You are here: Home / Exposures / Purvis, Smith, Koizumi, Butera, 2007 / Intrinsic Bursters Increase the Robustness of Rythm Generation in an Excitatory Network: Single Pacemaker Cell

Model Mathematics

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Component: environment

Component: membrane

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

Component: fast_sodium_current

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

Component: fast_sodium_current_m_gate

m_infinity = \frac{1}{1 + ⅇ^{\frac{V - theta_m}{omega_m}}}

Component: potassium_current

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

Component: potassium_current_n_gate

\frac{d}{d time} (n) = \frac{n_infinity - n}{tau_n} n_infinity = \frac{1}{1 + ⅇ^{\frac{V - theta_n}{omega_n}}} tau_n = \frac{tau_n_max}{\cosh (\frac{V - theta_n}{2 omega_n})}

Component: persistent_sodium_current

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

Component: persistent_sodium_current_m_gate

m_infinity = \frac{1}{1 + ⅇ^{\frac{V - theta_m}{omega_m}}}

Component: persistent_sodium_current_h_gate

\frac{d}{d time} (h) = \frac{h_infinity - h}{tau_h} h_infinity = \frac{1}{1 + ⅇ^{\frac{V - theta_h}{omega_h}}} tau_h = \frac{tau_h_max}{\cosh (\frac{V - theta_h}{2 omega_h})}

Component: leakage_current

i_leak = g_leak \frac{1}{1000} (V - E_leak)

Component: tonic_current

i_tonic_e = g_tonic_e \frac{1}{1000} (V - E_syn_e)

Source: Derived from workspace Purvis, Smith, Koizumi, Butera, 2007 at changeset d75208ca718c.

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