Model Mathematics

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Component: synaptic_coupling

sum_g_syn_e_s_1 = g_syn_e_1_2 s1 + g_syn_e_1_3 s1 + g_syn_e_1_4 s1 + g_syn_e_1_5 s1 sum_g_syn_e_s_2 = g_syn_e_2_1 s2 + g_syn_e_2_3 s2 + g_syn_e_2_4 s2 + g_syn_e_2_5 s2 sum_g_syn_e_s_3 = g_syn_e_3_1 s3 + g_syn_e_3_2 s3 + g_syn_e_3_4 s3 + g_syn_e_3_5 s3 sum_g_syn_e_s_4 = g_syn_e_4_1 s4 + g_syn_e_4_2 s4 + g_syn_e_4_3 s4 + g_syn_e_4_5 s4 sum_g_syn_e_s_5 = g_syn_e_5_1 s5 + g_syn_e_5_2 s5 + g_syn_e_5_3 s5 + g_syn_e_5_4 s5

Component: single_neuron_model

Component: environment

Component: membrane

\frac{d}{d time} (V) = \frac{(- (i_NaP + i_Na + i_K + i_L + i_tonic_e + i_syn_e)) + i_app}{C}

Component: fast_sodium_current

i_Na = g_Na {m_infinity}^{3.0} (1.0 - n) (V - E_Na)

Component: fast_sodium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

Component: fast_sodium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

Component: potassium_current

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

Component: potassium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

Component: persistent_sodium_current

i_NaP = g_NaP m_infinity h (V - E_Na)

Component: persistent_sodium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

Component: persistent_sodium_current_h_gate

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_h}{sigma_h}}} tau_h = \frac{tau_h_max}{\cosh (\frac{V - theta_h}{2.0 sigma_h})}

Component: leakage_current

i_L = g_L (V - E_L)

Component: tonic_current

i_tonic_e = g_tonic_e (V - E_syn_e)

Component: synaptic_input

i_syn_e = sum_g_syn_e_s (V - E_syn_e) s_infinity = \frac{1}{1 + ⅇ^{\frac{V - theta_s}{sigma_s}}} \frac{d}{d time} (s) = \frac{(1 - s) s_infinity - (- (kr s))}{tau_s}

Component: synaptic_coupling

sum_g_syn_e_s = g_syn_e_1_2 s1 + g_syn_e_1_3 s1 + g_syn_e_1_4 s1 + g_syn_e_1_5 s1

Component: single_neuron_model

Component: environment

Component: membrane

\frac{d}{d time} (V) = \frac{(- (i_NaP + i_Na + i_K + i_L + i_tonic_e + i_syn_e)) + i_app}{C}

Component: fast_sodium_current

i_Na = g_Na {m_infinity}^{3.0} (1.0 - n) (V - E_Na)

Component: fast_sodium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

Component: fast_sodium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

Component: potassium_current

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

Component: potassium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

Component: persistent_sodium_current

i_NaP = g_NaP m_infinity h (V - E_Na)

Component: persistent_sodium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

Component: persistent_sodium_current_h_gate

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_h}{sigma_h}}} tau_h = \frac{tau_h_max}{\cosh (\frac{V - theta_h}{2.0 sigma_h})}

Component: leakage_current

i_L = g_L (V - E_L)

Component: tonic_current

i_tonic_e = g_tonic_e (V - E_syn_e)

Component: synaptic_input

i_syn_e = sum_g_syn_e_s (V - E_syn_e) s_infinity = \frac{1}{1 + ⅇ^{\frac{V - theta_s}{sigma_s}}} \frac{d}{d time} (s) = \frac{(1 - s) s_infinity - (- (kr s))}{tau_s}

Component: synaptic_coupling

sum_g_syn_e_s = g_syn_e_1_2 s1 + g_syn_e_1_3 s1 + g_syn_e_1_4 s1 + g_syn_e_1_5 s1

Component: single_neuron_model

Component: environment

Component: membrane

\frac{d}{d time} (V) = \frac{(- (i_NaP + i_Na + i_K + i_L + i_tonic_e + i_syn_e)) + i_app}{C}

Component: fast_sodium_current

i_Na = g_Na {m_infinity}^{3.0} (1.0 - n) (V - E_Na)

Component: fast_sodium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

Component: fast_sodium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

Component: potassium_current

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

Component: potassium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

Component: persistent_sodium_current

i_NaP = g_NaP m_infinity h (V - E_Na)

Component: persistent_sodium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

Component: persistent_sodium_current_h_gate

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_h}{sigma_h}}} tau_h = \frac{tau_h_max}{\cosh (\frac{V - theta_h}{2.0 sigma_h})}

Component: leakage_current

i_L = g_L (V - E_L)

Component: tonic_current

i_tonic_e = g_tonic_e (V - E_syn_e)

Component: synaptic_input

i_syn_e = sum_g_syn_e_s (V - E_syn_e) s_infinity = \frac{1}{1 + ⅇ^{\frac{V - theta_s}{sigma_s}}} \frac{d}{d time} (s) = \frac{(1 - s) s_infinity - (- (kr s))}{tau_s}

Component: synaptic_coupling

sum_g_syn_e_s = g_syn_e_1_2 s1 + g_syn_e_1_3 s1 + g_syn_e_1_4 s1 + g_syn_e_1_5 s1

Component: single_neuron_model

Component: environment

Component: membrane

\frac{d}{d time} (V) = \frac{(- (i_NaP + i_Na + i_K + i_L + i_tonic_e + i_syn_e)) + i_app}{C}

Component: fast_sodium_current

i_Na = g_Na {m_infinity}^{3.0} (1.0 - n) (V - E_Na)

Component: fast_sodium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

Component: fast_sodium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

Component: potassium_current

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

Component: potassium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

Component: persistent_sodium_current

i_NaP = g_NaP m_infinity h (V - E_Na)

Component: persistent_sodium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

Component: persistent_sodium_current_h_gate

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_h}{sigma_h}}} tau_h = \frac{tau_h_max}{\cosh (\frac{V - theta_h}{2.0 sigma_h})}

Component: leakage_current

i_L = g_L (V - E_L)

Component: tonic_current

i_tonic_e = g_tonic_e (V - E_syn_e)

Component: synaptic_input

i_syn_e = sum_g_syn_e_s (V - E_syn_e) s_infinity = \frac{1}{1 + ⅇ^{\frac{V - theta_s}{sigma_s}}} \frac{d}{d time} (s) = \frac{(1 - s) s_infinity - (- (kr s))}{tau_s}

Component: synaptic_coupling

sum_g_syn_e_s = g_syn_e_1_2 s1 + g_syn_e_1_3 s1 + g_syn_e_1_4 s1 + g_syn_e_1_5 s1

Component: single_neuron_model

Component: environment

Component: membrane

\frac{d}{d time} (V) = \frac{(- (i_NaP + i_Na + i_K + i_L + i_tonic_e + i_syn_e)) + i_app}{C}

Component: fast_sodium_current

i_Na = g_Na {m_infinity}^{3.0} (1.0 - n) (V - E_Na)

Component: fast_sodium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

Component: fast_sodium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

Component: potassium_current

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

Component: potassium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_n}{sigma_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2.0 sigma_n})}

Component: persistent_sodium_current

i_NaP = g_NaP m_infinity h (V - E_Na)

Component: persistent_sodium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_m}{sigma_m}}}

Component: persistent_sodium_current_h_gate

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_h}{sigma_h}}} tau_h = \frac{tau_h_max}{\cosh (\frac{V - theta_h}{2.0 sigma_h})}

Component: leakage_current

i_L = g_L (V - E_L)

Component: tonic_current

i_tonic_e = g_tonic_e (V - E_syn_e)

Component: synaptic_input

i_syn_e = sum_g_syn_e_s (V - E_syn_e) s_infinity = \frac{1}{1 + ⅇ^{\frac{V - theta_s}{sigma_s}}} \frac{d}{d time} (s) = \frac{(1 - s) s_infinity - (- (kr s))}{tau_s}

Component: synaptic_coupling

sum_g_syn_e_s = g_syn_e_1_2 s1 + g_syn_e_1_3 s1 + g_syn_e_1_4 s1 + g_syn_e_1_5 s1