Model Mathematics

\frac{d}{d time} (V) = \frac{- (i_Na + i_NaP + i_K + 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_NaP = g_NaP m h \frac{1}{1000} (V - E_Na)

\frac{d}{d time} (m) = \frac{{(1 + ⅇ^{\frac{- (V + 47.1)}{3.1}})}^{-1} - m}{\frac{1.0}{\cosh (\frac{V + 47.1}{6.2})}}

\frac{d}{d time} (h) = \frac{{(1 + ⅇ^{\frac{V + 60.0}{9.0}})}^{-1} - h}{\frac{5000.0}{\cosh (\frac{V + 60.0}{9.0})}}

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_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} (s_e) = \frac{- s_e}{tau_E}

g_synE = 0.43 + 0.03 S1 g_synI = 0.025 S3 + 0.225 S4