Model Mathematics

\frac{d}{d time} (MP) = vsP \frac{{KIP}^{n}}{{KIP}^{n} + {CN}^{n}} - (vmP \frac{MP}{KmP + MP} + kd MP)

\frac{d}{d time} (P0) = ksP MP + V2P \frac{P1}{K2P + P1} - (V1P \frac{P0}{K1P + P0} + kd P0)

\frac{d}{d time} (P1) = V1P \frac{P0}{K1P + P0} + V4P \frac{P2}{K4P + P2} - (V2P \frac{P1}{K2P + P1} + V3P \frac{P1}{K3P + P1} + kd P1)

\frac{d}{d time} (P2) = V3P \frac{P1}{K3P + P1} + k4 C - (V4P \frac{P2}{K4P + P2} + k3 P2 T2 + vdP \frac{P2}{KdP + P2} + kd P2) Pt = P0 + P1 + P2 + C + CN

\frac{d}{d time} (MT) = vsT \frac{{KIT}^{n}}{{KIT}^{n} + {CN}^{n}} - (vmT \frac{MT}{KmT + MT} + kd MT)

\frac{d}{d time} (T0) = ksT MT + V2T \frac{T1}{K2T + T1} - (V1T \frac{T0}{K1T + T0} + kd T0)

\frac{d}{d time} (T1) = V1T \frac{T0}{K1T + T0} + V4T \frac{T2}{K4T + T2} - (V2T \frac{T1}{K2T + T1} + V3T \frac{T1}{K3T + T1} + kd T1)

\frac{d}{d time} (T2) = V3T \frac{T1}{K3T + T1} + k4 C - (V4T \frac{T2}{K4T + T2} + k3 P2 T2 + vdT \frac{T2}{KdT + T2} + kd T2)

\frac{d}{d time} (C) = k3 P2 T2 + k2 CN - (k4 C + k1 C + kdC C)

\frac{d}{d time} (CN) = k1 C - (k2 CN + kdN CN)