You are here: Home / Exposures / Butera, Rinzel, Smith, 1999 / Models of Respiratory Rhythm Generation in the Pre-Botzinger Complex. I. Bursting Pacemaker Neurons: model 2 (which includes a slow potassium current)

Model Mathematics

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Component: environment

Component: membrane

\frac{d}{d time} (V) = \frac{(- (i_NaP + i_KS + i_Na + i_K + i_L + i_tonic_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: slow_potassium_current

i_KS = g_KS k (V - E_K)

Component: slow_potassium_current_k_gate

\frac{d}{d time} (k) = \frac{k_infinity - k}{tau_k} k_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V - theta_k}{sigma_k}}} tau_k = \frac{tau_k_max}{\cosh (\frac{V - theta_k}{2.0 sigma_k})}

Component: persistent_sodium_current

i_NaP = g_NaP m_infinity (V - E_Na)

Component: persistent_sodium_current_m_gate

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

Component: leakage_current

i_L = g_L (V - E_L)

Component: tonic_current

i_tonic_e = g_tonic_e (V - E_syn_e)

Source: Derived from workspace Butera, Rinzel, Smith, 1999 at changeset d4ce067eab26.

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