Model Mathematics

RT = \frac{R T 1}{1 e 6}

q_Na_o = c_Nae W_e q_Na_i = c_Nai W_i q_K_o = c_Ke W_e q_K_i = c_Ki W_i q_Pi = c_P_i W_i q_ADP = c_MgADP W_i q_ATP = c_MgATP W_i q_H = 10^{- pH} 1000 W_i

z_2 = - 1 - z_1 \frac{d}{d t} (q_1) = v_4 - v_1 \frac{d}{d t} (q_2) = v_1 - v_2 \frac{d}{d t} (q_3) = v_2 - v_3 \frac{d}{d t} (q_4) = v_3 - v_4 u_e = \frac{q_mem}{C_m} Q_1 = K_1 q_1 Q_2 = K_2 q_2 Q_3 = K_3 q_3 Q_4 = K_4 q_4 Q_Na_o = K_Nae q_Na_o Q_Na_i = K_Nai q_Na_i Q_K_o = K_Ke q_K_o Q_K_i = K_Ki q_K_i Q_ATP = K_ATP q_ATP Q_ADP = K_ADP q_ADP Q_Pi = K_Pi q_Pi Q_H = K_H q_H v_1 = kappa_1 (Q_1 {Q_K_o}^{2} - (Q_2 Q_Pi Q_H)) v_2 = kappa_2 (Q_2 Q_ATP - (Q_3 {Q_K_i}^{2})) v_3 = kappa_3 (Q_3 {Q_Na_i}^{3} - (Q_4 Q_ADP ⅇ^{\frac{z_1 F u_e}{RT}})) v_4 = kappa_4 (Q_4 - (Q_1 {Q_Na_o}^{3} ⅇ^{\frac{z_2 F u_e}{RT}})) q_tot = q_1 + q_2 + q_3 + q_4

Adenosine_tot = q_ATP + q_ADP + q_3 Phosphate_tot = 3 q_ATP + 2 q_ADP + q_Pi + q_1 + 3 q_3 + q_4

lambda_1_NKE = \frac{kappa_2}{kappa_4} lambda_2_NKE = \frac{K_1}{K_2} lambda_3_NKE = \frac{K_1}{K_3} lambda_4_NKE = \frac{K_1}{K_4} e_0 = ⅇ^{\frac{F u_e}{RT}} A_0_NKE = q_tot kappa_2 K_1 A_1_NKE = {(\frac{Q_Na_i}{Q_Na_o})}^{3} - (\frac{Q_ADP Q_Pi}{Q_ATP} {(\frac{Q_K_i}{Q_K_o})}^{2} e_0) A_2_NKE = \frac{Q_Pi}{Q_ATP {Q_K_o}^{2}} + \frac{lambda_2_NKE}{Q_ATP} A_3_NKE = \frac{Q_ADP Q_Pi}{Q_ATP} {(\frac{Q_K_i}{Q_K_o})}^{2} + \frac{lambda_2_NKE Q_ADP {Q_K_i}^{2}}{Q_ATP} + lambda_3_NKE Q_ADP + lambda_4_NKE {Q_Na_i}^{3} ⅇ^{\frac{(- z_1) F u_e}{RT}} A_4_NKE = \frac{lambda_1_NKE ⅇ^{\frac{z_1 F u_e}{RT}}}{{Q_Na_o}^{3}} + \frac{Q_Pi}{Q_ATP {Q_K_o}^{2}} e_0 AA_NKE = A_1_NKE A_2_NKE + A_3_NKE A_4_NKE v_NKE = \frac{A_0_NKE}{AA_NKE} ({(\frac{Q_Na_i}{Q_Na_o})}^{3} - (\frac{Q_ADP Q_Pi}{Q_ATP} {(\frac{Q_K_i}{Q_K_o})}^{2} e_0))

u_1 = RT \ln Q_1 u_2 = RT \ln Q_2 u_3 = RT \ln Q_3 u_4 = RT \ln Q_4 u_K_o = RT \ln Q_K_o u_K_i = RT \ln Q_K_i u_Na_o = RT \ln Q_Na_o u_Na_i = RT \ln Q_Na_i u_ATP = RT \ln Q_ATP u_ADP = RT \ln Q_ADP u_Pi = RT \ln Q_Pi u_f1 = u_1 + 2 u_K_o u_r1 = u_2 + u_Pi u_f2 = u_2 + u_ATP u_r2 = u_3 + 2 u_K_i u_f3 = u_3 + 3 u_Na_i u_r3 = u_4 + u_ADP + z_1 F u_e u_f4 = u_4 u_r4 = u_1 + 3 u_Na_o + z_2 F u_e Power_external = (2 u_K_o - u_Pi) v_1 + (u_ATP - (2 u_K_i)) v_2 + (3 u_Na_i - u_ADP - (z_1 F u_e)) v_3 - ((3 u_Na_o + z_2 F u_e) v_4) Power_dissipation = (u_f1 - u_r1) v_1 + (u_f2 - u_r2) v_2 + (u_f3 - u_r3) v_3 + (u_f4 - u_r4) v_4