Coupling and synchronization of oscillators in the sinoatrial node

Abstract

The sinoatrial node (SAN) is the primary pacemaker of the heart and its role is to generate the electrical signals that initiate the cardiac contraction. In this study, the frequency synchronization characteristics of the SAN were examined using experimentally validated mathematical models of individual SAN cells from different regions. These models were extended to describe cells as a function of location, and to take into account the constrained external environment of the SAN tissue. The synchronization of the cells was determined both as a function of the time that they were coupled, and as a function of the strength of the coupling. Three main coupling modalities were explored: constant-gap junction conductances which directly connected the cytosols of the neighbouring cells, voltage-dependent gap junction conductances and diffusive coupling due to ionic mixing in the interstitial space between neighbouring cells. The investigations show that only three to five active gap junctions are required for frequency synchronization of cell pairs. The critical coupling conductance, the minimum required for the frequency synchronization of neighbouring coupled cells, was found to linearly increase as a function of the difference between the cycle lengths of the coupled cells. Extending this to one- and two-dimensional networks, the critical coupling conductance was found to be higher than any individual pair within the networks, but still only a small number of active gap junction channels, indicating substantial redundancy in the biological system. Taking the voltage-dependent characteristics of the gap junctions into account, variations were found in the sub-critical synchronization behaviour, indicating that these features have important influences for systems with weak coupling. Diffusive coupling caused oscillations in the extracellular concentrations and cycle lengths of the cells. Alone this was insufficient to cause frequency entrainment between dissimilar neighbours. Combined with gap junction conductances however, the specific influence of the diffusive coupling was clearly visible, altering the critical conductance by up to 65%. This secondary coupling mechanism could be an important modulator of synchronization in the SAN.