Figure 1.

(a) Schema of the model of the generation of the cooling-induced electrical response (action potential in irritated zone, AP), (b) schema of interaction between neighboring cells, (c) and basic parameters of AP used in the current work. The model was based on our previous studies [11,29,53,57,58,59]; equations of the model are described in the File S1 (Supplementary Materials). The general model is composed of a two-dimensional group of cells (20 × 20 cells); each cell has its apoplast region. Each cell (excluding boundary cells) is connected with four neighboring cells. All cells are treated by cooling. E_m is a membrane potential; we analyze averaged E_m in the investigation (central 10 × 10 cells). E_m⁰ is the value of E_m before the initiation of cooling; T is temperature; A_AP is the amplitude of AP; Δt_th is the duration of cooling, which is necessary for the induction of E_m changes equaling to 50% of A_AP; and ΔT_th is magnitude of cooling, which is necessary for the induction of E_m changes equaling to 50% of A_AP. E_m^ij is the membrane potential in cell with coordinates i and j, and g is the electrical conductance between neighboring cells. j_C^r is the flux of ion r (Cl⁻, K⁺, Ca²⁺, or H⁺) through ion channels based on the Goldman–Hodgkin–Katz flux equation. Potential-dependent anion, inward, and outward K⁺ channels, Ca²⁺ channels, and H⁺ leakage (proton channels) are described. p_o and p_i are the probabilities of open and inactivated states of ion channels. k_+o(+i) and k_-o(-i) are velocity constants of transition from closed (open) to open (inactivated) states and vice versa. P_max is the maximal permeability of the ion channel and z is the charge of the ion. F, R, and T are standard thermodynamic constants. j_p is the flux of the ion through transport ATP-ases (H⁺-ATP-ase and Ca²⁺-ATP-ase described), which are described on the basis of the “two-state model”. k₊₁, k₋₁, k₊₂, and k₋₂ are velocity constants for the transitions between states of the transport ATP-ases. Initial activities of H⁺-ATP-ases in different cells are modified by multiplication on stochastic variable ξ, which has normal distribution (ξ = 1 ± SD, where SD is the standard deviation). j_p^K is the flux through an H⁺-K⁺ symporter and V^K is a parameter that is proportional to the rate of the transports of ions through the symporter. j_p^Cl is the flux through a 2H⁺-Cl⁻ antiporter and V^Cl is a parameter that is proportional to the rate of the transports of ions through the antiporter. B_in and BH_in are free and H⁺-bound buffer molecules are in the cytoplasm. B_out, BH_out, and BK_out are free, H⁺-bound and K⁺-bound buffer molecules are in the apoplast. Cooling is imitated by the decrease of T with 4 °C min⁻¹, 2 °C min⁻¹, and 0.5 °C min⁻¹ rates. Description of the modifications of transport enzymes activities are based on using Q₁₀ = 3.