Emergent activity, heterogeneity, and robustness in a calcium feedback model of the sinoatrial node

The sinoatrial node (SAN) is the primary pacemaker of the heart. SAN activity emerges at an early point in life and maintains a steady rhythm for the lifetime of the organism. The ion channel composition and currents of SAN cells can be influenced by a variety of factors. Therefore, the emergent activity and long-term stability imply some form of dynamical feedback control of SAN activity. We adapt a recent feedback model-previously utilized to describe control of ion conductances in neurons-to a model of SAN cells and tissue. The model describes a minimal regulatory mechanism of ion channel conductances via feedback between intracellular calcium and an intrinsic target calcium level. By coupling a SAN cell to the calcium feedback model, we show that spontaneous electrical activity emerges from quiescence and is maintained at steady state. In a 2D SAN tissue model, spatial variability in intracellular calcium targets lead to significant, self-organized heterogeneous ion channel expression and calcium transients throughout the tissue. Furthermore, multiple pacemaking regions appear, which interact and lead to time-varying cycle length, demonstrating that variability in heart rate is an emergent property of the feedback model. Finally, we demonstrate that the SAN tissue is robust to the silencing of leading cells or ion channel knockouts. Thus, the calcium feedback model can reproduce and explain many fundamental emergent properties of activity in the SAN that have been observed experimentally based on a minimal description of intracellular calcium and ion channel regulatory networks.