# Model Mathematics

### Component: Asc

$ddtimeAsc= gamma_Asc ⁢ Asc ⁢ C_Asc - Asc - pG + pDA ⁢ T_Asc ⁢ Asc$

### Component: Csc

$ddtimeCsc= gamma_Csc ⁢ Csc ⁢ C_Csc - Csc + gmax ⁢ GtnC 2.0 GtnC 2.0 + alpha_Csc 2.0 ⁢ Csc - pE + pDC + pP ⁢ T_Csc ⁢ Csc$

### Component: G

$ddtimeG= pG ⁢ T_Asc ⁢ Asc + k_gmax ⁢ 1.0 - AC 2.0 AC 2.0 + alpha_HA 2.0 ⁢ G - gamma_Fdmax ⁢ 1.0 - Fd 2.0 Fd 2.0 + alpha_Fd 2.0 ⁢ G + gamma_Gc ⁢ G$

### Component: DA

$ddtimeDA= pDA ⁢ T_Asc ⁢ Asc + k_dmax ⁢ AC 2.0 AC 2.0 + alpha_HA 2.0 ⁢ DA + gamma_Fdmax ⁢ 1.0 - Fd 2.0 Fd 2.0 + alpha_Fd 2.0 ⁢ DA - gamma_DA ⁢ DA$

### Component: DC

$ddtimeDC= pDC ⁢ T_Asc ⁢ Csc - gamma_DC ⁢ DC$

### Component: E

$ddtimeE= pE ⁢ T_Csc ⁢ Csc - gamma_E ⁢ E + k_Emax ⁢ GtnC 2.0 GtnC 2.0 + alpha_E 2.0 ⁢ E$

### Component: P

$ddtimeP= pP ⁢ T_Csc ⁢ Csc - gamma_P ⁢ P$

### Component: feedback_mechanisms

$pG=ⅇ- f ⁢ G 2.0 N_ 2.0 pDA=ⅇ- f ⁢ DA 2.0 N_ 2.0 pDC=ⅇ- f ⁢ DC 2.0 N_ 2.0 pP=ⅇ- f ⁢ P 2.0 N_ 2.0 pE=ⅇ- f ⁢ E 2.0 N_ 2.0$

### Component: GtnA

$ddtimeGtnA=- G ⁢ KNG1 ⁢ NE NE + alpha_NG1 ⁢ 1.0 + SA kSG ⁢ 1.0 + AC 2.0 AC 2.0 + kAG 2.0 + KNG2 ⁢ NC NC + alpha_NG2 ⁢ 1.0 + SA kSG ⁢ 1.0 + AC 2.0 AC 2.0 + kAG 2.0 + KFG ⁢ Fd Fd + alpha_Fd ⁢ 1.0 + SA kSG ⁢ 1.0 + AC 2.0 AC 2.0 + kAG 2.0 ⁢ kG + beta_G ⁢ GtnA$

### Component: GtnC

$ddtimeGtnC= beta_G ⁢ GtnA - kappa_G ⁢ GtnC$

### Component: SA

$ddtimeSA=- DA ⁢ KAS ⁢ AA AA + alpha_AS ⁢ 1.0 + SA kSS ⁢ 1.0 + NC kNS + KGS ⁢ NE NE + alpha_NS ⁢ 1.0 + SA kSS ⁢ 1.0 + NC kNS ⁢ kappa_S ⁢ SA$

### Component: SC

$ddtimeSC=- DC ⁢ KNS ⁢ NE NE + alpha_NS ⁢ 1.0 + SC kSS ⁢ 1.0 + NC kNS + KGS ⁢ GtnC GtnC + alpha_GS ⁢ 1.0 + SC kSS ⁢ 1.0 + NC kNS ⁢ kappa_S ⁢ SC$

### Component: HC

$ddtimeHC=- E ⁢ KNH ⁢ NE NE + alpha_NH ⁢ 1.0 + SC kSH + KGH ⁢ GtnC GtnC + alpha_GH ⁢ 1.0 + SC kSH ⁢ kappa_H ⁢ HC$

### Component: AC

$ddtimeAC=- P ⁢ KNA ⁢ NC NC + alpha_NA ⁢ 1.0 + SC kSA + HC HC + alpha_HA + KGA ⁢ GtnC GtnC + alpha_GA ⁢ 1.0 + SC kSA + KHA ⁢ HC HC + alpha_HA ⁢ 1.0 + SC kSA ⁢ hb ⁢ AC ⁢ BC + k_Fdmax ⁢ Fd Fd + alpha_Fd ⁢ AC + beta_A ⁢ AC$

### Component: AA

$ddtimeAA= beta_A ⁢ AC - kappa_A ⁢ AA$

### Component: BC

$ddtimeBC= k_BCmax ⁢ NC NC + alpha_NB - hb ⁢ AC ⁢ BC + beta_B ⁢ BC$

### Component: BA

$ddtimeBA= k_BAmax ⁢ NC NC + alpha_NB - hb ⁢ AA ⁢ BA + kappa_B ⁢ BA$

### Component: NC

$ddtimeNC= Nmax1 ⁢ Fd Fd + kFd ⁢ 1.0 + AC 2.0 AC 2.0 + kAN1 2.0 - kappa_NC ⁢ NC + Bas1$

### Component: NE

$ddtimeNE= Nmax2 ⁢ Fd Fd + kFd 2.0 ⁢ 1.0 + AC 2.0 AC 2.0 + kAN2 2.0 - kappa_NE ⁢ NE + Bas2$

### Component: model_parameters

Source
Derived from workspace Joseph, Zavros, Merchant, Kirschner, 2003 at changeset 29d74e7429bf.
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