Model Mathematics

\frac{d}{d time} (M_P) = v_sP \frac{{K_IP}^{n}}{{K_IP}^{n} + {C_N}^{n}} - (v_mP \frac{M_P}{K_mP + M_P}) - (k_d M_P) \frac{d}{d time} (M_T) = v_sT \frac{{K_IT}^{n}}{{K_IT}^{n} + {C_N}^{n}} - (v_mT \frac{M_T}{K_mT + M_T}) - (k_d M_T) \frac{d}{d time} (C_N) = k_1 C - (k_2 C_N) - (k_dN C_N)

\frac{d}{d time} (C) = (k_3 P_2 T_2 - (k_4 C) - (k_1 C)) + k_2 C_N - (k_dC C)

\frac{d}{d time} (P_0) = (k_sP M_P - (V_1P \frac{P_0}{K_1P + P_0})) + V_2P \frac{P_1}{K_2P + P_1} - (k_d P_0) \frac{d}{d time} (P_1) = (V_1P \frac{P_0}{K_1P + P_0} - (V_2P \frac{P_1}{K_2P + P_1}) - (V_3P \frac{P_1}{K_3P + P_1})) + V_4P \frac{P_2}{K_4P + P_2} - (k_d P_1) \frac{d}{d time} (P_2) = (V_3P \frac{P_1}{K_3P + P_1} - (V_4P \frac{P_2}{K_4P + P_2}) - (k_3 P_2 T_2)) + k_4 C - (v_dP \frac{P_2}{K_dP + P_2}) - (k_d P_2)

\frac{d}{d time} (T_0) = (k_sT M_T - (V_1T \frac{T_0}{K_1T + T_0})) + V_2T \frac{T_1}{K_2T + T_1} - (k_d T_0) \frac{d}{d time} (T_1) = (V_1T \frac{T_0}{K_1T + T_0} - (V_2T \frac{T_1}{K_2T + T_1}) - (V_3T \frac{T_1}{K_3T + T_1})) + V_4T \frac{T_2}{K_4T + T_2} - (k_d T_1) \frac{d}{d time} (T_2) = (V_3T \frac{T_1}{K_3T + T_1} - (V_4T \frac{T_2}{K_4T + T_2}) - (k_3 P_2 T_2)) + k_4 C - (v_dT \frac{T_2}{K_dT + T_2}) - (k_d T_2)

P_t = P_0 + P_1 + P_2 + C + C_N

T_t = T_0 + T_1 + T_2 + C + C_N