You are here: Home / Exposures / Gall, Susa, 1999 / Effect of Na/Ca Exchange on Plateau Fraction and [Ca]i in Models for Bursting in Pancreatic Beta-Cells (Model C)

Model Mathematics

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Component: environment

Component: membrane

\frac{d}{d time} (V) = \frac{- (i_K + i_Ca + i_K_Ca + i_Na_Ca)}{Cm}

Component: rapidly_activating_K_current

i_K = g_K n (V - V_K)

Component: rapidly_activating_K_current_n_gate

\frac{d}{d time} (n) = lamda \frac{n_infinity - n}{tau_n} n_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V_n - V}{S_n}}} tau_n = \frac{c}{ⅇ^{\frac{V - V_}{a}} + ⅇ^{\frac{V_- V}{b}}}

Component: calcium_current

i_Ca = g_Ca m_infinity (V - V_Ca)

Component: calcium_current_m_gate

m_infinity = \frac{1.0}{1.0 + ⅇ^{\frac{V_m - V}{S_m}}}

Component: calcium_activated_K_current

i_K_Ca = g_K_Ca \frac{Ca_i}{K_d + Ca_i} (V - V_K)

Component: Na_Ca_exchanger_current

i_Na_Ca = g_Na_Ca \frac{{Ca_i}^{nH}}{{K_1_2}^{nH} + {Ca_i}^{nH}} (V - V_Na_Ca) V_Na_Ca = RT_F 3.0 \ln (\frac{Na_o}{Na_i} - (\ln (\frac{Ca_o}{Ca_i})))

Component: ionic_concentrations

\frac{d}{d time} (Ca_i) = f ((- alpha) (i_Ca - (2.0 i_Na_Ca)) - (k_Ca Ca_i)) + k_rel (Ca_ret - Ca_i) - (k_pump Ca_i) \frac{d}{d time} (Ca_ret) = (- k_rel) (Ca_ret - Ca_i) + k_pump Ca_i

Source: Derived from workspace Gall, Susa, 1999 at changeset 6c79aa0371c3.

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