Skip to main content
SpringerLink
Log in

A Mathematical Model of Action Potential in Cells of Vascular Plants

  • Published:
Journal of Membrane Biology Aims and scope Submit manuscript

Abstract

A mathematical model of action potential (AP) in vascular plants cells has been worked out. The model takes into account actions of plasmalemma ion transport systems (K+, Cl− and Ca2+ channels; H+- and Ca2+-ATPases; 2H+/Cl− symporter; and H+/K+ antiporter), changes of ion concentrations in the cell and in the extracellular space, cytoplasmic and apoplastic buffer capacities and the temperature dependence of active transport systems. The model of AP simulates a stationary level of the membrane potential and ion concentrations, generation of AP induced by electrical stimulation and gradual cooling and the impact of external Ca2+ for AP development. The model supports a hypothesis about participation of H+-ATPase in AP generation.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7

Similar content being viewed by others

References

  • Barbier-Brygoo H, Vinauger M, Colcombet J, Ephritikhine G, Frachisse J-M, Maurel C (2000) Anion channels in higher plants: functional characterization, molecular structure and physiological role. Biochim Biophys Acta 1465:199–218

    Article  CAS  PubMed  Google Scholar 

  • Beilby MJ (1982) Cl− channels in Chara. Phil Trans R Soc London B 299:435–445

    Article  CAS  Google Scholar 

  • Beilby MJ (2007) Action potential in charophytes. Int Rev Cytol 257:43–82

    Article  CAS  PubMed  Google Scholar 

  • Beilby MJ, Shepherd VA (2001) Modeling the current–voltage characteristics of charophyte membranes. II. The effect of salinity on membranes of Lamprothamnium papulosum. J Membr Biol 181:77–89

    CAS  PubMed  Google Scholar 

  • Bentrup F-W (1990) Potassium ion channels in the plasmalemma. Physiol Plant 79:705–711

    Article  CAS  Google Scholar 

  • Berestovsky GN, Kataev AA (2005) Voltage-gated calcium and Ca2+-activated chloride channels and Ca2+ transients: voltage-clamp studies of perfused and intact cells of Chara. Eur Biophys J 34:973–986

    Article  CAS  PubMed  Google Scholar 

  • Blatt MR (1992) K+ channels of stomatal guard cells. J Gen Physiol 99:615–644

    Article  CAS  PubMed  Google Scholar 

  • Bulychev AA, Turovetsky VB (1983) Light-triggered changes of membrane potential in the cells of Anthoceros punctatus and their relation to activation of chloroplast ATPase. J Exp Bot 34:1181–1188

    Article  CAS  Google Scholar 

  • Bulychev AA, Kamzolkina NA, Luengviriya J, Rubin AB, Muller CS (2004) Effect of a single excitation stimulus on photosynthetic activity and light-dependent pH banding in Chara cells. J Membr Biol 202:11–19

    Article  CAS  PubMed  Google Scholar 

  • Bush DS (1993) Regulation of cytosolic calcium in plants. Plant Physiol 103:7–13

    CAS  PubMed  Google Scholar 

  • Davies E (2006) Electrical signals in plants: facts and hypotheses. In: Volkov AG (ed) Plant electrophysiology. Theory and methods. Springer, Berlin, pp 407–422

    Chapter  Google Scholar 

  • Felle HH, Zimmermann MR (2007) Systemic signaling in barley through action potentials. Planta 226:203–214

    Article  CAS  PubMed  Google Scholar 

  • Fromm J, Bauer T (1994) Action potentials in maize sieve tubes change phloem translocation. J Exp Bot 45:463–469

    Article  Google Scholar 

  • Fromm J, Lautner S (2007) Electrical signals and their physiological significance in plants. Plant Cell Environ 30:249–257

    Article  CAS  PubMed  Google Scholar 

  • Fromm J, Spanswick R (1993) Characteristics of action potentials in willow (Salix viminalis L.). J Exp Bot 44:1119–1125

    Article  Google Scholar 

  • Gradmann D (1976) “Metabolic” action potentials in Acetabularia. J Membr Biol 29:23–45

    Article  CAS  PubMed  Google Scholar 

  • Gradmann D (2001a) Models for oscillations in plants. Aust J Plant Physiol 28:577–590

    CAS  Google Scholar 

  • Gradmann D (2001b) Impact of apoplast volume on ionic relations in plant cells. J Membr Biol 184:61–69

    Article  CAS  PubMed  Google Scholar 

  • Gradmann D, Hoffstadt J (1998) Electrocoupling of ion transporters in plants: interaction with internal ion concentrations. J Membr Biol 166:51–59

    Article  CAS  PubMed  Google Scholar 

  • Gradmann D, Blatt MR, Thiel G (1993) Electrocoupling of ion transporters in plants. J Membr Biol 136:327–332

    CAS  PubMed  Google Scholar 

  • Hansen U-P, Gradmann D, Sanders D, Slayman CL (1981) Interpretation of current-voltage relationships for “active” ion transport systems: I. Steady-state reaction-kinetic analysis of class-I mechanisms. J Membr Biol 63:165–190

    Article  CAS  PubMed  Google Scholar 

  • Hodick D, Sievers A (1988) The action potential of Dionaea muscipula Ellis. Planta 174:8–18

    Article  CAS  Google Scholar 

  • Huang JW, Grunes DL, Kochian LV (1994) Voltage-dependent Ca2+ influx into right-side-out plasma membrane vesicles isolated from wheat roots: characterization of a putative Ca2+ channel. Proc Natl Acad Sci USA 91:3473–3477

    Article  CAS  PubMed  Google Scholar 

  • Iijima T, Sibaoka T (1985) Membrane potentials in excitable cells of Aldrovanda vesiculosa trap-lobes. Plant Cell Physiol 26:1–13

    CAS  Google Scholar 

  • Kinoshita T, Nishimura M, Shimazaki K (1995) Cytosolic concentration of Ca2+ regulates the plasma membrane H+-ATPase in guard cells of fava bean. Plant Cell 7:1333–1342

    Article  CAS  PubMed  Google Scholar 

  • Klusener B, Weiler EW (1999) A calcium-selective channel from root-tip endomembranes of garden cress. Plant Physiol 119:1399–1405

    Article  CAS  PubMed  Google Scholar 

  • Lewis BD, Karlin-Neumann G, Davis RW, Spalding EP (1997) Ca2+-activated anion channels and membrane depolarizations induced by blue light and cold in Arabidopsis seedlings. Plant Physiol 114:1324–1327

    Article  Google Scholar 

  • Moran M, Ehrenstein G, Iwasa K, Mischke C, Bare C, Satter RL (1988) Potassium channels in motor cells of Samanea saman. A patch-clamp study. Plant Physiol 88:643–648

    Article  PubMed  Google Scholar 

  • Mummert H, Gradmann D (1991) Action potentials in Acetabularia: measurement and simulation of voltage-gated fluxes. J Membr Biol 124:265–273

    Article  CAS  PubMed  Google Scholar 

  • Opritov VA, Retivin VG (1982) On the mechanism of propagating excitation in higher plants. Fiziol Rast 29:915–924

    CAS  Google Scholar 

  • Opritov VA, Pyatygin SS, Retivin VG (1991) Bioelectrogenesis in higher plants [in Russian]. Nauka, Moskow

    Google Scholar 

  • Opritov VA, Pyatygin SS, Vodeneev VA (2002) Direct coupling of action potential generation in cells of a higher plant (Cucurbita pepo) with the operation of an electrogenic pump. Russ J Plant Physiol 49:142–147

    Article  CAS  Google Scholar 

  • Pei Z-M, Baizabal-Aguirre VM, Allen GJ, Schroeder JL (1998) A transient outward-rectifying K+ channel current down-regulated by cytosolic Ca2+ in Arabidopsis thaliana guard cells. Proc Natl Acad Sci USA 95:6548–6553

    Article  CAS  PubMed  Google Scholar 

  • Pyatygin SS, Opritov VA, Khudyakhov VA (1992) Subthreshold changes in excitable membranes of Cucurbita pepo L. stem cells during cooling-induced action potential generation. Planta 186:161–165

    Article  CAS  Google Scholar 

  • Pyatygin SS, Opritov VA, Abramova NN, Vodeneev VA (1999a) Primary bioelectric response of higher plant cells to the combined action of stress factors. Russ J Plant Physiol 46:530–536

    CAS  Google Scholar 

  • Pyatygin SS, Opritov VA, Polovinkin AV, Vodeneev VA (1999b) Mechanism of generation of action potential in higher plants. Dokl Biophys 364–366:42–45

    Google Scholar 

  • Pyatygin SS, Opritov VA, Vodeneev VA (2008) Signaling role of action potential in higher plants. Russ J Plant Physiol 55:312–319

    Google Scholar 

  • Rodriguez-Navarro A (2000) Potassium transport in fungi and plants. Biochim Biophys Acta 1469:1–30

    CAS  PubMed  Google Scholar 

  • Samejima M, Sibaoka T (1982) Identification of the excitable cells in the petiole of Mimosa pudica by intracellular injection of procion yellow. Plant Cell Physiol 24:33–39

    Google Scholar 

  • Shimmen T, Mimura T, Kikuyama M, Tazawa M (1994) Characean cells as a tool for studying electrophysiological characteristics of plant cell. Cell Struct Funct 19:263–278

    Article  CAS  PubMed  Google Scholar 

  • Sukhov VS, Vodeneev VA (2005) Mathematical model of action potential in higher plant. In: Riznichenko GY (ed) Mathematics, computing, education [in Russian]. Regular and chaotic dynamics, Moskow-Izhevsk, pp 267–278

    Google Scholar 

  • Thomine S, Zimmermann S, Guern J, Barbier-Brygoo H (1995) ATP-dependent regulation of an anion channel at the plasma membrane of protoplasts from epidermal cells of Arabidopsis hypocotyls. Plant Cell 7:2091–2100

    Article  CAS  PubMed  Google Scholar 

  • Trebacz K, Dziubinska H, Krol E (2006) Electrical signals in long-distance communication in plants. In: Baluska F, Mancuso S, Volkmann D (eds) Communication in plants. Neuronal aspects of plant life. Springer, Berlin, pp 277–290

    Google Scholar 

  • Tyerman SD, Beilby M, Whittington J, Juswono U, Neyman L, Shabala S (2001) Oscillations in proton transport revealed from simultaneous measurements of net current and net proton fluxes from isolated root protopasts: MIFE meets patch-clamp. Aust J Plant Physiol 28:591–604

    CAS  Google Scholar 

  • Vodeneev VA, Opritov VA, Pyatygin SS (2006) Reversible changes of extracellular pH during action potential generation in a higher plant Cucurbita pepo. Russ J Plant Physiol 53:481–487

    Article  CAS  Google Scholar 

  • White PJ (1998) Calcium channels in the plasma membrane of root cells. Ann Bot 81:173–183

    Article  CAS  Google Scholar 

  • Zawadzki T, Davies E, Dziubinska H, Trebacz K (1991) Characteristics of action potential in Helianthus annuus. Physiol Plant 83:601–604

    Article  Google Scholar 

  • Zimmermann S, Sentenac H (1999) Plant ion channels: from molecular structures to physiological functions. Curr Opin Plant Biol 2:477–482

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgment

This work was supported by the Russian Foundation for Basic Research (grant 09-04-01413-a).

Author information

Authors and Affiliations

  1. Department of Biophysics, N.I. Lobachevsky State University of Nizhny Novgorod, Gagarin Avenue, 23, Nizhny Novgorod, 603950, Russia

    Vladimir Sukhov & Vladimir Vodeneev

Authors
  1. Vladimir Sukhov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vladimir Vodeneev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vladimir Sukhov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sukhov, V., Vodeneev, V. A Mathematical Model of Action Potential in Cells of Vascular Plants. J Membrane Biol 232, 59–67 (2009). https://doi.org/10.1007/s00232-009-9218-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00232-009-9218-9

Keywords

Search

Navigation