Model Mathematics

I_soma = I_Na + I_K_DR + I_h I_h = g_h h (V_s + 30) 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{- I_soma - (\frac{g_c}{p} (V_D - V_s))}{C_m}

R_pump = 18 \frac{p}{1 - p} g_L = 0.18 \frac{p}{1 - p} g_NMDA = 1.25 \frac{p}{1 - p} g_Na_NMDA = 1 \frac{p}{1 - p} f_NMDA = \frac{1}{1 + 0.141 ⅇ^{\frac{- V_D}{q}}} I_pump = \frac{\frac{R_pump p}{1 - p} {(V_D 1 + Na)}^{3}}{{K_p}^{3} + {(V_D 1 + Na)}^{3}} I_pump_ss = \frac{\frac{R_pump p}{1 - p} {Na_eq}^{3}}{{K_Na}^{3} + {Na_eq}^{3}} I_L = g_L (V_D - V_L) I_NMDA = g_NMDA f_NMDA V_D I_Na_NMDA = g_Na_NMDA f_NMDA (V_D - V_Na) I_D = (I_NMDA + I_pump - I_pump_ss) + I_L \frac{d}{d time} (V_D) = \frac{(- I_D) + \frac{g_c}{1 - p} (V_s - V_D)}{C_m} \frac{d}{d time} (Na) = alpha (- I_Na_NMDA - (3 (I_pump - I_pump_ss)))

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}}} r_infinity = \frac{1}{1 + ⅇ^{\frac{V_s + 80}{8}}} tau_h = 0.43 + \frac{0.86}{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)}} tau_mL = \frac{0.4}{5 ⅇ^{\frac{- (V_D + 11)}{8.3}} + \frac{\frac{- (V_D + 11)}{8.3}}{ⅇ^{\frac{- (V_D + 11)}{8.3}} - 1}} tau_r = 190 \frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} \frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n}