Modern perspectives on numerical modeling of cardiac pacemaker cell

Measuring and modeling the effects of vagus nerve stimulation on heart rate and laryngeal muscles

BACKGROUND

Reduced heart rate (HR) during vagus nerve stimulation (VNS) is associated with therapy for heart failure, but stimulation frequency and amplitude are limited by patient tolerance. An understanding of physiological responses to parameter adjustments would allow differential control of therapeutic and side effects. To investigate selective modulation of the physiological responses to VNS, we quantified the effects and interactions of parameter selection on two physiological outcomes: one related to therapy (reduced HR) and one related to side effects (laryngeal muscle EMG).

METHODS

We applied a broad range of stimulation parameters (mean pulse rates (MPR), intra-burst frequencies, and amplitudes) to the vagus nerve of anesthetized mice. We leveraged the in vivo recordings to parameterize and validate computational models of HR and laryngeal muscle activity across amplitudes and temporal patterns of VNS. We constructed a finite element model of excitation of fibers within the mouse cervical vagus nerve.

RESULTS

HR decreased with increased amplitude, increased MPR, and decreased intra-burst frequency. EMG increased with increased MPR. Preferential HR effects over laryngeal EMG effects required combined adjustments of amplitude and MPR. The model of HR responses highlighted contributions of ganglionic filtering to VNS-evoked changes in HR at high stimulation frequencies. Overlap in activation thresholds between small and large modeled fibers was consistent with the overlap in dynamic ranges of related physiological measures (HR and EMG).

CONCLUSION

The present study provides insights into physiological responses to VNS required for informed parameter adjustment to modulate selectively therapeutic effects and side effects.

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.

Coupling and heterogeneity modulate pacemaking capability in healthy and diseased two-dimensional sinoatrial node tissue models

Both experimental and modeling studies have attempted to determine mechanisms by which a small anatomical region, such as the sinoatrial node (SAN), can robustly drive electrical activity in the human heart. However, despite many advances from prior research, important questions remain unanswered. This study aimed to investigate, through mathematical modeling, the roles of intercellular coupling and cellular heterogeneity in synchronization and pacemaking within the healthy and diseased SAN. In a multicellular computational model of a monolayer of either human or rabbit SAN cells, simulations revealed that heterogenous cells synchronize their discharge frequency into a unique beating rhythm across a wide range of heterogeneity and intercellular coupling values. However, an unanticipated behavior appeared under pathological conditions where perturbation of ionic currents led to reduced excitability. Under these conditions, an intermediate range of intercellular coupling (900-4000 MΩ) was beneficial to SAN automaticity, enabling a very small portion of tissue (3.4%) to drive propagation, with propagation failure occurring at both lower and higher resistances. This protective effect of intercellular coupling and heterogeneity, seen in both human and rabbit tissues, highlights the remarkable resilience of the SAN. Overall, the model presented in this work allowed insight into how spontaneous beating of the SAN tissue may be preserved in the face of perturbations that can cause individual cells to lose automaticity. The simulations suggest that certain degrees of gap junctional coupling protect the SAN from ionic perturbations that can be caused by drugs or mutations.

Disorder in Ca2+ release unit locations confers robustness but cuts flexibility of heart pacemaking

Excitation-contraction coupling kinetics is dictated by the action potential rate of sinoatrial-nodal cells. These cells generate local Ca releases (LCRs) that activate Na/Ca exchanger current, which accelerates diastolic depolarization and determines the pace. LCRs are generated by clusters of ryanodine receptors, Ca release units (CRUs), residing in the sarcoplasmic reticulum. While CRU distribution exhibits substantial heterogeneity, its functional importance remains unknown. Using numerical modeling, here we show that with a square lattice distribution of CRUs, Ca-induced-Ca-release propagation during diastolic depolarization is insufficient for pacemaking within a broad range of realistic ICaL densities. Allowing each CRU to deviate randomly from its lattice position allows sparks to propagate, as observed experimentally. As disorder increases, the CRU distribution exhibits larger empty spaces and simultaneously CRU clusters, as in Poisson clumping. Propagating within the clusters, Ca release becomes synchronized, increasing action potential rate and reviving pacemaker function of dormant/nonfiring cells. However, cells with fully disordered CRU positions could not reach low firing rates and their β-adrenergic-receptor stimulation effect was substantially decreased. Inclusion of Cav1.3, a low-voltage activation L-type Ca channel isoform into ICaL, strongly increases recruitment of CRUs to fire during diastolic depolarization, increasing robustness of pacemaking and complementing effects of CRU distribution. Thus, order/disorder in CRU locations along with Cav1.3 expression regulates pacemaker function via synchronization of CRU firing. Excessive CRU disorder and/or overexpression of Cav1.3 boosts pacemaker function in the basal state, but limits the rate range, which may contribute to heart rate range decline with age and disease.

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.

Impact of mitochondria on local calcium release in murine sinoatrial nodal cells

Roles of mitochondria in sinoatrial nodal cells (SANCs) have not been fully clarified. We have previously demonstrated that mitochondrial Ca²⁺ efflux through the Na⁺-Ca²⁺ exchanger, NCXm, modulates sarcoplasmic reticulum (SR) Ca²⁺ content and automaticity of HL-1 cardiomyocytes. In this study, we extended this line of investigation to clarify the spatial and functional association between mitochondria and local calcium release (LCR) from the SR in murine SANCs. High-speed two dimensional (2D) and confocal line-scan imaging of SANCs revealed that LCRs in the early phase of the Ca²⁺ transient cycle length (CL) appeared with a higher probability near mitochondria. Although LCR increased toward the late phase of CL, no significant difference was noted in the occurrence of late LCRs near and distant from mitochondria. LCRs, especially in the late phase of CL, induced temporal and spatial heterogeneity of the Ca²⁺ transient amplitude. Attenuating mitochondrial Ca²⁺ efflux using an NCXm inhibitor, CGP-37157 (1 μM), reduced the amplitude, duration and size of LCR. It also attenuated early LCR occurrence, and simultaneously prolonged LCR period and CL. Additionally, CGP-37157 reduced caffeine-induced Ca²⁺ transient. Therefore, the inhibitory effect on LCR was attributable to the reduction of the SR Ca²⁺ content through NCXm inhibition. No obvious off-target effects of 1 μM CGP-37157 were found on T- and L-type voltage-gated Ca²⁺ currents and hyperpolarization-activated inward current. Taken together, these results suggest that mitochondria are involved in LCR generation by modulating the SR Ca²⁺ content through NCXm-mediated Ca²⁺ efflux in murine SANCs.

The Cardiac Pacemaker Story-Fundamental Role of the Na+/Ca2+ Exchanger in Spontaneous Automaticity

The electrophysiological mechanism of the sinus node automaticity was previously considered exclusively regulated by the so-called "funny current". However, parallel investigations increasingly emphasized the importance of the Ca²⁺-homeostasis and Na⁺/Ca²⁺ exchanger (NCX). Recently, increasing experimental evidence, as well as insight through mechanistic in silico modeling demonstrates the crucial role of the exchanger in sinus node pacemaking. NCX had a key role in the exciting story of discovery of sinus node pacemaking mechanisms, which recently settled with a consensus on the coupled-clock mechanism after decades of debate. This review focuses on the role of the Na⁺/Ca²⁺ exchanger from the early results and concepts to recent advances and attempts to give a balanced summary of the characteristics of the local, spontaneous, and rhythmic Ca²⁺ releases, the molecular control of the NCX and its role in the fight-or-flight response. Transgenic animal models and pharmacological manipulation of intracellular Ca²⁺ concentration and/or NCX demonstrate the pivotal function of the exchanger in sinus node automaticity. We also highlight where specific hypotheses regarding NCX function have been derived from computational modeling and require experimental validation. Nonselectivity of NCX inhibitors and the complex interplay of processes involved in Ca²⁺ handling render the design and interpretation of these experiments challenging.

A physiology based model of heart rate variability

Heart rate variability (HRV) is governed by the autonomic nervous system (ANS) and is routinely used to estimate the state of body and mind. At the same time, recorded HRV features can vary substantially between people. A model for HRV that (1) correctly simulates observed HRV, (2) reliably functions for multiple scenarios, and (3) can be personalised using a manageable set of parameters, would be a significant step forward toward understanding individual responses to external influences, such as physical and physiological stress. Current HRV models attempt to reproduce HRV characteristics by mimicking the statistical properties of measured HRV signals. The model presented here for the simulation of HRV follows a radically different approach, as it is based on an approximation of the physiology behind the triggering of a heart beat and the biophysics mechanisms of how the triggering process-and thereby the HRV-is governed by the ANS. The model takes into account the metabolisation rates of neurotransmitters and the change in membrane potential depending on transmitter and ion concentrations. It produces an HRV time series that not only exhibits the features observed in real data, but also explains a reduction of low frequency band-power for physically or psychologically high intensity scenarios. Furthermore, the proposed model enables the personalisation of input parameters to the physiology of different people, a unique feature not present in existing methods. All these aspects are crucial for the understanding and application of future wearable health.

Positive Feedback Mechanisms among Local Ca Releases, NCX, and ICaL Ignite Pacemaker Action Potentials

Recent data suggest that cardiac pacemaker cell function is determined by numerous time-, voltage-, and Ca-dependent interactions of cell membrane electrogenic proteins (M-clock) and intracellular Ca cycling proteins (Ca-clock), forming a coupled-clock system. Many aspects of the coupled-clock system, however, remain underexplored. The key players of the system are Ca release channels (ryanodine receptors), generating local Ca releases (LCRs) from sarcoplasmic reticulum, electrogenic Na/Ca exchanger (NCX) current, and L-type Ca current (I_CaL). We combined numerical model simulations with experimental simultaneous recordings of action potentials (APs) and Ca to gain further insight into the complex interactions within the system. Our simulations revealed a positive feedback mechanism, dubbed AP ignition, which accelerates the diastolic depolarization (DD) to reach AP threshold. The ignition phase begins when LCRs begin to occur and the magnitude of inward NCX current begins to increase. The NCX current, together with funny current and T-type Ca current accelerates DD, bringing the membrane potential to I_CaL activation threshold. During the ignition phase, I_CaL-mediated Ca influx generates more LCRs via Ca-induced Ca release that further activates inward NCX current, creating a positive feedback. Simultaneous recordings of membrane potential and confocal Ca images support the model prediction of the positive feedback among LCRs and I_CaL, as diastolic LCRs begin to occur below and continue within the voltage range of I_CaL activation. The ignition phase onset (identified within the fine DD structure) begins when DD starts to notably accelerate (∼0.15 V/s) above the recording noise. Moreover, the timing of the ignition onset closely predicted the duration of each AP cycle in the basal state, in the presence of autonomic receptor stimulation, and in response to specific inhibition of either the M-clock or Ca-clock, thus indicating general importance of the new coupling mechanism for regulation of the pacemaker cell cycle duration, and ultimately the heart rate.

Cellular Mechanisms of Sinus Node Dysfunction in Carriers of the SCN5A-E161K Mutation and Role of the H558R Polymorphism

Background: Carriers of the E161K mutation in the SCN5A gene, encoding the Na_V1.5 pore-forming α-subunit of the ion channel carrying the fast sodium current (I_Na), show sinus bradycardia and occasional exit block. Voltage clamp experiments in mammalian expression systems revealed a mutation-induced 2.5- to 4-fold reduction in I_Na peak current density as well as a +19 mV shift and reduced steepness of the steady-state activation curve. The highly common H558R polymorphism in Na_V1.5 limits this shift to +13 mV, but also introduces a -10 mV shift in steady-state inactivation. Aim: We assessed the cellular mechanism by which the E161K mutation causes sinus node dysfunction in heterozygous mutation carriers as well as the potential role of the H558R polymorphism. Methods: We incorporated the mutation-induced changes in I_Na into the Fabbri-Severi model of a single human sinoatrial node cell and the Maleckar et al. human atrial cell model, and carried out simulations under control conditions and over a wide range of acetylcholine levels. Results: In absence of the H558R polymorphism, the E161K mutation increased the basic cycle length of the sinoatrial node cell from 813 to 866 ms. In the simulated presence of 10 and 25 nM acetylcholine, basic cycle length increased from 1027 to 1131 and from 1448 to 1795 ms, respectively. The increase in cycle length was the result of a significant slowing of diastolic depolarization. The mutation-induced reduction in I_Na window current had reduced the contribution of the mutant component of I_Na to the net membrane current during diastolic depolarization to effectively zero. Highly similar results were obtained in presence of the H558R polymorphism. Atrial excitability was reduced, both in absence and presence of the H558R polymorphism, as reflected by an increase in threshold stimulus current and a concomitant decrease in capacitive current of the atrial cell. Conclusion: We conclude that the experimentally identified mutation-induced changes in I_Na can explain the clinically observed sinus bradycardia and potentially the occasional exit block. Furthermore, we conclude that the common H558R polymorphism does not significantly alter the effects of the E161K mutation and can thus not explain the reduced penetrance of the E161K mutation.

A coupled-clock system drives the automaticity of human sinoatrial nodal pacemaker cells

The spontaneous rhythmic action potentials generated by the sinoatrial node (SAN), the primary pacemaker in the heart, dictate the regular and optimal cardiac contractions that pump blood around the body. Although the heart rate of humans is substantially slower than that of smaller experimental animals, current perspectives on the biophysical mechanisms underlying the automaticity of sinoatrial nodal pacemaker cells (SANCs) have been gleaned largely from studies of animal hearts. Using human SANCs, we demonstrated that spontaneous rhythmic local Ca2+ releases generated by a Ca2+ clock were coupled to electrogenic surface membrane molecules (the M clock) to trigger rhythmic action potentials, and that Ca2+-cAMP-protein kinase A (PKA) signaling regulated clock coupling. When these clocks became uncoupled, SANCs failed to generate spontaneous action potentials, showing a depolarized membrane potential and disorganized local Ca2+ releases that failed to activate the M clock. β-Adrenergic receptor (β-AR) stimulation, which increases cAMP concentrations and clock coupling in other species, restored spontaneous, rhythmic action potentials in some nonbeating "arrested" human SANCs by increasing intracellular Ca2+ concentrations and synchronizing diastolic local Ca2+ releases. When β-AR stimulation was withdrawn, the clocks again became uncoupled, and SANCs reverted to a nonbeating arrested state. Thus, automaticity of human pacemaker cells is driven by a coupled-clock system driven by Ca2+-cAMP-PKA signaling. Extreme clock uncoupling led to failure of spontaneous action potential generation, which was restored by recoupling of the clocks. Clock coupling and action potential firing in some of these arrested cells can be restored by β-AR stimulation-induced augmentation of Ca2+-cAMP-PKA signaling.

Age-related pacemaker deterioration is due to impaired intracellular and membrane mechanisms: Insights from numerical modeling

Pacemaker function deteriorates in advanced age. Behar and Yaniv show that both intracellular and membrane mechanisms are responsible for age-associated pacemaker function deterioration and explain why the maximal beating rate is restored as a result of changes in sensitivity of HCN₄ to cAMP and phospholamban to PKA.

Age-related deterioration of pacemaker function has been documented in mammals, including humans. In aged isolated sinoatrial node tissues and cells, reduction in the spontaneous action potential (AP) firing rate was associated with deterioration of intracellular and membrane mechanisms; however, their relative contribution to age-associated deficient pacemaker function is not known. Interestingly, pharmacological interventions that increase posttranslation modification signaling activities can restore the basal and maximal AP firing rate, but the identities of the protein targets responsible for AP firing rate restoration are not known. Here, we developed a numerical model that simulates the function of a single mouse pacemaker cell. In addition to describing membrane and intracellular mechanisms, the model includes descriptions of autonomic receptor activation pathways and posttranslation modification signaling cascades. The numerical model shows that age-related deterioration of pacemaker function is related to impaired intracellular and membrane mechanisms: HCN₄, T-type channels, and phospholamban functions, as well as the node connecting these mechanisms, i.e., intracellular Ca²⁺ and posttranslation modification signaling. To explain the restored maximal beating rate in response to maximal phosphodiesterase (PDE) inhibition, autonomic receptor stimulation, or infused cyclic adenosine monophosphate (cAMP), the model predicts that phospholamban phosphorylation by protein kinase A (PKA) and HCN₄ sensitivity to cAMP are altered in advanced age. Moreover, alteration in PKA and cAMP sensitivity can also explain age-reduced sensitivity to PDE inhibition and autonomic receptor stimulation. Finally, the numerical model suggests two pharmacological approaches and one gene manipulation method to restore the basal beating rate of aged pacemaker cells to that of normal adult cells. In conclusion, our numerical model shows that impaired membrane and intracellular mechanisms and the nodes that couple them can lead to deteriorated pacemaker function. By increasing posttranslation modification signaling, the deteriorated basal and maximal age-associated beating rate can be restored to adult levels.

Regularity of beating of small clusters of embryonic chick ventricular heart-cells: experiment vs. stochastic single-channel population model

The transmembrane potential is recorded from small isopotential clusters of 2-4 embryonic chick ventricular cells spontaneously generating action potentials. We analyze the cycle-to-cycle fluctuations in the time between successive action potentials (the interbeat interval or IBI). We also convert an existing model of electrical activity in the cluster, which is formulated as a Hodgkin-Huxley-like deterministic system of nonlinear ordinary differential equations describing five individual ionic currents, into a stochastic model consisting of a population of ∼20 000 independently and randomly gating ionic channels, with the randomness being set by a real physical stochastic process (radio static). This stochastic model, implemented using the Clay-DeFelice algorithm, reproduces the fluctuations seen experimentally: e.g., the coefficient of variation (standard deviation/mean) of IBI is 4.3% in the model vs. the 3.9% average value of the 17 clusters studied. The model also replicates all but one of several other quantitative measures of the experimental results, including the power spectrum and correlation integral of the voltage, as well as the histogram, Poincaré plot, serial correlation coefficients, power spectrum, detrended fluctuation analysis, approximate entropy, and sample entropy of IBI. The channel noise from one particular ionic current (I_Ks), which has channel kinetics that are relatively slow compared to that of the other currents, makes the major contribution to the fluctuations in IBI. Reproduction of the experimental coefficient of variation of IBI by adding a Gaussian white noise-current into the deterministic model necessitates using an unrealistically high noise-current amplitude. Indeed, a major implication of the modelling results is that, given the wide range of time-scales over which the various species of channels open and close, only a cell-specific stochastic model that is formulated taking into consideration the widely different ranges in the frequency content of the channel-noise produced by the opening and closing of several different types of channels will be able to reproduce precisely the various effects due to membrane noise seen in a particular electrophysiological preparation.

RyR2R420Q catecholaminergic polymorphic ventricular tachycardia mutation induces bradycardia by disturbing the coupled clock pacemaker mechanism

Catecholaminergic polymorphic ventricular tachycardia (CPVT) is a lethal genetic arrhythmia that manifests syncope or sudden death in children and young adults under stress conditions. CPVT patients often present bradycardia and sino-atrial node (SAN) dysfunction. However, the mechanism remains unclear. We analyzed SAN function in two CPVT families and in a novel knock-in (KI) mouse model carrying the RyR2R420Q mutation. Humans and KI mice presented slower resting heart rate. Accordingly, the rate of spontaneous intracellular Ca2+ ([Ca2+]i) transients was slower in KI mouse SAN preparations than in WT, without any significant alteration in the "funny" current (If ). The L-type Ca2+ current was reduced in KI SAN cells in a [Ca2+]i-dependent way, suggesting that bradycardia was due to disrupted crosstalk between the "voltage" and "Ca2+" clock, and the mechanisms of pacemaking was induced by aberrant spontaneous RyR2- dependent Ca2+ release. This finding was consistent with a higher Ca2+ leak during diastolic periods produced by long-lasting Ca2+ sparks in KI SAN cells. Our results uncover a mechanism for the CPVT-causing RyR2 N-terminal mutation R420Q, and they highlight the fact that enhancing the Ca2+ clock may slow the heart rhythm by disturbing the coupling between Ca2+ and voltage clocks.

The end effector of circadian heart rate variation: the sinoatrial node pacemaker cell

Cardiovascular function is regulated by the rhythmicity of circadian, infradian and ultradian clocks. Specific time scales of different cell types drive their functions: circadian gene regulation at hours scale, activation-inactivation cycles of ion channels at millisecond scales, the heart's beating rate at hundreds of millisecond scales, and low frequency autonomic signaling at cycles of tens of seconds. Heart rate and rhythm are modulated by a hierarchical clock system: autonomic signaling from the brain releases neurotransmitters from the vagus and sympathetic nerves to the heart’s pacemaker cells and activate receptors on the cell. These receptors activating ultradian clock functions embedded within pacemaker cells include sarcoplasmic reticulum rhythmic spontaneous Ca²⁺ cycling, rhythmic ion channel current activation and inactivation, and rhythmic oscillatory mitochondria ATP production. Here we summarize the evidence that intrinsic pacemaker cell mechanisms are the end effector of the hierarchical brain-heart circadian clock system. [BMB Reports 2015; 48(12): 677-684]

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.

Computational models of atrial cellular electrophysiology and calcium handling, and their role in atrial fibrillation

The complexity of the heart makes an intuitive understanding of the relative contribution of ion channels, transporters and signalling pathways to cardiac electrophysiology challenging. Computational modelling of cardiac cellular electrophysiology has proven useful to integrate experimental findings, extrapolate results obtained in expression systems or animal models to other systems, test quantitatively ideas based on experimental data and provide novel hypotheses that are experimentally testable. While the bulk of computational modelling has traditionally been directed towards ventricular bioelectricity, increasing recognition of the clinical importance of atrial arrhythmias, particularly atrial fibrillation, has led to widespread efforts to apply computational approaches to understanding atrial electrical function. The increasing availability of detailed, atrial-specific experimental data has stimulated the development of novel computational models of atrial-cellular electrophysiology and Ca(2+) handling. To date, more than 300 studies have employed mathematical simulations to enhance our understanding of atrial electrophysiology, arrhythmogenesis and therapeutic responses. Future modelling studies are likely to move beyond current whole-cell models by incorporating new data on subcellular architecture, macromolecular protein complexes, and localized ion-channel regulation by signalling pathways. At the same time, more integrative multicellular models that take into account regional electrophysiological and Ca(2+) handling properties, mechano-electrical feedback and/or autonomic regulation will be needed to investigate the mechanisms governing atrial arrhythmias. A combined experimental and computational approach is expected to provide the more comprehensive understanding of atrial arrhythmogenesis that is required to develop improved diagnostic and therapeutic options. Here, we review this rapidly expanding area, with a particular focus on Ca(2+) handling, and provide ideas about potential future directions.

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.

The functions of atrial strands interdigitating with and penetrating into sinoatrial node: a theoretical study of the problem

The sinoatrial node (SAN)-atrium system is closely involved with the activity of heart beating. The impulse propagation and phase-locking behaviors of this system are of theoretical interest. Some experiments have revealed that atrial strands (ASs) interdigitate with and penetrate into the SAN, whereby the SAN-atrium system works as a complex network. In this study, the functions of ASs are numerically investigated using realistic cardiac models. The results indicate that the ASs penetrating into the central region of the SAN play a major role in propagating excitation into the atrium. This is because the threshold SAN-AS coupling for an AS to function as an alternative path for propagation is lower at the center than at the periphery. However, ASs penetrating into the peripheral region have a great effect in terms of enlarging the 1:1 entrainment range of the SAN because the automaticity of the SAN is evidently reduced by ASs. Moreover, an analytical formula for approximating the enlargement of the 1:1 range is derived.

Potential effects of intrinsic heart pacemaker cell mechanisms on dysrhythmic cardiac action potential firing

The heart's regular electrical activity is initiated by specialized cardiac pacemaker cells residing in the sinoatrial node. The rate and rhythm of spontaneous action potential firing of sinoatrial node cells are regulated by stochastic mechanisms that determine the level of coupling of chemical to electrical clocks within cardiac pacemaker cells. This coupled-clock system is modulated by autonomic signaling from the brain via neurotransmitter release from the vagus and sympathetic nerves. Abnormalities in brain-heart clock connections or in any molecular clock activity within pacemaker cells lead to abnormalities in the beating rate and rhythm of the pacemaker tissue that initiates the cardiac impulse. Dysfunction of pacemaker tissue can lead to tachy-brady heart rate alternation or exit block that leads to long atrial pauses and increases susceptibility to other cardiac arrhythmia. Here we review evidence for the idea that disturbances in the intrinsic components of pacemaker cells may be implemented in arrhythmia induction in the heart.

From two competing oscillators to one coupled-clock pacemaker cell system

At the beginning of this century, debates regarding “what are the main control mechanisms that ignite the action potential (AP) in heart pacemaker cells” dominated the electrophysiology field. The original theory which prevailed for over 50 years had advocated that the ensemble of surface membrane ion channels (i.e., “M-clock”) is sufficient to ignite rhythmic APs. However, more recent experimental evidence in a variety of mammals has shown that the sarcoplasmic reticulum (SR) acts as a “Ca²⁺-clock” rhythmically discharges diastolic local Ca²⁺ releases (LCRs) beneath the cell surface membrane. LCRs activate an inward current (likely that of the Na⁺/Ca²⁺ exchanger) that prompts the surface membrane “M-clock” to ignite an AP. Theoretical and experimental evidence has mounted to indicate that this clock “crosstalk” operates on a beat-to-beat basis and determines both the AP firing rate and rhythm. Our review is focused on the evolution of experimental definition and numerical modeling of the coupled-clock concept, on how mechanisms intrinsic to pacemaker cell determine both the heart rate and rhythm, and on future directions to develop further the coupled-clock pacemaker cell concept.