Mathematical modelling of the train station of the heart: the atrio-ventricular node

Abstract

In mammals, each normal heart beat requires sequential and directed movement of the electrical triggering event, the action potential (AP), proximal and then distal to the atrioventricular (A-V) node. This is the basis for, and ensures, a one-to-one ratio between activation and contraction of the atria and the ventricles. Equally importantly, the delay produced in part by the relatively slow conduction across the A-V node is essential for providing the time window needed for the ventricles to fill with blood before they contract. Given these essential physiological functions, it is not surprising that this critical ‘station within the heart’ has been studied in detail using anatomical, electrophysiological, molecular and mathematical simulation methods (Markowitz & Lerman, 2018). Nonetheless, key aspects of its functional properties (such as the basis for the delay of the AP just when it leaves the atria and enters the A-V node) and the conduction slowing across the node are not fully understood (Choi et al, 2023). It is well known, however, that these features are fundamental to the altered dynamics of the A-V node in response to changes in heart rate (Billette & Nattel, 1994) as well as in the setting of some supraventricular rhythm disturbances (Markowitz & Lerman, 2018).

A timely and comprehensive paper, aimed at obtaining an improved understanding of A-V node function, is published in this issue of The Journal of Physiology (Bartolucci et al., 2024). It is based on mathematical modelling of a typical myocyte isolated from the A-V node of the adult mouse heart. The authors make use of new experimental data to advance knowledge of the ways in which the constellation of ion channels, transporters and electrogenic pumps that are expressed in these A-V node isolated myocytes act in combination to regulate both (1) their action potential waveform and (2) their latent, or secondary, pacemaker activity. One set of novel findings provide important insights into the ways in which the integral membrane proteins that form the L-type channel complex regulate Ca²⁺ influx. This Ca²⁺ conductance provides much of the depolarizing current that generates the initial regenerative depolarization of the ‘slow response’ APs in these A-V node myocytes. The revised mathematical model also takes semiquantitative account of the intracellular Ca²⁺. Thus, it can be used to guide ongoing research into Ca²⁺-induced Ca²⁺ release in these myocytes as well as Ca²⁺-dependent intercellular coupling and/or Ca²⁺-dependent gene transcription in response to maintained changes in A-V node firing rate. This comprehensive work is made possible by the complementary expertise of the two main collaborating groups. The Mangoni group have well established expertise in the challenging task of isolating and then carrying out detailed electrophysiological studies on these single myocytes. The Severi group complement this based on their ability to objectively analyse these data sets, extract key features that anchor their computational approaches, and then account for the interesting intrinsic variability of ion channel expression in theses single myocytes.

An appreciation for the new findings in this paper leads to speculation concerning how these insights could be leveraged to obtain a more complete understanding of the electrophysiological dynamics in the A-V nodes. Examples include the following.

As noted, the A-V node in all mammalian hearts is a 3-D structure consisting (in the adult mouse heart) of several thousand myocytes that are coupled electrotonically (Spitzer et al., 1997) by very sparse expression of connexins. Bartolucci et al. (2024) focus on the electrophysiological basis for the AP waveform, and some aspects of the latent pacemaker depolarization in a single isolated myocyte. Interestingly, recent publications by the Simula group (Jæger, Trotter et al., 2024; Jæger & Tveito, 2024) have developed a mathematical basis and parallel computing platform that, in principle, could allow this type of single myocyte model to be mapped onto a 2- or 3-D mesh corresponding to the entire adult mouse A-V node. Their approach offers the spatial and temporal resolution that can account for each single myocyte AP, and also calculate the related changes in extracellular potentials.

Bartolucci et al. (2024) provide a comprehensive biophysical basis for rate-induced changes in Na⁺, K⁺ or Ca²⁺ within the single A-V node myocyte. This information could be explored in more detail. A primary reason for this is that the intrinsic properties of the A-V node myocyte (small size and very low current densities) result in this interesting ‘train station within the heart’ functioning as a high resistance current source during the entire time course or duty cycle of each heartbeat. This property has the consequence that even very small changes in net transmembrane current can significantly alter the action potential waveform and/or the maximum diastolic potential and slope of the latent pacemaker depolarization in the A-V node. We note that Bartolucci et al. (2024) have preassigned a relatively high in silico expression density or turnover rate for the electrogenic Na⁺/K⁺ pump. This should be further explored in terms of the contributions of this pump-mediated current to the action potential wave form and to the exact value of the maximum diastolic potential. In neurophysiological systems, coupling of cellular metabolism to electrical activity is important under both physiological and pathophysiological conditions (Howarth et al., 2012).

Improved understanding of the functional role(s) of Ca²⁺ fluxes in the A-V node myocyte motivates additional studies that focus on changes produced by alterations in autonomic tone (Hucker et al., 2007; Markowitz & Lerman, 2018. In addition, adenosine (Wang et al., 1996) is well known in both experimental and clinical settings to result in transient changes in A-V node function. Some of these are due to decreases in the L-type Ca²⁺ current.

The revised mathematical model developed by Bartolucci et al, 2024 could also be applied in an attempt to understand the functional roles of the different types of myocytes that are found in the mammalian A-V node (Inada et al, 2009). This approach may also be able to be extended in attempts to understand the ‘dual pathway’ conduction phenomena with the A-V node (George et al (2017). Finally, the comprehensive work in this paper may provide a basis for re-examining the mechanisms that underlie conduction block that occurs within or very near the A-V node in a variety of cardiovascular diseases (Sabzwari & Tzou, 2023).