Model Mathematics

\frac{d}{d t} (q_K_i) = - v_KACh \frac{d}{d t} (q_K_o) = v_KACh \frac{d}{d t} (q_mem) = I_mem_KACh V_mem = \frac{q_mem}{C_m}

mu_K_i = R T \ln (K_K_i q_K_i) mu_K_o = R T \ln (K_K_o q_K_o) mu_Gibetagamma = R T \ln (K_Gibetagamma q_Gibetagamma) Am_KACh = zK F V_mem Af_KACh = mu_K_i + zK F V_mem + mu_Gibetagamma Ar_KACh = mu_K_o v_KACh = \{\begin{matrix} kappa_KACh (ⅇ^{\frac{Af_KACh}{R T}} - (ⅇ^{\frac{Ar_KACh}{R T}})) if Am_KACh = 0 \\ \frac{\frac{kappa_KACh Am_KACh}{R T}}{ⅇ^{\frac{Am_KACh}{R T}} - 1} (ⅇ^{\frac{Af_KACh}{R T}} - (ⅇ^{\frac{Ar_KACh}{R T}})) otherwise \end{matrix} I_mem_KACh = (- zK) F v_KACh