Abstract
Mathematical action potential (AP) modeling is a well-established but still-developing area of research to better understand physiological and pathological processes. In particular, changes in AP mechanisms in the isoproterenol (ISO) -induced hypertrophic heart model are incompletely understood. Here we present a mathematical model of the rat AP based on recordings from rat ventricular myocytes. In our model, for the first time, all channel kinetics are defined with a single type of function that is simple and easy to apply. The model AP and channels dynamics are consistent with the APs recorded from rats for both Control (absence of ISO) and ISO-treated cases. Our mathematical model helps us to understand the reason for the prolongation in AP duration after ISO application while ISO treatment helps us to validate our mathematical model. We reveal that the smaller density and the slower gating kinetics of the transient K+ current help explain the prolonged AP duration after ISO treatment and the increasing amplitude of the rapid and the slow inward rectifier currents also contribute to this prolongation alongside the flux in Ca2+ currents. ISO induced an increase in the density of the Na+ current that can explain the faster upstroke. We believe that AP dynamics from rat ventricular myocytes can be reproduced very well with this mathematical model and that it provides a powerful tool for improved insights into the underlying dynamics of clinically important AP properties such as ISO application.
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Abbreviations
- AP:
-
Action potential
- APD:
-
Action potential duration
- HH:
-
Hodgkin–Huxley
- HW/TL:
-
Hearth weight/tibia length
- I Na :
-
The Fast Na+ current
- I CaL :
-
TL-Type Ca2+ current
- ICaT :
-
T-Type Ca2+ current
- I to :
-
Transient K+ current
- I K1 :
-
Inward rectifier K+ current
- I Kr :
-
Rapidly activated outward rectifier K+ current
- I Ks :
-
Slowly activated outward rectifier K+ current
- I f :
-
Hyperpolarization-activated current
- I BNa :
-
Background Na+ current
- I BCa :
-
Background Ca2+ current
- I BK :
-
Background K+ current
- I BCl :
-
Background Cl− current
- ICaP :
-
Sarcolemmal Ca2+ pump current
- INaCa :
-
Na+-Ca2+ exchanger (NCX) current
- INaK :
-
Na+-K+ pump current
- ISO:
-
Isoproterenol
- JSR:
-
Junctional sarcoplasmic reticulum
- LR:
-
Luo and rudy
- NCX:
-
Na+-Ca2+ exchanger
- NDE:
-
Nonlinear differential equation system
- NSR:
-
Network SR
- PO:
-
Peak overshoot
- RyR:
-
Ryanodine receptor
- SEM:
-
Standard error of the mean
- SERCA:
-
Sa Ca2+-ATPase
- SR:
-
Sarcoplasmic reticulum
References
Agus ZS, Dukes ID, Morad M (1991) Divalent cations modulate the transient outward current in rat ventricular myocytes. Am J Physiol Cell Physiol 261(2):C310–C318. https://doi.org/10.1152/ajpcell.1991.261.2.c310
Avila G, Medina IM, Jimenez E, Elizondo G, Aguilar CI (2007) Transforming growth factor-beta1 decreases cardiac muscle L-type Ca2+ current and charge movement by acting on the Cav1.2 mRNA. Am J Physiol Heart Circ Physiol 292(1):622–631
Beeler GW, Reuter H (1977) Reconstruction of the action potential of ventricular myocardial fibres. J Physiol 268(1):177–210. https://doi.org/10.1113/jphysiol.1977.sp011853
Bueno-Orovio A, Sánchez C, Pueyo E, Rodriguez B (2013) Na/K pump regulation of cardiac repolarization: insights from a systems biology approach. Pflügers Archiv Eur J Physiol 466(2):183–193. https://doi.org/10.1007/s00424-013-1293-1
Caroni P, Carafoli E (1980) An ATP-dependent Ca2+-pumping system in dog heart sarcolemma. Nature 283(5749):765–767. https://doi.org/10.1038/283765a0
Cha CY, Nakamura Y, Himeno Y, Wang J, Fujimoto S, Inagaki N, Noma A (2011) Ionic mechanisms and Ca2+ dynamics underlying the glucose response of pancreatic β cells: a simulation study. J General Physiol 138(1):21–37. https://doi.org/10.1085/jgp.201110611
Cha CY, Himeno Y, Shimayoshi T, Amano A, Noma A (2009) A Novel method to quantify contribution of channels and transporters to membrane potential dynamics. Biophys J 97(12):3086–3094. https://doi.org/10.1016/j.bpj.2009.08.060
Conforti L, Tohse N, Sperelakis N (1993) Tetrodotoxin-sensitive sodium current in rat fetal ventricular myocytes - contribution to the plateau phase of action potential. J Molecular Cell Cardiol 25(2):159–173. https://doi.org/10.1006/jmcc.1993.1019
Cortassa S, Aon MA, O’Rourke B, Jacques R, Tseng H, Marbán E, Winslow RL (2006) A computational model integrating electrophysiology, contraction, and mitochondrial bioenergetics in the ventricular myocyte. Biophys J 91(4):1564–1589. https://doi.org/10.1529/biophysj.105.076174
Crampin EJ, Smith NP (2006) A dynamic model of excitation-contraction coupling during acidosis in cardiac ventricular myocytes. Biophys J 90(9):3074–3090. https://doi.org/10.1529/biophysj.105.070557
Danielsson C, Brask J, Sköld A, Genead R, Andersson A, Andersson U, Elinder F (2012) Exploration of human, rat, and rabbit embryonic cardiomyocytes suggests K-channel block as a common teratogenic mechanism. Cardiovas Res 97(1):23–32. https://doi.org/10.1093/cvr/cvs296
DiFrancesco D (1985) The cardiac hyperpolarizing-activated current, if origins and developments. Progress Biophys Molecular Biol 46(3):163–183. https://doi.org/10.1016/0079-6107(85)90008-2
DiFrancesco D, Noble D (1985) A model of cardiac electrical activity incorporating ionic pumps and concentration changes. Philosoph Transact Royal Soc 307(1133):353–398. https://doi.org/10.1098/rstb.1985.0001
Fares N, Gomez JP, Potreau D (1996) T-type calcium current is expressed in dedifferentiated adult rat ventricularcells in primary culture. C R Acad Sci Paris Sci de la vie / Life Sci 319:569–576
Farès N, Bois P, Lenfant J, Potreau D (1998) Characterization of a hyperpolarization-activated current in dedifferentiated adult rat ventricular cells in primary culture. J Physiol 506(1):73–82. https://doi.org/10.1111/j.1469-7793.1998.073bx.x
Grandi E, Pasqualini FS, Puglisi JL, Bers DM (2009) A novel computational model of the human ventricular action potential and Ca transient. Biophys J 96(3):664a–665a. https://doi.org/10.1016/j.bpj.2008.12.3513
Gu M, Zhu Y, Yin X, Zhang D (2018) Small-conductance Ca2+-activated K+ channels: insights into their roles in cardiovascular disease. Experim Molecul Med. https://doi.org/10.1038/s12276-018-0043-z
Hansen PB (2015) Functional importance of T-type voltage-gated calcium channels in the cardiovascular and renal system: news from the world of knockout mice. Am J Physiol Regul Integ Compar Physiol 308(4):R227–R237. https://doi.org/10.1152/ajpregu.00276.2014
Hashambhoy YL, Winslow RL, Greeinstein JL (2009) CaMKII-induced shift in modal gating explains L-type Ca2+ current facilitation: A modeling study. Biophys J 96:1770–1785. https://doi.org/10.1016/j.bpj.2008.11.055
Hodgkin AL, Huxley AF (1952) The components of membrane conductance in the giant axon of Loligo. J Physiol 116(4):473–496. https://doi.org/10.1113/jphysiol.1952.sp004718
Iyer V, Mazhari R, Winslow RL (2004) A computational model of the human left-ventricular epicardial myocyte. Biophysl J 87(3):1507–1525. https://doi.org/10.1529/biophysj.104.043299
Jafri MS, Rice JJ, Winslow RL (1998) Cardiac Ca2+ dynamics: the roles of ryanodine receptor adaptation and sarcoplasmic reticulum load. Biophys J 74(3):1149–1168. https://doi.org/10.1016/s0006-3495(98)77832-4
Javidgonbadi D, Andersson B, Abdon N, Schaufelberger M, Östman-Smith I (2019) Factors influencing long-term heart failure mortality in patients with obstructive hypertrophic cardiomyopathy in Western Sweden: probable dose-related protection from beta-blocker therapy. Open Heart 6(1):e000963. https://doi.org/10.1136/openhrt-2018-000963
Kamiya K, Guo W, Yasui K, Toyama J (1999) Hypoxia inhibits the changes in action potentials and ion channels during primary culture of neonatal rat ventricular myocytes. J Molec Cell Cardiol 31(9):1591–1598. https://doi.org/10.1006/jmcc.1999.0992
Katsube Y, Yokoshiki H, Nguyen L, Yamamoto M, Sperelakis N (1998) L-type Ca2+ currents in ventricular myocytes from neonatal and adult rats. Canad J Physiol Pharmacol 76(9):873–881. https://doi.org/10.1139/cjpp-76-9-873
Keizer J, Levine L (1996) Ryanodine receptor adaptation and Ca2+(-)induced Ca2+ release-dependent Ca2+ oscillations. Biophys J 71(6):3477–3487. https://doi.org/10.1016/s0006-3495(96)79543-7
Korhonen T, Hänninen SL, Tavi P (2009) Model of excitation-contraction coupling of rat neonatal ventricular myocytes. Biophys J 96(3):1189–1209. https://doi.org/10.1016/j.bpj.2008.10.026
Lang D, Holzem K, Kang C, Xiao M, Hwang HJ, Ewald GA, Efimov IR (2015) Arrhythmogenic remodeling of β 2 versus β 1 adrenergic signaling in the human failing heart. Circul Arrhythmia Electrophysiol 8(2):409–419. https://doi.org/10.1161/circep.114.002065
Lee H, Lu T, Weintraub NL, VanRollins M, Spector AA, Shibata EF (1999) Effects of epoxyeicosatrienoic acids on the cardiac sodium channels in isolated rat ventricular myocytes. J Physiol 519(1):153–168. https://doi.org/10.1111/j.1469-7793.1999.0153o.x
Li X, Zhang J, Shuai J (2014) Isoprenaline: a potential contributor in sick sinus syndrome—insights from a mathematical model of the rabbit sinoatrial node. Scient World J 2014:1–11. https://doi.org/10.1155/2014/540496
Luo CH, Rudy Y (1994) A dynamic model of the cardiac ventricular action potential. I simulations of ionic currents and concentration changes. Circul Res 74(6):1071–1096. https://doi.org/10.1161/01.res.74.6.1071
Mahajan A, Shiferaw Y, Sato D, Baher A, Olcese R, Xie L, Weiss JN (2008) A rabbit ventricular action potential model replicating cardiac dynamics at rapid heart rates. Biophys J 94(2):392–410. https://doi.org/10.1529/biophysj.106.98160
Matsuoka S, Sarai N, Kuratomi S, Ono K, Noma A (2003) Role of individual ionic current systems in ventricular cells hypothesized by a model study. Japan J Physiol 53(2):105–123. https://doi.org/10.2170/jjphysiol.53.105
Mullins LJ (1979) The generation of electric currents in cardiac fibers by Na/Ca exchange. Am J Physiol Cell Physiol 236(3):C103–C110. https://doi.org/10.1152/ajpcell.1979.236.3.c103
Nichtova Z, Novotova M, Kralova E, Stankovicova T (2012) Morphological and functional characteristics of models of experimental myocardial injury induced by isoproterenol. General Physiol Biophys 31(02):141–151. https://doi.org/10.4149/gpb_2012_015
Noble D (1960) Cardiac action and pacemaker potentials based on the Hodgkin-Huxley equations. Nature 188(4749):495–497. https://doi.org/10.1038/188495b0
Noble D (2007) From the Hodgin-Huxley axon to the virtual heart. J Physiol 580(1):15–22. https://doi.org/10.1113/jphysiol.2006.119370
Osadchii OE (2017) Role of abnormal repolarization in the mechanism of cardiac arrhythmia. Acta Physiol 220:1–71. https://doi.org/10.1111/apha.12902
Pandit SV, Clark RB, Giles WR, Demir SS (2001) A mathematical model of action potential heterogeneity in adult rat left ventricular myocytes. Biophysical J 81(6):3029–3051. https://doi.org/10.1016/s0006-3495(01)75943-7
Pond AL, Scheve BK, Benedict AT, Petrecca K, Van Wagoner DR, Shrier A, Nerbonne JM (2000) Expression of distinct ERG proteins in rat, mouse, and human heart. J Biolog Chem 275(8):5997–6006. https://doi.org/10.1074/jbc.275.8.5997
Pásek M, Šimurda J, Orchard CH, Christé G (2008) A model of the guinea-pig ventricular cardiac myocyte incorporating a transverse–axial tubular system. Progress Biophys Molec Biol 96(1–3):258–280. https://doi.org/10.1016/j.pbiomolbio.2007.07.022
Ramirez RJ, Nattel S, Courtemanche M (2000) Mathematical analysis of canine atrial action potentials: rate, regional factors, and electrical remodeling. Am J Physiol Heart Circul Physiol 279(4):H1767–H1785. https://doi.org/10.1152/ajpheart.2000.279.4.h1767
Richard S, Charnet P, Nerbonne JM (1993) Interconversion between distinct gating pathways of the high threshold calcium channel in rat ventricular myocytes. J Physiol 462(1):197–228. https://doi.org/10.1113/jphysiol.1993.sp019551
Şengül S, Clewley R, Bertram R, Tabak J (2014) Determining the contributions of divisive and subtractive feedback in the Hodgkin-Huxley model. J Comput Neurosci 37(3):403–415. https://doi.org/10.1007/s10827-014-0511-y
Shannon TR, Wang F, Puglisi J, Weber C, Bers DM (2004) A mathematical treatment of integrated Ca dynamics within the ventricular myocyte. Biophys J 87(5):3351–3371. https://doi.org/10.1529/biophysj.104.047449
Shi W, Wymore R, Yu H, Wu J, Wymore RT, Pan Z, Cohen IS (1999) Distribution and prevalence of hyperpolarization-activated cation channel (HCN) mRNA expression in cardiac tissues. Circul Res. https://doi.org/10.1161/01.res.85.1.e1
Sobie EA (2009) Parameter sensitivity analysis in electrophysiological models using multivariable regression. Biophys J 96(4):1264–1274. https://doi.org/10.1016/j.bpj.2008.10.056
Stengl M, Carmeliet E, Mubagwa K, Flameng W (1998) Modulation of transient outward current by extracellular protons and Cd2+in rat and human ventricular myocytes. J Physiol 511(3):827–836. https://doi.org/10.1111/j.1469-7793.1998.827bg.x
Sun L, Fan J, Clark JW, Palade PT (2000) A model of the L-type Ca2+channel in rat ventricular myocytes: ion selectivity and inactivation mechanisms. J Physiol 529(1):139–158. https://doi.org/10.1111/j.1469-7793.2000.00139.x
Ten Tusscher K, Bernus O, Hren R, Panfilov A (2006) Comparison of electrophysiological models for human ventricular cells and tissues. Progress Biophys Molec Biol 90(1–3):326–345. https://doi.org/10.1016/j.pbiomolbio.2005.05.015
Ten Tusscher KH, Noble D, Noble PJ, Panfilov AV (2004) A model for human ventricular tissue. Am J Physiol Heart Circul Physiol 286(4):H1573–H1589. https://doi.org/10.1152/ajpheart.00794.2003
Umehara S, Tan X, Okamoto Y, Ono K, Noma A, Amano A, Himeno Y (2019) Mechanisms underlying spontaneous action potential generation induced by catecholamine in pulmonary vein cardiomyocytes: a simulation study. Int J Molec Sci 20(12):2913. https://doi.org/10.3390/ijms20122913
Wahler GM (1992) Developmental increases in the inwardly rectifying potassium current of rat ventricular myocytes. Am J Physiol-Cell Physiol 262(5):C1266–C1272. https://doi.org/10.1152/ajpcell.1992.262.5.c1266
Wallis W, Cooklin M, Sheridan D, Fry C (2001) The action of isoprenaline on the electrophysiological properties of hypertrophied left ventricular myocytes. Arch Physiol Biochem 109(2):117–126. https://doi.org/10.1076/apab.109.2.117.4266
Wettwer E, Ravens U (1993) Recording cardiac potassium currents with the whole-cell voltage clamp technique. Pract Methods Cardiovas Res. https://doi.org/10.1007/3-540-26574-0_18
Winslow RL, Cortassa S, O'Rourke B, Hashambhoy YL, Rice JJ, Greenstein JL (2010) Integrative modeling of the cardiac ventricular myocyte. Wiley Interdisciplinary Rev Syst Biol Med 3(4):392–413. https://doi.org/10.1002/wsbm.122
Winslow RL, Rice J, Jafri S, Marbán E, O’Rourke B (1999) Mechanisms of altered excitation-contraction coupling in canine tachycardia-induced heart failure II. Circul Res 84(5):571–586. https://doi.org/10.1161/01.res.84.5.571
Zhang X, Coulibaly ZA, Chen WC, Ledford HA, Lee JH, Sirish P, Chiamvimonvat N (2018) Coupling of SK channels, L-type Ca2+ channels, and ryanodine receptors in cardiomyocytes. Scient Rep. https://doi.org/10.1038/s41598-018-22843-3
Zorn-Pauly K, Schaffer P, Pelzmann B, Bernhart E, Lang P, Koidl B (2004) L-type and T-type Ca2+ current in cultured ventricular guinea pig myocytes. Physiol Res 53(4):369–377
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This study was supported by The Scientific and Technological Research Council of Turkey (TUBITAK, Project No: 117F020). These funding sources had no involvement in study design, writing of the report, decision to publish, or the collection, analysis, and interpretation of data.
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SSA and AKS designed the studies; SSA, AKS & NY performed simulation and experimental research; SSA, AKS, MA and AK analysed data; SSA and MA wrote the paper. All authors have seen and approved the final version of the manuscript.
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Şengül Ayan, S., Sırcan, A.K., Abewa, M. et al. Mathematical model of the ventricular action potential and effects of isoproterenol-induced cardiac hypertrophy in rats. Eur Biophys J 49, 323–342 (2020). https://doi.org/10.1007/s00249-020-01439-8
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DOI: https://doi.org/10.1007/s00249-020-01439-8