Model Mathematics

\frac{d}{d time} (V) = (- (\frac{1.0}{Cm})) (i_Na + i_Ca + i_K + i_K_A + i_K_Ca + i_L)

i_Na = g_Na m^{3.0} h (V - E_Na)

alpha_m = \frac{(-0.6) (V + 30.0)}{ⅇ^{(-0.1) (V + 30.0)} - 1.0} beta_m = 20.0 ⅇ^{\frac{- (V + 55.0)}{18.0}} \frac{d}{d time} (m) = alpha_m (1.0 - m) - (beta_m m)

alpha_h = 0.4 ⅇ^{\frac{- (V + 50.0)}{20.0}} beta_h = \frac{6.0}{ⅇ^{(-0.1) (V + 20.0)} + 1.0} \frac{d}{d time} (h) = alpha_h (1.0 - h) - (beta_h h)

i_Ca = g_Ca c^{3.0} (V - E_Ca) E_Ca = \frac{R T}{2.0 F} \ln (\frac{Ca_e}{Ca_i})

alpha_c = \frac{(-0.3) (V + 13.0)}{ⅇ^{(-0.1) (V + 13.0)} - 1.0} beta_c = 10.0 ⅇ^{\frac{- (V + 38.0)}{18.0}} \frac{d}{d time} (c) = alpha_c (1.0 - c) - (beta_c c)

i_K = g_K n^{4.0} (V - E_K)

alpha_n = \frac{(-0.02) (V + 40.0)}{ⅇ^{(-0.1) (V + 40.0)} - 1.0} beta_n = 0.4 ⅇ^{\frac{- (V + 50.0)}{80.0}} \frac{d}{d time} (n) = alpha_n (1.0 - n) - (beta_n n)

i_K_A = g_K_A a^{3.0} h (V - E_K)

alpha_a = \frac{(-0.006) (V + 90.0)}{ⅇ^{(-0.1) (V + 90.0)} - 1.0} beta_a = 0.1 ⅇ^{\frac{- (V + 30.0)}{10.0}} \frac{d}{d time} (a) = alpha_a (1.0 - a) - (beta_a a)

alpha_h = 0.04 ⅇ^{\frac{- (V + 70.0)}{20.0}} beta_h = \frac{0.6}{ⅇ^{(-0.1) (V + 40.0)} + 1.0} \frac{d}{d time} (h) = alpha_h (1.0 - h) - (beta_h h)

i_K_Ca = g_K_Ca (V - E_K) g_K_Ca_gate = g_K_Ca \frac{{(\frac{Ca_i}{Ca_diss})}^{2.0}}{1.0 + {(\frac{Ca_i}{Ca_diss})}^{2.0}}

i_L = g_L (V - E_L)

\frac{d}{d time} (Ca_i) = \frac{(-3.0) i_Ca}{2.0 F r} - (\frac{Ca_i - Ca_res}{tau_Ca})