Key points

• • Computational models of the electrical activity of sinoatrial cells (SANCs) have been proposed to gain a deeper understanding of the cellular basis of cardiac pacemaking.

• • However, they fail to reproduce a number of experimental data, among which are effects measured after modifications of the ‘funny' (I_f) current.

• • We developed a novel SANC mathematical model by updating the description of membrane currents and intracellular mechanisms on the basis of experimental acquisitions, in an attempt to reproduce pacemaker activity and its physiological and pharmacological modulation.

• • Our model describes satisfactorily experimental data on pacemaking regulation due to neural modulation, I_f block and inhibition of the intracellular Ca²⁺ handling.

• • Computer simulation results suggest that a detailed description of the intracellular Ca²⁺ fluxes is fully compatible with the observation that I_f is a major component of pacemaking and heart rate modulation.

Abstract

The cellular basis of cardiac pacemaking is still debated. Reliable computational models of the sinoatrial node (SAN) action potential (AP) may help gain a deeper understanding of the phenomenon. Recently, novel models incorporating detailed Ca²⁺-handling dynamics have been proposed, but they fail to reproduce a number of experimental data, and more specifically effects of ‘funny' (I_f) current modifications. We therefore developed a SAN AP model, based on available experimental data, in an attempt to reproduce physiological and pharmacological heart rate modulation. Cell compartmentalization and intracellular Ca²⁺-handling mechanisms were formulated as in the Maltsev–Lakatta model, focusing on Ca²⁺-cycling processes. Membrane current equations were revised on the basis of published experimental data. Modifications of the formulation of currents/pumps/exchangers to simulate I_f blockers, autonomic modulators and Ca²⁺-dependent mechanisms (ivabradine, caesium, acetylcholine, isoprenaline, BAPTA) were derived from experimental data. The model generates AP waveforms typical of rabbit SAN cells, whose parameters fall within the experimental ranges: 352 ms cycle length, 80 mV AP amplitude, -58 mV maximum diastolic potential (MDP), 108 ms APD₅₀, and 7.1 V s^-1 maximum upstroke velocity. Rate modulation by I_f-blocking drugs agrees with experimental findings: 20% and 22% caesium-induced (5 mM) and ivabradine-induced (3 µM) rate reductions, respectively, due to changes in diastolic depolarization (DD) slope, with no changes in either MDP or take-off potential (TOP). The model consistently reproduces the effects of autonomic modulation: 20% rate decrease with 10 nMacetylcholine and 28% increase with 1 µM isoprenaline, again entirely due to increase in the DD slope, with no changes in either MDP or TOP. Model testing of BAPTA effects showed slowing of rate, -26%, without cessation of beating. Our up-to-date model describes satisfactorily experimental data concerning autonomic stimulation, funny-channel blockade and inhibition of the Ca²⁺-related system by BAPTA, making it a useful tool for further investigation. Simulation results suggest that a detailed description of the intracellular Ca²⁺fluxes is fully compatible with the observation that I_f is a major component of pacemaking and rate modulation.