Model Mathematics

\frac{d}{d 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)

\frac{d}{d 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)

\frac{d}{d 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)

\frac{d}{d 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)

\frac{d}{d 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)

\frac{d}{d time} (pEGFR_Akt) = k1_pEGFR_Akt pEGFR Akt - (k2_pEGFR_Akt pEGFR_Akt + k1_Akt_phosphorylation pEGFR_Akt)

\frac{d}{d time} (Akt) = k2_pEGFR_Akt pEGFR_Akt + k1_pAkt_dephosphorylation pAkt - (k1_pEGFR_Akt pEGFR Akt)

\frac{d}{d 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)

\frac{d}{d time} (pAkt_S6) = k1_pAkt_S6 pAkt S6 - (k2_pAkt_S6 pAkt_S6 + k1_S6_phosphorylation pAkt_S6)

\frac{d}{d time} (S6) = k2_pAkt_S6 pAkt_S6 + k1_pS6_dephosphorylation pS6 - (k1_pAkt_S6 pAkt S6)

\frac{d}{d time} (pS6) = k1_S6_phosphorylation pAkt_S6 - (k1_pS6_dephosphorylation pS6)

pEGFR_total = (pEGFR + pEGFR_Akt) pEGFR_scalefactor

pAkt_total = (pAkt + pAkt_S6) pAkt_scalefactor

pS6_total = pS6 pS6_scalefactor