Model Mathematics

\frac{d}{d time} (q_K_i) = - v_funny_K \frac{d}{d time} (q_K_o) = v_funny_K \frac{d}{d time} (q_Na_i) = - v_funny_Na \frac{d}{d time} (q_Na_o) = v_funny_Na \frac{d}{d time} (q_mem) = I_mem_funny

Am_K = zK F V_mem Am_Na = zNa F V_mem mu_K_i = R T \ln (K_K_i q_K_i) mu_K_o = R T \ln (K_K_o q_K_o) Af_K = mu_x1_funny + mu_K_i + Am_K Ar_K = mu_x1_funny + mu_K_o mu_Na_i = R T \ln (K_Na_i q_Na_i) mu_Na_o = R T \ln (K_Na_o q_Na_o) Af_Na = mu_x1_funny + mu_Na_i + Am_Na Ar_Na = mu_x1_funny + mu_Na_o v_funny_K = \{\begin{matrix} 1 kappa_funny_K (ⅇ^{\frac{Af_K}{R T}} - (ⅇ^{\frac{Ar_K}{R T}})) if Am_K = 0 \\ \frac{\frac{1 kappa_funny_K Am_K}{R T}}{ⅇ^{\frac{Am_K}{R T}} - 1} (ⅇ^{\frac{Af_K}{R T}} - (ⅇ^{\frac{Ar_K}{R T}})) otherwise \end{matrix} v_funny_Na = \{\begin{matrix} 1 kappa_funny_Na (ⅇ^{\frac{Af_Na}{R T}} - (ⅇ^{\frac{Ar_Na}{R T}})) if Am_Na = 0 \\ \frac{\frac{1 kappa_funny_Na Am_Na}{R T}}{ⅇ^{\frac{Am_Na}{R T}} - 1} (ⅇ^{\frac{Af_Na}{R T}} - (ⅇ^{\frac{Ar_Na}{R T}})) otherwise \end{matrix} V_mem = \frac{q_mem}{C_m} I_mem_funny = F ((- zK) v_funny_K + zNa v_funny_Na + z_xfr v_xf - (z_xff v_xf))

mu_x0_funny = R T \ln (K_x0_funny q_x0_funny) mu_x1_funny = R T \ln (K_x1_funny q_x1_funny) Af_R_xf = mu_x0_funny + z_xff F V_mem Ar_R_xf = mu_x1_funny + z_xfr F V_mem v_xf = kappa_R_xf (ⅇ^{\frac{Af_R_xf}{R T}} - (ⅇ^{\frac{Ar_R_xf}{R T}})) \frac{d}{d t} (q_x0_funny) = - v_xf \frac{d}{d t} (q_x1_funny) = v_xf