Model Mathematics

Component based math viewer is available

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 + g_syn_e_1_6 s1 + g_syn_e_1_7 s1 + g_syn_e_1_8 s1 + g_syn_e_1_9 s1 + g_syn_e_1_10 s1 + g_syn_e_2_1 s2 + g_syn_e_2_3 s2 + g_syn_e_2_4 s2 + g_syn_e_2_5 s2 + g_syn_e_2_6 s2 + g_syn_e_2_7 s2 + g_syn_e_2_8 s2 + g_syn_e_2_9 s2 + g_syn_e_2_10 s2 + g_syn_e_3_1 s3 + g_syn_e_3_2 s3 + g_syn_e_3_4 s3 + g_syn_e_3_5 s3 + g_syn_e_3_6 s3 + g_syn_e_3_7 s3 + g_syn_e_3_8 s3 + g_syn_e_3_9 s3 + g_syn_e_3_10 s3 + g_syn_e_4_1 s4 + g_syn_e_4_2 s4 + g_syn_e_4_3 s4 + g_syn_e_4_5 s4 + g_syn_e_4_6 s4 + g_syn_e_4_7 s4 + g_syn_e_4_8 s4 + g_syn_e_4_9 s4 + g_syn_e_4_10 s4 + g_syn_e_5_1 s5 + g_syn_e_5_2 s5 + g_syn_e_5_3 s5 + g_syn_e_5_4 s5 + g_syn_e_5_6 s5 + g_syn_e_5_7 s5 + g_syn_e_5_8 s5 + g_syn_e_5_9 s5 + g_syn_e_5_10 s5 + g_syn_e_6_1 s6 + g_syn_e_6_2 s6 + g_syn_e_6_3 s6 + g_syn_e_6_4 s6 + g_syn_e_6_5 s6 + g_syn_e_6_7 s6 + g_syn_e_6_8 s6 + g_syn_e_6_9 s6 + g_syn_e_6_10 s6 + g_syn_e_7_1 s7 + g_syn_e_7_2 s7 + g_syn_e_7_3 s7 + g_syn_e_7_4 s7 + g_syn_e_7_5 s7 + g_syn_e_7_6 s7 + g_syn_e_7_8 s7 + g_syn_e_7_9 s7 + g_syn_e_7_10 s7 + g_syn_e_8_1 s8 + g_syn_e_8_2 s8 + g_syn_e_8_3 s8 + g_syn_e_8_4 s8 + g_syn_e_8_5 s8 + g_syn_e_8_6 s8 + g_syn_e_8_7 s8 + g_syn_e_8_9 s8 + g_syn_e_8_10 s8 + g_syn_e_9_1 s9 + g_syn_e_9_2 s9 + g_syn_e_9_3 s9 + g_syn_e_9_4 s9 + g_syn_e_9_5 s9 + g_syn_e_9_6 s9 + g_syn_e_9_7 s9 + g_syn_e_9_8 s9 + g_syn_e_9_10 s9 + g_syn_e_10_1 s10 + g_syn_e_10_2 s10 + g_syn_e_10_3 s10 + g_syn_e_10_4 s10 + g_syn_e_10_5 s10 + g_syn_e_10_6 s10 + g_syn_e_10_7 s10 + g_syn_e_10_8 s10 + g_syn_e_10_9 s10

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{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}

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{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}

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{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}

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{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}

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{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}

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{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}

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{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}

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{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}

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{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}

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{1.0}{1.0 + ⅇ^{\frac{V - theta_s}{sigma_s}}} s = \frac{(1.0 - s) s_infinity - (- (kr s))}{tau_s}