# Model Mathematics

### Component: EGFR

$dd time EGFR = EGF_binding_kb ⁢ EGF_EGFR + inhibitor_binding_kb ⁢ EGFR_i + EGFR_turnover ⁢ pro_EGFR - EGFR - EGF_binding_kf ⁢ EGF ⁢ EGFR + inhibitor_binding_kf ⁢ inhibitor ⁢ EGFR$

### Component: EGF_EGFR

$dd time EGF_EGFR = EGF_binding_kf ⁢ EGF ⁢ EGFR + inhibitor_binding_kb ⁢ EGF_EGFR_i - EGF_binding_kb ⁢ EGF_EGFR + inhibitor_binding_kf ⁢ inhibitor ⁢ EGF_EGFR + k1_EGFR_phosphorylation ⁢ EGF_EGFR$

### Component: EGFR_i

$dd time EGFR_i = EGF_binding_kb ⁢ EGF_EGFR_i + inhibitor_binding_kf ⁢ inhibitor ⁢ EGFR - EGF_binding_kf ⁢ EGF ⁢ EGFR_i + inhibitor_binding_kb ⁢ EGFR_i + EGFR_turnover ⁢ EGFR_i$

### Component: EGF_EGFR_i

$dd time EGF_EGFR_i = EGF_binding_kf ⁢ EGF ⁢ EGFR_i + inhibitor_binding_kf ⁢ inhibitor ⁢ EGF_EGFR - EGF_binding_kb ⁢ EGF_EGFR_i + inhibitor_binding_kb ⁢ EGF_EGFR_i$

### Component: pEGFR

$dd time pEGFR = k1_EGFR_phosphorylation ⁢ EGF_EGFR + k1_Akt_phosphorylation ⁢ pEGFR_Akt + k2_pEGFR_Akt ⁢ pEGFR_Akt - k1_pEGFR_degradation ⁢ pEGFR + k1_pEGFR_Akt ⁢ pEGFR ⁢ Akt$

### Component: pEGFR_Akt

$dd time pEGFR_Akt = k1_pEGFR_Akt ⁢ pEGFR ⁢ Akt - k2_pEGFR_Akt ⁢ pEGFR_Akt + k1_Akt_phosphorylation ⁢ pEGFR_Akt$

### Component: Akt

$dd time Akt = k2_pEGFR_Akt ⁢ pEGFR_Akt + k1_pAkt_dephosphorylation ⁢ pAkt - k1_pEGFR_Akt ⁢ pEGFR ⁢ Akt$

### Component: pAkt

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

### 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: pEGFR_total

$pEGFR_total = pEGFR + pEGFR_Akt ⁢ pEGFR_scalefactor$

### 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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