A model of the autonomic control of heart rate at the pacemaker cell level through G-proteins

A mathematical model of the pacemaker cell of the mammal sinoatrial node, based upon the Yanagihara-Noma-Irisawa equations, is presented here. Its aim is to mimic the control of the pacemaker cell, as measured on the resulting heart rate, by both branches of the autonomic nervous system (ANS). It is a simplification of the original model by the suppression of some variables (but no ionic current being removed). It also uses a dynamical model of the G-proteins as actuators of this control in the system, and a construction of the sympathetic and vagal impulses, reflecting respiratory sinus arrhythmia and baroreflex influence. These characteristics make it a model compatible with what is known of the electrophysiological mechanisms of pacemaking at the single cell level, and with the observed spectral characteristics of short-term (respiratory) heart rate variability at the whole heart (electrocardiographic) level, thus partly bridging a gap between these two representation levels of the ANS