Model Mathematics

\frac{d}{d time} (RS) = k_r R_T - ((k_r + \frac{k_p L}{K_1 + L}) RS) - (k_r RS_p)

\frac{d}{d time} (RS_p) = L (\frac{k_p RS}{K_1 + L} - (\frac{k_e RS_p}{K_2 + L}))

\frac{d}{d time} (G) = k_a (delta + rho_r) (G_T - G) - (k_d G)

\frac{d}{d time} (IP_3) = \frac{r_h PIP_2}{N_a v} - (k_deg IP_3)

\frac{d}{d time} (PIP_2) = ((- (r_h + r_r)) PIP_2 - (r_r N_a v IP_3)) + r_r PIP_2_T

r_h = \frac{alpha C}{K_c + C} G

rho_r = \frac{L RS}{xi R_T (K_1 + L)}

\frac{d}{d time} (C) = beta (epsilon_r (eta_1 {m_infinit}^{3} h^{3} + eta_2) (C_ER - C) - (\frac{eta_3 C^{2}}{{k_3}^{2} + C^{2}}))

\frac{d}{d time} (h) = \frac{h_infinit - h}{tau_h}

tau_h = {(a_2 (zeta + C))}^{- 1}

h_infinit = \frac{zeta}{zeta + C}

zeta = \frac{d_2 (IP_3 + d_1)}{IP_3 + d_3}

m_infinit = \frac{\frac{IP_3}{d_1 + IP_3} C}{d_5 + C}

beta = {(1 + \frac{K_e B_e}{{(K_e + C)}^{2}} + \frac{K_x B_x}{{(K_x + C)}^{2}})}^{- 1}

gamma = {(1 + \frac{B_e}{K_e + C} + \frac{B_x}{K_x + C})}^{- 1}

C_ER = \frac{K_ER}{B_ER epsilon_r} (C_T - (\frac{C}{gamma}))

RS_E = \frac{k_r (1 + \frac{\frac{k_p}{k_e} (K_2 + L)}{K_1 + L})}{k_r + \frac{k_p L}{K_1 + L} + \frac{\frac{k_r k_p}{k_e} (K_2 + L)}{K_1 + L}} xi R_T + (1 - xi) R_T