Hyperpolarization-activated current, If, in mathematical models of rabbit sinoatrial node pacemaker cells

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.

Bidirectional flow of the funny current (If) during the pacemaking cycle in murine sinoatrial node myocytes

Sinoatrial node myocytes (SAMs) act as cardiac pacemaker cells by firing spontaneous action potentials (APs) that initiate each heartbeat. The funny current (If) is critical for the generation of these spontaneous APs; however, its precise role during the pacemaking cycle remains unresolved. Here, we used the AP-clamp technique to quantify If during the cardiac cycle in mouse SAMs. We found that If is persistently active throughout the sinoatrial AP, with surprisingly little voltage-dependent gating. As a consequence, it carries both inward and outward current around its reversal potential of -30 mV. Despite operating at only 2 to 5% of its maximal conductance, If carries a substantial fraction of both depolarizing and repolarizing net charge movement during the firing cycle. We also show that β-adrenergic receptor stimulation increases the percentage of net depolarizing charge moved by If, consistent with a contribution of If to the fight-or-flight increase in heart rate. These properties were confirmed by heterologously expressed HCN4 channels and by mathematical models of If Modeling further suggested that the slow rates of activation and deactivation of the HCN4 isoform underlie the persistent activity of If during the sinoatrial AP. These results establish a new conceptual framework for the role of If in pacemaking, in which it operates at a very small fraction of maximal activation but nevertheless drives membrane potential oscillations in SAMs by providing substantial driving force in both inward and outward directions.

Isoform-specific regulation of HCN4 channels by a family of endoplasmic reticulum proteins

Ion channels in excitable cells function in macromolecular complexes in which auxiliary proteins modulate the biophysical properties of the pore-forming subunits. Hyperpolarization-activated, cyclic nucleotide-sensitive HCN4 channels are critical determinants of membrane excitability in cells throughout the body, including thalamocortical neurons and cardiac pacemaker cells. We previously showed that the properties of HCN4 channels differ dramatically in different cell types, possibly due to the endogenous expression of auxiliary proteins. Here, we report the discovery of a family of endoplasmic reticulum (ER) transmembrane proteins that associate with and modulate HCN4. Lymphoid-restricted membrane protein (LRMP, Jaw1) and inositol trisphosphate receptor-associated guanylate kinase substrate (IRAG, Mrvi1, and Jaw1L) are homologous proteins with small ER luminal domains and large cytoplasmic domains. Despite their homology, LRMP and IRAG have distinct effects on HCN4. LRMP is a loss-of-function modulator that inhibits the canonical depolarizing shift in the voltage dependence of HCN4 in response to the binding of cAMP. In contrast, IRAG causes a gain of HCN4 function by depolarizing the basal voltage dependence in the absence of cAMP. The mechanisms of action of LRMP and IRAG are independent of trafficking and cAMP binding, and they are specific to the HCN4 isoform. We also found that IRAG is highly expressed in the mouse sinoatrial node where computer modeling predicts that its presence increases HCN4 current. Our results suggest important roles for LRMP and IRAG in the regulation of cellular excitability, as tools for advancing mechanistic understanding of HCN4 channel function, and as possible scaffolds for coordination of signaling pathways.

Calibration of ionic and cellular cardiac electrophysiology models

Cardiac electrophysiology models are among the most mature and well-studied mathematical models of biological systems. This maturity is bringing new challenges as models are being used increasingly to make quantitative rather than qualitative predictions. As such, calibrating the parameters within ion current and action potential (AP) models to experimental data sets is a crucial step in constructing a predictive model. This review highlights some of the fundamental concepts in cardiac model calibration and is intended to be readily understood by computational and mathematical modelers working in other fields of biology. We discuss the classic and latest approaches to calibration in the electrophysiology field, at both the ion channel and cellular AP scales. We end with a discussion of the many challenges that work to date has raised and the need for reproducible descriptions of the calibration process to enable models to be recalibrated to new data sets and built upon for new studies. This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease Models of Systems Properties and Processes > Cellular Models.

Cardiac Pacemaker Activity and Aging

A progressive decline in maximum heart rate (mHR) is a fundamental aspect of aging in humans and other mammals. This decrease in mHR is independent of gender, fitness, and lifestyle, affecting in equal measure women and men, athletes and couch potatoes, spinach eaters and fast food enthusiasts. Importantly, the decline in mHR is the major determinant of the age-dependent decline in aerobic capacity that ultimately limits functional independence for many older individuals. The gradual reduction in mHR with age reflects a slowing of the intrinsic pacemaker activity of the sinoatrial node of the heart, which results from electrical remodeling of individual pacemaker cells along with structural remodeling and a blunted β-adrenergic response. In this review, we summarize current evidence about the tissue, cellular, and molecular mechanisms that underlie the reduction in pacemaker activity with age and highlight key areas for future work.

A computational model of induced pluripotent stem-cell derived cardiomyocytes incorporating experimental variability from multiple data sources

Key points

Induced pluripotent stem cell‐derived cardiomyocytes (iPSC‐CMs) capture patient‐specific genotype–phenotype relationships, as well as cell‐to‐cell variability of cardiac electrical activity

Computational modelling and simulation provide a high throughput approach to reconcile multiple datasets describing physiological variability, and also identify vulnerable parameter regimes

We have developed a whole‐cell model of iPSC‐CMs, composed of single exponential voltage‐dependent gating variable rate constants, parameterized to fit experimental iPSC‐CM outputs

We have utilized experimental data across multiple laboratories to model experimental variability and investigate subcellular phenotypic mechanisms in iPSC‐CMs

This framework links molecular mechanisms to cellular‐level outputs by revealing unique subsets of model parameters linked to known iPSC‐CM phenotypes

Abstract

There is a profound need to develop a strategy for predicting patient‐to‐patient vulnerability in the emergence of cardiac arrhythmia. A promising in vitro method to address patient‐specific proclivity to cardiac disease utilizes induced pluripotent stem cell‐derived cardiomyocytes (iPSC‐CMs). A major strength of this approach is that iPSC‐CMs contain donor genetic information and therefore capture patient‐specific genotype–phenotype relationships. A cited detriment of iPSC‐CMs is the cell‐to‐cell variability observed in electrical activity. We postulated, however, that cell‐to‐cell variability may constitute a strength when appropriately utilized in a computational framework to build cell populations that can be employed to identify phenotypic mechanisms and pinpoint key sensitive parameters. Thus, we have exploited variation in experimental data across multiple laboratories to develop a computational framework for investigating subcellular phenotypic mechanisms. We have developed a whole‐cell model of iPSC‐CMs composed of simple model components comprising ion channel models with single exponential voltage‐dependent gating variable rate constants, parameterized to fit experimental iPSC‐CM data for all major ionic currents. By optimizing ionic current model parameters to multiple experimental datasets, we incorporate experimentally‐observed variability in the ionic currents. The resulting population of cellular models predicts robust inter‐subject variability in iPSC‐CMs. This approach links molecular mechanisms to known cellular‐level iPSC‐CM phenotypes, as shown by comparing immature and mature subpopulations of models to analyse the contributing factors underlying each phenotype. In the future, the presented models can be readily expanded to include genetic mutations and pharmacological interventions for studying the mechanisms of rare events, such as arrhythmia triggers.

Induced pluripotent stem cell‐derived cardiomyocytes (iPSC‐CMs) capture patient‐specific genotype–phenotype relationships, as well as cell‐to‐cell variability of cardiac electrical activity

Computational modelling and simulation provide a high throughput approach to reconcile multiple datasets describing physiological variability, and also identify vulnerable parameter regimes

We have developed a whole‐cell model of iPSC‐CMs, composed of single exponential voltage‐dependent gating variable rate constants, parameterized to fit experimental iPSC‐CM outputs

We have utilized experimental data across multiple laboratories to model experimental variability and investigate subcellular phenotypic mechanisms in iPSC‐CMs

This framework links molecular mechanisms to cellular‐level outputs by revealing unique subsets of model parameters linked to known iPSC‐CM phenotypes

Tachycardia-bradycardia syndrome: Electrophysiological mechanisms and future therapeutic approaches (Review)

Sick sinus syndrome (SSS) encompasses a group of disorders whereby the heart is unable to perform its pacemaker function, due to genetic and acquired causes. Tachycardia‑bradycardia syndrome (TBS) is a complication of SSS characterized by alternating tachycardia and bradycardia. Techniques such as genetic screening and molecular diagnostics together with the use of pre-clinical models have elucidated the electrophysiological mechanisms of this condition. Dysfunction of ion channels responsible for initiation or conduction of cardiac action potentials may underlie both bradycardia and tachycardia; bradycardia can also increase the risk of tachycardia, and vice versa. The mainstay treatment option for SSS is pacemaker implantation, an effective approach, but has disadvantages such as infection, limited battery life, dislodgement of leads and catheters to be permanently implanted in situ. Alternatives to electronic pacemakers are gene‑based bio‑artificial sinoatrial node and cell‑based bio‑artificial pacemakers, which are promising techniques whose long-term safety and efficacy need to be established. The aim of this article is to review the different ion channels involved in TBS, examine the three‑way relationship between ion channel dysfunction, tachycardia and bradycardia in TBS and to consider its current and future therapies.

Potassium currents in the heart: functional roles in repolarization, arrhythmia and therapeutics

This is the second of the two White Papers from the fourth UC Davis Cardiovascular Symposium Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias (3-4 March 2016), a biennial event that brings together leading experts in different fields of cardiovascular research. The theme of the 2016 symposium was 'K⁺ channels and regulation', and the objectives of the conference were severalfold: (1) to identify current knowledge gaps; (2) to understand what may go wrong in the diseased heart and why; (3) to identify possible novel therapeutic targets; and (4) to further the development of systems biology approaches to decipher the molecular mechanisms and treatment of cardiac arrhythmias. The sessions of the Symposium focusing on the functional roles of the cardiac K⁺ channel in health and disease, as well as K⁺ channels as therapeutic targets, were contributed by Ye Chen-Izu, Gideon Koren, James Weiss, David Paterson, David Christini, Dobromir Dobrev, Jordi Heijman, Thomas O'Hara, Crystal Ripplinger, Zhilin Qu, Jamie Vandenberg, Colleen Clancy, Isabelle Deschenes, Leighton Izu, Tamas Banyasz, Andras Varro, Heike Wulff, Eleonora Grandi, Michael Sanguinetti, Donald Bers, Jeanne Nerbonne and Nipavan Chiamvimonvat as speakers and panel discussants. This article summarizes state-of-the-art knowledge and controversies on the functional roles of cardiac K⁺ channels in normal and diseased heart. We endeavour to integrate current knowledge at multiple scales, from the single cell to the whole organ levels, and from both experimental and computational studies.

The Autonomic Nervous System Regulates the Heart Rate through cAMP-PKA Dependent and Independent Coupled-Clock Pacemaker Cell Mechanisms

Sinoatrial nodal cells (SANCs) generate spontaneous action potentials (APs) that control the cardiac rate. The brain modulates SANC automaticity, via the autonomic nervous system, by stimulating membrane receptors that activate (adrenergic) or inactivate (cholinergic) adenylyl cyclase (AC). However, these opposing afferents are not simply additive. We showed that activation of adrenergic signaling increases AC-cAMP/PKA signaling, which mediates the increase in the SANC AP firing rate (i.e., positive chronotropic modulation). However, there is a limited understanding of the underlying internal pacemaker mechanisms involved in the crosstalk between cholinergic receptors and the decrease in the SANC AP firing rate (i.e., negative chronotropic modulation). We hypothesize that changes in AC-cAMP/PKA activity are crucial for mediating either decrease or increase in the AP firing rate and that the change in rate is due to both internal and membrane mechanisms. In cultured adult rabbit pacemaker cells infected with an adenovirus expressing the FRET sensor AKAR3, PKA activity and AP firing rate were tightly linked in response to either adrenergic receptor stimulation (by isoproterenol, ISO) or cholinergic stimulation (by carbachol, CCh). To identify the main molecular targets that mediate between PKA signaling and pacemaker function, we developed a mechanistic computational model. The model includes a description of autonomic-nervous receptors, post- translation signaling cascades, membrane molecules, and internal pacemaker mechanisms. Yielding results similar to those of the experiments, the model simulations faithfully reproduce the changes in AP firing rate in response to CCh or ISO or a combination of both (i.e., accentuated antagonism). Eliminating AC-cAMP-PKA signaling abolished the core effect of autonomic receptor stimulation on the AP firing rate. Specifically, disabling the phospholamban modulation of the SERCA activity resulted in a significantly reduced effect of CCh and a failure to increase the AP firing rate under ISO stimulation. Directly activating internal pacemaker mechanisms led to a similar extent of changes in the AP firing rate with respect to brain receptor stimulation. Thus, Ca²⁺ and cAMP/PKA-dependent phosphorylation limits the rate and magnitude of chronotropic changes in the spontaneous AP firing rate.

Pacemaker Created in Human Ventricle by Depressing Inward-Rectifier K⁺ Current: A Simulation Study

Cardiac conduction disorders are common diseases which cause slow heart rate and syncope. The best way to treat these diseases by now is to implant electronic pacemakers, which, yet, have many disadvantages, such as the limited battery life and infection. Biopacemaker has been expected to replace the electronic devices. Automatic ventricular myocytes (VMs) could show pacemaker activity, which was induced by depressing inward-rectifier K⁺ current (I_K1). In this study, a 2D model of human biopacemaker was created from the ventricular endocardial myocytes. We examined the stability of the created biopacemaker and investigated its driving capability by finding the suitable size and spatial distribution of the pacemaker for robust pacing and driving the surrounding quiescent cardiomyocytes. Our results suggest that the rhythm of the pacemaker is similar to that of the single cell at final stable state. The driving force of the biopacemaker is closely related to the pattern of spatial distribution of the pacemaker.

Dynamics of PKA phosphorylation and gain of function in cardiac pacemaker cells: a computational model analysis

Cardiac pacemaker cell function is regulated by a coupled-clock system that integrates molecular cues on the cell-membrane surface (i.e., membrane clock) and on the sarcoplasmic reticulum (SR) (i.e., Ca(2+) clock). A recent study has shown that cotransfection of spontaneous beating cells (HEK293 cells and neonatal rat myocytes) with R524Q-mutant human hyperpolarization-activated cyclic nucleotide-gated molecules (the dominant component of funny channels) increases the funny channel's sensitivity to cAMP and leads to a decrease in spontaneous action potential (AP) cycle length (i.e., tachycardia). We hypothesize that in rabbit pacemaker cells, the same behavior is expected, and because of the coupled-clock system, the resultant steady-state decrease in AP cycle length will embody contributions from both clocks: the initial decrease in the spontaneous AP beating interval, arising from increased sensitivity of the f-channel to cAMP, will be accompanied by an increase in the adenylyl cyclase (AC)-cAMP-PKA-dependent phosphorylation activity, which will further decrease this interval. To test our hypothesis, we used the recently developed Yaniv-Lakatta pacemaker cell numerical model. This model predicts the cAMP signaling dynamics, as well as the kinetics and magnitude of protein phosphorylation in both normal and mutant pacemaker cells. We found that R524Q-mutant pacemaker cells have a shorter AP firing rate than that of wild-type cells and that gain in pacemaker function is the net effect of the R514Q mutation on the functioning of the coupled-clock system. Specifically, our results directly support the hypothesis that changes in Ca(2+)-activated AC-cAMP-PKA signaling are involved in the development of tachycardia in R524Q-mutant pacemaker cells.

Cell-specific Dynamic Clamp analysis of the role of funny If current in cardiac pacemaking

We used the Dynamic Clamp technique for i) comparative validation of conflicting computational models of the hyperpolarization-activated funny current, If, and ii) quantification of the role of If in mediating autonomic modulation of heart rate. Experimental protocols based on the injection of a real-time recalculated synthetic If current in sinoatrial rabbit cells were developed. Preliminary results of experiments mimicking the autonomic modulation of If demonstrated the need for a customization procedure to compensate for cellular heterogeneity. For this reason, we used a cell-specific approach, scaling the maximal conductance of the injected current based on the cell's spontaneous firing rate. The pacemaking rate, which was significantly reduced after application of Ivabradine, was restored by the injection of synthetic current based on the Severi-DiFrancesco formulation, while the injection of synthetic current based on the Maltsev-Lakatta formulation did not produce any significant variation. A positive virtual shift of the If activation curve, mimicking the Isoprenaline effects, led to a significant increase in pacemaking rate (+17.3 ± 6.7%, p < 0.01), although of lower magnitude than that induced by real Isoprenaline (+45.0 ± 26.1%). Similarly, a negative virtual shift of the activation curve significantly lowered the pacemaking rate (-11.8 ± 1.9%, p < 0.001), as did the application of real Acetylcholine (-20.5 ± 5.1%). The Dynamic Clamp approach, applied to the If study in cardiomyocytes for the first time and rate-adapted to manage intercellular variability, indicated that: i) the quantitative description of the If current in the Severi-DiFrancesco model accurately reproduces the effects of the real current on rabbit sinoatrial cell pacemaking rate and ii) a significant portion (50-60%) of the physiological autonomic rate modulation is due to the shift of the If activation curve.

The importance of Ca(2+)-dependent mechanisms for the initiation of the heartbeat

Mechanisms underlying pacemaker activity in the sinus node remain controversial, with some ascribing a dominant role to timing events in the surface membrane (“membrane clock”) and others to uptake and release of calcium from the sarcoplasmic reticulum (SR) (“calcium clock”). Here we discuss recent evidence on mechanisms underlying pacemaker activity with a particular emphasis on the many roles of calcium. There are particular areas of controversy concerning the contribution of calcium spark-like events and the importance of I(f) to spontaneous diastolic depolarisation, though it will be suggested that neither of these is essential for pacemaking. Sodium-calcium exchange (NCX) is most often considered in the context of mediating membrane depolarisation after spark-like events. We present evidence for a broader role of this electrogenic exchanger which need not always depend upon these spark-like events. Short (milliseconds or seconds) and long (minutes) term influences of calcium are discussed including direct regulation of ion channels and NCX, and control of the activity of calcium-dependent enzymes (including CaMKII, AC1, and AC8). The balance between the many contributory factors to pacemaker activity may well alter with experimental and clinical conditions, and potentially redundant mechanisms are desirable to ensure the regular spontaneous heart rate that is essential for life. This review presents evidence that calcium is central to the normal control of pacemaking across a range of temporal scales and seeks to broaden the accepted description of the “calcium clock” to cover these important influences.

Effects of maximal sodium and potassium conductance on the stability of Hodgkin-Huxley model

Hodgkin-Huxley (HH) equation is the first cell computing model in the world and pioneered the use of model to study electrophysiological problems. The model consists of four differential equations which are based on the experimental data of ion channels. Maximal conductance is an important characteristic of different channels. In this study, mathematical method is used to investigate the importance of maximal sodium conductance g-Na and maximal potassium conductance g-K. Applying stability theory, and taking g-Na and g-K as variables, we analyze the stability and bifurcations of the model. Bifurcations are found when the variables change, and bifurcation points and boundary are also calculated. There is only one bifurcation point when g-Na is the variable, while there are two points when g-K is variable. The (g-Na,  g-K) plane is partitioned into two regions and the upper bifurcation boundary is similar to a line when both g-Na and g-K are variables. Numerical simulations illustrate the validity of the analysis. The results obtained could be helpful in studying relevant diseases caused by maximal conductance anomaly.

Modern perspectives on numerical modeling of cardiac pacemaker cell

Cardiac pacemaking is a complex phenomenon that is still not completely understood. Together with experimental studies, numerical modeling has been traditionally used to acquire mechanistic insights in this research area. This review summarizes the present state of numerical modeling of the cardiac pacemaker, including approaches to resolve present paradoxes and controversies. Specifically we discuss the requirement for realistic modeling to consider symmetrical importance of both intracellular and cell membrane processes (within a recent "coupled-clock" theory). Promising future developments of the complex pacemaker system models include the introduction of local calcium control, mitochondria function, and biochemical regulation of protein phosphorylation and cAMP production. Modern numerical and theoretical methods such as multi-parameter sensitivity analyses within extended populations of models and bifurcation analyses are also important for the definition of the most realistic parameters that describe a robust, yet simultaneously flexible operation of the coupled-clock pacemaker cell system. The systems approach to exploring cardiac pacemaker function will guide development of new therapies such as biological pacemakers for treating insufficient cardiac pacemaker function that becomes especially prevalent with advancing age.

I(f) blocking potency of ivabradine is preserved under elevated endotoxin levels in human atrial myocytes

Lower heart rate is associated with better survival in patients with multiple organ dysfunction syndrome (MODS), a disease mostly caused by sepsis. The benefits of heart rate reduction by ivabradine during MODS are currently being investigated in the MODI_fY clinical trial. Ivabradine is a selective inhibitor of the pacemaker current I_f and since I_f is impaired by lipopolysaccharide (LPS, endotoxin), a trigger of sepsis, we aimed to explore I_f blocking potency of ivabradine under elevated endotoxin levels in human atrial cardiomyocytes. Treatment of myocytes with S-LPS (containing the lipid A moiety, a core oligosaccharide and an O-polysaccharide chain) but not R595 (an O-chain lacking LPS-form) caused I_f inhibition under acute and chronic septic conditions. The specific interaction of S-LPS but not R595 to pacemaker channels HCN2 and HCN4 proves the necessity of O-chain for S-LPS–HCN interaction. The efficacy of ivabradine to block I_f was reduced under septic conditions, an observation that correlated with lower intracellular ivabradine concentrations in S-LPS- but not R595-treated cardiomyocytes. Computational analysis using a sinoatrial pacemaker cell model revealed that despite a reduction of I_f under septic conditions, ivabradine further decelerated pacemaking activity. This novel finding, i.e. I_f inhibition by ivabradine under elevated endotoxin levels in vitro, may provide a molecular understanding for the efficacy of this drug on heart rate reduction under septic conditions in vivo, e.g. the MODI_fY clinical trial.

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S-LPS impairs I_f via interaction of its O-chain to HCN channels.

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Efficacy of ivabradine for I_f blockage is reduced under elevated endotoxin levels.

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S-LPS reduces intracellular ivabradine concentrations.

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Ivabradine is efficient to decelerate sinoatrial pacemaking activity under septic conditions in silico.