# Model Mathematics

### Component: R

$ddtimeR= phi_2_ ⁢ O - phi_2 ⁢ p ⁢ R + phi_1 ⁢ R + l_2_ + k_1_ ⁢ I_1$

### Component: O

$ddtimeO= phi_2 ⁢ p ⁢ R - phi_2_ + phi_4 + phi_3 ⁢ O + phi_4_ ⁢ A + k_3_ ⁢ S$

### Component: A

$ddtimeA= phi_4 ⁢ O - phi_4_ ⁢ A + phi_5 ⁢ A + k_1_ + l_2_ ⁢ I_2$

### Component: I_1

$ddtimeI_1= phi_1 ⁢ R - k_1_ + l_2_ ⁢ I_1$

### Component: I_2

$ddtimeI_2= phi_5 ⁢ A - k_1_ + l_2_ ⁢ I_2$

### Component: S

$ddtimeS= phi_3 ⁢ O - k_3_ ⁢ S$

### Component: P_IPR

$P_IPR= 0.1 ⁢ O + 0.9 ⁢ A 4.0$

### Component: IPR_parameters

$phi_1 = k_1 ⁢ L_1 + l_2 ⁢ c L_1 + c ⁢ 1.0 + L_1 L_3 phi_2 = k_2 ⁢ L_3 + l_4 ⁢ c L_3 + c ⁢ 1.0 + L_3 L_1 phi_2_ = k_2_ + l_4_ ⁢ c 1.0 + c L_5 phi_3 = k_3 ⁢ L_5 c + L_5 phi_4 = k_4 ⁢ L_5 + l_6 ⁢ c c + L_5 phi_4_ = k_1 ⁢ L_1 + l_2 ⁢ c c + L_1 phi_5 = L_1 ⁢ k_4_ + l_6_ ⁢ c c + L_1$

### Component: P_RyR

$P_RyR = w ⁢ 1.0 + c Kb 3.0 1.0 + Ka c 4.0 + c Kb 3.0 w_infinity_c = 1.0 + Ka c 4.0 + c Kb 3.0 1.0 + 1.0 Kc + Ka c 4.0 + c Kb 3.0 Ka = ka_minus ka_plus Kb = kb_minus kb_plus Kc = kc_minus kc_plus ddtime w = kc_minus ⁢ w_infinity_c - w w_infinity_c$

### Component: calcium

$∂∂ time c = Dc ⁢ c_x2 + k_f ⁢ P_IPR + v_1 ⁢ P_RyR + J_er ⁢ c_e - c + delta ⁢ J_in ⁢ p - J_pm - J_serca + J_mito ∂ 2.0 ∂ x 2.0 c = c_x2 dd time c_e = gamma ⁢ J_serca - k_f ⁢ P_IPR + v_1 ⁢ P_RyR + J_er ⁢ c_e - c$

### Component: plasma_membrane_calcium_pump

$J_pm = V_pm ⁢ c 2.0 K_pm 2.0 + c 2.0$

### Component: SERCA_pump

$J_serca = V_serca ⁢ c K_serca + c ⁢ 1.0 c_e$

### Component: mitochondrial_uptake

$J_mito = V_mito ⁢ c 1.0 + 1.0 c 2.0$

### Component: influx_from_outside_the_cell

$J_in = 0.2 + 0.05 ⁢ p$

### Component: IP3_dynamics

$p = p0 ⁢ⅇ -0.8 ⁢ time$
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