A novel conceptual model of heart rate autonomic modulation based on a small-world modular structure of the sinoatrial node

Abstract

The present view on heartbeat initiation is that a primary pacemaker cell or a group of cells in the sinoatrial node (SAN) center paces the rest of the SAN and the atria. However, recent high-resolution imaging studies show a more complex paradigm of SAN function that emerges from heterogeneous signaling, mimicking brain cytoarchitecture and function. Here, we developed and tested a new conceptual numerical model of SAN organized similarly to brain networks featuring a modular structure with small-world topology. In our model, a lower rate module leads action potential (AP) firing in the basal state and during parasympathetic stimulation, whereas a higher rate module leads during β-adrenergic stimulation. Such a system reproduces the respective shift of the leading pacemaker site observed experimentally and a wide range of rate modulation and robust function while conserving energy. Since experimental studies found functional modules at different scales, from a few cells up to the highest scale of the superior and inferior SAN, the SAN appears to feature hierarchical modularity, i.e., within each module, there is a set of sub-modules, like in the brain, exhibiting greater robustness, adaptivity, and evolvability of network function. In this perspective, our model offers a new mainframe for interpreting new data on heterogeneous signaling in the SAN at different scales, providing new insights into cardiac pacemaker function and SAN-related cardiac arrhythmias in aging and disease.

Keywords: autonomic modulation of heart rate; cell heterogeneity; heartbeat; numerical model; pacemaker mechanism; shift of the leading pacemaker site; sinoatrial node; small-world network.

FIGURE 1

Development of the 3D model of SAN tissues with brain-like modular structure and function. (A) An example of the model, which consists of two modules. Nodes in the network designate cells, and the edges imply electrical coupling between the cells: 242 HRM cells (red circles) and 243 LRM cells (blue circles), each connection has the intracellular resistivity ρ = 3,750 MΩ*m. The interactive 3D view of the model is provided in Supplementary Figure S2. (B) Probability distribution of the number of connections between cells in the SAN model in panel (A). (C–E) Results of the parametric sensitivity analysis of βAR and ChR stimulation in individual isolated SAN cells with respect to the basal conductance of I _CaL (g _CaL, x-axis) and sarcoplasmic reticulum Ca pumping rate (P _up, y-axis). The image shows the result of 97 (x)*61 (y) = 5,917 simulations (each pixel = 0.0025 nS/pF * 0.2 mM/s). The fork-like dash lines outline the bifurcation borders between non-firing (blue), firing (gradual red shades), and chaotic firing (mosaic red shades within the lower part of the fork). Red shades code AP firing rates from 0 (black) to 4 Hz (pure red). The HRM and LRM were populated with cells with parameters marked by green and magenta circles, respectively.

FIGURE 2

Performance of our small-world SAN model under different conditions. (A–C) Simulated AP traces in, respectively, the basal state (in the absence of autonomic modulation), in ChR stimulation, and βAR stimulation in each pacemaker module: HRM (orange traces) and LRM (blue traces). The respective leading/pacing rates are shown at the top of each panel. Histograms of the average AP cycle length of each cell in each module under each condition are provided in Supplementary Figure S3.