Model Mathematics

I_Na = g_Na h (V_s - V_Na) {m_infinity}^{3} I_K_DR = g_K_DR (V_s - V_K) n^{2} \frac{d}{d time} (V_s) = \frac{- (1000.0 (I_K_DR + I_Na + \frac{g_c}{p} (V_s - V_D)))}{C_m}

I_D = I_NMDA + I_pump + I_L I_L = g_L (V_D - V_L) I_pump = R_pump (phi_Na - phi_Na_eq) phi_Na = \frac{{Na}^{3}}{{Na}^{3} + {K_p}^{3}} phi_Na_eq = \frac{{Na_eq}^{3}}{{Na_eq}^{3} + {K_p}^{3}} I_NMDA = \frac{g_NMDA}{1 + \frac{Mg_o}{K_Mg} ⅇ^{- (\frac{V_D}{q})}} (V_D - V_NMDA) I_Na_NMDA = \frac{g_Na_NMDA}{1 + \frac{Mg_o}{K_Mg} ⅇ^{- (\frac{V_D}{q})}} (V_D - V_Na) \frac{d}{d time} (V_D) = \frac{- (1000.0 (I_NMDA + I_pump + I_L + \frac{g_c}{1 - p} (V_D - V_s)))}{C_m} \frac{d}{d time} (Na) = alpha (- I_Na_NMDA - (3 I_pump))

m_infinity = \frac{1}{1 + ⅇ^{\frac{- (V_s + 35)}{6.2}}} n_infinity = \frac{1}{1 + ⅇ^{\frac{- (V_s + 31)}{5.3}}} h_infinity = \frac{1}{1 + ⅇ^{\frac{V_s + 30}{8.3}}} tau_h = 0.4 (1 + \frac{2}{1 + ⅇ^{\frac{V_s + 25}{5}}}) tau_n = \frac{0.8 + \frac{1.6}{1 + ⅇ^{0.1 (V_s + 25)}}}{1 + ⅇ^{(- 0.1) (V_s + 70)}} \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} \frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n}