Model Mathematics

j_IP3 = J_IP3 ⅇ^{(- k_0) time} \frac{d}{d time} (IP3) = D_IP3 IP3 - (k_degr (IP3 - IP3_0))

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

J_Ca = \{\begin{matrix} gamma (Ca - Ca_c) if Ca > Ca_c \\ 0.0 otherwise \end{matrix}