Model Mathematics

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Component: environment

Component: PI3K

\frac{d}{d time} (R) = (- kf1) R HRG + kb1 R_HRG \frac{d}{d time} (HRG) = (- kf1) R HRG + kb1 R_HRG \frac{d}{d time} (R_HRG) = kf1 R HRG - (kb1 R_HRG) - (two (kf2 R_HRG R_HRG - (kb2 R_HRG2))) \frac{d}{d time} (R_HRG2) = (kf2 R_HRG R_HRG - (kb2 R_HRG2) - (kf3 R_HRG2 - (kb3 RP))) + \frac{V4 RP}{k4 + RP} \frac{d}{d time} (RP) = ((kf3 R_HRG2 - (kb3 RP) - (\frac{V4 RP}{k4 + RP}) - (kf5 RP Shc - (kb5 R_Shc))) + (kf8 R_ShP - (kb8 ShGS RP)) - (kf23 RP PI3K - (kb23 R_PI3K))) + (kf25 R_PI3Kstar - (kb25 RP PI3Kstar)) - (kf34 RP - (kb34 Internalisation)) \frac{d}{d time} (Internalisation) = kf34 RP - (kb34 Internalisation) \frac{d}{d time} (R_Shc) = kf5 RP Shc - (kb5 R_Shc) - (kf6 R_Shc - (kb6 R_ShP)) \frac{d}{d time} (Shc) = (- (kf5 RP Shc - (kb5 R_Shc))) + \frac{V10 ShP}{k10 + ShP} \frac{d}{d time} (R_ShP) = kf6 R_Shc - (kb6 R_ShP) - (kf7 R_ShP - (kb7 R_ShGS)) \frac{d}{d time} (GS) = (- (kf7 R_ShP - (kb7 R_ShGS))) + (kf9 ShGS - (kb9 GS ShP)) \frac{d}{d time} (ShP) = kf9 ShGS - (kb9 GS ShP) - (\frac{V10 ShP}{k10 + ShP}) \frac{d}{d time} (R_ShGS) = kf7 R_ShP - (kb7 R_ShGS) - (kf8 R_ShP - (kb8 ShGS RP)) \frac{d}{d time} (ShGS) = kf8 R_ShP - (kb8 ShGS RP) - (kf9 ShGS - (kb9 GS ShP)) \frac{d}{d time} (R_PI3K) = kf23 RP PI3K - (kb23 R_PI3K) - (kf24 R_PI3K - (kb24 R_PI3Kstar)) \frac{d}{d time} (PI3K) = (- (kf23 RP PI3K - (kb23 R_PI3K))) + \frac{V26 PI3Kstar}{k26 + PI3Kstar} \frac{d}{d time} (R_PI3Kstar) = kf24 R_PI3K - (kb24 R_PI3Kstar) - (kf25 R_PI3Kstar - (kb25 RP PI3Kstar)) \frac{d}{d time} (PI3Kstar) = kf25 R_PI3Kstar - (kb25 RP PI3Kstar) - (\frac{V26 PI3Kstar}{k26 + PI3Kstar})

Component: RasGDPtoRasGTP

\frac{d}{d time} (RasGDP) = (- (\frac{kf11 ShGS RasGDP}{k11 + RasGDP})) + \frac{V12 RasGTP}{k12 + RasGTP} \frac{d}{d time} (RasGTP) = \frac{kf11 ShGS RasGDP}{k11 + RasGDP} - (\frac{V12 RasGTP}{k12 + RasGTP})

Component: RAF

\frac{d}{d time} (RAF) = \frac{kf14 (Akt_PIPP + E) RAF_star}{k14 + RAF_star} - (\frac{kf13 RasGTP RAF}{k13 + RAF}) \frac{d}{d time} (RAF_star) = (- (\frac{kf14 (Akt_PIPP + E) RAF_star}{k14 + RAF_star})) + \frac{kf13 RasGTP RAF}{k13 + RAF}

Component: Akt

\frac{d}{d time} (P) = \frac{V28 PIP3}{k28 + PIP3} - (\frac{kf27 PI3Kstar P}{k27 + P}) \frac{d}{d time} (PIP3) = (- (\frac{V28 PIP3}{k28 + PIP3})) + \frac{kf27 PI3Kstar P}{k27 + P} - (kf29 PIP3 Akt - (kb29 Akt_PIP3)) \frac{d}{d time} (Akt) = - (kf29 PIP3 Akt - (kb29 Akt_PIP3)) \frac{d}{d time} (Akt_PIP3) = (kf29 PIP3 Akt - (kb29 Akt_PIP3) - (\frac{V30 Akt_PIP3}{k30 (one + \frac{Akt_PIP}{k32}) + Akt_PIP3})) + \frac{kf31 PP2A Akt_PIP}{k31 (one + \frac{MEKP}{k16} + \frac{MEKPP}{k18} + \frac{Akt_PIPP}{k33}) + Akt_PIP} \frac{d}{d time} (Akt_PIP) = (\frac{V30 Akt_PIP3}{k30 (one + \frac{Akt_PIP}{k32}) + Akt_PIP3} - (\frac{kf31 PP2A Akt_PIP}{k31 (one + \frac{MEKP}{k16} + \frac{MEKPP}{k18} + \frac{Akt_PIPP}{k33}) + Akt_PIP}) - (\frac{V32 Akt_PIP}{k32 (one + \frac{Akt_PIP3}{k30}) + Akt_PIP})) + \frac{kf33 PP2A Akt_PIPP}{k33 (one + \frac{MEKP}{k16} + \frac{MEKPP}{k18} + \frac{Akt_PIP}{k31}) + Akt_PIPP} \frac{d}{d time} (Akt_PIPP) = \frac{V32 Akt_PIP}{k32 (one + \frac{Akt_PIP3}{k30}) + Akt_PIP} - (\frac{kf33 PP2A Akt_PIPP}{k33 (one + \frac{MEKP}{k16} + \frac{MEKPP}{k18} + \frac{Akt_PIP}{k31}) + Akt_PIPP})

Component: MEK

\frac{d}{d time} (MEK) = (- (\frac{kf15 RAF_star MEK}{k15 (one + \frac{MEKP}{k17}) + MEK})) + \frac{kf16 PP2A MEKP}{k16 (one + \frac{MEKPP}{k18} + \frac{Akt_PIP}{k31} + \frac{Akt_PIPP}{k33}) + MEKP} \frac{d}{d time} (MEKP) = (\frac{kf15 RAF_star MEK}{k15 (one + \frac{MEKP}{k17}) + MEK} - (\frac{kf16 PP2A MEKP}{k16 (one + \frac{MEKPP}{k18} + \frac{Akt_PIP}{k31} + \frac{Akt_PIPP}{k33}) + MEKP}) - (\frac{kf17 RAF_star MEKP}{k17 (one + \frac{MEK}{k15}) + MEKP})) + \frac{kf18 PP2A MEKPP}{k18 (one + \frac{MEKP}{k16} + \frac{Akt_PIP}{k31} + \frac{Akt_PIPP}{k33}) + MEKPP} \frac{d}{d time} (MEKPP) = \frac{kf17 RAF_star MEKP}{k17 (one + \frac{MEK}{k15}) + MEKP} - (\frac{kf18 PP2A MEKPP}{k18 (one + \frac{MEKP}{k16} + \frac{Akt_PIP}{k31} + \frac{Akt_PIPP}{k33}) + MEKPP})

Component: ERK

\frac{d}{d time} (ERK) = (- (\frac{kf19 MEKPP ERK}{k19 (one + \frac{ERKP}{k21}) + ERK})) + \frac{kf20 MKP3 ERKP}{k20 (one + \frac{ERKPP}{k22}) + ERKP} \frac{d}{d time} (ERKPP) = \frac{kf21 MEKPP ERKP}{k21 (one + \frac{ERK}{k19}) + ERKP} - (\frac{kf22 MKP3 ERKPP}{k22 (one + \frac{ERKP}{k20}) + ERKPP}) \frac{d}{d time} (ERKP) = (\frac{kf19 MEKPP ERK}{k19 (one + \frac{ERKP}{k21}) + ERK} - (\frac{kf20 MKP3 ERKP}{k20 (one + \frac{ERKPP}{k22}) + ERKP}) - (\frac{kf21 MEKPP ERKP}{k21 (one + \frac{ERK}{k19}) + ERKP})) + \frac{kf22 MKP3 ERKPP}{k22 (one + \frac{ERKP}{k20}) + ERKPP}