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.

The Synthesis, Structure, and Luminescent Properties of TmMgB5O10 Crystals.

TmMgB5O10 spontaneous crystals were synthesized via the flux-growth technique from a K2Mo3O10-based solvent. The crystal structure of the compound was solved and refined within the space group P21/n. The first principles calculations of the electronic structure reveal that TmMg-pentaborate with an ideal not defected crystal structure is an insulator with an indirect energy band gap of approximately 6.37 eV. Differential scanning calorimetry measurements and powder X-ray diffraction studies of heat-treated solids show that TmMgB5O10 is an incongruent melting compound. A characteristic band of the Tm3+ cation corresponding to the 3H6 → 1D2 transition is observed in the photoluminescence excitation spectra of TmMg-borate. The as-obtained crystals exhibit intense blue emission with the emission peaks centered at 455, 479, 667, and 753 nm. The most intensive band corresponds to the 1D2 → 3F4 transition. TmMgB5O10 solids demonstrate the thermal stability of photoluminescence.

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.

Phase Relations in the Ln2O3-Cr2O3-B2O3 (Ln = Gd-Lu) Ternary Oxide Systems.

In this work, isothermal sections of the Ln2O3-Cr2O3-B2O3 (Ln = Gd-Lu) ternary oxide systems at 900, 1000, and 1100 °C were constructed by determining the phase relations by using a powder X-ray diffraction technique. As a result, these systems were divided into subsidiary subsystems. Two types of double borates, LnCr3(BO3)4 (Ln = Gd-Er) and LnCr(BO3)2 (Ln = Ho-Lu), were observed in the investigated systems. Regions of phase stability for LnCr3(BO3)4 and LnCr(BO3)2 were determined. It was shown that the LnCr3(BO3)4 compounds crystallized in rhombohedral and monoclinic polytype modifications up to 1100 °C; above this temperature and up to the melting points, the monoclinic modification was predominantly formed. The LnCr3(BO3)4 (Ln = Gd-Er) and LnCr(BO3)2 (Ln = Ho-Lu) compounds were characterized by using a powder X-ray diffraction method and thermal analysis.

Adenosine reduces sinoatrial node cell action potential firing rate by uncoupling its membrane and calcium clocks.

The spontaneous action potential (AP) firing rate of sinoatrial nodal cells (SANC) is regulated by a system of intracellular Ca2+ and membrane ion current clocks driven by Ca2+-calmodulin-activated adenylyl cyclase-protein kinase-A signaling. The mean AP-cycle length (APCL) and APCL variability inform on the effectiveness of clock coupling. Endogenous ATP metabolite adenosine binds to adenosine receptors (A1, A3) that couple to Gi protein-coupled receptors, reducing spontaneous AP firing rate via Gßγ signaling that activates IKAch,Ado. Adenosine also inhibits adenylyl cyclase activity via Gαi signaling, impacting cAMP-mediated protein kinase-A-dependent protein phosphorylation. We hypothesize that in addition to IKAch,Ado activation, adenosine impacts also Ca2+ via Gαi signaling and that both effects reduce AP firing rate by reducing the effectiveness of the Ca2+ and membrane clock coupling. To this end, we measured Ca2+ and membrane potential characteristics in enzymatically isolated single rabbit SANC. 10 µM adenosine substantially increased both the mean APCL (on average by 43%, n = 10) and AP beat-to-beat variability from 5.1 ± 1.7% to 7.2 ± 2.0% (n = 10) measured via membrane potential and 5.0 ± 2.2% to 10.6 ± 5.9% (n = 40) measured via Ca2+ (assessed as the coefficient of variability = SD/mean). These effects were mediated by hyperpolarization of the maximum diastolic membrane potential (membrane clock effect) and suppression of diastolic local Ca2+releases (LCRs) (Ca2+-clock effect): as LCR size distributions shifted to smaller values, the time of LCR occurrence during diastolic depolarization (LCR period) became prolonged, and the ensemble LCR signal became reduced. The tight linear relationship of coupling between LCR period to the APCL in the presence of adenosine "drifted" upward and leftward, i.e. for a given LCR period, APCL was prolonged, becoming non-linear indicating clock uncoupling. An extreme case of uncoupling occurred at higher adenosine concentrations (>100 µM): small stochastic LCRs failed to self-organize and synchronize to the membrane clock, thus creating a failed attempt to generate an AP resulting in arrhythmia and cessation of AP firing. Thus, the effects of adenosine to activate Gßγ and IKACh,Ado and to activate Gαi, suppressing adenylyl cyclase activity, both contribute to the adenosine-induced increase in the mean APCL and APCL variability by reducing the fidelity of clock coupling and AP firing rate.

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.

Phosphoprotein Phosphatase 1 but Not 2A Activity Modulates Coupled-Clock Mechanisms to Impact on Intrinsic Automaticity of Sinoatrial Nodal Pacemaker Cells.

Spontaneous AP (action potential) firing of sinoatrial nodal cells (SANC) is critically dependent on protein kinase A (PKA) and Ca2+/calmodulin-dependent protein kinase II (CaMKII)-dependent protein phosphorylation, which are required for the generation of spontaneous, diastolic local Ca2+ releases (LCRs). Although phosphoprotein phosphatases (PP) regulate protein phosphorylation, the expression level of PPs and phosphatase inhibitors in SANC and the impact of phosphatase inhibition on the spontaneous LCRs and other players of the oscillatory coupled-clock system is unknown. Here, we show that rabbit SANC express both PP1, PP2A, and endogenous PP inhibitors I-1 (PPI-1), dopamine and cyclic adenosine 3',5'-monophosphate (cAMP)-regulated phosphoprotein (DARPP-32), kinase C-enhanced PP1 inhibitor (KEPI). Application of Calyculin A, (CyA), a PPs inhibitor, to intact, freshly isolated single SANC: (1) significantly increased phospholamban (PLB) phosphorylation (by 2-3-fold) at both CaMKII-dependent Thr17 and PKA-dependent Ser16 sites, in a time and concentration dependent manner; (2) increased ryanodine receptor (RyR) phosphorylation at the Ser2809 site; (3) substantially increased sarcoplasmic reticulum (SR) Ca2+ load; (4) augmented L-type Ca2+ current amplitude; (5) augmented LCR's characteristics and decreased LCR period in intact and permeabilized SANC, and (6) increased the spontaneous basal AP firing rate. In contrast, the selective PP2A inhibitor okadaic acid (100 nmol/L) had no significant effect on spontaneous AP firing, LCR parameters, or PLB phosphorylation. Application of purified PP1 to permeabilized SANC suppressed LCR, whereas purified PP2A had no effect on LCR characteristics. Our numerical model simulations demonstrated that PP inhibition increases AP firing rate via a coupled-clock mechanism, including respective increases in the SR Ca2+ pumping rate, L-type Ca2+ current, and Na+/Ca2+-exchanger current. Thus, PP1 and its endogenous inhibitors modulate the basal spontaneous firing rate of cardiac pacemaker cells by suppressing SR Ca2+ cycling protein phosphorylation, the SR Ca2+ load and LCRs, and L-type Ca2+ current.

Ca2+ and Membrane Potential Transitions During Action Potentials Are Self-Similar to Each Other and to Variability of AP Firing Intervals Across the Broad Physiologic Range of AP Intervals During Autonomic Receptor Stimulation.

Ca2+ and V m transitions occurring throughout action potential (AP) cycles in sinoatrial nodal (SAN) cells are cues that (1) not only regulate activation states of molecules operating within criticality (Ca2+ domain) and limit-cycle (V m domain) mechanisms of a coupled-clock system that underlies SAN cell automaticity, (2) but are also regulated by the activation states of the clock molecules they regulate. In other terms, these cues are both causes and effects of clock molecular activation (recursion). Recently, we demonstrated that Ca2+ and V m transitions during AP cycles in single SAN cells isolated from mice, guinea pigs, rabbits, and humans are self-similar (obey a power law) and are also self-similar to trans-species AP firing intervals (APFIs) of these cells in vitro, to heart rate in vivo, and to body mass. Neurotransmitter stimulation of ß-adrenergic receptor or cholinergic receptor-initiated signaling in SAN cells modulates their AP firing rate and rhythm by impacting on the degree to which SAN clocks couple to each other, creating the broad physiologic range of SAN cell mean APFIs and firing interval variabilities. Here we show that Ca2+ and V m domain kinetic transitions (time to AP ignition in diastole and 90% AP recovery) occurring within given AP, the mean APFIs, and APFI variabilities within the time series of APs in 230 individual SAN cells are self-similar (obey power laws). In other terms, these long-range correlations inform on self-similar distributions of order among SAN cells across the entire broad physiologic range of SAN APFIs, regardless of whether autonomic receptors of these cells are stimulated or not and regardless of the type (adrenergic or cholinergic) of autonomic receptor stimulation. These long-range correlations among distributions of Ca2+ and V m kinetic functions that regulate SAN cell clock coupling during each AP cycle in different individual, isolated SAN cells not in contact with each other. Our numerical model simulations further extended our perspectives to the molecular scale and demonstrated that many ion currents also behave self-similar across autonomic states. Thus, to ensure rapid flexibility of AP firing rates in response to different types and degrees of autonomic input, nature "did not reinvent molecular wheels within the coupled-clock system of pacemaker cells," but differentially engaged or scaled the kinetics of gears that regulate the rate and rhythm at which the "wheels spin" in a given autonomic input context.

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

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

Self-Similar Synchronization of Calcium and Membrane Potential Transitions During Action Potential Cycles Predict Heart Rate Across Species.

OBJECTIVES: The purpose of this study was to discover regulatory universal mechanisms of normal automaticity in sinoatrial nodal (SAN) pacemaker cells that are self-similar across species. BACKGROUND: Translation of knowledge of SAN automaticity gleaned from animal studies to human dysrhythmias (e.g., "sick sinus" syndrome [SSS]) requiring electronic pacemaker insertion has been suboptimal, largely because heart rate varies widely across species. METHODS: Subcellular Ca2+ releases, whole cell action potential (AP)-induced Ca2+ transients, and APs were recorded in isolated mouse, guinea pig, rabbit, and human SAN cells. Ca2+-Vm kinetic parameters during phases of AP cycles from their ignition to recovery were quantified. RESULTS: Although both AP cycle lengths (APCLs) and Ca2+-Vm kinetic parameters during AP cycles differed across species by 10-fold, trans-species scaling of these during AP cycles and scaling of these to APCL in cells in vitro, electrocardiogram RR intervals in vivo, and body mass (BM) were self-similar (obeyed power laws) across species. Thus, APCL in vitro, heart rate in vivo, and BM of any species can be predicted by Ca2+-Vm kinetics during AP cycles in SAN cells measured in any single species in vitro. CONCLUSIONS: In designing optimal heart rate to match widely different BM and energy requirements from mice to humans, nature did not "reinvent pacemaker cell wheels," but differentially scaled kinetics of gears that regulate the rates at which the "wheels spin." This discovery will facilitate the development of novel pharmacological and biological pacemakers featuring a normal, wide-range rate regulation in animal models and the translation of these to humans to target recalcitrant human SSS.

cAMP-Dependent Signaling Restores AP Firing in Dormant SA Node Cells via Enhancement of Surface Membrane Currents and Calcium Coupling.

Action potential (AP) firing rate and rhythm of sinoatrial nodal cells (SANC) are controlled by synergy between intracellular rhythmic local Ca2+ releases (LCRs) ("Ca2+ clock") and sarcolemmal electrogenic mechanisms ("membrane clock"). However, some SANC do not fire APs (dormant SANC). Prior studies have shown that ß-adrenoceptor stimulation can restore AP firing in these cells. Here we tested whether this relates to improvement of synchronization of clock coupling. We characterized membrane potential, ion currents, Ca2+ dynamics, and phospholamban (PLB) phosphorylation, regulating Ca2+ pump in enzymatically isolated single guinea pig SANC prior to, during, and following ß-adrenoceptor stimulation (isoproterenol) or application of cell-permeant cAMP (CPT-cAMP). Phosphorylation of PLB (Serine 16) was quantified in the same cells following Ca2+ measurement. In dormant SANC LCRs were small and disorganized at baseline, membrane potential was depolarized (-38 ± 1 mV, n = 46), and ICaL, If, and IK densities were smaller vs SANC firing APs. ß-adrenoceptor stimulation or application of CPT-cAMP led to de novo spontaneous AP generation in 44 and 46% of dormant SANC, respectively. The initial response was an increase in size, rhythmicity and synchronization of LCRs, paralleled with membrane hyperpolarization and small amplitude APs (rate ∼1 Hz). During the transition to steady-state AP firing, LCR size further increased, while LCR period shortened. LCRs became more synchronized resulting in the growth of an ensemble LCR signal peaked in late diastole, culminating in AP ignition; the rate of diastolic depolarization, AP amplitude, and AP firing rate increased. ICaL, IK, and If amplitudes in dormant SANC increased in response to ß-adrenoceptor stimulation. During washout, all changes reversed in order. Total PLB was higher, but the ratio of phosphorylated PLB (Serine 16) to total PLB was lower in dormant SANC. ß-adrenoceptor stimulation increased this ratio in AP-firing cells. Thus, transition of dormant SANC to AP firing is linked to the increased functional coupling of membrane and Ca2+ clock proteins. The transition occurs via (i) an increase in cAMP-mediated phosphorylation of PLB accelerating Ca2+ pumping, (ii) increased spatiotemporal LCR synchronization, yielding a larger diastolic LCR ensemble signal resulting in an earlier increase in diastolic INCX; and (iii) increased current densities of If, ICaL, and IK.

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.

Crystal Chemistry of High-Temperature Borates.

In recent years borate-based crystals has attracted substantial interest among the research community. The overall importance of this family of materials is reflected in miscellaneous articles and several reviews that have been published over the years. Crystalline borate materials exhibit numerous interesting physical properties, which make them promising for further practical applications. Diversity of functional characteristics results from their high structural flexibility caused in the linkage of planar/non-planar BO3 groups and BO4 tetrahedra, which can occur as isolated or condensed structural units. This report is a brief review on crystal chemistry and structure features of anhydrous/high-temperature borates. Polymorphism of boron-oxygen radicals has been considered basing on cations' nature and synthesis conditions. Analysis of the laws governing borates structures and general principles of their systematics was discussed. As a result, an alternative classification of anhydrous compounds has been considered. It is based on four orders of their subdivision: (1) by the variety of anion formers, (2) by the cation charge, (3) by the N = NM:NB, i.e., ratio of metal atoms number to the ratio of boron atoms number (N-factor) value indicating the borate structural type (if it is known), (4) by the cation type and size.

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.