Model Mathematics

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Component: environment

x_tot = x_P1 + x_P3 + x_P6 + x_P13 + x_P7 + x_P14

x_Nae = c_Nae W_e x_Nai = c_Nai W_i x_Ke = c_Ke W_e x_Ki = c_Ki W_i x_P_i = c_P_i W_i x_MgADP = c_MgADP W_i x_MgATP = c_MgATP W_i x_H = 10^{- pH} 1000 W_i

zF_5 = z_5 F zF_8 = z_8 F v_H = v_R13 mu_H = R T \ln (K_H x_H) v_Ke = (- 2) v_R8 mu_Ke = R T \ln (K_Ke x_Ke) v_Ki = 2 v_R1 mu_Ki = R T \ln (K_Ki x_Ki) v_MgADP = v_R6 mu_MgADP = R T \ln (K_MgADP x_MgADP) v_MgATP = - v_R15 mu_MgATP = R T \ln (K_MgATP x_MgATP) v_Nae = 3 v_R8 mu_Nae = R T \ln (K_Nae x_Nae) v_Nai = (- 3) v_R3 mu_Nai = R T \ln (K_Nai x_Nai) v_P7 = v_R6 - v_R8 \frac{d}{d t} (x_P7) = v_P7 mu_P7 = R T \ln (K_7 x_P7) v_P_i = v_R13 mu_P_i = R T \ln (K_P x_P_i) I_mem = zF_5 v_R3 + zF_8 v_R8 V_mem = \frac{q_mem}{C_m} Af_R13 = mu_P13 Ar_R13 = mu_P14 + mu_P_i + mu_H v_R13 = kappa_13 (ⅇ^{\frac{Af_R13}{R T}} - (ⅇ^{\frac{Ar_R13}{R T}})) Af_R15 = mu_P14 + mu_MgATP Ar_R15 = mu_P1 v_R15 = kappa_15 (ⅇ^{\frac{Af_R15}{R T}} - (ⅇ^{\frac{Ar_R15}{R T}})) Af_R6 = mu_P6 Ar_R6 = mu_P7 + mu_MgADP v_R6 = kappa_6 (ⅇ^{\frac{Af_R6}{R T}} - (ⅇ^{\frac{Ar_R6}{R T}})) v_P14 = v_R13 - v_R15 \frac{d}{d t} (x_P14) = v_P14 mu_P14 = R T \ln (K_14 x_P14) v_P1 = v_R15 - v_R1 \frac{d}{d t} (x_P1) = v_P1 mu_P1 = R T \ln (K_1 x_P1) v_P3 = v_R1 - v_R3 \frac{d}{d t} (x_P3) = v_P3 mu_P3 = R T \ln (K_3 x_P3) v_P6 = v_R3 - v_R6 \frac{d}{d t} (x_P6) = v_P6 mu_P6 = R T \ln (K_6 x_P6) Af_R1 = mu_P1 Ar_R1 = mu_P3 + 2 mu_Ki v_R1 = kappa_1 (ⅇ^{\frac{Af_R1}{R T}} - (ⅇ^{\frac{Ar_R1}{R T}})) Af_R3 = mu_P3 + 3 mu_Nai Ar_R3 = zF_5 V_mem + mu_P6 v_R3 = kappa_3 (ⅇ^{\frac{Af_R3}{R T}} - (ⅇ^{\frac{Ar_R3}{R T}})) v_P13 = v_R8 - v_R13 \frac{d}{d t} (x_P13) = v_P13 mu_P13 = R T \ln (K_13 x_P13) Af_R8 = mu_P7 + 2 mu_Ke Ar_R8 = mu_P13 + 3 mu_Nae + zF_8 V_mem v_R8 = kappa_8 (ⅇ^{\frac{Af_R8}{R T}} - (ⅇ^{\frac{Ar_R8}{R T}}))