Model Mathematics

mu_Nai = R T \ln (K_Nai q_Nai) mu_Nao = R T \ln (K_Nao q_Nao) mu_Hi = R T \ln (K_Hi q_Hi) mu_Ho = R T \ln (K_Ho q_Ho) mu_1 = R T \ln (K_1 q_1) \frac{d}{d t} (q_1) = v_1 mu_2 = R T \ln (K_2 q_2) \frac{d}{d t} (q_2) = v_2 mu_3 = R T \ln (K_3 q_3) \frac{d}{d t} (q_3) = v_3 mu_4 = R T \ln (K_4 q_4) \frac{d}{d t} (q_4) = v_4 mu_5 = R T \ln (K_5 q_5) \frac{d}{d t} (q_5) = v_5 mu_6 = R T \ln (K_6 q_6) \frac{d}{d t} (q_6) = v_6 V_Vm = V0_Vm A_f_r1 = nNa mu_Nao + mu_1 A_r_r1 = mu_2 A_f_r2 = mu_2 A_r_r2 = mu_3 A_f_r3 = mu_3 A_r_r3 = mu_4 + nNa mu_Nai A_f_r4 = mu_4 + mu_Hi A_r_r4 = mu_5 A_f_r5 = mu_5 A_r_r5 = mu_6 A_f_r6 = mu_6 A_r_r6 = mu_1 + mu_Ho A_f_r7 = mu_1 A_r_r7 = mu_4 v_r1 = kappa_r1 (ⅇ^{\frac{A_f_r1}{R T}} - (ⅇ^{\frac{A_r_r1}{R T}})) v_r2 = kappa_r2 (ⅇ^{\frac{A_f_r2}{R T}} - (ⅇ^{\frac{A_r_r2}{R T}})) v_r3 = kappa_r3 (ⅇ^{\frac{A_f_r3}{R T}} - (ⅇ^{\frac{A_r_r3}{R T}})) v_r4 = kappa_r4 (ⅇ^{\frac{A_f_r4}{R T}} - (ⅇ^{\frac{A_r_r4}{R T}})) v_r5 = kappa_r5 (ⅇ^{\frac{A_f_r5}{R T}} - (ⅇ^{\frac{A_r_r5}{R T}})) v_r6 = kappa_r6 (ⅇ^{\frac{A_f_r6}{R T}} - (ⅇ^{\frac{A_r_r6}{R T}})) v_r7 = kappa_r7 (ⅇ^{\frac{A_f_r7}{R T}} - (ⅇ^{\frac{A_r_r7}{R T}})) v_1 = v_r6 - v_r1 - v_r7 v_2 = v_r1 - v_r2 v_3 = v_r2 - v_r3 v_4 = v_r3 + v_r7 - v_r4 v_5 = v_r4 - v_r5 v_6 = v_r5 - v_r6

V0_Vm = V_E q_Nai = Nai V_i q_Nao = Nao V_o q_Hi = Hi V_i q_Ho = Ho V_o \frac{d}{d t} (V_E) = 0