Clusters of calcium release channels harness the Ising phase transition to confine their elementary intracellular signals.

Intracellular Ca signals represent a universal mechanism of cell function. Messages carried by Ca are local, rapid, and powerful enough to be delivered over the thermal noise. A higher signal-to-noise ratio is achieved by a cooperative action of Ca release channels such as IP3 receptors or ryanodine receptors arranged in clusters (release units) containing a few to several hundred release channels. The channels synchronize their openings via Ca-induced Ca release, generating high-amplitude local Ca signals known as puffs in neurons and sparks in muscle cells. Despite the positive feedback nature of the activation, Ca signals are strictly confined in time and space by an unexplained termination mechanism. Here we show that the collective transition of release channels from an open to a closed state is identical to the phase transition associated with the reversal of magnetic field in an Ising ferromagnet. Our simple quantitative criterion closely predicts the Ca store depletion level required for spark termination for each cluster size. We further formulate exact requirements that a cluster of release channels should satisfy in any cell type for our mapping to the Ising model and the associated formula to remain valid. Thus, we describe deterministically the behavior of a system on a coarser scale (release unit) that is random on a finer scale (release channels), bridging the gap between scales. Our results provide exact mapping of a nanoscale biological signaling model to an interacting particle system in statistical physics, making the extensive mathematical apparatus available to quantitative biology.

Mechanisms of Calcium Leak from Cardiac Sarcoplasmic Reticulum Revealed by Statistical Mechanics.

Heart muscle contraction is normally activated by a synchronized Ca release from sarcoplasmic reticulum (SR), a major intracellular Ca store. However, under abnormal conditions, Ca leaks from the SR, decreasing heart contraction amplitude and increasing risk of life-threatening arrhythmia. The mechanisms and regimes of SR operation generating the abnormal Ca leak remain unclear. Here, we employed both numerical and analytical modeling to get mechanistic insights into the emergent Ca leak phenomenon. Our numerical simulations using a detailed realistic model of the Ca release unit reveal sharp transitions resulting in Ca leak. The emergence of leak is closely mapped mathematically to the Ising model from statistical mechanics. The system steady-state behavior is determined by two aggregate parameters: the analogs of magnetic field (h) and the inverse temperature (ß) in the Ising model, for which we have explicit formulas in terms of SR [Ca] and release channel opening and closing rates. The classification of leak regimes takes the shape of a phase ß-h diagram, with the regime boundaries occurring at h = 0 and a critical value of ß (ß∗) that we estimate using a classical Ising model and mean field theory. Our theory predicts that a synchronized Ca leak will occur when h > 0 and ß >ß∗, and a disordered leak occurs when ß <ß∗ and h is not too negative. The disorder leak is distinguished from synchronized leak (in long-lasting sparks) by larger Peierls contour lengths, an output parameter reflecting degree of disorder. Thus, in addition to our detailed numerical model approach, we also offer an instantaneous computational tool using analytical formulas of the Ising model for respective ryanodine receptor parameters and SR Ca load that describe and classify phase transitions and leak emergence.

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 (ICaL). 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 ICaL activation threshold. During the ignition phase, ICaL-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 ICaL, as diastolic LCRs begin to occur below and continue within the voltage range of ICaL 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.

Electrophysiological heterogeneity of pacemaker cells in the rabbit intercaval region, including the SA node: insights from recording multiple ion currents in each cell.

Cardiac pacemaker cells, including cells of the sinoatrial node, are heterogeneous in size, morphology, and electrophysiological characteristics. The exact extent to which these cells differ electrophysiologically is unclear yet is critical to understanding their functioning. We examined major ionic currents in individual intercaval pacemaker cells (IPCs) sampled from the paracristal, intercaval region (including the sinoatrial node) that were spontaneously beating after enzymatic isolation from rabbit hearts. The beating rate was measured at baseline and after inhibition of the Ca2+ pump with cyclopiazonic acid. Thereafter, in each cell, we consecutively measured the density of funny current ( If), delayed rectifier K+ current ( IK) (a surrogate of repolarization capacity), and L-type Ca2+ current ( ICa,L) using whole cell patch clamp. The ionic current densities varied to a greater extent than previously appreciated, with some IPCs demonstrating very small or zero If . The density of none of the currents was correlated with cell size, while ICa,L and If densities were related to baseline beating rates. If density was correlated with IK density but not with that of ICa,L. Inhibition of Ca2+ cycling had a greater beating rate slowing effect in IPCs with lower If densities. Our numerical model simulation indicated that 1) IPCs with small (or zero) If or small ICa,L can operate via a major contribution of Ca2+ clock, 2) If-Ca2+-clock interplay could be important for robust pacemaking function, and 3) coupled If- IK function could regulate maximum diastolic potential. Thus, we have demonstrated marked electrophysiological heterogeneity of IPCs. This heterogeneity is manifested in basal beating rate and response to interference of Ca2+ cycling, which is linked to If. NEW & NOTEWORTHY In the present study, a hitherto unrecognized range of heterogeneity of ion currents in pacemaker cells from the intercaval region is demonstrated. Relationships between basal beating rate and L-type Ca2+ current and funny current ( If) density are uncovered, along with a positive relationship between If and delayed rectifier K+ current. Links are shown between the response to Ca2+ cycling blockade and If density.

Stabilization of diastolic calcium signal via calcium pump regulation of complex local calcium releases and transient decay in a computational model of cardiac pacemaker cell with individual release channels.

Intracellular Local Ca releases (LCRs) from sarcoplasmic reticulum (SR) regulate cardiac pacemaker cell function by activation of electrogenic Na/Ca exchanger (NCX) during diastole. Prior studies demonstrated the existence of powerful compensatory mechanisms of LCR regulation via a complex local cross-talk of Ca pump, release and NCX. One major obstacle to study these mechanisms is that LCR exhibit complex Ca release propagation patterns (including merges and separations) that have not been characterized. Here we developed new terminology, classification, and computer algorithms for automatic detection of numerically simulated LCRs and examined LCR regulation by SR Ca pumping rate (Pup) that provides a major contribution to fight-or-flight response. In our simulations the faster SR Ca pumping accelerates action potential-induced Ca transient decay and quickly clears Ca under the cell membrane in diastole, preventing premature releases. Then the SR generates an earlier, more synchronized, and stronger diastolic LCR signal activating an earlier and larger inward NCX current. LCRs at higher Pup exhibit larger amplitudes and faster propagation with more collisions to each other. The LCRs overlap with Ca transient decay, causing an elevation of the average diastolic [Ca] nadir to ~200 nM (at Pup = 24 mM/s). Background Ca (in locations lacking LCRs) quickly decays to resting Ca levels (<100 nM) at high Pup, but remained elevated during slower decay at low Pup. Release propagation is facilitated at higher Pup by a larger LCR amplitude, whereas at low Pup by higher background Ca. While at low Pup LCRs show smaller amplitudes, their larger durations and sizes combined with longer transient decay stabilize integrals of diastolic Ca and NCX current signals. Thus, the local interplay of SR Ca pump and release channels regulates LCRs and Ca transient decay to insure fail-safe pacemaker cell operation within a wide range of rates.

Electrochemical Na+ and Ca2+ gradients drive coupled-clock regulation of automaticity of isolated rabbit sinoatrial nodal pacemaker cells.

Coupling of an intracellular Ca(2+) clock to surface membrane ion channels, i.e., a "membrane clock, " via coupling of electrochemical Na(+) and Ca(2+) gradients (ENa and ECa, respectively) has been theorized to regulate sinoatrial nodal cell (SANC) normal automaticity. To test this hypothesis, we measured responses of [Na(+)]i, [Ca(2+)]i, membrane potential, action potential cycle length (APCL), and rhythm in rabbit SANCs to Na(+)/K(+) pump inhibition by the digitalis glycoside, digoxigenin (DG, 10-20 µmol/l). Initial small but significant increases in [Na(+)]i and [Ca(2+)]i and reductions in ENa and ECa in response to DG led to a small reduction in maximum diastolic potential (MDP), significantly enhanced local diastolic Ca(2+) releases (LCRs), and reduced the average APCL. As [Na(+)]i and [Ca(2+)]i continued to increase at longer times following DG exposure, further significant reductions in MDP, ENa, and ECa occurred; LCRs became significantly reduced, and APCL became progressively and significantly prolonged. This was accompanied by increased APCL variability. We also employed a coupled-clock numerical model to simulate changes in ENa and ECa simultaneously with ion currents not measured experimentally. Numerical modeling predicted that, as the ENa and ECa monotonically reduced over time in response to DG, ion currents (ICaL, ICaT, If, IKr, and IbNa) monotonically decreased. In parallel with the biphasic APCL, diastolic INCX manifested biphasic changes; initial INCX increase attributable to enhanced LCR ensemble Ca(2+) signal was followed by INCX reduction as ENCX (ENCX = 3ENa - 2ECa) decreased. Thus SANC automaticity is tightly regulated by ENa, ECa, and ENCX via a complex interplay of numerous key clock components that regulate SANC clock coupling.

Contribution of sodium channel neuronal isoform Nav1.1 to late sodium current in ventricular myocytes from failing hearts.

KEY POINTS: Late Na(+) current (INaL) contributes to action potential remodelling and Ca(2+)/Na(+) changes in heart failure. The molecular identity of INaL remains unclear. The contributions of different Na(+) channel isoforms, apart from the cardiac isoform, remain unknown. We discovered and characterized a substantial contribution of neuronal isoform Nav1.1 to INaL. This new component is physiologically relevant to the control of action potential shape and duration, as well as to cell Ca(2+) dynamics, especially in heart failure. ABSTRACT: Late Na(+) current (INaL) contributes to action potential (AP) duration and Ca(2+) handling in cardiac cells. Augmented INaL was implicated in delayed repolarization and impaired Ca(2+) handling in heart failure (HF). We tested if Na(+) channel (Nav) neuronal isoforms contribute to INaL and Ca(2+) cycling defects in HF in 17 dogs in which HF was achieved via sequential coronary artery embolizations. Six normal dogs served as control. Transient Na(+) current (INaT ) and INaL in left ventricular cardiomyocytes (VCMs) were recorded by patch clamp while Ca(2+) dynamics was monitored using Fluo-4. Virally delivered short interfering RNA (siRNA) ensured Nav1.1 and Nav1.5 post-transcriptional silencing. The expression of six Navs was observed in failing VCMs as follows: Nav1.5 (57.3%) > Nav1.2 (15.3%) > Nav1.1 (11.6%) > Nav2.1 (10.7%) > Nav1.3 (4.6%) > Nav1.6 (0.5%). Failing VCMs showed up-regulation of Nav1.1 expression, but reduction of Nav1.6 mRNA. A similar Nav expression pattern was found in samples from human hearts with ischaemic HF. VCMs with silenced Nav1.5 exhibited residual INaT and INaL (∼30% of control) with rightwardly shifted steady-state activation and inactivation. These currents were tetrodotoxin sensitive but resistant to MTSEA, a specific Nav1.5 blocker. The amplitude of the tetrodotoxin-sensitive INaL was 0.1709 ± 0.0299 pA pF(-1) (n = 7 cells) and the decay time constant was τ = 790 ± 76 ms (n = 5). This INaL component was lacking in VCMs with a silenced Nav1.1 gene, indicating that, among neuronal isoforms, Nav1.1 provides the largest contribution to INaL. At -10 mV this contribution is ∼60% of total INaL. Our further experimental and in silico examinations showed that this new Nav1.1 INaL component contributes to Ca(2+) accumulation in failing VCMs and modulates AP shape and duration. In conclusion, we have discovered an Nav1.1-originated INaL component in dog heart ventricular cells. This component is physiologically relevant to controlling AP shape and duration, as well as to cell Ca(2+) dynamics.

Na+ channel function, regulation, structure, trafficking and sequestration.

This paper is the second of a series of three reviews published in this issue resulting from the University of California Davis Cardiovascular Symposium 2014: Systems approach to understanding cardiac excitation-contraction coupling and arrhythmias: Na(+) channel and Na(+) transport. The goal of the symposium was to bring together experts in the field to discuss points of consensus and controversy on the topic of sodium in the heart. The present review focuses on Na(+) channel function and regulation, Na(+) channel structure and function, and Na(+) channel trafficking, sequestration and complexing.

RyR-NCX-SERCA local cross-talk ensures pacemaker cell function at rest and during the fight-or-flight reflex.

RATIONALE: A recent study published in Circulation Research by Gao et al used sinoatrial node (SAN)-targeted, incomplete Ncx1 knockout in mice to explore the role of the Na(+)/Ca(2+) exchanger (NCX) in cardiac pacemaker. The authors concluded that NCX is required for increasing sinus rates, but not for maintaining resting heart rate. This conclusion was based, in part, on numeric model simulations performed by Gao et al that reproduced their experimental results of unchanged action potentials in the knockout SAN cells. The authors, however, did not simulate the NCX current (INCX), that is, the subject of the study. OBJECTIVE: We extended numeric examinations to simulate INCX in their incomplete knockout SAN cells that is crucial to interpret the study results. METHODS AND RESULTS: INCX and Ca(2+) dynamics were simulated using different contemporary numeric models of SAN cells. We found that minimum diastolic Ca(2+) levels and INCX amplitudes generated by remaining NCX molecules (only 20% of control) remained almost unchanged. Simulations using a new local Ca(2+) control model indicate that these powerful compensatory mechanisms involve complex local cross-talk of Ca(2+) cycling proteins and NCX. Specifically, lower NCX expression facilitates Ca(2+)-induced Ca(2+) release and larger local Ca(2+) releases that stabilize diastolic INCX. Further reduction of NCX expression results in arrhythmia and halt of automaticity. CONCLUSIONS: Remaining NCX molecules in the incomplete knockout model likely produce almost the same diastolic INCX as in wild-type cells. INCX contribution is crucially important for both basal automaticity of SAN cells and during the fight-or-flight reflex.

Sarcoplasmic reticulum Ca2+ cycling protein phosphorylation in a physiologic Ca2+ milieu unleashes a high-power, rhythmic Ca2+ clock in ventricular myocytes: relevance to arrhythmias and bio-pacemaker design.

Basal phosphorylation of sarcoplasmic reticulum (SR) Ca(2+) proteins is high in sinoatrial nodal cells (SANC), which generate partially synchronized, spontaneous, rhythmic, diastolic local Ca(2+) releases (LCRs), but low in ventricular myocytes (VM), which exhibit rare diastolic, stochastic SR-generated Ca(2+) sparks. We tested the hypothesis that in a physiologic Ca(2+) milieu, and independent of increased Ca(2+) influx, an increase in basal phosphorylation of SR Ca(2+) cycling proteins will convert stochastic Ca(2+) sparks into periodic, high-power Ca(2+) signals of the type that drives SANC normal automaticity. We measured phosphorylation of SR-associated proteins, phospholamban (PLB) and ryanodine receptors (RyR), and spontaneous local Ca(2+) release characteristics (LCR) in permeabilized single, rabbit VM in physiologic [Ca(2+)], prior to and during inhibition of protein phosphatase (PP) and phosphodiesterase (PDE), or addition of exogenous cAMP, or in the presence of an antibody (2D12), that specifically inhibits binding of the PLB to SERCA-2. In the absence of the aforementioned perturbations, VM could only generate stochastic local Ca(2+) releases of low power and low amplitude, as assessed by confocal Ca(2+) imaging and spectral analysis. When the kinetics of Ca(2+) pumping into the SR were increased by an increase in PLB phosphorylation (via PDE and PP inhibition or addition of cAMP) or by 2D12, self-organized, "clock-like" local Ca(2+) releases, partially synchronized in space and time (Ca(2+) wavelets), emerged, and the ensemble of these rhythmic local Ca(2+) wavelets generated a periodic high-amplitude Ca(2+) signal. Thus, a Ca(2+) clock is not specific to pacemaker cells, but can also be unleashed in VM when SR Ca(2+) cycling increases and spontaneous local Ca(2+) release becomes partially synchronized. This unleashed Ca(2+) clock that emerges in a physiological Ca(2+) milieu in VM has two faces, however: it can provoke ventricular arrhythmias; or if harnessed, can be an important feature of novel bio-pacemaker designs.

Modern concepts concerning the origin of the heartbeat.

Physiological processes governing the heart beat have been under investigation for several hundred years. Major advances have been made in the recent past. A review of the present paradigm is presented here, including a look back at important steps that led us to where we are today, alongside a glimpse into the exciting future of pacemaker research.

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.

Mechanisms of beat-to-beat regulation of cardiac pacemaker cell function by Ca²âº cycling dynamics.

Whether intracellular Ca(2+) cycling dynamics regulate cardiac pacemaker cell function on a beat-to-beat basis remains unknown. Here we show that under physiological conditions, application of low concentrations of caffeine (2-4 mM) to isolated single rabbit sinoatrial node cells acutely reduces their spontaneous action potential cycle length (CL) and increases Ca(2+) transient amplitude for several cycles. Numerical simulations, using a modified Maltsev-Lakatta coupled-clock model, faithfully reproduced these effects, and also the effects of CL prolongation and dysrhythmic spontaneous beating (produced by cytosolic Ca(2+) buffering) and an acute CL reduction (produced by flash-induced Ca(2+) release from a caged Ca(2+) buffer), which we had reported previously. Three contemporary numerical models (including the original Maltsev-Lakatta model) failed to reproduce the experimental results. In our proposed new model, Ca(2+) releases acutely change the CL via activation of the Na(+)/Ca(2+) exchanger current. Time-dependent CL reductions after flash-induced Ca(2+) releases (the memory effect) are linked to changes in Ca(2+) available for pumping into sarcoplasmic reticulum which, in turn, changes the sarcoplasmic reticulum Ca(2+) load, diastolic Ca(2+) releases, and Na(+)/Ca(2+) exchanger current. These results support the idea that Ca(2+) regulates CL in cardiac pacemaker cells on a beat-to-beat basis, and suggest a more realistic numerical mechanism of this regulation.

Numerical models based on a minimal set of sarcolemmal electrogenic proteins and an intracellular Ca(2+) clock generate robust, flexible, and energy-efficient cardiac pacemaking.

Recent evidence supports the idea that robust and, importantly, FLEXIBLE automaticity of cardiac pacemaker cells is conferred by a coupled system of membrane ion currents (an "M-clock") and a sarcoplasmic reticulum (SR)-based Ca(2+) oscillator ("Ca(2+)clock") that generates spontaneous diastolic Ca(2+) releases. This study identified numerical models of a human biological pacemaker that features robust and flexible automaticity generated by a minimal set of electrogenic proteins and a Ca(2+)clock. Following the Occam's razor principle (principle of parsimony), M-clock components of unknown molecular origin were excluded from Maltsev-Lakatta pacemaker cell model and thirteen different model types of only 4 or 5 components were derived and explored by a parametric sensitivity analysis. The extended ranges of SR Ca(2+) pumping (i.e. Ca(2+)clock performance) and conductance of ion currents were sampled, yielding a large variety of parameter combination, i.e. specific model sets. We tested each set's ability to simulate autonomic modulation of human heart rate (minimum rate of 50 to 70bpm; maximum rate of 140 to 210bpm) in response to stimulation of cholinergic and ß-adrenergic receptors. We found that only those models that include a Ca(2+)clock (including the minimal 4-parameter model "ICaL+IKr+INCX+Ca(2+)clock") were able to reproduce the full range of autonomic modulation. Inclusion of If or ICaT decreased the flexibility, but increased the robustness of the models (a relatively larger number of sets did not fail during testing). The new models comprised of components with clear molecular identity (i.e. lacking IbNa & Ist) portray a more realistic pacemaking: A smaller Na(+) influx is expected to demand less energy for Na(+) extrusion. The new large database of the reduced coupled-clock numerical models may serve as a useful tool for the design of biological pacemakers. It will also provide a conceptual basis for a general theory of robust, flexible, and energy-efficient pacemaking based on realistic components.

New evidence for coupled clock regulation of the normal automaticity of sinoatrial nodal pacemaker cells: bradycardic effects of ivabradine are linked to suppression of intracellular Ca²âº cycling.

Beneficial clinical bradycardic effects of ivabradine (IVA) have been interpreted solely on the basis of If inhibition, because IVA specifically inhibits If in sinoatrial nodal pacemaker cells (SANC). However, it has been recently hypothesized that SANC normal automaticity is regulated by crosstalk between an "M clock," the ensemble of surface membrane ion channels, and a "Ca(2+) clock," the sarcoplasmic reticulum (SR). We tested the hypothesis that crosstalk between the two clocks regulates SANC automaticity, and that indirect suppression of the Ca(2+) clock further contributes to IVA-induced bradycardia. IVA (3 µM) not only reduced If amplitude by 45 ± 6% in isolated rabbit SANC, but the IVA-induced slowing of the action potential (AP) firing rate was accompanied by reduced SR Ca(2+) load, slowed intracellular Ca(2+) cycling kinetics, and prolonged the period of spontaneous local Ca(2+) releases (LCRs) occurring during diastolic depolarization. Direct and specific inhibition of SERCA2 by cyclopiazonic acid (CPA) had effects similar to IVA on LCR period and AP cycle length. Specifically, the LCR period and AP cycle length shift toward longer times almost equally by either direct perturbations of the M clock (IVA) or the Ca(2+) clock (CPA), indicating that the LCR period reports the crosstalk between the clocks. Our numerical model simulations predict that entrainment between the two clocks that involves a reduction in INCX during diastolic depolarization is required to explain the experimentally AP firing rate reduction by IVA. In summary, our study provides new evidence that a coupled-clock system regulates normal cardiac pacemaker cell automaticity. Thus, IVA-induced bradycardia includes a suppression of both clocks within this system.

Elementary intracellular Ca signals approximated as a transition of release channel system from a metastable state.

Cardiac muscle contraction is initiated by an elementary Ca signal (called Ca spark) which is achieved by collective action of Ca release channels in a cluster. The mechanism of this synchronization remains uncertain. We approached Ca spark activation as an emergent phenomenon of an interactive system of release channels. We constructed a weakly lumped Markov chain that applies an Ising model formalism to such release channel clusters and probable open channel configurations and demonstrated that spark activation is described as a system transition from a metastable to an absorbing state, analogous to the pressure required to overcome surface tension in bubble formation. This yielded quantitative estimates of the spark generation probability as a function of various system parameters. We performed numerical simulations to find spark probabilities as a function of sarcoplasmic reticulum Ca concentration, obtaining similar values for spark activation threshold as our analytic model, as well as those reported in experimental studies. Our parametric sensitivity analyses also showed that the spark activation threshold decreased as Ca sensitivity of RyR activation and RyR cluster size increased.

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

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 ß-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.

A coupled SYSTEM of intracellular Ca2+ clocks and surface membrane voltage clocks controls the timekeeping mechanism of the heart's pacemaker.

Ion channels on the surface membrane of sinoatrial nodal pacemaker cells (SANCs) are the proximal cause of an action potential. Each individual channel type has been thoroughly characterized under voltage clamp, and the ensemble of the ion channel currents reconstructed in silico generates rhythmic action potentials. Thus, this ensemble can be envisioned as a surface "membrane clock" (M clock). Localized subsarcolemmal Ca(2+) releases are generated by the sarcoplasmic reticulum via ryanodine receptors during late diastolic depolarization and are referred to as an intracellular "Ca(2+) clock," because their spontaneous occurrence is periodic during voltage clamp or in detergent-permeabilized SANCs, and in silico as well. In spontaneously firing SANCs, the M and Ca(2+) clocks do not operate in isolation but work together via numerous interactions modulated by membrane voltage, subsarcolemmal Ca(2+), and protein kinase A and CaMKII-dependent protein phosphorylation. Through these interactions, the 2 subsystem clocks become mutually entrained to form a robust, stable, coupled-clock system that drives normal cardiac pacemaker cell automaticity. G protein-coupled receptors signaling creates pacemaker flexibility, ie, effects changes in the rhythmic action potential firing rate, by impacting on these very same factors that regulate robust basal coupled-clock system function. This review examines evidence that forms the basis of this coupled-clock system concept in cardiac SANCs.

The "funny" current (I(f)) inhibition by ivabradine at membrane potentials encompassing spontaneous depolarization in pacemaker cells.

Recent clinical trials have shown that ivabradine (IVA), a drug that inhibits the funny current (I(f)) in isolated sinoatrial nodal cells (SANC), decreases heart rate and reduces morbidity and mortality in patients with cardiovascular diseases. While IVA inhibits I(f), this effect has been reported at essentially unphysiological voltages, i.e., those more negative than the spontaneous diastolic depolarization (DD) between action potentials (APs). We tested the relative potency of IVA to block I(f) over a wide range of membrane potentials, including those that encompass DD governing to the SANC spontaneous firing rate. A clinically relevant IVA concentration of 3 µM to single, isolated rabbit SANC slowed the spontaneous AP firing rate by 15%. During voltage clamp the maximal I(f) was 18 ± 3 pA/pF (at -120 mV) and the maximal I(f) reduction by IVA was 60 ± 8% observed at -92 ± 4 mV. At the maximal diastolic depolarization (~-60 mV) I(f) amplitude was only -2.9 ± 0.4 pA/pF, and was reduced by only 41 ± 6% by IVA. Thus, I(f) amplitude and its inhibition by IVA at physiologically relevant membrane potentials are substantially less than that at unphysiological (hyperpolarized) membrane potentials. This novel finding more accurately describes how IVA affects SANC function and is of direct relevance to numerical modeling of SANC automaticity.