Numerical models based on a minimal set of sarcolemmal electrogenic proteins and an intracellular Ca(2+) clock generate robust, flexible, and energy-efficient cardiac pacemaking.

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 70bpm; maximum rate of 140 to 210bpm) 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 "ICaL+IKr+INCX+Ca(2+)clock") were able to reproduce the full range of autonomic modulation. Inclusion of If or ICaT 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 IbNa & Ist) 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.