Model Mathematics

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Component: environment

Component: S1

S1 = \sum_{k = 1}^{50} ({s_e}^{k})

Component: S2

S2 = \frac{1}{3} \sum_{k = 1}^{50} ({s_i}^{k})

Component: S3

S3 = \frac{1}{3} \sum_{k = 1}^{50} ({s_i}^{k})

Component: S4

S4 = \frac{1}{3} \sum_{k = 1}^{50} ({s_i}^{k})

Component: model_parameters

Component: pre_I

Component: V

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

Component: i_Na

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

Component: i_Na_m_gate

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

Component: i_Na_h_gate

\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})}}

Component: i_NaP

i_NaP = g_NaP m h \frac{1}{1000} (V - E_Na)

Component: i_NaP_m_gate

\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})}}

Component: i_NaP_h_gate

\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})}}

Component: i_K

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

Component: i_K_m_gate

\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}}

Component: i_L

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

Component: i_synE

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

Component: i_synI

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

Component: s_e

\frac{d}{d time} (s_e) = \frac{- s_e}{tau_E}

Component: model_parameters

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

Component: early_I

Component: V

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

Component: i_Na

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

Component: i_Na_m_gate

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

Component: i_Na_h_gate

\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})}}

Component: i_K

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

Component: i_K_m_gate

\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}}

Component: i_Ca

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

Component: i_Ca_m_gate

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

Component: i_Ca_h_gate

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

Component: i_KCa

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

Component: i_KCa_m_gate

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

Component: i_L

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

Component: i_synE

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

Component: i_synI

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

Component: Ca

\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}

Component: s_i

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

Component: model_parameters

g_synE = 0.7 + 0.034 S1 g_synI = 0.145 S3 + 0.4 S4 E_Ca = 13.27 \log_{10} (\frac{4.0}{Ca})

Component: post_I

Component: V

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

Component: i_Na

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

Component: i_Na_m_gate

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

Component: i_Na_h_gate

\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})}}

Component: i_K

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

Component: i_K_m_gate

\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}}

Component: i_Ca

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

Component: i_Ca_m_gate

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

Component: i_Ca_h_gate

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

Component: i_KCa

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

Component: i_KCa_m_gate

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

Component: i_L

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

Component: i_synE

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

Component: i_synI

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

Component: Ca

\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}

Component: s_i

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

Component: model_parameters

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

Component: aug_E

Component: V

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

Component: i_Na

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

Component: i_Na_m_gate

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

Component: i_Na_h_gate

\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})}}

Component: i_K

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

Component: i_K_m_gate

\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}}

Component: i_Ca

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

Component: i_Ca_m_gate

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

Component: i_Ca_h_gate

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

Component: i_KCa

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

Component: i_KCa_m_gate

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

Component: i_L

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

Component: i_synE

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

Component: i_synI

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

Component: Ca

\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}

Component: s_i

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

Component: model_parameters

E_Ca = 13.27 \log_{10} (\frac{4.0}{Ca}) g_synI = 0.115 S2 + 0.32 S4