Model Mathematics

\frac{d}{d time} (c) = (J_IPR - J_serca) + delta (J_in - J_pm)

\frac{d}{d time} (ce) = gamma (J_serca - J_IPR)

J_IPR = (kf {(0.1 O + 0.9 A)}^{4.0} + g1) (ce - c)

\frac{d}{d time} (R) = (phi_2_O - (phi_2 p R + phi_1 R)) + (l_2_+ k_1_) I_1

\frac{d}{d time} (O) = (phi_2 p R - ((phi_2_+ phi_4 + 1 phi_3) O)) + phi_4_A + k_3_S

\frac{d}{d time} (I_1) = phi_1 R - ((k_1_+ l_2_) I_1)

\frac{d}{d time} (I_2) = phi_5 A - ((k_1_+ l_2_) I_2)

\frac{d}{d time} (S) = 1 phi_3 O - (k_3_S)

\frac{d}{d time} (A) = (phi_4 O - (phi_4_A + phi_5 A)) + (k_1_+ l_2_) I_2

phi_1 = \frac{(k_1 L_1 + l_2) c}{L_1 + c (1.0 + \frac{L_1}{L_3})} phi_2 = \frac{k_2 L_3 + l_4 c}{L_3 + c (1.0 + \frac{L_3}{L_1})} phi_2_= \frac{k_2_+ l_4_c}{1.0 + \frac{c}{L_5}} phi_3 = \frac{k_3 L_5}{c + L_5} phi_4 = \frac{(k_4 L_5 + l_6) c}{c + L_5} phi_4_= \frac{L_1 (k_4_+ l_6_)}{c + L_1} phi_5 = \frac{(k_1 L_1 + l_2) c}{c + L_1}

J_serca = \frac{Vs c}{Ks + c} \frac{1.0}{ce}

J_pm = \frac{Vp c^{2.0}}{{Kp}^{2.0} + c^{2.0}}

J_in = alpha1 + alpha2 p