Figure 2.

Mathematical description of transporter activities. (A) Voltage dependence of the background conductance I_background = I_BG = I_BGmax× (1 − exp[−(V − V₀) × F/(RT)])/(1 + exp[−(V − V₀) × F/(RT)]); here V₀ = −100 mV (black curves) or V₀ = −50 mV (gray curve); I_BGmax = 20 fA/μm² (solid lines), I_BGmax = 10 fA/μm² (dotted line). (B,C) Voltage dependencies of the (B) H/P and (C) H/C cotransporters were approximated by first-order Taylor approximation. (B) I_H/P = G_H/P× (V − RT/F × [2 × ln(H_apo/H_cyt) + ln(P_apo/P_cyt)]); G_H/P = 200 fA/(μm²× V) (solid line), G_H/P = 400 fA/(μm²× V) (dashed line), G_H/P = 100 fA/(μm²× V) (dotted line). P_cyt = 2 mM, P_apo = 10 μM, pH_cyt = 7.0, pH_apo = 6.0, i.e. E_H/P = −17.3 mV. (C) I_H/C = 200 fA/(μm²× V) × (V − RT/F × [ln(H_apo/H_cyt) + ln(C_apo/C_cyt)]); C_cyt = 2 mM (solid lines), C_cyt = 4 mM (dashed line), C_cyt = 1 mM (dotted line), C_apo = 10 μM (black lines) or C_apo = 2 mM (gray line). The basic settings of the transporter network were: ${\text{P}}_{\text{cyt}}^{\text{plant}}$ = 1.5 mM, ${\text{P}}_{\text{cyt}}^{\text{fungus}}$ = 3.0 mM, ${\text{C}}_{\text{cyt}}^{\text{plant}}$ = 2 mM, ${\text{C}}_{\text{cyt}}^{\text{fungus}}$ = 1 mM, pH_apo = 6.0, p${\text{H}}_{\text{cyt}}^{\text{plant}}$ = 7.0, p${\text{H}}_{\text{cyt}}^{\text{fungus}}$ = 7.0, ${\text{G}}_{\text{H}/\text{P}}^{\text{plant}}$ = 200 fA/(μm² × V), ${\text{G}}_{\text{H}/\text{P}}^{\text{fungus}}$ = 200 fA/(μm² × V), ${\text{G}}_{\text{H}/\text{C}}^{\text{plant}}$ = 200 fA/(μm² × V), ${\text{G}}_{\text{H}/\text{C}}^{\text{fungus}}$ = 200 fA/(μm² × V), ${\text{I}}_{\text{BGmax}}^{\text{plant}}$ = 20 fA/μm², ${\text{I}}_{\text{BGmax}}^{\text{fungus}}$ = 20 fA/μm², ${\text{V}}_{\text{p}}^0$ = ${\text{V}}_0^{\text{plant}}$ = −75 mV, ${\text{V}}_{\text{f}}^0$ = ${\text{V}}_0^{\text{fungus}}$ = −75 mV. The free-running parameters in in silico simulations were the apoplastic concentrations P_apo and C_apo, and the voltages at the plant and fungal plasma membrane V_p, V_f.