Mathematical model of action potential in higher plants with account for the involvement of vacuole in the electrical signal generation

Electrical signals, including action potential (AP), play an important role in plant adaptation to the changing environmental conditions. Experimental and theoretical investigations of the mechanisms of AP generation are required to understand the relationships between environmental factors and electrical activity of plants. In this work we have elaborated a mathematical model of AP generation, which takes into account the participation of vacuole in the generation of electrical response. The model describes the transporters of the plasma membrane (Ca²⁺, Cl^–, and K⁺ channels, H⁺- and Ca²⁺-ATPases, H⁺/K⁺ antiporter, and 2H⁺/Cl^– symporter) and the tonoplast (Ca²⁺, Cl^–, and K⁺ channels; H⁺- and Ca²⁺-ATPases; H⁺/K⁺, 2H⁺/Cl^–, and 3H⁺/Ca²⁺ antiporters), with due consideration of their regulation by second messengers (Ca²⁺ and IP3). The apoplastic, cytoplasmic and vacuolar buffers are also described. The properties of the simulated AP are in good agreement with experimental data. The AP model describes the attenuation of electrical signal with an increase in the vacuole area and volume; this effect is related to a decrease in the Ca²⁺ spike magnitude. The electrical signal was weakly influenced by the K⁺ and Cl^– content in the vacuole. It was also shown that the contribution of vacuolar IP₃-dependent Ca²⁺ channels into the generation of calcium spike during AP was insignificant with the given parameters of the model. The results provide theoretical evidence for the significance of the vacuolar area and volume in plant cell excitability.