Models of cardiac excitation-contraction coupling in ventricular myocytes

Mathematical Biosciences

Volumn 226, Issue 1, 2010, Pages 1-15

  Williams, George S B ^a   Smith, Gregory D ^c   Sobie, Eric A ^a,b,d   Jafri, M Saleet ^a,b  

^a GEORGE MASON UNIVERSITY   (United States)

^b UNIVERSITY OF MARYLAND BIOTECHNOLOGY INSTITUTE   (United States)

^c The College of William and Mary   (United States)

^d MOUNT SINAI SCHOOL OF MEDICINE   (United States)

Author keywords

Calcium; Calcium spark; Excitation contraction coupling; Heart; Model

Indexed keywords

CALCIUM DYNAMICS; CELLULAR MODEL; COMPUTATIONAL MODELING; EXCITATION-CONTRACTION COUPLING; EXPERIMENTAL STUDIES; HEART MODEL; HEART MUSCLES; MOLECULAR COMPONENTS; MOMENT CLOSURE; NOVEL METHODS; PHYSIOLOGICAL DATA; PROBABILITY DENSITIES; TIME COURSE; VENTRICULAR MYOCYTES; WHOLE CELL; WHOLE-HEART MODEL;

CALCIUM; COMPUTATIONAL EFFICIENCY; ELECTRIC SPARKS; PROBABILITY DENSITY FUNCTION;

HEART;

CALCIUM; CALCIUM CHANNEL L TYPE; RYANODINE RECEPTOR;

CALCIUM; CARDIOLOGY; CARDIOVASCULAR SYSTEM; MODELING; NUMERICAL MODEL;

BIOPHYSICS; CALCIUM TRANSPORT; CHANNEL GATING; EXCITATION CONTRACTION COUPLING; HEART CONTRACTION; HEART ELECTROPHYSIOLOGY; HEART FUNCTION; HEART MUSCLE CELL; HEART MUSCLE EXCITABILITY; HEART VENTRICLE; HUMAN; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MONTE CARLO METHOD; NONHUMAN; PROBABILITY; REVIEW; TIME;

ACTION POTENTIALS; ANIMALS; CALCIUM SIGNALING; DOGS; EXCITATION CONTRACTION COUPLING; GUINEA PIGS; HEART FAILURE; HUMANS; MODELS, CARDIOVASCULAR; MONTE CARLO METHOD; MYOCARDIAL CONTRACTION; MYOCYTES, CARDIAC; PROBABILITY THEORY; RYANODINE RECEPTOR CALCIUM RELEASE CHANNEL; VENTRICULAR FUNCTION;

EID: 77953123168     PISSN: 00255564     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mbs.2010.03.005     Document Type: Review

References (94)

1. Noble D. A modification of the Hodgkin-Huxley equations applicable to Purkinje fibre action and pace-maker potentials. J. Physiol. 1962, 160:317.
2. Hodgkin A., Huxley A. The components of membrane conductance in the giant axon of loligo. J. Physiol. 1952, 116(4):473.
3. McAllister R., Noble D., Tsien R. Reconstruction of the electrical activity of cardiac Purkinje fibres. J. Physiol. 1975, 251(1):1.
4. DiFrancesco D., Noble D. A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philos. Trans. Roy. Soc. Lond. B: Biol. Sci. 1985, 307(1133):353.
5. Hilgemann D., Noble D. Excitation-contraction coupling and extracellular calcium transients in rabbit atrium: reconstruction of basic cellular mechanisms. Philos. Trans. Roy. Soc. Lond. B: Biol. Sci. 1987, 230(1259):163.
6. Demir S., Clark J., Murphey C.R., Giles W.R. A mathematical model of a rabbit sinoatrial cell. Am. J. Physiol. 1994, 266(3 Pt. 1):C832.
7. Beeler G., Reuter H. Reconstruction of the action potential of ventricular myocardial fibres. J. Physiol. 1977, 268(1):177.
8. Luo C., Rudy Y. A model of the ventricular cardiac action potential: depolarization, repolarization, and their interaction. Circ. Res. 1991, 68(6):1501.
9. Luo C., Rudy Y. A dynamic model of the cardiac ventricular action potential. I. Simulations of ionic currents and concentration changes. Circ. Res. 1994, 74(6):1071.
10. Luo C., Rudy Y. A dynamic model of the cardiac ventricular action potential. II. Afterdepolarizations, triggered activity, and potentiation. Circ. Res. 1994, 74(6):1097.
11. Noble D. Computational models of the heart and their use in assessing the actions of drugs. J. Pharmacol. Sci. 2008, 107(2):107.
12. 2+ and electrical alternans in cardiac myocytes: role of CamKII and repolarizing currents. Am. J. Physiol. Heart Circ. Physiol. 2007, 292(6):H2854.
13. Decker K., Heijman J., Silva J., Hund T., Rudy Y. Properties and ionic mechanisms of action potential adaptation, restitution, and accommodation in canine epicardium. Am. J. Physiol. Heart Circ. Physiol. 2009, 296(4):H1017.
14. Zeng J., Rudy Y. Early afterdepolarizations in cardiac myocytes: mechanism and rate dependence. Biophys. J. 1995, 68(3):949.
15. Stern M. Theory of excitation-contraction coupling in cardiac muscle. Biophys. J. 1992, 63(2):497.
16. 2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys. J. 1998, 74(3):1149.
17. 2+ channel inactivation in cardiac muscle. Am. J. Physiol. Heart Circ. Physiol. 2004, 286(3):H1154.
18. Pandit S., Clark R., Giles W.R., Demir S. A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophys. J. 2001, 81(6):3029.
19. Winslow R., Rice J., Jafri S., Marbán E., O'Rourke B. Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure, II: model studies. Circ. Res. 1999, 84(5):571.
20. Shannon T., Wang F., Puglisi J., Weber C., Bers D. A mathematical treatment of integrated Ca dynamics within the ventricular myocyte. Biophys. J. 2004, 87(5):3351.
21. 2+ oscillations. Biophys. J. 1996, 71(6):3477.
22. Irvine L., Jafri M., Winslow R. Cardiac sodium channel markov model with temperature dependence and recovery from inactivation. Biophys. J. 1999, 76(4):1868.
23. Rudy Y. From genome to physiome: integrative models of cardiac excitation. Ann. Biomed. Eng. 2000, 28(8):945.
24. Clancy C., Zhu Z., Rudy Y. Pharmacogenetics and anti-arrhythmic drug therapy: a theoretical investigation. Am. J. Physiol. Heart Circ. Physiol. 2007, 292(3):H1641.
25. Clancy C., Rudy Y. Linking a genetic defect to its cellular phenotype in a cardiac arrhythmia. Nature 1999, 400(6744):566.
26. 2+ channels. Neuron 1994, 12(6):1301.
27. 2+ release in heart. Science (New York, NY) 1993, 260(5109):807.
28. Rice J., Winslow R., Hunter W. Comparison of putative cooperative mechanisms in cardiac muscle: length dependence and dynamic responses. Am. J. Physiol. 1999, 276(5 Pt. 2):H1734.
29. Bassani J., Yuan W., Bers D. Fractional sr ca release is regulated by trigger ca and sr ca content in cardiac myocytes. Am. J. Physiol. 1995, 268(5 Pt. 1):C1313.
30. Linz K., Meyer R. Control of L-type calcium current during the action potential of guinea-pig ventricular myocytes. J. Physiol. 1998, 513(Pt. 2):425.
31. Bers D. Excitation-Contraction Coupling and Cardiac Contractile Force 1992, Kluwer Academic Publishers, Dordrecht. second ed.
32. Rice J., Jafri M., Winslow R. Modeling short-term interval-force relations in cardiac muscle. Am. J. Physiol. Heart Circ. Physiol. 2000, 278(3):H913.
33. Wier W., Yue D. Intracellular calcium transients underlying the short-term force-interval relationship in ferret ventricular myocardium. J. Physiol. 1986, 376:507.
34. 2+-mobility in the sarcoplasmic reticulum of ventricular myocytes is low. Biophys. J. 2008, 95(3):1412.
35. Zima A., Picht E., Bers D., Blatter L. Partial inhibition of sarcoplasmic reticulum ca release evokes long-lasting ca release events in ventricular myocytes: role of luminal ca in termination of ca release. Biophys. J. 2008, 94(5):1867.
36. Winslow R., Scollan D., Holmes A., Yung C., Zhang J., Jafri M. Electrophysiological modeling of cardiac ventricular function: from cell to organ. Ann. Rev. Biomed. Eng. 2000, 2:119.
37. Shiferaw Y., Watanabe M., Garfinkel A., Weiss J., Karma A. Model of intracellular calcium cycling in ventricular myocytes. Biophys. J. 2003, 85(6):3666.
38. Restrepo J., Weiss J., Karma A. Calsequestrin-mediated mechanism for cellular calcium transient alternans. Biophys. J. 2008, 95(8):3767.
39. Restrepo J., Karma A. Spatiotemporal intracellular calcium dynamics during cardiac alternans. Chaos (Woodbury, NY) 2009, 19(3):037115.
40. Sato D., Shiferaw Y., Garfinkel A., Weiss J., Qu Z., Karma A. Spatially discordant alternans in cardiac tissue: role of calcium cycling. Circ. Res. 2006, 99(5):520.
41. Tao T., O'Neill S., Diaz M., Li Y., Eisner D., Zhang H. Alternans of cardiac calcium cycling in a cluster of ryanodine receptors: a simulation study. Am. J. Physiol. Heart Circ. Physiol. 2008, 295(2):H598.
42. Huertas M., Smith G., Györke S. Analysis of calcium alternans in a cardiac myocyte model that uses moment equations to represent heterogeneous junction sr calcium. Biophys. J. 2009, 96(Suppl. 1):277a.
43. Cheng H., Lederer W., Cannell M. Calcium sparks: elementary events underlying excitation-contraction coupling in heart muscle. Science 1993, 262(5134):740.
44. Stern M., Cheng H. Putting out the fire: what terminates calcium-induced calcium release in cardiac muscle?. Cell Calcium 2004, 35(6):591.
45. DeRemigio H., Smith G. The dynamics of stochastic attrition viewed as an absorption time on a terminating Markov chain. Cell Calcium 2005, 38(2):73.
46. 2+ channels. J. Theor. Biol. 2005, 235(1):121.
47. 2+ channels and release sites. J. Theor. Biol. 2007, 246(2):332.
48. 2+ release units and couplons in skeletal and cardiac muscles. Biophys. J. 1999, 77(3):1528.
49. Groff J., Smith G. Calcium-dependent inactivation and the dynamics of calcium puffs and sparks. J. Theor. Biol. 2008, 253(3):483.
50. 2+ sensing sites. Biophys. J. 1998, 75(6):2801.
51. Smith G., Keizer J., Stern M., Lederer W., Cheng H. A simple numerical model of calcium spark formation and detection in cardiac myocytes. Biophys. J. 1998, 75(1):15.
52. Stern M., Pizarro G., Ríos E. Local control model of excitation-contraction coupling in skeletal muscle. J. Gen. Physiol. 1997, 110(4):415.
53. 2+ sparks: an investigative mathematical model of calcium-induced calcium release. Biophys. J. 2002, 83(1):59.
54. 2+ oscillations. Biophys. J. 1994, 67(1):447.
55. 2+ blinks: rapid nanoscopic store calcium signaling. Proc. Natl. Acad. Sci. USA 2005, 102(8):3099.
56. 2+ reserve. Circ. Res. 2003, 93(1):40.
57. 2+ release in cardiac myocytes. Circ. Res. 2002, 91(5):414.
58. Terentyev D., Viatchenko-Karpinski S., Györke I., Volpe P., Williams S., Györke S. Calsequestrin determines the functional size and stability of cardiac intracellular calcium stores: mechanism for hereditary arrhythmia. Proc. Natl. Acad. Sci. USA 2003, 100(20):11759.
59. 2+ diffusion. Circ. Res. 2008, 103(8):e105.
60. 2+ release refractoriness in heart muscle. Circ. Res. 2004, 95(8):807.
61. 2+ release in rat ventricular myocytes. J. Physiol. 2005, 565(Pt 2):441.
62. 2+ efflux theory and practice. Prog. Biophys. Mol. Biol. 2005, 90(1-3):172.
63. Duke T., Bray D. Heightened sensitivity of a lattice of membrane receptors. Proc. Natl. Acad. Sci. USA 1999, 96(18):10104.
64. Duke T., Le Novère N., Bray D. Conformational spread in a ring of proteins: a stochastic approach to allostery. J. Mol. Biol. 2001, 308(3):541.
65. Groff J., Smith G. Ryanodine receptor allosteric coupling and the dynamics of calcium sparks. Biophys. J. 2008, 95(1):135.
66. Stern M.D., Song L.S., Cheng H., Sham J.S., Yang H.T., Boheler K.R., Ríos E. Local control models of cardiac excitation-contraction coupling. A possible role for allosteric interactions between ryanodine receptors. J. Gen. Physiol. 1999, 113(3):469.
67. 2+ sparks. Biophys. J. 2001, 80(1):88.
68. Izu L., Wier W., Balke C. Evolution of cardiac calcium waves from stochastic calcium sparks. Biophys. J. 2001, 80(1):103.
69. Ramay H., Sobie E., Lederer W., Jafri M. A model of calcium dynamics in the rat ventricular sarcomere. Biophys. J. 2004, 86(1 Pt. 2 Suppl. S):112A.
70. Ramay H.R., Sobie E.A., Lederer W.J., Jafri M.S. A Monte Carlo simulation study of spontaneous calcium waves in the heart. Biophys. J. 2007, (Suppl. S):257A.
71. Tan W., Fu C., Fu C., Xie W., Cheng H. An anomalous subdiffusion model for calcium spark in cardiac myocytes. Appl. Phys. Lett. 2007, 91(18):183901.
72. Fabiato A. Time and calcium dependence of activation and inactivation of calcium-induced release of calcium from the sarcoplasmic reticulum of a skinned canine cardiac purkinje cell. J. Gen. Physiol. 1985, 85(2):247.
73. Cannell M., Berlin J., Lederer W. Effect of membrane potential changes on the calcium transient in single rat cardiac muscle cells. Science 1987, 238(4832):1419.
74. 2+ transient in feline ventricular myocytes. Am. J. Physiol. 1989, 257(3 Pt. 2):H746.
75. i transients in guinea pig ventricular myocytes. Circ. Res. 1987, 61(1):148.
76. 2+ release in the functional unit of the cardiac diadic space. Biophys. J. 1999, 77(4):1871.
77. 2+ release. Biophys. J. 2002, 83(6):2918.
78. Chikando A.C., Ramay H.R., Sobie E.A., Jafri M.S. A detailed computational study of calcium dynamics incorporating rogue ryanodine receptors contribution. Biophys. J. 2007, (Suppl. S):137A.
79. Hinch R., Greenstein J., Tanskanen A., Xu L., Winslow R. A simplified local control model of calcium-induced calcium release in cardiac ventricular myocytes. Biophys. J. 2004, 87(6):3723.
80. Greenstein J., Hinch R., Winslow R. Mechanisms of excitation-contraction coupling in an integrative model of the cardiac ventricular myocyte. Biophys. J. 2006, 90(1):77.
81. Hinch R., Greenstein J., Winslow R. Multi-scale models of local control of calcium-induced calcium release. Prog. Biophys. Mol. Biol. 2006, 90(1-3):136.
82. Williams G.S.B., Huertas M.A., Sobie E.A., Jafri M.S., Smith G.D. A probability density approach to modeling local control of calcium-induced calcium release in cardiac myocytes. Biophys. J. 2007, 92(7):2311.
83. Bertram R., Sherman A. Population dynamics of synaptic release sites. SIAM J. Appl. Math. 1998, 58(1):142.
84. Nykamp D., Tranchina D. A population density approach that facilitates large-scale modeling of neural networks: analysis and an application to orientation tuning. J. Comput. Neurosci. 2000, 8(1):19.
85. Huertas M., Smith G. A multivariate population density model of the dLGN/PGN relay. J. Comput. Neurosci. 2006, 21(2):171.
86. Williams G., Huertas M., Sobie E., Jafri M., Smith G. Moment closure for local control models of calcium-induced calcium release in cardiac myocytes. Biophys. J. 2008, 95(4):1689.
87. DeRemigio H., Kemper P., LaMar M., Smith G. Markov chain models of coupled intracellular calcium channels: Kronecker structured representations and benchmark stationary distribution calculations. Phys. Biol. 2008, 5(3):36003.
88. Y. Hao, P. Kemper, G. Smith, Reduction of calcium release site models via fast/slow analysis and iterative aggregation/disaggregation, Chaos. Focus issue: intracellular calcium dynamics - a change of modeling paradigm? 5 (3) (2009) 36003.
89. Greenstein J., Tanskanen A., RL W. Modeling the actions of beta-adrenergic signaling on excitation-contraction coupling processes. Ann. N. Y. Acad. Sci. 2004, 1015:16.
90. Saucerman J., McCulloch A. Cardiac beta-adrenergic signaling: from subcellular microdomains to heart failure. Ann. N. Y. Acad. Sci. 2006, 1080:348.
91. 2+ in cardiac myocytes. Biophys. J. 2008, 95(10):4597.
92. 2+ current facilitation: a modeling study. Biophys. J. 2009, 96(5):1770.
93. Cortassa S., O'Rourke B., Winslow R., Aon M. Control and regulation of mitochondrial energetics in an integrated model of cardiomyocyte function. Biophys. J. 2009, 96(6):2466.
94. 2+, and regulation of ion pumps in ventricular myocyte. Biophys. J. 2001, 81(2):614.