# Model Mathematics

### Component: IP3_dynamics

$j_IP3 = J_IP3 ⁢ⅇ- k_0 ⁢ time ddtimetime=- k_degr ⁢ IP3 - IP3_0$

### Component: Calcium_dynamics

$ddtimetime= alpha ⁢ J_channel +- J_pump + J_leak + R_buffering$

### Component: Channel_kinetics

$J_channel = J_max ⁢ IP3 IP3 + K_IP3 ⁢ Ca Ca + K_act ⁢ h 3.0 ⁢ 1.0 - Ca Ca_ER dd time time = k_on ⁢ K_inh - h ⁢ Ca + K_inh$

### Component: SERCA_pump_kinetics

$J_pump = V_max ⁢ Ca 2.0 Ca 2.0 + K_p 2.0$

### Component: Leak

$J_leak = L ⁢ 1.0 - Ca Ca_ER$

### Component: Calcium_buffering

$R_buffering = R1 + R2 R1 =- k1_on ⁢ Ca ⁢ B1 + k1_off ⁢ CaB1 R2 =- k2_on ⁢ Ca ⁢ B2 + k2_off ⁢ CaB2 dd time time = R1 dd time time =- R1 dd time time = R2 dd time time =- R2 K1 = k1_off k1_on K2 = k2_off k2_on$

### Component: Plasma_membrane_extrusion_mechanisms

$gamma = gamma_s ifsoma_or_neurite≦0 gamma_n otherwise gamma_s = gamma_0 ⁢ sigma delta ⁢ sigma_neurite_2D ⁢ w_n + sigma_soma_2D ⁢ w_s gamma_n = gamma_0 ⁢ sigma ⁢ delta delta ⁢ sigma_neurite_2D ⁢ w_n + sigma_soma_2D ⁢ w_s j_Ca = gamma ⁢ Ca - Ca_c if Ca > Ca_c 0.0 otherwise$
Source
Derived from workspace Fink, Slepchenko, Moraru, Watras, Schaff, Loew, 2000 at changeset 62f9650b5ecb.
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