Biological Cybernetics

, Volume 102, Issue 2, pp 109–121 | Cite as

Bistable dynamics of cardiac cell models coupled by dynamic gap junctions linked to Cardiac Memory

  • Gairik Sachdeva
  • Kanakapriya Kalyanasundaram
  • J. Krishnan
  • V. S. Chakravarthy
Original Paper


In an earlier study, we suggested that adaptive gap junctions (GJs) might be a basis of cardiac memory, a phenomenon which refers to persistent electrophysiological response of the heart to external pacing. Later, it was also shown that the proposed mechanism of adaptation of GJs is consistent with known electrophysiology of GJs. In the present article, we show that a pair of cardiac cell models coupled by dynamic, voltage-sensitive GJs exhibits bistable behavior under certain conditions. Three kinds of cell pairs are considered: (1) a Noble–Noble cell pair that represents adjacent cells in Purkinje network, (2) a pair of DiFranceso–Noble cells that represents adjacent SA nodal cells, and (3) a model of Noble cell coupled to Luo–Rudy cell model, which represents an interacting pair of a Purkinje fiber and a ventricular myocyte. Bistability is demonstrated in all the three cases. We suggest that this bistability might be an underlying factor behind cardiac memory. Focused analysis of a pair of Noble cell models showed that bistability is obtained only when the properties of GJs “match” with the properties of the pair of cells that is coupled by the GJs. This novel notion of match between GJs and cardiac cell types might give an insight into specialized distributions of various connexin proteins in cardiac tissue.


Voltage-sensitive gap junctions Hysteresis Hebbian mechanisms Noble cardiac cell model Luo–Rudy model DiFrancesco model 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Baigent S, Jaroslav S, Warner A (1997) Modeling the effect of gap junction nonlinearities in systems of coupled cells. J Theor Biol 186: 223–239CrossRefGoogle Scholar
  2. Coppen SR, Severs NJ, Gourdie RG (1999a) Connexin45 (α 6) expression declineates an extended conduction system in the embryonic and mature rodent heart. Dev Genet 24: 82–90CrossRefPubMedGoogle Scholar
  3. Coppen SR, Kodama I, Boyett MR, Dobrzynski H, Takagishi Y, Honjo H, Yeh HI, Severs NJ (1999b) Connexin45, a major connexin of the rabbit sinoatrial node, is co-expressed with connexin43 in a restricted zone at the Nodal–Crista terminals border. J Histochem Cytochem 47: 907–918PubMedGoogle Scholar
  4. Chakravarthy VS, Ghosh J (1997) On Hebbian-like adaption in heart muscle: a proposal for “Cardiac Memory”. Biol Cybern 76: 207–215CrossRefPubMedGoogle Scholar
  5. Chatterjee K, Harri A, Davies G, Leatham A (1969) Electrocardiographic changes subsequent to artificial ventricular depolarization. Br Heart J 31: 770–779CrossRefPubMedGoogle Scholar
  6. De Mello WC (1998) Cell to cell communication in the failing heart. In: De Mello WC, Janse MJ (eds) Heart cell communication in health and disease. Kluwer Academic Publishers, Boston, pp 149–173Google Scholar
  7. Del Balzo U, Rosen MR (1992) T-wave changes persisting after ventricular pacing in canine heart are altered by 4-aminopyridine but not by lidocaine: implications with respect to phenomenon of “cardiac memory”. Circulation 85: 1464–1472PubMedGoogle Scholar
  8. Dhein S, Krusemann K, Schaefer T (1999) Effects of the gap junction uncoupler palmitoleic acid on the activation and repolarization wavefronts in isolated rabbit hearts. Br J Pharmacol 128: 1375–1384CrossRefPubMedGoogle Scholar
  9. DiFrancesco D, Noble D (1985) A model of electric activity incorporating ionic pumps and concenteration changes. Phil Trans R Soc Lond B307: 353–398Google Scholar
  10. Gibbs HM, McCall SL, Venkatesan TNC (1980) Optical bistable devices: the basic components of all-optical systems. Opt Eng 19: 463–468Google Scholar
  11. Gourdie RG, Lo CW (2000) Cx43 (α 1) gap junctions in cardiac development and disease. Curr Top Membr 49: 581–602CrossRefGoogle Scholar
  12. Gourdie RG, Severs NJ, Green CR, Rothery S, Germroth P, Thompson RP (1993) The spatial distribution and relative abundance of gap junctional connexin40 and connexin43 correlate to functional properties of components of the cardiac atrioventricular conduction system. J Cell Sci 105: 985–991PubMedGoogle Scholar
  13. Gros DB, Jongsma HJ (1996) Connexin in mammalian heart function. Bioessays 18: 719–730CrossRefPubMedGoogle Scholar
  14. Guyton AC, Hall JE (2000) Textbook of Medical Physiology, 10th edn. W.B. Saunders, PhiladelphiaGoogle Scholar
  15. Haefliger JA, Polikar R, Schnyder G, Burdet M, Sutter E, Pexieder T, Nicod P, Meda P (2000) Connexin37 in normal and pathological development of mouse heart and great arteries. Dev Dyn 218: 331–344CrossRefPubMedGoogle Scholar
  16. Harris ALM, Hutter OF, Noble D (1983) Control of intercellular communication by voltage dependence of gap junctional conductance. J Neurosci 3: 79–100PubMedGoogle Scholar
  17. Henriquez AP, Vogel R, Muller-Borer BJ, Henriquez CS, Weingart R, Cascio WE (2001) Influence of dynamic gap junction resistance on impulse propagation in ventricular myocardium: a computer simulation study. Biophys J 81: 2112–2121CrossRefPubMedGoogle Scholar
  18. Krishnan J, Chakravarthy VS, Radhakrishnan S (2005) On the role of gap junctions on cardiac memory effect. Comput Cardiol 32: 13–17CrossRefGoogle Scholar
  19. Krishnan J, Sachdeva G, Chakravarthy VS, Radhakrishnan S (2008) Interpreting voltage-sensitivity of gap junctions as a mechanism of cardiac memory. Math Biosci 212(2): 132–148CrossRefPubMedGoogle Scholar
  20. Lin X, Gemel J, Beyer EC, Veenstra RD (2004) Dynamic model for ventricular junctional conductance during the cardiac action potential. Am J Physiol Heart Circ Physiol 288: H1113–H1123CrossRefPubMedGoogle Scholar
  21. Luke RA, Saffitz JE (1991) Remodeling of ventricular conduction pathways in healed canine infarct border zones. J Clin Invest 87: 1594–1602CrossRefPubMedGoogle Scholar
  22. Luo CH, Rudy Y (1991) A model of the ventricular cardiac action potential. Circ Res 68(6): 1501–1526PubMedGoogle Scholar
  23. Luo–Rudy Model from the CellML Repository,
  24. Michaels DC, Matyas EP, Jalife J (1986) Dynamic interactions and mutual synchronization of sinoatrial node pacemaker cells: a mathematical model. Circ Res 58: 706–720PubMedGoogle Scholar
  25. Montague PR, Sejnowski TJ (1994) The predictive brain: temporal coincidence and temporal order in synaptic learning mechanisms. Learn Mem 1: 1–33PubMedGoogle Scholar
  26. Noble D (1960) A Modification of the Hodgkin–Huxley equations applicable to Purkinje fibre action and pacemaker potentials. J Physiol 160: 317–352Google Scholar
  27. Patel PM, Plotnikov A, Kanagaratnam P, Shvilkin A, Sheehan CT, Xiong W, Danilo P Jr, Rosen MR, Peters NS (2001) Altering ventricular activation remodels gap junction distribution in canine heart. Cardiovasc Electrophysiol 12: 570–577CrossRefGoogle Scholar
  28. Peters NS, Green CR, Poole-Wilson PA, Severs NJ (1993) Reduced content of connexin43 gap junctions in ventricular myocardium from hypertrophied and ischemic human hearts. Circulation 88: 864–875PubMedGoogle Scholar
  29. Phelan P, Starich TA (2001) Innexins get into the gap. BioEssays 23: 388–396CrossRefPubMedGoogle Scholar
  30. Plotnikov AN, Yu H, Geller JC, Gainullin RZ, Chandra P, Patberg KW, Friezema S, Danilo P, Cohen IS, Feinmark SJ, Rosen MR (2003) Role of L-type calcium channels in pacing-induced short-term and long-term cardiac memory in canine heart. Circulation 107(22): 2844–2849CrossRefPubMedGoogle Scholar
  31. Pradhan B, Batabyal SK, Pal AJ (2006) Electrical bistability and memory phenomenon in carbon nanotube-conjugated polymer matrixes. Phys Chem B 110(16): 8274–8277CrossRefGoogle Scholar
  32. Rohr S (2004) Role of gap junctions in the propagation of the cardiac action potential. Cardiovasc Res 62(2): 309–322CrossRefPubMedGoogle Scholar
  33. Rosen MR (2001) The heart remembers: clinical applications. Lancet 357: 468–471CrossRefPubMedGoogle Scholar
  34. Rosen MR, Binah O, Marom S (2003) Cardiac memory and cortical memory: do learning patterns in neural networks impact on cardiac arrhythmias? Circulation 108: 1784–1789CrossRefPubMedGoogle Scholar
  35. Rosenbaum MB, Blanco HH, Elizari MV, Lazzari JO, Davidenko JM (1982) Electronic modulation of the T wave and cardiac memory. Am J Cardiol 50: 213–222CrossRefPubMedGoogle Scholar
  36. Saffitz JE (1997) Gap junctions: functional effects of molecular structure and tissue distribution. Adv Exp Med Biol 430: 291–301PubMedGoogle Scholar
  37. Saffitz JE, Kanter HL, Green KG, Tolley TK, Beyer EC (1994) Tissue-specific determinants of anisotropic conduction velocity in canine atrial and ventricular myocardium. Circ Res 74: 1065–1070PubMedGoogle Scholar
  38. Severs NJ (1994) Pathophysiology of gap junctions in heart disease. J Cardiovasc Electrophysiol 5: 462–475CrossRefPubMedGoogle Scholar
  39. Shvilkin A, Danilo P Jr, Wang J, Burkhoff D, Anyukhovsky EP, Sosunov EA, Hara M, Rosen MR (1998) The evolution and resolution of long-term cardiac memory. Circulation 97: 1810–1817PubMedGoogle Scholar
  40. Smith CG (1997) Bistable memory element. U.S. Patent No. 5677823Google Scholar
  41. Van Kempen MJA, Ten Velde I, Wessels A, Oosthock PW, Gros D, Jongsma HJ, Moorman AFM, Lamers WH (1995) Differential connexin distribution accommodates cardiac function in different species. Microsc Res Tech 31: 420–436CrossRefPubMedGoogle Scholar
  42. Veenstra RD, Wang HZ, Westphale EM, Beyer EC (1992) Multiple connexins confer distinct regulatory and conductance properties of gap junctions in developing heart. Circ Res 71: 1277–1283PubMedGoogle Scholar
  43. Vogel R, Weingart R (1998) Mathematical model of vertebrate gap junctions derived from electrical measurements on homotypic and heterotypic channels. J Physiol 510(Pt 1): 177–189CrossRefPubMedGoogle Scholar
  44. Winslow RL, Cai D, Lai YC (1994) Network models of the SA node. Proceedings of the IFAC Symposium on Modeling and Control in Biomedical Systems, pp 86–92Google Scholar

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • Gairik Sachdeva
    • 1
  • Kanakapriya Kalyanasundaram
    • 1
  • J. Krishnan
    • 2
  • V. S. Chakravarthy
    • 1
  1. 1.Department of BiotechnologyIndian Institute of Technology, MadrasChennaiIndia
  2. 2.Department of Instrumentation EngineeringAnnamalai UniversityAnnamalai NagarIndia

Personalised recommendations