Synergism of coupled subsarcolemmal Ca2+ clocks and sarcolemmal voltage clocks confers robust and flexible pacemaker function in a novel pacemaker cell model.

Recent experimental studies have demonstrated that sinoatrial node cells (SANC) generate spontaneous, rhythmic, local subsarcolemmal Ca(2+) releases (Ca(2+) clock), which occur during late diastolic depolarization (DD) and interact with the classic sarcolemmal voltage oscillator (membrane clock) by activating Na(+)-Ca(2+) exchanger current (I(NCX)). This and other interactions between clocks, however, are not captured by existing essentially membrane-delimited cardiac pacemaker cell numerical models. Using wide-scale parametric analysis of classic formulations of membrane clock and Ca(2+) cycling, we have constructed and initially explored a prototype rabbit SANC model featuring both clocks. Our coupled oscillator system exhibits greater robustness and flexibility than membrane clock operating alone. Rhythmic spontaneous Ca(2+) releases of sarcoplasmic reticulum (SR)-based Ca(2+) clock ignite rhythmic action potentials via late DD I(NCX) over much broader ranges of membrane clock parameters [e.g., L-type Ca(2+) current (I(CaL)) and/or hyperpolarization-activated ("funny") current (I(f)) conductances]. The system Ca(2+) clock includes SR and sarcolemmal Ca(2+) fluxes, which optimize cell Ca(2+) balance to increase amplitudes of both SR Ca(2+) release and late DD I(NCX) as SR Ca(2+) pumping rate increases, resulting in a broad pacemaker rate modulation (1.8-4.6 Hz). In contrast, the rate modulation range via membrane clock parameters is substantially smaller when Ca(2+) clock is unchanged or lacking. When Ca(2+) clock is disabled, the system parametric space for fail-safe SANC operation considerably shrinks: without rhythmic late DD I(NCX) ignition signals membrane clock substantially slows, becomes dysrhythmic, or halts. In conclusion, the Ca(2+) clock is a new critical dimension in SANC function. A synergism of the coupled function of Ca(2+) and membrane clocks confers fail-safe SANC operation at greatly varying rates.

[1]  D. Noble,et al.  A model of sino-atrial node electrical activity based on a modification of the DiFrancesco-Noble (1984) equations , 1984, Proceedings of the Royal Society of London. Series B. Biological Sciences.

[2]  Donald M. Bers,et al.  Ca2+ Scraps: Local Depletions of Free [Ca2+] in Cardiac Sarcoplasmic Reticulum During Contractions Leave Substantial Ca2+ Reserve , 2003, Circulation research.

[3]  K. Sampson,et al.  Autonomic Control of Cardiac Action Potentials: Role of Potassium Channel Kinetics in Response to Sympathetic Stimulation , 2005, Circulation research.

[4]  D DiFrancesco,et al.  Basal responses of the L‐type Ca2+ and hyperpolarization‐activated currents to autonomic agonists in the rabbit sino‐atrial node. , 1996, The Journal of physiology.

[5]  Michael D Stern,et al.  Diastolic calcium release controls the beating rate of rabbit sinoatrial node cells: numerical modeling of the coupling process. , 2004, Biophysical journal.

[6]  E. Lakatta,et al.  Rhythmic Ryanodine Receptor Ca2+ Releases During Diastolic Depolarization of Sinoatrial Pacemaker Cells Do Not Require Membrane Depolarization , 2004, Circulation research.

[7]  Hiroaki Kitano,et al.  Biological robustness , 2008, Nature Reviews Genetics.

[8]  E. Lakatta,et al.  Dynamic interactions of an intracellular Ca2+ clock and membrane ion channel clock underlie robust initiation and regulation of cardiac pacemaker function. , 2008, Cardiovascular research.

[9]  Yasutaka Kurata,et al.  Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell. , 2002, American journal of physiology. Heart and circulatory physiology.

[10]  Edward G Lakatta,et al.  The emergence of a general theory of the initiation and strength of the heartbeat. , 2006, Journal of pharmacological sciences.

[11]  Stefan Herrmann,et al.  HCN4 provides a ‘depolarization reserve’ and is not required for heart rate acceleration in mice , 2007, The EMBO journal.

[12]  D. Noble,et al.  Facilitation of the L-type calcium current in rabbit sino-atrial cells: effect on cardiac automaticity. , 2000, Cardiovascular research.

[13]  Itsuo Kodama,et al.  Are We Lost in the Labyrinth of the Sinoatrial Node Pacemaker Mechanism? , 2002, Journal of cardiovascular electrophysiology.

[14]  Zhilin Qu,et al.  Dynamics and Cardiac Arrhythmias , 2006, Journal of cardiovascular electrophysiology.

[15]  E. Lakatta,et al.  The Integration of Spontaneous Intracellular Ca2+ Cycling and Surface Membrane Ion Channel Activation Entrains Normal Automaticity in Cells of the Heart's Pacemaker , 2006, Annals of the New York Academy of Sciences.

[16]  E. Lakatta,et al.  Membrane Potential Fluctuations Resulting From Submembrane Ca2+ Releases in Rabbit Sinoatrial Nodal Cells Impart an Exponential Phase to the Late Diastolic Depolarization That Controls Their Chronotropic State , 2006, Circulation research.

[17]  D. Bers,et al.  Cardiac pacemaking: If vs. Ca2+, is it really that simple? , 2003 .

[18]  E. Bozler TONUS CHANGES IN CARDIAC MUSCLE AND THEIR SIGNIFICANCE FOR THE INITIATION OF IMPULSES , 1943 .

[19]  Michael D. Stern,et al.  Local Control Models of Cardiac Excitation–Contraction Coupling , 1999, The Journal of general physiology.

[20]  D. Noble Modeling the Heart--from Genes to Cells to the Whole Organ , 2002, Science.

[21]  Satoshi Matsuoka,et al.  Role of individual ionic current systems in the SA node hypothesized by a model study. , 2003, The Japanese journal of physiology.

[22]  H. T. ter Keurs,et al.  Calcium and arrhythmogenesis. , 2007, Physiological reviews.

[23]  E. Lakatta,et al.  Sinoatrial Nodal Cell Ryanodine Receptor and Na + -Ca 2+ Exchanger: Molecular Partners in Pacemaker Regulation , 2001, Circulation research.

[24]  Matteo E Mangoni,et al.  Genesis and regulation of the heart automaticity. , 2008, Physiological reviews.

[25]  E. Lakatta,et al.  Constitutive Phosphodiesterase Activity Restricts Spontaneous Beating Rate of Cardiac Pacemaker Cells by Suppressing Local Ca2+ Releases , 2008, Circulation research.

[26]  M. Boyett,et al.  Desensitization to acetylcholine in single sinoatrial node cells isolated from rabbit hearts. , 1992, The American journal of physiology.

[27]  D. Terrar,et al.  Protein kinase C enhances the rapidly activating delayed rectifier potassium current, IKr, through a reduction in C‐type inactivation in guinea‐pig ventricular myocytes , 2000, The Journal of physiology.

[28]  Ronald Wilders,et al.  Computer modelling of the sinoatrial node , 2007, Medical & Biological Engineering & Computing.

[29]  D. Noble Cardiac Action and Pacemaker Potentials based on the Hodgkin-Huxley Equations , 1960, Nature.

[30]  M R Boyett,et al.  Correlation between electrical activity and the size of rabbit sino‐atrial node cells. , 1993, The Journal of physiology.

[31]  Stanley Nattel,et al.  Time-dependent transients in an ionically based mathematical model of the canine atrial action potential. , 2002, American journal of physiology. Heart and circulatory physiology.

[32]  R. Tsien,et al.  Cellular and subcellular mechanisms of cardiac pacemaker oscillations. , 1979, The Journal of experimental biology.

[33]  R L Winslow,et al.  Dynamics of abnormal pacemaking activity in cardiac Purkinje fibers. , 1994, Journal of theoretical biology.

[34]  J. H. Wang,et al.  Dependence of cardiac sarcoplasmic reticulum calcium pump activity on the phosphorylation status of phospholamban. , 1991, The Journal of biological chemistry.

[35]  S. Penckofer,et al.  Letter by Wallis and Penckofer regarding article, "Calcium/vitamin D supplementation and cardiovascular events". , 2007, Circulation.

[36]  D. Terrar,et al.  Fundamental importance of Na+–Ca2+ exchange for the pacemaking mechanism in guinea‐pig sino‐atrial node , 2006, The Journal of physiology.

[37]  Denis Noble,et al.  Role of pacemaking current in cardiac nodes: insights from a comparative study of sinoatrial node and atrioventricular node. , 2008, Progress in biophysics and molecular biology.

[38]  John W. Clark,et al.  Parasympathetic modulation of sinoatrial node pacemaker activity in rabbit heart: a unifying model. , 1999, American journal of physiology. Heart and circulatory physiology.

[39]  D. Rubenstein,et al.  Mechanisms of automaticity in subsidiary pacemakers from cat right atrium. , 1989, Circulation research.

[40]  J. Lenfant,et al.  Mechanism of muscarinic control of the high-threshold calcium current in rabbit sino-atrial node myocytes , 1993, Pflügers Archiv.

[41]  D. Noble,et al.  Rectifying Properties of Heart Muscle , 1960, Nature.

[42]  J. Clark,et al.  A mathematical model of a rabbit sinoatrial node cell. , 1994, The American journal of physiology.

[43]  Trine Krogh-Madsen,et al.  An ionic model for rhythmic activity in small clusters of embryonic chick ventricular cells. , 2005, American journal of physiology. Heart and circulatory physiology.

[44]  E. Lakatta,et al.  The Missing Link in the Mystery of Normal Automaticity of Cardiac Pacemaker Cells , 2008, Annals of the New York Academy of Sciences.

[45]  Donald M Bers,et al.  A mathematical treatment of integrated Ca dynamics within the ventricular myocyte. , 2004, Biophysical journal.

[46]  E. Lakatta Beyond Bowditch: the convergence of cardiac chronotropy and inotropy. , 2004, Cell calcium.

[47]  D DiFrancesco,et al.  Reciprocal role of the inward currents ib, Na and if in controlling and stabilizing pacemaker frequency of rabbit sino-atrial node cells , 1992, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[48]  H Honjo,et al.  Sarcoplasmic Reticulum Ca2+ Release Is Not a Dominating Factor in Sinoatrial Node Pacemaker Activity , 2003, Circulation research.

[49]  E. Lakatta,et al.  Calcium Cycling Protein Density and Functional Importance to Automaticity of Isolated Sinoatrial Nodal Cells Are Independent of Cell Size , 2007, Circulation research.

[50]  D. Kass,et al.  Wall Tension Is a Potent Negative Regulator of In Vivo Thrombomodulin Expression , 2003, Circulation Research.

[51]  Dario DiFrancesco,et al.  Direct activation of cardiac pacemaker channels by intracellular cyclic AMP , 1991, Nature.

[52]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[53]  S. Matsuoka,et al.  Ionic mechanisms underlying the positive chronotropy induced by beta1-adrenergic stimulation in guinea pig sinoatrial node cells: a simulation study. , 2008, The journal of physiological sciences : JPS.

[54]  H. Cheng,et al.  Sinoatrial node pacemaker activity requires Ca(2+)/calmodulin-dependent protein kinase II activation. , 2000, Circulation research.

[55]  J Jalife,et al.  Mutual entrainment and electrical coupling as mechanisms for synchronous firing of rabbit sino‐atrial pace‐maker cells. , 1984, The Journal of physiology.

[56]  C. Luo,et al.  A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. , 1994, Circulation research.

[57]  E. Lakatta,et al.  High Basal Protein Kinase A–Dependent Phosphorylation Drives Rhythmic Internal Ca2+ Store Oscillations and Spontaneous Beating of Cardiac Pacemaker Cells , 2006, Circulation research.

[58]  Jürgen Kurths,et al.  Synchronization: Phase locking and frequency entrainment , 2001 .

[59]  E. Lakatta,et al.  Cardiac pacemaker cell failure with preserved I(f), I(CaL), and I(Kr): a lesson about pacemaker function learned from ischemia-induced bradycardia. , 2007, Journal of molecular and cellular cardiology.

[60]  D DiFrancesco,et al.  The contribution of the ‘pacemaker’ current (if) to generation of spontaneous activity in rabbit sino‐atrial node myocytes. , 1991, The Journal of physiology.

[61]  C Antzelevitch,et al.  Electrotonic Modulation of Pacemaker Activity Further Biological and Mathematical Observations on the Behavior of Modulated Parasystole , 1982, Circulation.

[62]  W. Trautwein,et al.  Relaxation of the ACh-induced potassium current in the rabbit sinoatrial node cell , 1978, Pflügers Archiv.

[63]  A E Becker,et al.  Functional and Morphological Organization of the Rabbit Sinus Node , 1980, Circulation research.

[64]  D. Bers The beat goes on: diastolic noise that just won't quit. , 2006, Circulation research.

[65]  H Zhang,et al.  Mathematical models of action potentials in the periphery and center of the rabbit sinoatrial node. , 2000, American journal of physiology. Heart and circulatory physiology.

[66]  E. Lakatta,et al.  Cyclic Variation of Intracellular Calcium: A Critical Factor for Cardiac Pacemaker Cell Dominance , 2003, Circulation research.

[67]  Christopher J. Davidson,et al.  A novel mechanism of pacemaker control that depends on high levels of cAMP and PKA-dependent phosphorylation: a precisely controlled biological clock. , 2006, Circulation research.

[68]  S Guan,et al.  A discussion about the DiFrancesco-Noble model. , 1997, Journal of theoretical biology.

[69]  Zhengfeng Zhou,et al.  Na(+)‐Ca2+ exchange current in latent pacemaker cells isolated from cat right atrium. , 1993, The Journal of physiology.

[70]  Yasutaka Kurata,et al.  Roles of L-type Ca2+ and delayed-rectifier K+ currents in sinoatrial node pacemaking: insights from stability and bifurcation analyses of a mathematical model. , 2003, American journal of physiology. Heart and circulatory physiology.

[71]  Jörg Hüser,et al.  Intracellular Ca2+ release contributes to automaticity in cat atrial pacemaker cells , 2000, The Journal of physiology.

[72]  Edward G Lakatta,et al.  &bgr;-Adrenergic Stimulation Modulates Ryanodine Receptor Ca2+ Release During Diastolic Depolarization to Accelerate Pacemaker Activity in Rabbit Sinoatrial Nodal Cells , 2002, Circulation research.

[73]  Y Rudy,et al.  Ionic charge conservation and long-term steady state in the Luo-Rudy dynamic cell model. , 2001, Biophysical journal.