Model Mathematics

Cc = \frac{1}{Vc 6.022 e 2} Cp = \frac{1}{Vc Rpc} Cpc = \frac{Cc}{Cp} \frac{d}{d t} (P) = J13 - (J9 + J8) \frac{d}{d t} (Pg) = J9 - (J11 + J13) \frac{d}{d t} (Pc) = J8 + J12 - J10 \frac{d}{d t} (Pcg) = J10 + J11 - J12 J13 = kf13 Pg J12 = kf12 Pcg kr11 = kf11 Kd11 J11 = kf11 Pg Ca - (kr11 Pcg) J10 = kf10 Pc Gt - (kr10 Pcg) J8 = kf8 P Ca - (kr8 Pc) J9 = kf9 P Gt - (kr9 Pg) J16 = kf16 IP3 J14 = \frac{kf14 Pc PIP2}{\frac{Km14}{Cpc} + PIP2} J15 = \frac{kf15 Pcg PIP2}{\frac{Km15}{Cpc} + PIP2} \frac{d}{d t} (IP3) = Cpc (J14 + J15) - J16 \frac{d}{d t} (Gd) = J7 + J13 + J12 - (J2 + J3) \frac{d}{d t} (Gt) = J6 - (J7 + J9 + J10) J7 = kf7 Gt \frac{d}{d t} (Ca) = Cpc (- 1) (J8 + J11) L = \{\begin{matrix} \frac{Ls}{1 + ⅇ^{(- 80) (t - ts - 0.05)}} if t < ts + 0.15 \land t \geq ts \\ Ls if t \geq ts + 0.15 \\ 0 otherwise \end{matrix} kr1 = kf1 Kd1 J1 = kf1 R L - (kr1 Rl) kr2 = kf2 Kd2 J2 = kf2 R Gd - (kr2 Rg) \frac{d}{d t} (R) = (- 1) (J1 + J2) J3 = kf3 Rl Gd - (kr3 Rlg) \frac{d}{d t} (Rl) = J1 + J6 - J3 kr4 = kf4 Kd4 J4 = kf4 L Rg - (kr4 Rlg) \frac{d}{d t} (Rg) = J2 - J4 J5 = kf5 Rlg \frac{d}{d t} (Rlgp) = J5 J6 = kf6 Rlg \frac{d}{d t} (Rlg) = (J3 - J5) + J4 - J6