Cycle length restitution in sinoatrial node cells: a theory for understanding spontaneous action potential dynamics

Intracellular ion accumulation in the genesis of complex action potential dynamics under cardiac diseases

Intracellular ions, including sodium (Na^{+}), calcium (Ca^{2+}), and potassium (K^{+}), etc., accumulate slowly after a change of the state of the heart, such as a change of the heart rate. The goal of this study is to understand the roles of slow ion accumulation in the genesis of cardiac memory and complex action-potential duration (APD) dynamics that can lead to lethal cardiac arrhythmias. We carry out numerical simulations of a detailed action potential model of ventricular myocytes under normal and diseased conditions, which exhibit memory effects and complex APD dynamics. We develop a low-dimensional iterated map (IM) model to describe the dynamics of Na^{+}, Ca^{2+}, and APD and use it to uncover the underlying dynamical mechanisms. The development of the IM model is informed by simulation results under the normal condition. We then use the IM model to perform linear stability analyses and computer simulations to investigate the bifurcations and complex APD dynamics, which depend on the feedback loops between APD and intracellular Ca^{2+} and Na^{+} concentrations and the steepness of the APD response to the ion concentrations. When the feedback between APD and Ca^{2+} concentration is positive, a Hopf bifurcation leading to periodic oscillatory behavior occurs as the steepness of the APD response to the ion concentrations increases. The negative feedback loop between APD and Na^{+} concentration is required for the Hopf bifurcation. When the feedback between APD and Ca^{2+} concentration is negative, period-doubling bifurcations leading to high periodicity and chaos occurs. In this case, Na^{+} accumulation plays little role in the dynamics. Finally, we carry out simulations of the detailed action potential model under two diseased conditions, which exhibit steep APD responses to ion concentrations. Under both conditions, Hopf bifurcations leading to slow oscillations or period-doubling bifurcations leading to high periodicity and chaotic APD dynamics occur, depending on the strength of the ion pump-Na^{+}-Ca^{2+} exchanger. Using functions reconstructed from the simulation data, the IM model accurately captures the bifurcations and dynamics under the two diseased conditions. In conclusion, besides using computer simulations of a detailed high-dimensional action-potential model to investigate the effects of slow ion accumulation and short-term memory on bifurcations and genesis of complex APD dynamics in cardiac myocytes under diseased conditions, this study also provides a low-dimensional mathematical tool, i.e., the IM model, to allow stability analyses for uncovering the underlying mechanisms.

The virtual sinoatrial node: What did computational models tell us about cardiac pacemaking?

Since its discovery, the sinoatrial node (SAN) has represented a fascinating and complex matter of research. Despite over a century of discoveries, a full comprehension of pacemaking has still to be achieved. Experiments often produced conflicting evidence that was used either in support or against alternative theories, originating intense debates. In this context, mathematical descriptions of the phenomena underlying the heartbeat have grown in importance in the last decades since they helped in gaining insights where experimental evaluation could not reach. This review presents the most updated SAN computational models and discusses their contribution to our understanding of cardiac pacemaking. Electrophysiological, structural and pathological aspects - as well as the autonomic control over the SAN - are taken into consideration to reach a holistic view of SAN activity.

Functional Heterogeneity of Cell Populations Increases Robustness of Pacemaker Function in a Numerical Model of the Sinoatrial Node Tissue

Each heartbeat is initiated by specialized pacemaker cells operating within the sinoatrial node (SAN). While individual cells within SAN tissue exhibit substantial heterogeneity of their electrophysiological parameters and Ca cycling, the role of this heterogeneity for cardiac pacemaker function remains mainly unknown. Here we investigated the problem numerically in a 25 × 25 square grid of connected coupled-clock Maltsev-Lakatta cell models. The tissue models were populated by cells with different degree of heterogeneity of the two key model parameters, maximum L-type Ca current conductance (g_CaL) and sarcoplasmic reticulum Ca pumping rate (P_up). Our simulations showed that in the areas of P_up-g_CaL parametric space at the edge of the system stability, where action potential (AP) firing is absent or dysrhythmic in SAN tissue models populated with identical cells, rhythmic AP firing can be rescued by populating the tissues with heterogeneous cells. This robust SAN function is synergistic with respect to heterogeneity in g_CaL and P_up and can be further strengthened by clustering of cells with similar properties. The effect of cell heterogeneity is not due to a simple summation of activity of intrinsically firing cells naturally present in heterogeneous SAN; rather AP firing cells locally and critically interact with non-firing/dormant cells. When firing cells prevail, they recruit many dormant cells to fire, strongly enhancing overall SAN function; and vice versa, prevailing dormant cells suppress AP firing in cells with intrinsic automaticity and halt SAN function. The transitions between firing and non-firing states of the system are sharp, resembling phase transitions in statistical physics. Furthermore, robust function of heterogeneous SAN tissue requires weak cell coupling, a known property of the central area of SAN where cardiac impulse emerges; stronger cell coupling reduces AP firing rate and ultimately halts SAN automaticity at the edge of stability.

Pacemaking function of two simplified cell models

Simplified nonlinear models of biological cells are widely used in computational electrophysiology. The models reproduce qualitatively many of the characteristics of various organs, such as the heart, brain, and intestine. In contrast to complex cellular ion-channel models, the simplified models usually contain a small number of variables and parameters, which facilitates nonlinear analysis and reduces computational load. In this paper, we consider pacemaking variants of the Aliev-Panfilov and Corrado two-variable excitable cell models. We conducted a numerical simulation study of these models and investigated the main nonlinear dynamic features of both isolated cells and 1D coupled pacemaker-excitable systems. Simulations of the 2D sinoatrial node and 3D intestine tissue as application examples of combined pacemaker-excitable systems demonstrated results similar to obtained previously. The uniform formulation for the conventional excitable cell models and proposed pacemaker models allows a convenient and easy implementation for the construction of personalized physiological models, inverse tissue modeling, and development of real-time simulation systems for various organs that contain both pacemaker and excitable cells.

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

The heartbeat is initiated by pacemaker cells residing in the sinoatrial node (SAN). SAN cells generate spontaneous action potentials (APs), i.e., normal automaticity. The sympathetic nervous system increases the heart rate commensurate with the cardiac output demand via stimulation of SAN β-adrenergic receptors (βAR). While SAN cells reportedly represent a highly heterogeneous cell population, the current dogma is that, in response to βAR stimulation, all cells increase their spontaneous AP firing rate in a similar fashion. The aim of the present study was to investigate the cell-to-cell variability in the responses of a large population of SAN cells. We measured the βAR responses among 166 single SAN cells isolated from 33 guinea pig hearts. In contrast to the current dogma, the SAN cell responses to βAR stimulation substantially varied. In each cell, changes in the AP cycle length were highly correlated (R2 = 0.97) with the AP cycle length before βAR stimulation. While, as expected, on average, the cells increased their pacemaker rate, greater responses were observed in cells with slower basal rates, and vice versa: cells with higher basal rates showed smaller responses, no responses, or even decreased their rate. Thus, βAR stimulation synchronized the operation of the SAN cell population toward a higher average rate, rather than uniformly shifting the rate in each cell, creating a new paradigm of βAR-driven fight-or-flight responses among individual pacemaker cells.

Adherens junction engagement regulates functional patterning of the cardiac pacemaker cell lineage

Cardiac pacemaker cells (CPCs) rhythmically initiate the electrical impulses that drive heart contraction. CPCs display the highest rate of spontaneous depolarization in the heart despite being subjected to inhibitory electrochemical conditions that should theoretically suppress their activity. While several models have been proposed to explain this apparent paradox, the actual molecular mechanisms that allow CPCs to overcome electrogenic barriers to their function remain poorly understood. Here, we have traced CPC development at single-cell resolution and uncovered a series of cytoarchitectural patterning events that are critical for proper pacemaking. Specifically, our data reveal that CPCs dynamically modulate adherens junction (AJ) engagement to control characteristics including surface area, volume, and gap junctional coupling. This allows CPCs to adopt a structural configuration that supports their overall excitability. Thus, our data have identified a direct role for local cellular mechanics in patterning critical morphological features that are necessary for CPC electrical activity.

Restitution metrics in Brugada syndrome: a systematic review and meta-analysis

BACKGROUND

Brugada syndrome (BrS) is an ion channelopathy that predisposes affected subjects to ventricular tachycardia/fibrillation (VT/VF) and sudden cardiac death. Restitution analysis has been examined in BrS patients but not all studies have reported significant differences between BrS patients and controls. Therefore, we conducted a systematic review and meta-analysis to investigate the different restitution indices used in BrS.

METHODS

PubMed and Embase were searched until April 7, 2019, identifying 20 and 27 studies.

RESULTS

A total of ten studies involving 178 BrS (mean age 38 years old, 63% male) and 102 controls (mean age 31 years old, 42% male) were included in this systematic review. Pacing was carried out at the right ventricular outflow tract (RVOT)/right ventricular apex (RPA) (n = 4), RPA (n = 4), or right atrium (RA) (n = 1). Basic cycle lengths of 400 (n = 4), 500 (n = 2), 600 (n = 6) and 750 ms (n = 1) were used. Recording methods include electrograms (n = 4), monophasic action potentials (n = 5), and electrocardiograms (n = 1). Signals were obtained from the RVOT (n = 8), RVA (n = 3), RA (n = 1), or the body surface (n = 1). The maximum restitution slope for endocardial repolarization at the RVOT was 0.87 for BrS patients (n = 5; 95% confidence interval [CI] 0.68-1.07) compared with 0.74 in control subjects (n = 4; 95% CI 0.42-1.06), with a significant mean difference of 0.40 (n = 4; 95% CI 0.11-0.69; P = 0.007).

CONCLUSIONS

Steeper endocardial repolarization restitution slopes are found in BrS patients compared with controls at baseline. Restitution analysis can provide important information for risk stratification in BrS.

Bifurcations Caused by Feedback between Voltage and Intracellular Ion Concentrations in Ventricular Myocytes

We develop an iterated map model to describe the bifurcations and complex dynamics caused by the feedback between voltage and intracellular Ca^{2+} and Na^{+} concentrations in paced ventricular myocytes. Voltage and Ca^{2+} can form either a positive or a negative feedback loop, while voltage and Na^{+} form a negative feedback loop. Under certain diseased conditions, when the feedback between voltage and Ca^{2+} is positive, Hopf bifurcations occur, leading to periodic oscillatory behaviors. When this feedback is negative, period-doubling bifurcation routes to alternans and chaos occur.

Understanding the Beat-to-Beat Variations of P-Waves Morphologies in AF Patients During Sinus Rhythm: A Scoping Review of the Atrial Simulation Studies

The remarkable advances in high-performance computing and the resulting increase of the computational power have the potential to leverage computational cardiology toward improving our understanding of the pathophysiological mechanisms of arrhythmias, such as Atrial Fibrillation (AF). In AF, a complex interaction between various triggers and the atrial substrate is considered to be the leading cause of AF initiation and perpetuation. In electrocardiography (ECG), P-wave is supposed to reflect atrial depolarization. It has been found that even during sinus rhythm (SR), multiple P-wave morphologies are present in AF patients with a history of AF, suggesting a higher dispersion of the conduction route in this population. In this scoping review, we focused on the mechanisms which modify the electrical substrate of the atria in AF patients, while investigating the existence of computational models that simulate the propagation of the electrical signal through different routes. The adopted review methodology is based on a structured analytical framework which includes the extraction of the keywords based on an initial limited bibliographic search, the extensive literature search and finally the identification of relevant articles based on the reference list of the studies. The leading mechanisms identified were classified according to their scale, spanning from mechanisms in the cell, tissue or organ level, and the produced outputs. The computational modeling approaches for each of the factors that influence the initiation and the perpetuation of AF are presented here to provide a clear overview of the existing literature. Several levels of categorization were adopted while the studies which aim to translate their findings to ECG phenotyping are highlighted. The results denote the availability of multiple models, which are appropriate under specific conditions. However, the consideration of complex scenarios taking into account multiple spatiotemporal scales, personalization of electrophysiological and anatomical models and the reproducibility in terms of ECG phenotyping has only partially been tackled so far.

LongQt: A cardiac electrophysiology simulation platform

Mathematical modeling has been used for over half a century to advance our understanding of cardiac electrophysiology and arrhythmia mechanisms. Notably, computational studies using mathematical models of the cardiac action potential (AP) have provided important insight into the fundamental nature of cell excitability, mechanisms underlying both acquired and inherited arrhythmia, and potential therapies. Ultimately, an approach that tightly integrates mathematical modeling and experimental techniques has great potential to accelerate discovery. Despite the increasing acceptance of mathematical modeling as a powerful tool in cardiac electrophysiology research, there remain significant barriers to its more widespread use in the field, due in part to the increasing complexity of models and growing need for specialization. To help bridge the gap between experimental and theoretical worlds that stands as a barrier to transformational breakthroughs, we present LongQt, which has the following key features:

•

Cross-platform, threaded application with accessible graphical user interface.

•

Facilitates advanced computational cardiac electrophysiology and arrhythmia studies.

•

Does not require advanced programming skills.

Two-Pore K+ Channel TREK-1 Regulates Sinoatrial Node Membrane Excitability

Background

Two‐pore K⁺ channels have emerged as potential targets to selectively regulate cardiac cell membrane excitability; however, lack of specific inhibitors and relevant animal models has impeded the effort to understand the role of 2‐pore K⁺ channels in the heart and their potential as a therapeutic target. The objective of this study was to determine the role of mechanosensitive 2‐pore K⁺ channel family member TREK‐1 in control of cardiac excitability.

Methods and Results

Cardiac‐specific TREK‐1–deficient mice (αMHC‐Kcnk^f/f) were generated and found to have a prevalent sinoatrial phenotype characterized by bradycardia with frequent episodes of sinus pause following stress. Action potential measurements from isolated αMHC‐Kcnk2^f/f sinoatrial node cells demonstrated decreased background K⁺ current and abnormal sinoatrial cell membrane excitability. To identify novel pathways for regulating TREK‐1 activity and sinoatrial node excitability, mice expressing a truncated allele of the TREK‐1–associated cytoskeletal protein β_IV‐spectrin (qv^4J mice) were analyzed and found to display defects in cell electrophysiology as well as loss of normal TREK‐1 membrane localization. Finally, the β_IV‐spectrin/TREK‐1 complex was found to be downregulated in the right atrium from a canine model of sinoatrial node dysfunction and in human cardiac disease.

Conclusions

These findings identify a TREK‐1–dependent pathway essential for normal sinoatrial node cell excitability that serves as a potential target for selectively regulating sinoatrial node cell function.

Role of sinoatrial node architecture in maintaining a balanced source-sink relationship and synchronous cardiac pacemaking

Normal heart rhythm (sinus rhythm) depends on regular activity of the sinoatrial node (SAN), a heterogeneous collection of specialized myocytes in the right atrium. SAN cells, in general, possess a unique electrophysiological profile that promotes spontaneous electrical activity (automaticity). However, while automaticity is required for normal pacemaking, it is not necessarily sufficient. Less appreciated is the importance of the elaborate structure of the SAN complex for proper pacemaker function. Here, we review the important structural features of the SAN with a focus on how these elements help manage a precarious balance between electrical charge generated by the SAN (“source”) and the charge needed to excite the surrounding atrial tissue (“sink”). We also discuss how compromised “source-sink” balance due, for example to fibrosis, may promote SAN dysfunction, characterized by slow and/or asynchronous pacemaker activity and even failure, in the setting of cardiovascular disease (e.g., heart failure, atrial fibrillation). Finally, we discuss implications of the “source-sink” balance in the SAN complex for cell and gene therapies aimed at creating a biological pacemaker as replacement or bridge to conventional electronic pacemakers.