Model Mathematics

\frac{d}{d time} (V) = \frac{- (i_Na + i_K + i_Ca + i_KCa + i_L + i_synE + i_synI)}{C}

i_Na = g_Na m^{3} h \frac{1}{1000} (V - E_Na)

\frac{d}{d time} (m) = \frac{{(1 + ⅇ^{\frac{- (V + 43.8)}{6}})}^{-1} - m}{\frac{0.252}{\cosh (\frac{V + 43.8}{14})}}

\frac{d}{d time} (h) = \frac{{(1 + ⅇ^{\frac{V + 67.5}{10.8}})}^{-1} - h}{\frac{8.456}{\cosh (\frac{V + 67.5}{12.8})}}

i_K = g_K m^{4} \frac{1}{1000} (V - E_K)

\frac{d}{d time} (m) = a - ((a + b) m) a = \frac{0.001 (V + 44.0)}{1 - (ⅇ^{\frac{- (V + 44.0)}{5.0}})} b = 0.17 ⅇ^{\frac{- (V + 49.0)}{40.0}}

i_Ca = g_Ca m h \frac{1}{1000} (V - E_Ca)

\frac{d}{d time} (m) = \frac{{(1 + ⅇ^{\frac{- (V + 27.4)}{5.7}})}^{-1} - m}{0.5}

\frac{d}{d time} (h) = \frac{{(1 + ⅇ^{\frac{V + 52.4}{5.2}})}^{-1} - h}{18.0}

i_KCa = g_KCa m^{2} \frac{1}{1000} (V - E_K)

\frac{d}{d time} (m) = \frac{1.25 e 8 {Ca}^{2} - ((1.25 e 8 {Ca}^{2} + 2.5) m)}{1000.0 kappa}

i_L = g_L \frac{1}{1000} (V - E_L)

i_synE = g_synE \frac{1}{1000} (V - E_synE)

i_synI = g_synI \frac{1}{1000} (V - E_synI)

\frac{d}{d time} (Ca) = (-2.072 e -5) \frac{Ca + 0.001}{Ca + 0.031} i_Ca + \frac{5 e -5 - Ca}{500.00}

\frac{d}{d time} (s_i) = \frac{- s_i}{tau_I}

E_Ca = 13.27 \log_{10} (\frac{4.0}{Ca}) g_synI = 0.04 S2 + 0.01 S3