A three-dimensional simulation model of cardiomyocyte integrating excitation-contraction coupling and metabolism.

Recent studies have revealed that Ca(2+) not only regulates the contraction of cardiomyocytes, but can also function as a signaling agent to stimulate ATP production by the mitochondria. However, the spatiotemporal resolution of current experimental techniques limits our investigative capacity to understand this phenomenon. Here, we created a detailed three-dimensional (3D) cardiomyocyte model to study the subcellular regulatory mechanisms of myocardial energetics. The 3D cardiomyocyte model was based on the finite-element method, with detailed subcellular structures reproduced, and it included all elementary processes involved in cardiomyocyte electrophysiology, contraction, and ATP metabolism localized to specific loci. The simulation results were found to be reproducible and consistent with experimental data regarding the spatiotemporal pattern of cytosolic, intrasarcoplasmic-reticulum, and mitochondrial changes in Ca(2+); as well as changes in metabolite levels. Detailed analysis suggested that although the observed large cytosolic Ca(2+) gradient facilitated uptake by the mitochondrial Ca(2+) uniporter to produce cyclic changes in mitochondrial Ca(2+) near the Z-line region, the average mitochondrial Ca(2+) changes slowly. We also confirmed the importance of the creatine phosphate shuttle in cardiac energy regulation. In summary, our 3D model provides a powerful tool for the study of cardiac function by overcoming some of the spatiotemporal limitations of current experimental approaches.

[1]  D. Bers Sources and Sinks of Activator Calcium , 2001 .

[2]  H. Sugi,et al.  Unloaded shortening increases peak of Ca2+ transients but accelerates their decay in rat single cardiac myocytes. , 2003, American journal of physiology. Heart and circulatory physiology.

[3]  M. Stern,et al.  Measurement of mitochondrial calcium in single living cardiomyocytes by selective removal of cytosolic indo 1. , 1997, The American journal of physiology.

[4]  Antonis A Armoundas,et al.  Role of Sodium-Calcium Exchanger in Modulating the Action Potential of Ventricular Myocytes From Normal and Failing Hearts , 2003, Circulation research.

[5]  D. Nicholls,et al.  Intracellular calcium homeostasis. , 1986, British medical bulletin.

[6]  G. Rutter,et al.  ATP Regulation in Adult Rat Cardiomyocytes , 2006, Journal of Biological Chemistry.

[7]  H. Eppenberger,et al.  In situ compartmentation of creatine kinase in intact sarcomeric muscle: The acto-myosin overlap zone as a molecular sieve , 1992, Journal of Muscle Research & Cell Motility.

[8]  R. Balaban,et al.  Gated in vivo examination of cardiac metabolites with 31P nuclear magnetic resonance. , 1986, The American journal of physiology.

[9]  D. Bers,et al.  Mitochondrial free calcium regulation during sarcoplasmic reticulum calcium release in rat cardiac myocytes. , 2009, Journal of molecular and cellular cardiology.

[10]  P. Dan,et al.  Distribution of proteins implicated in excitation-contraction coupling in rat ventricular myocytes. , 2000, Biophysical journal.

[11]  J A Negroni,et al.  A cardiac muscle model relating sarcomere dynamics to calcium kinetics. , 1996, Journal of molecular and cellular cardiology.

[12]  Marko Vendelin,et al.  Analysis of functional coupling: mitochondrial creatine kinase and adenine nucleotide translocase. , 2004, Biophysical journal.

[13]  M R Boyett,et al.  The effects of mechanical loading and changes of length on single guinea‐pig ventricular myocytes. , 1995, The Journal of physiology.

[14]  M. Jabůrek,et al.  Kinetics and ion specificity of Na+/Ca2+ exchange mediated by the reconstituted beef heart mitochondrial Na+/Ca2+ antiporter , 2004 .

[15]  Toshiaki Hisada,et al.  Three-dimensional simulation of calcium waves and contraction in cardiomyocytes using the finite element method. , 2005, American journal of physiology. Cell physiology.

[16]  D. Bers,et al.  Simultaneous measurements of mitochondrial NADH and Ca(2+) during increased work in intact rat heart trabeculae. , 2002, Biophysical journal.

[17]  B. Corkey,et al.  Determination of the matrix free Ca2+ concentration and kinetics of Ca2+ efflux in liver and heart mitochondria. , 1982, The Journal of biological chemistry.

[18]  V. Saks,et al.  Mathematical model of compartmentalized energy transfer: Its use for analysis and interpretation of 31P-NMR studies of isolated heart of creatine kinase deficient mice , 2004, Molecular and Cellular Biochemistry.

[19]  F. Brette,et al.  beta-adrenergic stimulation restores the Ca transient of ventricular myocytes lacking t-tubules. , 2004, Journal of molecular and cellular cardiology.

[20]  S. Matsuoka,et al.  Simulation of ATP metabolism in cardiac excitation-contraction coupling. , 2004, Progress in biophysics and molecular biology.

[21]  V. Ramesh,et al.  Transport of Ca2+ from Sarcoplasmic Reticulum to Mitochondria in Rat Ventricular Myocytes , 2000, Journal of bioenergetics and biomembranes.

[22]  W. Lederer,et al.  Calcium sparks: elementary events underlying excitation-contraction coupling in heart muscle. , 1993, Science.

[23]  G. Gros,et al.  Protein diffusion in living skeletal muscle fibers: dependence on protein size, fiber type, and contraction. , 2000, Biophysical journal.

[24]  H. Llewelyn Roderick,et al.  The spatial pattern of atrial cardiomyocyte calcium signalling modulates contraction , 2004, Journal of Cell Science.

[25]  Josep Roca,et al.  Modeling of spatial metabolite distributions in the cardiac sarcomere. , 2007, Biophysical journal.

[26]  C. Orchard,et al.  t-Tubules and sarcoplasmic reticulum function in cardiac ventricular myocytes. , 2007, Cardiovascular research.

[27]  J. R. Abney,et al.  Dynamics, structure, and function are coupled in the mitochondrial matrix. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[28]  Donald M. Bers,et al.  Excitation-Contraction Coupling and Cardiac Contractile Force , 1991, Developments in Cardiovascular Medicine.

[29]  E. Griffiths Species dependence of mitochondrial calcium transients during excitation-contraction coupling in isolated cardiomyocytes. , 1999, Biochemical and biophysical research communications.

[30]  K. Nicolay,et al.  In vivo 31P-NMR diffusion spectroscopy of ATP and phosphocreatine in rat skeletal muscle , 2000 .

[31]  L. Izu,et al.  Evolution of cardiac calcium waves from stochastic calcium sparks. , 2001, Biophysical Journal.

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

[33]  A Miyawaki,et al.  Beat‐to‐beat oscillations of mitochondrial [Ca2+] in cardiac cells , 2001, The EMBO journal.

[34]  B. O’Rourke,et al.  Mitochondrial Ca2+ uptake: tortoise or hare? , 2009, Journal of molecular and cellular cardiology.

[35]  V. Mootha,et al.  Ca2+ activation of heart mitochondrial oxidative phosphorylation: role of the F0/F1-ATPase , 2000 .

[36]  Donald M. Bers,et al.  Na+-Ca2+ Exchange Current and Submembrane [Ca2+] During the Cardiac Action Potential , 2002, Circulation research.

[37]  T. Wiesner,et al.  Underlying mechanisms of symmetric calcium wave propagation in rat ventricular myocytes. , 2001, Biophysical journal.

[38]  Greg Lemon,et al.  Fire-diffuse-fire calcium waves in confined intracellular spaces , 2004, Bulletin of mathematical biology.

[39]  A S Verkman,et al.  Monte Carlo analysis of obstructed diffusion in three dimensions: application to molecular diffusion in organelles. , 1998, Biophysical journal.

[40]  D. Bers Cardiac excitation–contraction coupling , 2002, Nature.

[41]  G H Pollack,et al.  Passive and active tension in single cardiac myofibrils. , 1994, Biophysical journal.

[42]  D. Bers,et al.  Spatiotemporal characteristics of SR Ca(2+) uptake and release in detubulated rat ventricular myocytes. , 2005, Journal of molecular and cellular cardiology.

[43]  Daniel A Beard,et al.  Analysis of cardiac mitochondrial Na+–Ca2+ exchanger kinetics with a biophysical model of mitochondrial Ca2+ handing suggests a 3: 1 stoichiometry , 2008, The Journal of physiology.

[44]  G. Langer,et al.  Calcium concentration and movement in the diadic cleft space of the cardiac ventricular cell. , 1996, Biophysical journal.

[45]  Brian O'Rourke,et al.  Elevated Cytosolic Na+ Decreases Mitochondrial Ca2+ Uptake During Excitation–Contraction Coupling and Impairs Energetic Adaptation in Cardiac Myocytes , 2006, Circulation research.

[46]  Toshiaki Hisada,et al.  Multiphysics simulation of left ventricular filling dynamics using fluid-structure interaction finite element method. , 2004, Biophysical journal.

[47]  J. Hoerter,et al.  Water content and its intracellular distribution in intact and saline perfused rat hearts revisited. , 2002, Cardiovascular research.

[48]  K. Gunter,et al.  Mitochondrial calcium transport: physiological and pathological relevance. , 1994, The American journal of physiology.

[49]  Michael J. Holst,et al.  Numerical Analysis of Ca2+ Signaling in Rat Ventricular Myocytes with Realistic Transverse-Axial Tubular Geometry and Inhibited Sarcoplasmic Reticulum , 2010, PLoS Comput. Biol..

[50]  Y. Saeki,et al.  Transverse stiffness of myofibrils of skeletal and cardiac muscles studied by atomic force microscopy. , 2006, The journal of physiological sciences : JPS.

[51]  L. Blatter,et al.  Mitochondrial Calcium in Heart Cells: Beat-to-Beat Oscillations or Slow Integration of Cytosolic Transients? , 2000, Journal of bioenergetics and biomembranes.

[52]  Christian Soeller,et al.  Three-dimensional distribution of ryanodine receptor clusters in cardiac myocytes. , 2006, Biophysical journal.

[53]  R. Balaban,et al.  Role of calcium in metabolic signaling between cardiac sarcoplasmic reticulum and mitochondria in vitro. , 2003, American journal of physiology. Cell physiology.

[54]  W. Cascio,et al.  Mitochondrial calcium transients in adult rabbit cardiac myocytes: inhibition by ruthenium red and artifacts caused by lysosomal loading of Ca(2+)-indicating fluorophores. , 2000, Biophysical journal.

[55]  J. V. van Beek Adenine nucleotide-creatine-phosphate module in myocardial metabolic system explains fast phase of dynamic regulation of oxidative phosphorylation. , 2007, American journal of physiology. Cell physiology.

[56]  C. Soeller,et al.  Examination of the transverse tubular system in living cardiac rat myocytes by 2-photon microscopy and digital image-processing techniques. , 1999, Circulation research.

[57]  D. Bers,et al.  Cytosolic and mitochondrial Ca2+ signals in patch clamped mammalian ventricular myocytes , 1998, The Journal of physiology.

[58]  H. Yamashita,et al.  Coupling between myosin ATPase cycle and creatinine kinase cycle facilitates cardiac actomyosin sliding in vitro. A clue to mechanical dysfunction during myocardial ischemia. , 1996, Circulation.

[59]  V. Saks,et al.  Mathematical model of compartmentalized energy transfer: Its use for analysis and interpretation of 31 P-NMR studies of isolated heart of creatine kinase deficient mice , 1998 .

[60]  K. W. Linz,et al.  Profile and kinetics of L-type calcium current during the cardiac ventricular action potential compared in guinea-pigs, rats and rabbits , 2000, Pflügers Archiv.

[61]  E. Page,et al.  Morphometry of rat heart mitochondrial subcompartments and membranes: application to myocardial cell atrophy after hypophysectomy. , 1976, Journal of ultrastructure research.

[62]  L. Blatter,et al.  Integration of rapid cytosolic Ca2+ signals by mitochondria in cat ventricular myocytes. , 2006, American journal of physiology. Cell physiology.

[63]  R. Winslow,et al.  An integrated model of cardiac mitochondrial energy metabolism and calcium dynamics. , 2003, Biophysical journal.

[64]  T. Gunter,et al.  Kinetics of Mitochondrial Calcium Transport , 2001 .

[65]  Raimond L Winslow,et al.  A computational model integrating electrophysiology, contraction, and mitochondrial bioenergetics in the ventricular myocyte. , 2006, Biophysical journal.

[66]  Bence Ölveczky,et al.  Rapid Diffusion of Green Fluorescent Protein in the Mitochondrial Matrix , 1998, The Journal of cell biology.

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

[68]  Michal Pásek,et al.  A model of the guinea-pig ventricular cardiac myocyte incorporating a transverse-axial tubular system. , 2008, Progress in biophysics and molecular biology.

[69]  G. Hajnóczky,et al.  Calcium signal transmission between ryanodine receptors and mitochondria in cardiac muscle. , 2001, Trends in cardiovascular medicine.

[70]  Gregery T. Buzzard,et al.  Modeling Mitochondrial Bioenergetics with Integrated Volume Dynamics , 2010, PLoS Comput. Biol..

[71]  C. Soeller,et al.  Numerical simulation of local calcium movements during L-type calcium channel gating in the cardiac diad. , 1997, Biophysical journal.

[72]  F. Yin,et al.  A multiaxial constitutive law for mammalian left ventricular myocardium in steady-state barium contracture or tetanus. , 1998, Journal of biomechanical engineering.

[73]  A McCulloch,et al.  Model study of ATP and ADP buffering, transport of Ca(2+) and Mg(2+), and regulation of ion pumps in ventricular myocyte. , 2001, Biophysical journal.

[74]  Y Rudy,et al.  Two components of the delayed rectifier K+ current in ventricular myocytes of the guinea pig type. Theoretical formulation and their role in repolarization. , 1995, Circulation research.

[75]  Kunio Tanaka,et al.  Cyclical changes in high-energy phosphates during the cardiac cycle by pacing-Gated 31P nuclear magnetic resonance. , 2002, Circulation journal : official journal of the Japanese Circulation Society.

[76]  M. Morad,et al.  ‘Pressure–flow‘‐triggered intracellular Ca2+ transients in rat cardiac myocytes: possible mechanisms and role of mitochondria , 2008, The Journal of physiology.

[77]  Ave Minajeva,et al.  Energetic Crosstalk Between Organelles: Architectural Integration of Energy Production and Utilization , 2001, Circulation research.

[78]  M. Forbes,et al.  Membrane systems of guinea pig myocardium: Ultrastructure and morphometric studies , 1988, The Anatomical Record.

[79]  Miss A.O. Penney (b) , 1974, The New Yale Book of Quotations.

[80]  Control of Mitochondrial Respiration in the Heart In Vivo , 1990 .

[81]  R. Meyer,et al.  Control of L‐type calcium current during the action potential of guinea‐pig ventricular myocytes , 1998, The Journal of physiology.

[82]  E. Lakatta,et al.  Measurement of mitochondrial free Ca2+ concentration in living single rat cardiac myocytes. , 1991, The American journal of physiology.

[83]  M. Aimi,et al.  Molecular organizations of myofibrils of skeletal muscle studied by atomic force microscopy. , 2003, Advances in experimental medicine and biology.

[84]  J. Humphrey,et al.  Determination of a constitutive relation for passive myocardium: II. Parameter estimation. , 1990, Journal of biomechanical engineering.

[85]  L. Blatter,et al.  Mitochondrial Ca2+ and the heart. , 2008, Cell calcium.