ЗАКЛЮЧЕНИЕ. 1. Дано дальнейшее развитие электронно-конформационной модели RyR-канала и кластера RyR-каналов на мембране саркоплазматического ретикулюма в высвобождающей

ОСНОВНЫЕ РЕЗУЛЬТАТЫ И ВЫВОДЫ

1. Дано дальнейшее развитие электронно-конформационной модели RyR-канала и кластера RyR-каналов на мембране саркоплазматического ретикулюма в высвобождающей единице. Впервые в ЭК-модели предложено введение дополнительного, инактивационного состояния. Предложена новая модель взаимодействия ионов Са²⁺ с активационным центром RyR-канала, учитывающая вероятности заполнения мест присоединения активационного центра ионами Са²⁺. Дана детализация модели туннельных переходов, включающая введение «зоны разрешенного туннельного перехода» вблизи минимума конформационного потенциала RyR-канала.

2. Разработан многоцелевой компьютерный комплекс, реализующий алгоритмы численного решения уравнений электронно-конформационной модели и единой модели Са²⁺ высвобождающей единицы, на базе которого проводились серии экспериментов по изучению динамики одиночного RyR-канала, кластера RyR-каналов и Са²⁺ высвобождающей единицы.

3. Впервые в рамках электронно-конформационной модели воспроизведены и объяснены основные экспериментально наблюдаемые особенности функционирования одиночного RyR-канала:

- экстремальная зависимость вероятности пребывания RyR-канала в открытом состоянии от концентрации Са²⁺;

- влияние ионов Mg²⁺ на процесс активации RyR-канала;

- эффект адаптации RyR-канала к продолжительной стимуляции.

4. Разработана единая модель Са²⁺ высвобождающей единицы, объединяющая электронно-конформационную модель функционирования кластера RyR-каналов с моделью динамики ионов Са²⁺ между отделами высвобождающей единицы.

5. Впервые в рамках ЭК-модели исследована изолированная Са²⁺ высвобождающая единица в клетках водителя сердечного ритма (Ca²⁺-«часы»). Численные эксперименты показали, что изолированная ВЕ в широком диапазоне параметров может вести себя как самоподдерживающийся кальциевый осциллятор. Выявлена различные режимы функционирования изолированной ВЕ. Отмечено, что в физиологическом режиме при повышении частоты увеличивается амплитуда осцилляций Са²⁺-«часов», что на молекулярном уровне объясняет принцип Боудича «чаще-сильнее» работы сердечных клеток.

7. Впервые исследовано влияние взаимодействия между RyR-каналами на стабильность работы Са²⁺-«часов». Показано, что включение конформационного взаимодействия между каналами приводит к стабилизации осцилляций по частоте и амплитуде.

8. Впервые обнаружен и исследован эффект случайной остановки осцилляций Са²⁺-«часов» при достаточно сильном взаимодействии между RyR-каналами в ВЕ.

Список литературы

1. Bers, D., Excitation-contraction coupling and cardiac contractile force. Vol. 237. 2001: Kluwer Academic Pub.

2. Wehrens, X.H. and A.R. Marks, Ryanodine Receptors: Structure, function and dysfunction in clinical disease. Vol. 254. 2004: Springer.

3. Moskvin, A.S., et al., Electron-conformational model of ryanodine receptor lattice dynamics. Progress in biophysics and molecular biology, 2006. 90(1): p. 88-103.

4. Moskvin, A.S., et al. Electron-conformational model of nonlinear dynamics of the ryanodine channel lattice in cardiomyocytes. Doklady Biochemistry and Biophysics. 2005. Springer.

5. Moskvin, A.S., et al. Biophysical adaptation of the theory of photo-induced phase transition: model of cooperative gating of cardiac ryanodine receptors. in Journal of Physics: Conference Series. 2005. IOP Publishing.

6. Коньков Л. Е. и др. Нелинейная динамика клеточного рианодинового канала //Нелинейная динамика. – 2008. – Т. 4. – №. 2. – С. 181-192.

7. Беркинблит, М.Б. and Е.Г. Глаголева, Электричество в живых организмах. 1988: Наука.

8. Гоффман, Б., и др., Электрофизиология сердца: Пер. с англ. 1962: Изд-во иностр. лит.

9. Морман, Д., Хеллер Л., Физиология сердечно-сосудистой системы. СПб.: Питер, 2000. 250: стр. 15.

10. Katz, A.M., Physiology of the Heart. 2010: Lippincott Williams & Wilkins.

11. Bers, D.M., Cardiac action potential and ion channels, in Excitation-Contraction Coupling and Cardiac Contractile Force. 2001, Springer. p. 63-100.

12. Williams, A.J., D.J. West, and R. Sitsapesan, Light at the end of the Ca²⁺-release channel tunnel: structures and mechanisms involved in ion translocation in ryanodine receptor channels. Quarterly reviews of biophysics, 2001. 34(1): p. 61.

13. Yin, C.-C., L.M. Blayney, and F. Anthony Lai, Physical coupling between ryanodine receptor–calcium release channels. Journal of molecular biology, 2005. 349 (3): p. 538-546.

14. Marx, S.O., et al., Coupled gating between cardiac calcium release channels (ryanodine receptors). Circulation research, 2001. 88 (11): p. 1151-1158.

15. Wehrens, X.H.T., et al., FKBP12. 6 deficiency and defective calcium release channel (ryanodine receptor) function linked to exercise-induced sudden cardiac death. Cell, 2003. 113(7): p. 829-840.

16. Copello, J., et al., Differential activation by Ca2+, ATP and caffeine of cardiac and skeletal muscle ryanodine receptors after block by Mg²⁺. Journal of Membrane Biology, 2002. 187 (1): p. 51-64.

17. Laver, D., et al., Cytoplasmic Ca²⁺ inhibits the ryanodine receptor from cardiac muscle. The Journal of membrane biology, 1995. 147 (1): p. 7-22.

18. 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. The Journal of general physiology, 1985. 85 (2): p. 247-289.

19. Zahradnikova, A., J. Bak, and L.G. Meszaros, Heterogeneity of the cardiac calcium release channel as assessed by its response to ADP-ribose. Biochemical and biophysical research communications, 1995. 210(2): p. 457-463.

20. Malev, V., et al., Kinetics of opening and closure of syringomycin E channels formed in lipid bilayers. Membrane & cell biology, 2001. 14 (6): p. 813.

21. Zahradnikova, A., J. Bak, and L.G. Meszaros, Heterogeneity of the cardiac calcium release channel as assessed by its response to ADP-ribose. Biochemical and biophysical research communications, 1995. 210 (2): p. 457-463.

22. Fill, M., et al., Ryanodine receptor adaptation. The Journal of general physiology, 2000. 116(6): p. 873-882.

23. Armisen R., Sierralta J., Vélez P., Naranjo D., Suarez-Isla B.A. Modal gating in neuronal and skeletal muscle ryanodine-sensitive Ca²⁺ release channels. Am J Physiol Cell Physiol, 1996. 271: р. 144–153.

24. Gyorke, I. and S. Gyorke, Regulation of the Cardiac Ryanodine Receptor Channel by Luminal Ca²⁺ Involves Luminal Ca²⁺ Sensing Sites. Biophysical journal, 1998. 75(6): p. 2801-2810.

25. Gyorke, S. and D. Terentyev, Modulation of ryanodine receptor by luminal calcium and accessory proteins in health and cardiac disease. Cardiovascular research, 2008. 77(2): p. 245-255.

26. Bordner, A.J., Predicting small ligand binding sites in proteins using backbone structure. Bioinformatics, 2008. 24(24): p. 2865-2871.

27. Bertram, R., et al., Tutorials in Mathematical Biosciences II: Mathematical Modeling of Calcium Dynamics and Signal Transduction. Vol. 2. 2005: Springer.

28. Fill M., C.J., Ryanodine Receptor Calcium Release Channels. Physiol Rev, 2002. 82: p. 893-922.

29. Gyorke, S. and M. Fill, Ryanodine receptor adaptation: control mechanism of Ca (2+)-induced Ca2+ release in heart. Science, 1993. 260(5109): p. 807-809.

30. Fill, M. and J.A. Copello, Ryanodine receptor calcium release channels. Physiological reviews, 2002. 82(4): p. 893-922.

31. Keizer, J. and L. Levine, Ryanodine receptor adaptation and Ca2+ (-) induced Ca2+ release-dependent Ca2+ oscillations. Biophysical journal, 1996. 71(6): p. 3477-3487.

32. M. Fill, A.Z.e.a., Ryanodine Receptor Adaptation. J. Gen. Physiol., 2000. 116: p. 873-882.

33. Valdivia, H.H., et al., Rapid adaptation of cardiac ryanodine receptors: modulation by Mg2+ and phosphorylation. Science, 1995. 267(5206): p. 1997-2000.

34. Laver, D.R., Ca2+ stores regulate ryanodine receptor Ca²⁺ release channels via luminal and cytosolic Ca²⁺ sites. Clinical and experimental pharmacology and physiology, 2007. 34(9): p. 889-896.

35. Laver, D.R. and B.A. Curtis, Response of ryanodine receptor channels to Ca2+ steps produced by rapid solution exchange. Biophysical journal, 1996. 71(2): p. 732-741.

36. Sobie E. A. et al. Termination of Cardiac Ca²⁺ Sparks: An Investigative Mathematical Model of Calcium-Induced Calcium Release //Biophysical journal. – 2002. – Т. 83. – №. 1. – С. 59-78.

37. Rosales, R.A., M. Fill, and A.L. Escobar, Calcium regulation of single ryanodine receptor channel gating analyzed using HMM/MCMC statistical methods. The Journal of general physiology, 2004. 123 (5): p. 533-553.

38. Zahradnikova, A. and I. Zahradnik, A minimal gating model for the cardiac calcium release channel. Biophysical journal, 1996. 71(6): p. 2996-3012.

39. Zahradnikova, A. and I. Zahradnik, Analysis of calcium-induced calcium release in cardiac sarcoplasmic reticulum vesicles using models derived from single-channel data. Biochimica et Biophysica Acta (BBA)-Biomembranes, 1999. 1418(2): p. 268-284.

40. Bassingthwaighte, J.B., L.S. Liebovitch, and B.J. West, Fractal physiology. Vol. 2. 1994: Amer Physiological Society.

41. Гриневич, А., М. Асташев, and В. Казаченко, Мультифрактальная кинетика воротного механизма ионных каналов в биологических мембранах. Биологические мембраны: Журнал мембранной и клеточной биологии, 2007. 24 (4): p. 316-332.

42. Liebovitch, L.S., J. Fischbarg, and J.P. Koniarek, Ion channel kinetics: a model based on fractal scaling rather than multistate Markov processes. Mathematical Biosciences, 1987. 84 (1): p. 37-68.

43. Oswald R.E., Millhause G.L., Carter A.A. Diffusion model in ion channel gating. Extension to agonist-acti-vated ion channels // Biophys. J. 1991. V. 59. P. 1136–1142.

44. Liebovitch L.S. Analysis of fractal ion channel gating kinetics: Kinetics rates energy levels and activation energies // Math. Biosci. 1989. V. 93. P. 97–115

45. Шайтан, К., К. Терешкина, Молекулярная динамика белков и пептидов. 2004: Ойкос М.

46. Шайтан, К., Конформационная подвижность белка с точки зрения физики. Соросовский образовательный журнал, 1999. 5: p. 8-13.

47. Liebovitch L.S., Lullivan J.M. Fractal analysis of a voltage-dependent potassium channel from cultured mouse hippocampal neurons // Biophys. J. 1987. V. 52. P. 979–988.

48. Liebovitch L.S., Krekora P. The physical basis of ion channel kinetics: the impotance of dynamics // Proc. Inst. Math. and its Appl. Univer. Minnessota. 2002. V. 129. P. 27–52.

49. Varanda W.A., Liebovitch L.S., Figueiroa J.N., Nogueira R.A. Hurst analysis applied the study of single calcium-activated potassium channel kinetics // J. íheor. Biol. 2000. V. 206. P. 343–353.

50. Bers, D.M., Cardiac excitation-contraction coupling. Nature, 2002. 415(6868): p. 198-205.

51. Bers, D.M., Calcium cycling and signaling in cardiac myocytes. Annu. Rev. Physiol., 2008. 70: p. 23-49.

52. Tsugorka A., Rios E., Blatter L. A. Imaging elementary events of calcium release in skeletal muscle cells //Science. – 1995. – Т. 269. – №. 5231. – С. 1723-1726.

52. Cheng H., Lederer W. J., Cannell M. B. Calcium sparks: elementary events underlying excitation-contraction coupling in heart muscle //Science. – 1993. – Т. 262. – №. 5134. – С. 740-744.

53. Wier, W.G. and C.W. Balke, Ca2+ release mechanisms, Ca2+ sparks, and local control of excitation-contraction coupling in normal heart muscle. Circulation research, 1999. 85 (9): p. 770-776.

54. Shirokova, N., et al., Calcium sparks: release packets of uncertain origin and fundamental role. The Journal of general physiology, 1999. 113 (3): p. 377-384.

55. Stern, M., Theory of excitation-contraction coupling in cardiac muscle. Biophys J, 1992. 63: p. 497–517.

56. Winslow, R.L., Rice, J.J., Jafri, M.S., Marban, E. and O’Rourke, B., Mechanisms of Altered Excitation-Contraction Coupling in Canine Tachycardia-Induced Heart Failure. II. Model Studies. Circ. Res., 1999. 84: p. 571–586. 104, 105, 106, 108, 122, 123

57. Noble, D., Varghese, A., Kohl, P. and Noble, P., Inproved Guinea-pig ventricular cell model incorporating a diadic space, Ikr and Iks, and length- and tension-dependent processes. Can. J. Cardiol., 1998. 14: p. 123–134. 104

58. Puglisi, J.L., Wang, F. and Bers, D.M., Modeling the isolated cardiac myocyte. Prog Biophys Mol Biol, 2004. 85(2-3): p. 163–78. 104

59. Faber, G.M. and Rudy, Y., Action potential and contractility changes in (i) overloaded cardiac myocytes: a simulation study. Biophys J, 2000. 78: p. 2392–404. 104

60. Luo, C.H. and Rudy, Y., A dynamic model of the cardiac ventricular action potential: I. Simulations of ionic currents and concentration changes. Circ Res, 1994. 74: p. 1071–1096. 104, 105, 106

61. Priebe, L. and Beuckelmann, D.J., Simulation study of cellular electric properties in heart failure. Circ Res, 1998. 82(11): p. 1206–23. 104

62. Rice, J.J., Jafri, M.S. and Winslow, R.L., Modeling short-term interval-force relations in cardiac muscle. Am J Physiol, 2000. 278: p. H913

63. Stern, M.D., Song, L.S., Cheng, H., Sham, J.S., Yang, H.T., Boheler, K.R. and Rios, E., Local control models of cardiac excitation-contraction coupling. A pos-sible role for allosteric interactions between ryanodine receptors. J Gen Physiol, 1999. 113: p. 469–89. 107, 114

64. Soeller C., Cannell M. B. Analysing cardiac excitation–contraction coupling with mathematical models of local control //Progress in biophysics and molecular biology. – 2004. – Т. 85. – №. 2. – С. 141-162.

65. Polyakova, E., et al., Local calcium release activation by DHPR calcium channel openings in rat cardiac myocytes. The Journal of physiology, 2008. 586(16): p. 3839-3854.

66. Santana, L.F., E.G. Kranias, and W.J. Lederer, Calcium Sparks and ExcitationContraction Coupling in Phospholamban‐Deficient Mouse Ventricular Myocytes. The Journal of physiology, 1997. 503(1): p. 21-29.

67. Cannell, M.B. and C. Soeller, Mechanisms underlying calcium sparks in cardiac muscle. The Journal of general physiology, 1999. 113(3): p. 373-376.

68. Ferrier, G.R., R.H. Smith, and S.E. Howlett, Calcium sparks in mouse ventricular myocytes at physiological temperature. American Journal of Physiology-Heart and Circulatory Physiology, 2003. 285(4): p. H1495-H1505.

69. Zima, A.V., et al., Termination of cardiac Ca2+ sparks role of intra-SR [Ca²⁺], release flux, and intra-SR Ca²⁺ diffusion. Circulation research, 2008. 103(8): p. e105-e115.

70. Мазуров, М., Ритмогенез в синоатриальном узле сердца. Биофизика, 2006. 51(6): p. 1092-1099.

71. Tsien, R.W., R.S. Kass, and R. Weingart, Cellular and subcellular mechanisms of cardiac pacemaker oscillations. The Journal of experimental biology, 1979. 81(1): p. 205-215.

72. Irisawa, H., H.F. Brown, and W. Giles, Cardiac pacemaking in the sinoatrial node. Physiological reviews, 1993. 73(1): p. 197-227.

73. Krebs, J. and M. Michalak, Calcium: A Matter of Life or Death: A Matter of Life or Death. Vol. 41. 2007: Elsevier Science.

74. Покровский В. М. Формирование ритма сердца в организме человека и животных. – Кубань-Книга, 2007.

75. Барабанов С. В. и др. Физиология сердца //СПБ, Специальная литература. – 1998.

76. Verkerk, A.O., A.C.G. van Ginneken, and R. Wilders, Pacemaker activity of the human sinoatrial node: Role of the hyperpolarization-activated current,I_f. International journal of cardiology, 2009. 132(3): p. 318-336.

77. Baruscotti M., Bucchi A., DiFrancesco D. Physiology and pharmacology of the cardiac pacemaker (“funny”) current //Pharmacology & therapeutics. – 2005. – Т. 107. – №. 1. – С. 59-79.

78. Wilders, R., Computer modelling of the sinoatrial node. Medical & biological engineering & computing, 2007. 45(2): p. 189-207.

79. Priebe, L. and D.J. Beuckelmann, Simulation study of cellular electric properties in heart failure. Circulation Research, 1998. 82(11): p. 1206-1223.

80. Bozler, E., Tonus changes in cardiac muscle and their significance for the initiation of impulses. American Journal of Physiology--Legacy Content, 1943. 139(3): p. 477-480.

81. Rosen, M.R., et al., Genes, stem cells and biological pacemakers. Cardiovascular research, 2004. 64(1): p. 12-23.

82. Vinogradova, T.M., et al., Rhythmic ryanodine receptor Ca2+ releases during diastolic depolarization of sinoatrial pacemaker cells do not require membrane depolarization. Circulation research, 2004. 94(6): p. 802-809.

83. Kurata, Y., 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. American Journal of Physiology-Heart and Circulatory Physiology, 2003. 285(6): p. H2804-H2819.

84. Lakatta, E.G., V.A. Maltsev, and T.M. Vinogradova, A coupled SYSTEM of intracellular Ca²⁺ clocks and surface membrane voltage clocks controls the timekeeping mechanism of the heart’s pacemaker. Circulation research, 2010. 106(4): p. 659-673.

85. Vinogradova, T.M., et al., High Basal Protein Kinase A–Dependent Phosphorylation Drives Rhythmic Internal Ca²⁺ Store Oscillations and Spontaneous Beating of Cardiac Pacemaker Cells. Circulation research, 2006. 98(4): p. 505-514.

86. Bogdanov, K.Y., et al., Modulation of the transient outward current in adult rat ventricular myocytes by polyunsaturated fatty acids. American Journal of Physiology-Heart and Circulatory Physiology, 1998. 274(2): p. H571-H579.

87. Bogdanov, K.Y., T.M. Vinogradova, and E.G. Lakatta, Sinoatrial Nodal Cell Ryanodine Receptor and Na⁺-Ca²⁺ Exchanger Molecular Partners in Pacemaker Regulation. Circulation research, 2001. 88(12): p. 1254-1258.

88. Kurata, Y., et al., Dynamical description of sinoatrial node pacemaking: improved mathematical model for primary pacemaker cell. American Journal of Physiology-Heart and Circulatory Physiology, 2002. 283(5): p. H2074-H2101.

89. Maltsev, V.A., T.M. Vinogradova, and E.G. Lakatta, The emergence of a general theory of the initiation and strength of the heartbeat. Journal of pharmacological sciences, 2006. 100(5): p. 338-369.

90. Maltsev, V.A. and E.G. Lakatta, Synergism of coupled subsarcolemmal Ca²⁺ clocks and sarcolemmal voltage clocks confers robust and flexible pacemaker function in a novel pacemaker cell model. American Journal of Physiology-Heart and Circulatory Physiology, 2009. 296(3): p. H594-H615.

91. Maltsev, V.A. and E.G. Lakatta, Dynamic interactions of an intracellular Ca²⁺ clock and membrane ion channel clock underlie robust initiation and regulation of cardiac pacemaker function. Cardiovascular research, 2008. 77(2): p. 274-284.

92. Maltsev, A.V., et al., Synchronization of Stochastic Ca²⁺ Release Units Creates a Rhythmic Ca²⁺ Clock in Cardiac Pacemaker Cells. Biophysical journal, 2011. 100(2): p. 271-283.

93. Shannon, T.R., et al., A mathematical treatment of integrated Ca dynamics within the ventricular myocyte. Biophysical journal, 2004. 87(5): p. 3351-3371.

94. Hamilton, S.L. and I.I. Serysheva, Ryanodine receptor structure: progress and challenges. Journal of Biological Chemistry, 2009. 284(7): p. 4047-4051.

95. Ashley, R.H. and A.J. Williams, Divalent cation activation and inhibition of single calcium release channels from sheep cardiac sarcoplasmic reticulum. The Journal of general physiology, 1990. 95(5): p. 981-1005.

96. Koshino, K. and T. Ogawa, Domino effects in photoinduced structural change in one-dimensional systems. Journal of the Physical Society of Japan, 1998. 67: p. 2174.

97. Koshino, K. and T. Ogawa, Photoinduced nucleation theory in one-dimensional systems. Physical Review B, 1998. 58(22): p. 14804.

98. Fujimoto, M., The physics of structural phase transitions. 2005: New York: Springer.

99. Nasu, K., Photoinduced phase transitions. 2004: World Scientific Publishing Company.

100. Шайтан, К., et al., Динамический молекулярный дизайн био-и наноструктур. Российский химический журнал, 2006. 50(2): p. 53-65.

101. Moskvin A. S. Photo-induced phase separation effect in cuprates //Journal of Physics: Conference Series. – IOP Publishing, 2005. – Т. 21. – №. 1. – С. 106.

102. Левич, В.Г., В.А. Мямлин, and Ю.А. Вдовин, Курс теоретической физики. Vol. 1. 1969: Наука.

103. Рубин, А., Биофизика: В 2-х кн. Учеб. для биол. спец вузов. Кн. 1. Теоретическая биофизика. М.: Высш. шк, 1987.

104. Иваницкий Г. Р., Кринский В. И., Сельков Е. Е. Математическая биофизика клетки. – Наука, 1978.

105. Coffey W. T., Kalmykov Y. P., Waldron J. T. The Langevin equation: with applications to stochastic problems in physics, chemistry, and electrical engineering. – World Scientific Publishing Company, 2004. – Т. 14.

106. Zahradnikova, A., et al., Rapid activation of the cardiac ryanodine receptor by submillisecond calcium stimuli. The Journal of general physiology, 1999. 114(6): p. 787-798.

107. Zahradnikova, A., M. Dura, and S. Gyorke, Modal gating transitions in cardiac ryanodine receptors during increases of Ca2+ concentration produced by photolysis of caged Ca2+. Pflugers Archiv, 1999. 438(3): p. 283-288.

108. Ландау, Л. and Е. Лифшиц, Квантовая механика. нерелятивистская теория, т. 3. ЛД Ландау, ЕМ Лифшиц–М.: Наука, 1989.

109. Atkins P. W., Friedman R. S. Molecular quantum mechanics. – Oxford: Oxford university press, 1997. – Т. 3.

110. Шайтан, К. and А. Рубин, Изотопные эффекты в реакциях туннелирования электронов в биологических системах и конформационная подвижность белков. Молекуляр. биология, 1981. 15(2): p. 368.

111. Keener, J.P. and J. Sneyd, Mathematical physiology. Vol. 8. 1998: Springer. 112. Greenstein, J.L., R. Hinch, and R.L. Winslow, Mechanisms of excitation-contraction coupling in an integrative model of the cardiac ventricular myocyte. Biophysical journal, 2006. 90(1): p. 77-91.

113. Greenstein, J.L. and R.L. Winslow, An Integrative Model of the Cardiac Ventricular Myocyte Incorporating Local Control of Ca²⁺ Release. Biophysical journal, 2002. 83(6): p. 2918-2945.

114. Maruyama, G., Continuous Markov processes and stochastic equations. Rendiconti del Circolo Matematico di Palermo, 1955. 4(1): p. 48-90.

115. Kloeden, P.E. and E. Platen, Numerical solution of stochastic differential equations. Vol. 23. 1992: Springer Verlag.

116. Федер Е., Данилов Ю. А., Шукуров А. Фракталы. – Мир, 1991. – Т. 254.

117. Иродов И. Е. Основные законы механики. – М.: Высш. шк., 1997.

118. Вентцель А. Д. Курс теории случайных процессов. – М.: Наука. Физматлит, 1975.

119. Sitsapesan, R., R.A. Montgomery, and A.J. Williams, New insights into the gating mechanisms of cardiac ryanodine receptors revealed by rapid changes in ligand concentration. Circulation research, 1995. 77(4): p. 765-772.

120. Terentyev, D., et al., Luminal Ca²⁺ controls termination and refractory behavior of Ca²⁺-induced Ca²⁺ release in cardiac myocytes. Circulation research, 2002. 91(5): p. 414-420.

121. Magleby, K.L. and B.S. Pallotta, Calcium dependence of open and shut interval distributions from calcium-activated potassium channels in cultured rat muscle. The Journal of physiology, 1983. 344(1): p. 585-604.

122. Laver, D.R. and B.N. Honen, Luminal Mg²⁺, a key factor controlling RYR2-mediated Ca²⁺ release: cytoplasmic and luminal regulation modeled in a tetrameric channel. The Journal of general physiology, 2008. 132(4): p. 429-446.

123. Copello, J., et al., Differential activation by Ca²⁺, ATP and caffeine of cardiac and skeletal muscle ryanodine receptors after block by Mg²⁺. Journal of Membrane Biology, 2002. 187(1): p. 51-64.

124. Pikovsky, A., M. Rosenblum, and J. Kurths, Synchronization: a universal concept in nonlinear sciences. Vol. 12. 2003: Cambridge university press.

125. Kut, C., V. Golkhou, and J.S. Bader, Analytical approximations for the amplitude and period of a relaxation oscillator. BMC systems biology, 2009. 3(1): p. 6.

126. Wehrens, X.H.T., et al., FKBP12. 6 deficiency and defective calcium release channel (ryanodine receptor) function linked to exercise-induced sudden cardiac death. Cell, 2003. 113(7): p. 829-840.

127. Chen, W., J.A. Wasserstrom, and Y. Shiferaw, Role of coupled gating between cardiac ryanodine receptors in the genesis of triggered arrhythmias. American Journal of Physiology-Heart and Circulatory Physiology, 2009. 297(1): p. H171-H180.

128. Vest, J.A., et al., Defective cardiac ryanodine receptor regulation during atrial fibrillation. Circulation, 2005. 111(16): p. 2025-2032.

129. Jiang, D., et al., Enhanced store overload induced Ca²⁺ release and channel sensitivity to luminal Ca²⁺ activation are common defects of RyR2 mutations linked to ventricular tachycardia and sudden death. Circulation research, 2005. 97(11): p. 1173-1181.

130. Lehnart, S.E., et al., Stabilization of cardiac ryanodine receptor prevents intracellular calcium leak and arrhythmias. Proceedings of the National Academy of Sciences, 2006. 103(20): p. 7906-7910.