Model Mathematics

\frac{d}{d time} (q_K_i) = - v_TO \frac{d}{d time} (q_K_o) = v_TO \frac{d}{d time} (q_mem) = I_mem_TO Vmem = \frac{q_mem}{C_m}

Am_TO = F V_mem u_K_i = R T \ln (K_K_i q_K_i) u_K_o = R T \ln (K_K_o q_K_o) Af_TO = mu_r1s1_TO + u_K_i + Am_TO Ar_TO = mu_r1s1_TO + u_K_o v_TO = \{\begin{matrix} 1 kappa_TO (ⅇ^{\frac{Af_TO}{R T}} - (ⅇ^{\frac{Ar_TO}{R T}})) if Am_TO = 0 \\ \frac{\frac{1 kappa_TO Am_TO}{R T}}{ⅇ^{\frac{Am_TO}{R T}} - 1} (ⅇ^{\frac{Af_TO}{R T}} - (ⅇ^{\frac{Ar_TO}{R T}})) otherwise \end{matrix} V_mem = \frac{q_mem}{C_m} I_mem_TO = F ((- zK) v_TO + (v_gTO_1 + v_gTO_2) (z_rTO_r - z_rTO_f) + (v_gTO_3 + v_gTO_4) (z_sTO_r - z_sTO_f))

Af_gTO_1 = mu_r0s0_TO + z_rTO_f F V_mem Ar_gTO_1 = mu_r1s0_TO + z_rTO_r F V_mem Af_gTO_3 = mu_r0s0_TO + z_sTO_f F V_mem Ar_gTO_3 = mu_r0s1_TO + z_sTO_r F V_mem Af_gTO_2 = mu_r0s1_TO + z_rTO_f F V_mem Ar_gTO_2 = mu_r1s1_TO + z_rTO_r F V_mem Af_gTO_4 = mu_r1s0_TO + z_sTO_f F V_mem Ar_gTO_4 = mu_r1s1_TO + z_sTO_r F V_mem v_gTO_1 = kappa_gTO_1 (ⅇ^{\frac{Af_gTO_1}{R T}} - (ⅇ^{\frac{Ar_gTO_1}{R T}})) v_gTO_3 = kappa_gTO_3 (ⅇ^{\frac{Af_gTO_3}{R T}} - (ⅇ^{\frac{Ar_gTO_3}{R T}})) v_gTO_2 = kappa_gTO_2 (ⅇ^{\frac{Af_gTO_2}{R T}} - (ⅇ^{\frac{Ar_gTO_2}{R T}})) v_gTO_4 = kappa_gTO_4 (ⅇ^{\frac{Af_gTO_4}{R T}} - (ⅇ^{\frac{Ar_gTO_4}{R T}})) v_r0s0_TO = (- v_gTO_1) + v_gTO_3 v_r1s0_TO = v_gTO_1 - v_gTO_4 v_r0s1_TO = (- v_gTO_2) + v_gTO_3 v_r1s1_TO = v_gTO_2 + v_gTO_4 mu_r0s0_TO = R T \ln (K_r0s0_TO q_r0s0_TO) mu_r1s0_TO = R T \ln (K_r1s0_TO q_r1s0_TO) mu_r0s1_TO = R T \ln (K_r0s1_TO q_r0s1_TO) mu_r1s1_TO = R T \ln (K_r1s1_TO q_r1s1_TO) \frac{d}{d t} (q_r0s0_TO) = v_r0s0_TO \frac{d}{d t} (q_r1s0_TO) = v_r1s0_TO \frac{d}{d t} (q_r0s1_TO) = v_r0s1_TO \frac{d}{d t} (q_r1s1_TO) = v_r1s1_TO