Model Mathematics

\frac{d}{d t} (q_K_o) = v_K_ATP \frac{d}{d t} (q_K_i) = - v_K_ATP

\frac{d}{d t} (q_mem) = I_mem_K_ATP

V_mem = \frac{q_mem}{C_m} mu_K_o = R T \ln (K_K_o q_K_o) mu_K_i = R T \ln (K_K_i q_K_i) Af_K_ATP = mu_K_i + zK F V_mem Am_K_ATP = zK F V_mem Ar_K_ATP = mu_K_o I_mem_K_ATP = F (- zK) v_K_ATP v_K_ATP = \{\begin{matrix} kappa_K_ATP (ⅇ^{\frac{Af_K_ATP}{R T}} - (ⅇ^{\frac{Ar_K_ATP}{R T}})) if Am_K_ATP = 0 \\ \frac{\frac{kappa_K_ATP Am_K_ATP}{R T}}{ⅇ^{\frac{Am_K_ATP}{R T}} - 1} (ⅇ^{\frac{Af_K_ATP}{R T}} - (ⅇ^{\frac{Ar_K_ATP}{R T}})) otherwise \end{matrix}