Synchronization of Pacemaking in the Sinoatrial Node: A Mathematical Modeling Study

Abstract

Computational studies using mathematical models of the sinoatrial node (SAN) cardiac action potential (AP) have provided important insight into the fundamental nature of cell excitability, cardiac arrhythmias, and potential therapies. While the impact of ion channel dynamics on SAN pacemaking has been studied, the governing dynamics responsible for regulating spatial and temporal control of SAN synchrony remain elusive. Here, we attempt to develop methods to explore cohesion in a network of coupled spontaneously active SAN cells. We present the updated version of a previously published graphical user interface LongQt: a cross-platform, threaded application for advanced cardiac electrophysiology studies that does not require advanced programming skills. We incorporated additional features to the existing LongQt platform that allows users to (1) specify heterogeneous gap junction conductivity across a multicellular grid, and (2) set heterogeneous ion channel conductance across a multicellular grid. We developed two methods of characterizing the synchrony of SAN tissue based on alignment of activation in time and similarity of voltage peaks among clusters of functionally related cells. In pairs and two-dimensional grids of coupled cells, we observed a range of conductivities (0.00014-0.00033 1/ -cm) in which the tissue was more susceptible to developing asynchronous spontaneous pro-arrhythmic behavior (e.g., spiral wave formation). We performed parameter sensitivity analysis to determine the relative impact of ion channel conductances on cycle length (CL), diastolic and peak voltage, and synchrony measurements in isolated and coupled cell pairs. We also defined measurements of evaluating synchrony based on peak AP voltage and the rate of wave propagation. Cell-to-cell coupling had a non-linear effect on the relationship between ion channel conductances, AP properties, and synchrony measurements. Our simulations demonstrate that conductivity plays an important role in regulating synchronous firing of heterogeneous SAN tissue, and demonstrate how to evaluate the role of coupling and ion channel conductance in pairs and grids of SAN cells. We anticipate that the approach outlined here will facilitate identification of key cell-and tissue-level factors responsible for cardiac disease.

β-Adrenergic Stimulation Synchronizes a Broad Spectrum of Action Potential Firing Rates of Cardiac Pacemaker Cells toward a Higher Population Average

“…Multicellular numerical models of SAN function have been developed in 1 dimension (as a linear chain of consecutive SAN cells) [49][50][51][52][53][54], in 2 dimensions [55][56][57], and even in 3 dimensions [58]. Those models have provided new insights about the importance of cell interactions; however, they have not tested the importance of dormant cells (with their subthreshold signaling) [10][11][12], cells operating at low rates found in intact SAN [8], and autonomic modulation.…”

Assembly of the Cardiac Pacemaking Complex: Electrogenic Principles of Sinoatrial Node Morphogenesis

“…Furthermore, the influence of the coupled atrial tissue is not typically considered when examining the process of synchronization. As described below, computational treatments of sinoatrial node function are continually adding increased complexity to our view of heterogeneity, including variations in gap junctional conductivities, ion channel conductance [ 45 ], cellular make up [ 46 , 47 ] and cell-to-cell connectivity [ 43 ]. In particular, recent models introduced by Gratz et al, Ly and Weinberg, Mata et al, and Sehgal et al may be able to account for all these features in future analysis of synchronization [ 43 , 45 , 46 , 48 ].…”

β-Adrenergic Stimulation Synchronizes a Broad Spectrum of Action Potential Firing Rates of Cardiac Pacemaker Cells towards a Higher Population Average

“…Testing new ideas and establishing exact mechanisms require new theoretical modeling. Multicellular numerical models of SAN function have been developed in 1 dimension (as a linear chain of consecutive SAN cells) [49][50][51][52][53][54], in 2 dimensions [55][56][57] and even in 3 dimensions [58]. Those models have provided new insights about the importance of cell interactions, but they have not tested importance of dormant cells (with their subthreshold signaling) [10][11][12], cells operating at low rates found in intact SAN [8], and autonomic modulation.…”