Model Mathematics

j_IP3 = J_IP3 ⅇ^{(- k_0) time} \frac{d}{d time} (time) = - (k_degr (IP3 - IP3_0))

\frac{d}{d time} (time) = alpha (J_channel + (- J_pump) + J_leak) + R_buffering

J_channel = J_max {(\frac{IP3}{IP3 + K_IP3} \frac{Ca}{Ca + K_act} h)}^{3.0} (1.0 - (\frac{Ca}{Ca_ER})) \frac{d}{d time} (time) = k_on (K_inh - (h (Ca + K_inh)))

J_pump = V_max \frac{{Ca}^{2.0}}{{Ca}^{2.0} + {K_p}^{2.0}}

J_leak = L (1.0 - (\frac{Ca}{Ca_ER}))

R_buffering = R1 + R2 R1 = (- (k1_on Ca B1)) + k1_off CaB1 R2 = (- (k2_on Ca B2)) + k2_off CaB2 \frac{d}{d time} (time) = R1 \frac{d}{d time} (time) = - R1 \frac{d}{d time} (time) = R2 \frac{d}{d time} (time) = - R2 K1 = \frac{k1_off}{k1_on} K2 = \frac{k2_off}{k2_on}

gamma = \{\begin{matrix} gamma_s if soma_or_neurite ≦ 0 \\ gamma_n otherwise \end{matrix} gamma_s = \frac{gamma_0 sigma}{delta sigma_neurite_2D w_n + sigma_soma_2D w_s} gamma_n = \frac{gamma_0 sigma delta}{delta sigma_neurite_2D w_n + sigma_soma_2D w_s} j_Ca = \{\begin{matrix} gamma (Ca - Ca_c) if Ca > Ca_c \\ 0.0 otherwise \end{matrix}