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.

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.

The paradigm shift: Heartbeat initiation without "the pacemaker cell".

The current dogma about the heartbeat origin is based on "the pacemaker cell," a specialized cell residing in the sinoatrial node (SAN) that exhibits spontaneous diastolic depolarization triggering rhythmic action potentials (APs). Recent high-resolution imaging, however, demonstrated that Ca signals and APs in the SAN are heterogeneous, with many cells generating APs of different rates and rhythms or even remaining non-firing (dormant cells), i.e., generating only subthreshold signals. Here we numerically tested a hypothesis that a community of dormant cells can generate normal automaticity, i.e., "the pacemaker cell" is not required to initiate rhythmic cardiac impulses. Our model includes 1) non-excitable cells generating oscillatory local Ca releases and 2) an excitable cell lacking automaticity. While each cell in isolation was not "the pacemaker cell", the cell system generated rhythmic APs: The subthreshold signals of non-excitable cells were transformed into respective membrane potential oscillations via electrogenic Na/Ca exchange and further transferred and integrated (computed) by the excitable cells to reach its AP threshold, generating rhythmic pacemaking. Cardiac impulse is an emergent property of the SAN cellular network and can be initiated by cells lacking intrinsic automaticity. Cell heterogeneity, weak coupling, subthreshold signals, and their summation are critical properties of the new pacemaker mechanism, i.e., cardiac pacemaker can operate via a signaling process basically similar to that of "temporal summation" happening in a neuron with input from multiple presynaptic cells. The new mechanism, however, does not refute the classical pacemaker cell-based mechanism: both mechanisms can co-exist and interact within SAN tissue.

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 ß-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.

Synchronized Cardiac Impulses Emerge From Heterogeneous Local Calcium Signals Within and Among Cells of Pacemaker Tissue.

OBJECTIVES: This study sought to identify subcellular Ca2+ signals within and among cells comprising the sinoatrial node (SAN) tissue. BACKGROUND: The current paradigm of SAN impulse generation: 1) is that full-scale action potentials (APs) of a common frequency are initiated at 1 site and are conducted within the SAN along smooth isochrones; and 2) does not feature fine details of Ca2+ signaling present in isolated SAN cells, in which small subcellular, subthreshold local Ca2+ releases (LCRs) self-organize to generate cell-wide APs. METHODS: Immunolabeling was combined with a novel technique to detect the occurrence of LCRs and AP-induced Ca2+ transients (APCTs) in individual pixels (chronopix) across the entire mouse SAN images. RESULTS: At high magnification, Ca2+ signals appeared markedly heterogeneous in space, amplitude, frequency, and phase among cells comprising an HCN4+/CX43- cell meshwork. The signaling exhibited several distinguishable patterns of LCR/APCT interactions within and among cells. Rhythmic APCTs that were apparently conducted within the meshwork were transferred to a truly conducting HCN4-/CX43+ network of striated cells via narrow functional interfaces where different cell types intertwine, that is, the SAN anatomic/functional unit. At low magnification, the earliest APCT of each cycle occurred within a small area of the HCN4 meshwork, and subsequent APCT appearance throughout SAN pixels was discontinuous and asynchronous. CONCLUSIONS: The study has discovered a novel, microscopic Ca2+ signaling paradigm of SAN operation that has escaped detection using low-resolution, macroscopic tissue isochrones employed in prior studies: synchronized APs emerge from heterogeneous subcellular subthreshold Ca2+ signals, resembling multiscale complex processes of impulse generation within clusters of neurons in neuronal networks.

Social heterogeneity drives complex patterns of the COVID-19 pandemic: insights from a novel Stochastic Heterogeneous Epidemic Model (SHEM).

In todays absence of a vaccine and impactful treatments, the most effective way to combat the virus is to find and implement mitigation strategies. An invaluable resource in this task is numerical modeling that can reveal key factors in COVID-19 pandemic development. On the other hand, it has become evident that regional infection curves of COVID-19 exhibit complex patterns which often differ from curves predicted by forecasting models. The wide variations in attack rate observed among different social strata suggest that this may be due to social heterogeneity not accounted for by regional models. We investigated this hypothesis by developing and using a new Stochastic Heterogeneous Epidemic Model (SHEM) that focuses on subpopulations that are vulnerable in the sense of having an increased likelihood of spreading infection among themselves. We found that the isolation or embedding of vulnerable sub-clusters in a major population hub generated complex stochastic infection patterns which included multiple peaks and growth periods, an extended plateau, a prolonged tail, or a delayed second wave of infection. Embedded vulnerable groups became hotspots that drove infection despite efforts of the main population to socially distance, while isolated groups suffered delayed but intense infection. Amplification of infection by these hotspots facilitated transmission from one urban area to another, causing the epidemic to hopscotch in a stochastic manner to places it would not otherwise reach, resembling a microcosm of the situation worldwide as of September 2020. Our results suggest that social heterogeneity is a key factor in the formation of complex infection propagation patterns. Thus, the mitigation of vulnerable groups is essential to control the COVID-19 pandemic worldwide. The design of our new model allows it to be applied in future studies of real-world scenarios on any scale, limited only by computing memory and the ability to determine the underlying topology and parameters.

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.

Heterogeneity of calcium clock functions in dormant, dysrhythmically and rhythmically firing single pacemaker cells isolated from SA node.

Current understanding of how cardiac pacemaker cells operate is based mainly on studies in isolated single sinoatrial node cells (SANC), specifically those that rhythmically fire action potentials similar to the in vivo behavior of the intact sinoatrial node. However, only a small fraction of SANC exhibit rhythmic firing after isolation. Other SANC behaviors have not been studied. Here, for the first time, we studied all single cells isolated from the sinoatrial node of the guinea pig, including traditionally studied rhythmically firing cells ('rhythmic SANC'), dysrhythmically firing cells ('dysrhythmic SANC') and cells without any apparent spontaneous firing activity ('dormant SANC'). Action potential-induced cytosolic Ca2+ transients and spontaneous local Ca2+ releases (LCRs) were measured with a 2D camera. LCRs were present not only in rhythmically firing SANC, but also in dormant and dysrhythmic SANC. While rhythmic SANC were characterized by large LCRs synchronized in space and time towards late diastole, dysrhythmic and dormant SANC exhibited smaller LCRs that appeared stochastically and were widely distributed in time. ß-adrenergic receptor (ßAR) stimulation increased LCR size and synchronized LCR occurrences in all dysrhythmic and a third of dormant cells (25 of 75 cells tested). In response to ßAR stimulation, these dormant SANC developed automaticity, and LCRs became coupled to spontaneous action potential-induced cytosolic Ca2+ transients. Conversely, dormant SANC that did not develop automaticity showed no significant change in average LCR characteristics. The majority of dysrhythmic cells became rhythmic in response to ßAR stimulation, with the rate of action potential-induced cytosolic Ca2+ transients substantially increasing. In summary, isolated SANC can be broadly categorized into three major populations: dormant, dysrhythmic, and rhythmic. We interpret our results based on simulations of a numerical model of SANC operating as a coupled-clock system. On this basis, the two previously unstudied dysrhythmic and dormant cell populations have intrinsically partially or completely uncoupled clocks. Such cells can be recruited to fire rhythmically in response to ßAR stimulation via increased rhythmic LCR activity and ameliorated coupling between the Ca2+ and membrane clocks.

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. ß-Adrenergic receptor (ß-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 ß-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 ß-AR stimulation-induced augmentation of Ca2+-cAMP-PKA signaling.

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.

Computer algorithms for automated detection and analysis of local Ca2+ releases in spontaneously beating cardiac pacemaker cells.

Local Ca2+ Releases (LCRs) are crucial events involved in cardiac pacemaker cell function. However, specific algorithms for automatic LCR detection and analysis have not been developed in live, spontaneously beating pacemaker cells. In the present study we measured LCRs using a high-speed 2D-camera in spontaneously contracting sinoatrial (SA) node cells isolated from rabbit and guinea pig and developed a new algorithm capable of detecting and analyzing the LCRs spatially in two-dimensions, and in time. Our algorithm tracks points along the midline of the contracting cell. It uses these points as a coordinate system for affine transform, producing a transformed image series where the cell does not contract. Action potential-induced Ca2+ transients and LCRs were thereafter isolated from recording noise by applying a series of spatial filters. The LCR birth and death events were detected by a differential (frame-to-frame) sensitivity algorithm applied to each pixel (cell location). An LCR was detected when its signal changes sufficiently quickly within a sufficiently large area. The LCR is considered to have died when its amplitude decays substantially, or when it merges into the rising whole cell Ca2+ transient. Ultimately, our algorithm provides major LCR parameters such as period, signal mass, duration, and propagation path area. As the LCRs propagate within live cells, the algorithm identifies splitting and merging behaviors, indicating the importance of locally propagating Ca2+-induced-Ca2+-release for the fate of LCRs and for generating a powerful ensemble Ca2+ signal. Thus, our new computer algorithms eliminate motion artifacts and detect 2D local spatiotemporal events from recording noise and global signals. While the algorithms were developed to detect LCRs in sinoatrial nodal cells, they have the potential to be used in other applications in biophysics and cell physiology, for example, to detect Ca2+ wavelets (abortive waves), sparks and embers in muscle cells and Ca2+ puffs and syntillas in neurons.

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.

Long-term HIF-1α transcriptional activation is essential for heat-acclimation-mediated cross tolerance: mitochondrial target genes.

An important adaptive feature of heat acclimation (HA) is the induction of cross tolerance against novel stressors (HACT) Reprogramming of gene expression leading to enhanced innate cytoprotective features by attenuating damage and/or enhancing the response of "help" signals plays a pivotal role. Hypoxia-inducible factor-1α (HIF-1α), constitutively upregulated by HA (1 mo, 34°C), is a crucial transcription factor in this program, although its specific role is as yet unknown. By using a rat HA model, we studied the impact of disrupting HIF-1α transcriptional activation [HIF-1α:HIF-1ß dimerization blockade by intraperitoneal acriflavine (4 mg/kg)] on its mitochondrial gene targets [phosphoinositide-dependent kinase-1 (PDK1), LON, and cyclooxygenase 4 (COX4) isoforms] in the HA rat heart. Physiological measures of cardiac HACT were infarct size after ischemia-reperfusion and time to rigor contracture during hypoxia in cardiomyocytes. We show that HACT requires transcriptional activation of HIF-1α throughout the course of HA and that this activation is accompanied by two metabolic switches: 1) profound upregulation of PDK1, which reduces pyruvate entry into the mitochondria, consequently increasing glycolytic lactate production; 2) remodeling of the COX4 isoform ratio, inducing hypoxic-tolerant COX4.2 dominance, and optimizing electron transfer and possibly ATP production during the ischemic and hypoxic insults. LON and COX4.2 transcript upregulation accompanied this shift. Loss of HACT despite elevated expression of the cytoprotective protein heat shock protein-72 concomitantly with disrupted HIF-1α dimerization suggests that HIF-1α is essential for HACT. The role of a PDK1 metabolic switch is well known in hypoxia acclimation but not in the HA model and its ischemic setting. Remodeling of COX4 isoforms by environmental acclimation is a novel finding.

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.

Hierarchical clustering of ryanodine receptors enables emergence of a calcium clock in sinoatrial node cells.

The sinoatrial node, whose cells (sinoatrial node cells [SANCs]) generate rhythmic action potentials, is the primary pacemaker of the heart. During diastole, calcium released from the sarcoplasmic reticulum (SR) via ryanodine receptors (RyRs) interacts with membrane currents to control the rate of the heartbeat. This "calcium clock" takes the form of stochastic, partially periodic, localized calcium release (LCR) events that propagate, wave-like, for limited distances. The detailed mechanisms controlling the calcium clock are not understood. We constructed a computational model of SANCs, including three-dimensional diffusion and buffering of calcium in the cytosol and SR; explicit, stochastic gating of individual RyRs and L-type calcium channels; and a full complement of voltage- and calcium-dependent membrane currents. We did not include an anatomical submembrane space or inactivation of RyRs, the two heuristic components that have been used in prior models but are not observed experimentally. When RyRs were distributed in discrete clusters separated by >1 µm, only isolated sparks were produced in this model and LCR events did not form. However, immunofluorescent staining of SANCs for RyR revealed the presence of bridging RyR groups between large clusters, forming an irregular network. Incorporation of this architecture into the model led to the generation of propagating LCR events. Partial periodicity emerged from the interaction of LCR events, as observed experimentally. This calcium clock becomes entrained with membrane currents to accelerate the beating rate, which therefore was controlled by the activity of the SERCA pump, RyR sensitivity, and L-type current amplitude, all of which are targets of ß-adrenergic-mediated phosphorylation. Unexpectedly, simulations revealed the existence of a pathological mode at high RyR sensitivity to calcium, in which the calcium clock loses synchronization with the membrane, resulting in a paradoxical decrease in beating rate in response to ß-adrenergic stimulation. The model indicates that the hierarchical clustering of surface RyRs in SANCs may be a crucial adaptive mechanism. Pathological desynchronization of the clocks may explain sinus node dysfunction in heart failure and RyR mutations.

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.

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.

Life and death of a cardiac calcium spark.

Calcium sparks in cardiac myocytes are brief, localized calcium releases from the sarcoplasmic reticulum (SR) believed to be caused by locally regenerative calcium-induced calcium release (CICR) via couplons, clusters of ryanodine receptors (RyRs). How such regeneration is terminated is uncertain. We performed numerical simulations of an idealized stochastic model of spark production, assuming a RyR gating scheme with only two states (open and closed). Local depletion of calcium in the SR was inevitable during a spark, and this could terminate sparks by interrupting CICR, with or without assumed modulation of RyR gating by SR lumenal calcium. Spark termination by local SR depletion was not robust: under some conditions, sparks could be greatly and variably prolonged, terminating by stochastic attrition-a phenomenon we dub "spark metastability." Spark fluorescence rise time was not a good surrogate for the duration of calcium release. Using a highly simplified, deterministic model of the dynamics of a couplon, we show that spark metastability depends on the kinetic relationship of RyR gating and junctional SR refilling rates. The conditions for spark metastability resemble those produced by known mutations of RyR2 and CASQ2 that cause life-threatening triggered arrhythmias, and spark metastability may be mitigated by altering the kinetics of the RyR in a manner similar to the effects of drugs known to prevent those arrhythmias. The model was unable to explain the distributions of spark amplitudes and rise times seen in chemically skinned cat atrial myocytes, suggesting that such sparks may be more complex events involving heterogeneity of couplons or local propagation among sub-clusters of RyRs.