A model of sinoatrial node cell regulation by the autonomic nervous system

Abstract

The primary function of the heart is to pump blood at a sufficient rate to ensure perfusion of all the organs. This vital task is achieved in large part by controlling the rate of cardiac contractions, which are initiated by cells in the sinoatrial node, the "pacemaker" of the heart. The oscillation rate of these spontaneously active cells is tightly regulated by the sympathetic and parasympathetic branches of the autonomic nervous system. Our understanding of sinoatrial node cell function has been greatly advanced by experimental and modeling efforts that quantitatively describe the numerous ionic currents responsible for the cell's spontaneous depolarization and generation of the action potential. Several models have also explored the effect of sympathetic and parasympathetic activity on specific ion channels and have reproduced the classic slowing and acceleration phenomena. However, a complete model of this interaction does not exist: current models lack the ability to simulate simultaneous sympathetic and parasympathetic activation or to reproduce heart rate dynamics in response to time-varying autonomic inputs. We addressed this need by constructing a bottom-up model of sinoatrial node cell regulation by the autonomic nervous system, with a focus on reproducing the full range of heart rates observed under simultaneous sympathetic and parasympathetic nerve stimulation, as well as the dynamic heart rate response to steps in sympathetic or parasympathetic stimulation rate. In constructing our model, we consolidate a large body of experimental data in a consistent mathematical framework. The model comprises 57 nonlinear coupled ordinary differential equations based on first principles and the current mechanistic understanding of the component reactions, fits well all the experimental data used to build the model, and reproduces high-level features of the system that were not explicitly fit when building the model. The detailed nature of the model also allows numerous conclusions to be drawn about the mechanisms of heart rate control. A better understanding of these mechanisms in health and disease may enable the development of better diagnostics for cardiovascular disease and more targeted drug design. We also identified a number of limitations in the present model that can be refined through further experimental and numerical efforts.