taken into consideration to reach a holistic view of SAN activity.

Cardiac pacemaking is a complex phenomenon that is still not completely understood. Together with experimental studies, numerical modeling has been traditionally used to acquire mechanistic insights in this research area. This review summarizes the present state of numerical modeling of the cardiac pacemaker, including approaches to resolve present paradoxes and controversies. Specifically we discuss the requirement for realistic modeling to consider symmetrical importance of both intracellular and cell membrane processes (within a recent “coupled-clock” theory). Promising future developments of the complex pacemaker system models include the introduction of local calcium control, mitochondria function, and biochemical regulation of protein phosphorylation and cAMP production. Modern numerical and theoretical methods such as multi-parameter sensitivity analyses within extended populations of models and bifurcation analyses are also important for the definition of the most realistic parameters that describe a robust, yet simultaneously flexible operation of the coupled-clock pacemaker cell system. The systems approach to exploring cardiac pacemaker function will guide development of new therapies such as biological pacemakers for treating insufficient cardiac pacemaker function that becomes especially prevalent with advancing age.

Whether intracellular Ca²⁺ cycling dynamics regulate cardiac pacemaker cell function on a beat-to-beat basis remains unknown. Here we show that under physiological conditions, application of low concentrations of caffeine (2–4 mM) to isolated single rabbit sinoatrial node cells acutely reduces their spontaneous action potential cycle length (CL) and increases Ca²⁺ transient amplitude for several cycles. Numerical simulations, using a modified Maltsev-Lakatta coupled-clock model, faithfully reproduced these effects, and also the effects of CL prolongation and dysrhythmic spontaneous beating (produced by cytosolic Ca²⁺ buffering) and an acute CL reduction (produced by flash-induced Ca²⁺ release from a caged Ca²⁺ buffer), which we had reported previously. Three contemporary numerical models (including the original Maltsev-Lakatta model) failed to reproduce the experimental results. In our proposed new model, Ca²⁺ releases acutely change the CL via activation of the Na⁺/Ca²⁺ exchanger current. Time-dependent CL reductions after flash-induced Ca²⁺ releases (the memory effect) are linked to changes in Ca²⁺ available for pumping into sarcoplasmic reticulum which, in turn, changes the sarcoplasmic reticulum Ca²⁺ load, diastolic Ca²⁺ releases, and Na⁺/Ca²⁺ exchanger current. These results support the idea that Ca²⁺ regulates CL in cardiac pacemaker cells on a beat-to-beat basis, and suggest a more realistic numerical mechanism of this regulation.

Recent evidence supports the idea that robust and, importantly, FLEXIBLE automaticity of cardiac pacemaker cells is conferred by a coupled system of membrane ion currents (an “M-clock”) and a sarcoplasmic reticulum (SR)-based Ca^2 + oscillator (“Ca^2 +clock”) that generates spontaneous diastolic Ca^2 + releases. This study identified numerical models of a human biological pacemaker that features robust and flexible automaticity generated by a minimal set of electrogenic proteins and a Ca^2 +clock. Following the Occam's razor principle (principle of parsimony), M-clock components of unknown molecular origin were excluded from Maltsev–Lakatta pacemaker cell model and thirteen different model types of only 4 or 5 components were derived and explored by a parametric sensitivity analysis. The extended ranges of SR Ca^2 + pumping (i.e. Ca^2 +clock performance) and conductance of ion currents were sampled, yielding a large variety of parameter combination, i.e. specific model sets. We tested each set's ability to simulate autonomic modulation of human heart rate (minimum rate of 50 to 70 bpm; maximum rate of 140 to 210 bpm) in response to stimulation of cholinergic and β-adrenergic receptors. We found that only those models that include a Ca^2 +clock (including the minimal 4-parameter model “I_CaL + I_Kr + I_NCX + Ca^2 +clock”) were able to reproduce the full range of autonomic modulation. Inclusion of I_f or I_CaT decreased the flexibility, but increased the robustness of the models (a relatively larger number of sets did not fail during testing). The new models comprised of components with clear molecular identity (i.e. lacking I_bNa & I_st) portray a more realistic pacemaking: A smaller Na⁺ influx is expected to demand less energy for Na⁺ extrusion. The new large database of the reduced coupled-clock numerical models may serve as a useful tool for the design of biological pacemakers. It will also provide a conceptual basis for a general theory of robust, flexible, and energy-efficient pacemaking based on realistic components.

Heart rate (HR) is determined by the pacemaker activity of cells from the sinoatrial node (SAN), located in the right atria. Spontaneous electrical activity of SAN cells results from a diastolic depolarization (DD). Despite controversy in the exact contribution of funny current (I_f) in pacemaking, it is a major contributor of DD. I_f is an inward Na⁺/K⁺ current, activated upon hyperpolarization and directly modulated by cyclic adenosine monophosphate. The f-proteins are hyperpolarization-activated cyclic nucleotide-gated channels, HCN4 being the main isoform of SAN. Ivabradine (IVA) decreases DD and inhibits I_f in a use-dependent manner. Under normal conditions IVA selectively reduces HR and limits exercise-induced tachycardia, in animals and young volunteers. Reduction in HR with IVA both decreases myocardial oxygen consumption and increases its supply due to prolongation of diastolic perfusion time. In animal models and in human with coronary artery disease (CAD), IVA has anti-anginal and anti-ischemic efficacy, equipotent to classical treatments, β-blockers, or calcium channel blockers. As expected from its selectivity for I_f, the drug is safe and well tolerated with minor visual side effects. As a consequence, IVA is the first inhibitor of I_f approved for the treatment of stable angina.

Available clinical data indicate that IVA could improve the management of stable angina in all patients including those treated with β-blockers. As chronic elevation of resting HR is an independent predictor of mortality, pure HR reduction by inhibition of I_f could, beyond the control of anti-anginal symptoms, improve the prognosis of CAD and heart failure; this therapeutic potential is currently under evaluation with IVA.