# Model Mathematics

### Component: TrkA

$dd time TrkA = k2_NGF_TrkA ⁢ NGF_TrkA + TrkA_turnover ⁢ pro_TrkA - TrkA - k1_NGF_TrkA ⁢ NGF ⁢ TrkA$

### Component: NGF_TrkA

$dd time NGF_TrkA = k1_NGF_TrkA ⁢ NGF ⁢ TrkA - k2_NGF_TrkA ⁢ NGF_TrkA + k1_TrkA_phosphorylation ⁢ NGF_TrkA$

### Component: pTrkA

$dd time pTrkA = k1_TrkA_phosphorylation ⁢ NGF_TrkA + k1_Akt_phosphorylation ⁢ pTrkA_Akt + k2_pTrkA_Akt ⁢ pTrkA_Akt - k1_pTrkA_degradation ⁢ pTrkA + k1_pTrkA_Akt ⁢ pTrkA ⁢ Akt$

### Component: pTrkA_Akt

$dd time pTrkA_Akt = k1_pTrkA_Akt ⁢ pTrkA ⁢ Akt - k2_pTrkA_Akt ⁢ pTrkA_Akt + k1_Akt_phosphorylation ⁢ pTrkA_Akt$

### Component: Akt

$dd time Akt = k2_pTrkA_Akt ⁢ pTrkA_Akt + k1_pAkt_dephosphorylation ⁢ pAkt - k1_pTrkA_Akt ⁢ pTrkA ⁢ Akt$

### Component: pAkt

$dd time pAkt = k1_Akt_phosphorylation ⁢ pTrkA_Akt + k2_pAkt_S6 ⁢ pAkt_S6 + k1_S6_phosphorylation ⁢ pAkt_S6 - k1_pAkt_dephosphorylation ⁢ pAkt + k1_pAkt_S6 ⁢ pAkt ⁢ S6$

### Component: pAkt_S6

$dd time pAkt_S6 = k1_pAkt_S6 ⁢ pAkt ⁢ S6 - k2_pAkt_S6 ⁢ pAkt_S6 + k1_S6_phosphorylation ⁢ pAkt_S6$

### Component: S6

$dd time S6 = k2_pAkt_S6 ⁢ pAkt_S6 + k1_pS6_dephosphorylation ⁢ pS6 - k1_pAkt_S6 ⁢ pAkt ⁢ S6$

### Component: pS6

$dd time pS6 = k1_S6_phosphorylation ⁢ pAkt_S6 - k1_pS6_dephosphorylation ⁢ pS6$

### Component: pTrkA_total

$pTrkA_total = pTrkA + pTrkA_Akt ⁢ pTrkA_scalefactor$

### Component: pAkt_total

$pAkt_total = pAkt + pAkt_S6 ⁢ pAkt_scalefactor$

### Component: pS6_total

$pS6_total = pS6 ⁢ pS6_scalefactor$

### Component: model_parameters

Source
Derived from workspace Fujita, Toyoshima, Uda, Ozaki, Kubota and Kuroda 2010 at changeset e404cee704e9.
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