An investigation of an action potential propagation in vascular plant using FitzHugh-Nagumo model

 pdf (2168K)  / Annotation

List of references:

  1. M. J. Beilby. C1–channels in Chara // Phil. Trans. R. Soc. London. B. — 1982. — V. 299. — P. 435–445. — DOI: 10.1098/rstb.1982.0142. — ads: 1982RSPTB.299..435B.
  2. P. C. Dauby, Th. Desaive, H. Croisier, Ph. Kolh. Standing waves in the FitzHugh–Nagumo model of cardiac electrical activity // Phys. Rev. E. — 2006. — V. 73. — P. 021908. — DOI: 10.1103/PhysRevE.73.021908. — ads: 2006PhRvE..73b1908D.
  3. E. Davies. Electrical signals in plants: facts and hypotheses / Plant Electrophysiology. Theory and Methods. — Ed. Volkov A. G. — Berlin-Heidelberg: Springer, 2006. — P. 407–422.
  4. H. Dziubinska. Ways of signal transmission and physiological role of electrical potential in plants // Acta Soc. Bot. Polon. — 2003. — V. 72. — P. 309–318. — DOI: 10.5586/asbp.2003.040.
  5. R. Fitzhugh. Impulses and physiological states in theoretical models of nerve membrane // Biophys J. — 1961. — V. 1. — P. 445–466. — DOI: 10.1016/S0006-3495(61)86902-6.
  6. J. Fromm. Long-distance electrical signaling and physiological functions in higher plants / Plant Electrophysiology. Theory and Methods. — Berlin-Heidelberg: Springer, 2006. — P. 269–285. — Ed. Volkov A. G.
  7. I. V. Garkusha, V. A. Petrov, V. A. Vasiliev, Yu. M. Romanovsky. Propagating of bioelectric potentials in green plants’conducting system. Mathematical modeling and experiment // Proc. SPIE. — 2002. — V. 4707. — P. 384–394. — DOI: 10.1117/12.475624. — ads: 2002SPIE.4707..384G.
  8. T. E. E. Grams, S. Lautner, H. H. Felle, R. Matyssek, J. Fromm. Heat-induced electrical signals affect cytoplasmic and apoplastic pH as well as photosynthesis during propagation through the maize leaf // Plant Cell. Environ. — 2009. — V. 32. — P. 319–326. — DOI: 10.1111/j.1365-3040.2008.01922.x. — ads: 2009pso..book.....G.
  9. C. Koziolek, T. E. E. Grams, U. Schreiber, R. Matyssek, J. Fromm. Transient knockout of photosynthesis mediated by electrical signals // New Phytologist. — 2003. — V. 161. — P. 715–722. — DOI: 10.1111/j.1469-8137.2004.00985.x.
  10. S. Lautner, T. E. E. Grams, R. Matyssek, J. Fromm. Characteristics of electrical signals in poplar and responses in photosynthesis // Plant. Physiol. — 2005. — V. 138. — P. 2200–2209. — DOI: 10.1104/pp.105.064196.
  11. H. Mummert, D. Gradmann. Action potentials in Acetabularia: measurement and simulation of voltagegated fluxes // J. Membrane Biol. — 1991. — V. 124. — P. 265–273. — DOI: 10.1007/BF01994359.
  12. E. V. Pankratova, A. V. Polovinkin, B. Spagnolo. Suppression of noise in FitzHugh–Nagumo model driven by a strong periodic signal // Phys. Let. A. — 2005. — V. 344. — P. 43–50. — DOI: 10.1016/j.physleta.2005.05.099. — ads: 2005PhLA..344...43P.
  13. T. K. Shajahan, A. R. Nayak, R. Pandit. Spiral-wave turbulence and its control in the presence of inhomogeneities in four mathematical models of cardiac tissue // PLoS ONE. — 2009. — V. 5. — P. e4738. — ads: 2009PLoSO...4.4738S.
  14. T. Sibaoka. Excitable cells in mimosa // Science. — 1962. — V. 137. — P. 226. — DOI: 10.1126/science.137.3525.226. — ads: 1962Sci...137..226S.
  15. T. Sibaoka. Rapid plant movements triggered by action potentials // Bot. Mag. Tokyo. — 1991. — V. 104. — P. 73–95. — DOI: 10.1007/BF02493405.
  16. B. E. Steinberg, L. Glass, A. Shrier, G. Dud. The role of heterogeneities and intercellular coupling in wave propagation in cardiac tissue // Phil. Trans. R. Soc. A. — 2006. — V. 364. — P. 1299–1311. — DOI: 10.1098/rsta.2006.1771. — MathSciNet: MR2243337. — ads: 2006RSPTA.364.1299S.
  17. V. S. Sukhov, V. A. Vodeneev. A mathematical model of action potential in cells of vascular plants // J. Membrane Biol. — 2009. — V. 232. — P. 59–67. — DOI: 10.1007/s00232-009-9218-9.
  18. K. H. W. J. Ten Tusscher, O. Bernus, R. Hren, A. V. Panfilov. Comparison of electrophysiological models for human ventricular cells and tissues // Prog. Biophys. Mol. Biol. — 2006. — V. 90. — P. 326–345. — DOI: 10.1016/j.pbiomolbio.2005.05.015.
  19. K. H. W. J. Ten Tusscher, A. V. Panfilov. Cell model for efficient simulation of wave propagation in human ventricular tissue under normal and pathological conditions // Phys. Med. Biol. — 2006. — V. 51. — P. 6141–6156. — DOI: 10.1088/0031-9155/51/23/014.
  20. K. Trebacz, H. Dziubinska, E. Krol. Electrical signals in long-distance communication in plants / Communication in plants. Neuronal aspects of plant life. — Berlin-Heidelberg: Springer, 2006. — P. 277–290. — Ed. Baluska F., Mancuso S., Volkmann D.
  21. В. А. Васильев, И. В. Гаркуша, В. А. Петров, Ю. М. Романовский, Ю. Х. Шогенов. Светоиндуцированная электрическая активность зеленых растений // Биофизика. — 2003. — Т. 48, № 4. — С. 706–716.
  22. В. А. Воденеев, В. А. Опритов, С. С. Пятыгин. Изменение внеклеточного pH при генерации потенциала действия у высшего растения Cucurbita pepo // Физиология растений. — 2006. — Т. 53, № 4. — С. 538–545.
  23. В. А. Опритов, С. С. Пятыгин, В. Г. Ретивин. Биоэлектрогенез высших растений. — М: Наука, 1991. — 213 с.
  24. А. Б. Рубин. Биофизика. — М: Высшая школа, 1987. — Т. 2. — 313 с.

Indexed in Scopus

Full-text version of the journal is also available on the web site of the scientific electronic library eLIBRARY.RU

The journal is included in the Russian Science Citation Index

The journal is included in the RSCI

International Interdisciplinary Conference "Mathematics. Computing. Education"