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A Systems Biology Approach to Cancer
Therapy and Early Detection
A Systems Biology Approach to Cancer
Therapy and Early Detection
Avijit Ghosh
Dhruv Pant, Rui Zou, Dave MillerYihua Wang, Hanbing Lin
Travis Hoppe, Aparna Kumar
Department of PhysicsDrexel University
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Special topics on Electrical and Systems Engineering 2007Systems Biology
Outline
Signal Transduction Overview
Mutations, Oncogenes, Proto-Oncogenes Mathematical Models
Enzymes Mutations
Predicting Putative Oncogenes using Systems Biology D. Pant A. Ghosh (2005) Biophys. Chem 113(3) 275-288
The Results Experimentally Validated Results New Predictions
Drugs! Spatio-Temporal Modeling CellSim Overview
Special topics on Electrical and Systems Engineering 2007Systems Biology
Signal Transduction
Controls behavior of cells Ion Channels Metabolic Pathways Cytoskeletal Proteins Gene Regulatory Proteins
Cell cycle Cytoskeletal rearrangement
D. Slish Mechanism of Tyrosine Kinase Receptors
U.Platt.
Special topics on Electrical and Systems Engineering 2007Systems Biology
The Normal Functioning MAPK Signal Cascade
Special topics on Electrical and Systems Engineering 2007Systems Biology
Signaling and Cell Growth
Input : EGF – Epidermal Growth
Factor Output:
Signal for gene transcription :: ERK
Activation: Phosphorylation GTP/GDP binding
Special topics on Electrical and Systems Engineering 2007Systems Biology
EGF stimulation and ERK response
Special topics on Electrical and Systems Engineering 2007Systems Biology
Oncogenes and Tumor Suppressor Genes
Oncogene - A gene (protein) that when mutated or inappropriately expressed contributes to cancer formation Mutations in signal transduction genes Mutations in Tumor Suppressor genes INHERITED
Activation Point Mutation Chromosomal rearrangement Gene amplification Viral Insertion
Special topics on Electrical and Systems Engineering 2007Systems Biology
The Ras Protein
Scheffzick et.al. (1997) Science 277 pp 333-338
• Ras Protein• Active – GTP Bound• Inactive – GDP Bound
•GAP (GTPase Activating Protein)
• Hydrolyzes GTP in Ras
•Gly12 – Stops Ras Gap Interactions•Gln61 – Stops hydrolysis
Special topics on Electrical and Systems Engineering 2007Systems Biology
Interactions
E+Sk1, fk1,b
← →⏐ ⏐ E.S
E.Sk2, f⏐ →⏐ ⏐ E + S*
1, 1, 2,
[ ][ ][ ] [ . ] [ . ]f b f
d Ek E S k E S k E S
dt=− + +
1, 1, 2,
[ . ][ ][ ] [ . ] [ . ]f b f
d E Sk E S k E S k E S
dt= − +
1, 1,
[ ][ ][ ] [ . ]f b
d Sk E S k E S
dt=− +
2,
[ *][ . ]f
d Sk E S
dt=
Special topics on Electrical and Systems Engineering 2007Systems Biology
EGF / MAPK / PLC / PLC-γ/ PKC / Calcium / PLA2 Pathways
#
# locations
# the volume is a optional parameter
# our volume units are L
location extracellular 1E-10 Ca-extlocation cytosol 1E-12location endosome 1.6E-13 Ca-sequester
# Channels
channel capacitive_Ca_entry* Ca-ext -> Ca :: 0.005channel Ca-leak-from-extracell Ca-ext -> Ca :: 0.004channel Ca-leak-to-cytoplasm Ca-sequester->Ca :: 8channel IP3R* Ca-sequester -> Ca :: 19.2
# conservationReactions
#conserve CaEPump :: Ca_CaEPump#conserve CaTransp-2Ca :: CaTransp#conserve mGluR :: Rec-Glu Rec-Glu-Gq Rec-Gq Blocked-rec-Gq#conserve PLC :: match /PLC-/#conserve PLA2-cytosolic :: match /PLA2/
# sum up#sum PKC-active :: PKC-DAG-AA* PKC-Ca-memb* PKC-Ca-AA* PKC-DAG-memb*# sumReactions
# (native units are #/compartment)
Ca + CaEPump <> Ca_CaEPump :: 0.003 288Ca_CaEPump -> CaEPump +Ca-ext :: 72 Ca.PLC_g + L.EGFR <> Ca.PLC_g_L.EGFR :: 5e-06 0.8Ca.PLC_g_L.EGFR -> L.EGFR +Ca.PLC_g* :: 0.2 SHC + L.EGFR <> SHC_L.EGFR :: 2e-06 0.8SHC_L.EGFR -> L.EGFR +SHC* :: 0.2 MAPK + MAPKK* <> MAPK_MAPKK* :: 2.7e-05 0.6MAPK_MAPKK* -> MAPKK* +MAPK-tyr :: 0.15 MAPK-tyr + MAPKK* <> MAPK-tyr_MAPKK* :: 2.7e-05 0.6MAPK-tyr_MAPKK* -> MAPKK* +MAPK* :: 0.15 MAPKK + Raf-GTP-Ras* <> MAPKK_Raf-GTP-Ras* :: 5.5e-06 0.42MAPKK_Raf-GTP-Ras* -> Raf-GTP-Ras* +MAPKK-ser :: 0.105 MAPKK-ser + Raf-GTP-Ras* <> MAPKK-ser_Raf-GTP-Ras* :: 5.5e-06 0.42MAPKK-ser_Raf-GTP-Ras* -> Raf-GTP-Ras* +MAPKK* :: 0.105 #craf-1 + PKC-active <> craf-1_PKC-active :: 5e-07 16#craf-1_PKC-active -> PKC-active +craf-1* :: 4 #GAP + PKC-active <> GAP_PKC-active :: 1e-05 16#GAP_PKC-active -> PKC-active +GAP* :: 4 #inact-GEF + PKC-active <> inact-GEF_PKC-active :: 1e-05 16#inact-GEF_PKC-active -> PKC-active +GEF* :: 4 craf-1 + PKC-DAG-AA* <> craf-1_PKC-DAG-AA* :: 5e-07 16craf-1_PKC-DAG-AA* -> PKC-DAG-AA* +craf-1* :: 4 GAP + PKC-DAG-AA* <> GAP_PKC-DAG-AA* :: 1e-05 16GAP_PKC-DAG-AA* -> PKC-DAG-AA* +GAP* :: 4 inact-GEF + PKC-DAG-AA* <> inact-GEF_PKC-DAG-AA* :: 1e-05 16inact-GEF_PKC-DAG-AA* -> PKC-DAG-AA* +GEF* :: 4 craf-1 + PKC-Ca-memb* <> craf-1_PKC-Ca-memb* :: 5e-07 16craf-1_PKC-Ca-memb* -> PKC-Ca-memb* +craf-1* :: 4 GAP + PKC-Ca-memb* <> GAP_PKC-Ca-memb* :: 1e-05 16GAP_PKC-Ca-memb* -> PKC-Ca-memb* +GAP* :: 4 inact-GEF + PKC-Ca-memb* <> inact-GEF_PKC-Ca-memb* :: 1e-05 16inact-GEF_PKC-Ca-memb* -> PKC-Ca-memb* +GEF* :: 4 craf-1 + PKC-Ca-AA* <> craf-1_PKC-Ca-AA* :: 5e-07 16craf-1_PKC-Ca-AA* -> PKC-Ca-AA* +craf-1* :: 4 GAP + PKC-Ca-AA* <> GAP_PKC-Ca-AA* :: 1e-05 16GAP_PKC-Ca-AA* -> PKC-Ca-AA* +GAP* :: 4 inact-GEF + PKC-Ca-AA* <> inact-GEF_PKC-Ca-AA* :: 1e-05 16inact-GEF_PKC-Ca-AA* -> PKC-Ca-AA* +GEF* :: 4 craf-1 + PKC-DAG-memb* <> craf-1_PKC-DAG-memb* :: 5e-07 16
craf-1_PKC-DAG-memb* -> PKC-DAG-memb* +craf-1* :: 4 GAP + PKC-DAG-memb* <> GAP_PKC-DAG-memb* :: 1e-05 16GAP_PKC-DAG-memb* -> PKC-DAG-memb* +GAP* :: 4 inact-GEF + PKC-DAG-memb* <> inact-GEF_PKC-DAG-memb* :: 1e-05 16inact-GEF_PKC-DAG-memb* -> PKC-DAG-memb* +GEF* :: 4 craf-1 + PKC-basal* <> craf-1_PKC-basal* :: 5e-07 16craf-1_PKC-basal* -> PKC-basal* +craf-1* :: 4 GAP + PKC-basal* <> GAP_PKC-basal* :: 1e-05 16GAP_PKC-basal* -> PKC-basal* +GAP* :: 4 inact-GEF + PKC-basal* <> inact-GEF_PKC-basal* :: 1e-05 16inact-GEF_PKC-basal* -> PKC-basal* +GEF* :: 4 craf-1 + PKC-AA* <> craf-1_PKC-AA* :: 5e-07 16craf-1_PKC-AA* -> PKC-AA* +craf-1* :: 4 GAP + PKC-AA* <> GAP_PKC-AA* :: 1e-05 16GAP_PKC-AA* -> PKC-AA* +GAP* :: 4 inact-GEF + PKC-AA* <> inact-GEF_PKC-AA* :: 1e-05 16inact-GEF_PKC-AA* -> PKC-AA* +GEF* :: 4 # end expandAPC + PLA2-Ca* <> APC_PLA2-Ca* :: 2.25e-06 21.6APC_PLA2-Ca* -> PLA2-Ca* +AA :: 5.4 APC + PIP2-PLA2* <> APC_PIP2-PLA2* :: 4.6e-06 44.16APC_PIP2-PLA2* -> PIP2-PLA2* +AA :: 11.04 APC + PIP2-Ca-PLA2* <> APC_PIP2-Ca-PLA2* :: 1.5e-05 144APC_PIP2-Ca-PLA2* -> PIP2-Ca-PLA2* +AA :: 36 APC + DAG-Ca-PLA2* <> APC_DAG-Ca-PLA2* :: 2.5e-05 240APC_DAG-Ca-PLA2* -> DAG-Ca-PLA2* +AA :: 60 APC + PLA2*-Ca <> APC_PLA2*-Ca :: 5e-05 480APC_PLA2*-Ca -> PLA2*-Ca +AA :: 120 PLA2-cytosolic + MAPK* <> PLA2-cytosolic_MAPK* :: 6.5e-06 80PLA2-cytosolic_MAPK* -> MAPK* +PLA2* :: 20 craf-1* + MAPK* <> craf-1*_MAPK* :: 3.25e-06 40craf-1*_MAPK* -> MAPK* +craf-1** :: 10 Sos + MAPK* <> Sos_MAPK* :: 3.25e-05 40Sos_MAPK* -> MAPK* +Sos* :: 10 MAPK-tyr + MKP-1 <> MAPK-tyr_MKP-1 :: 0.000125 4MAPK-tyr_MKP-1 -> MKP-1 +MAPK :: 1 MAPK* + MKP-1 <> MAPK*_MKP-1 :: 0.000125 4MAPK*_MKP-1 -> MKP-1 +MAPK-tyr :: 1 craf-1* + PPhosphatase2A <> craf-1*_PPhosphatase2A :: 3.3e-06 25craf-1*_PPhosphatase2A -> PPhosphatase2A +craf-1 :: 6 MAPKK* + PPhosphatase2A <> MAPKK*_PPhosphatase2A :: 3.3e-06 25MAPKK*_PPhosphatase2A -> PPhosphatase2A +MAPKK-ser :: 6 MAPKK-ser + PPhosphatase2A <> MAPKK-ser_PPhosphatase2A :: 3.3e-06 25MAPKK-ser_PPhosphatase2A -> PPhosphatase2A +MAPKK :: 6 craf-1** + PPhosphatase2A <> craf-1**_PPhosphatase2A :: 3.3e-06 25craf-1**_PPhosphatase2A -> PPhosphatase2A +craf-1* :: 6 inact-GEF + PKA-active <> inact-GEF_PKA-active :: 1e-05 36inact-GEF_PKA-active -> PKA-active +inact-GEF* :: 9 GDP-Ras + Shc*.Sos.Grb2 <> GDP-Ras_Shc*.Sos.Grb2 :: 3.3e-07 0.08GDP-Ras_Shc*.Sos.Grb2 -> Shc*.Sos.Grb2 +GTP-Ras :: 0.02 PIP2 + PLC-Ca <> PIP2_PLC-Ca :: 4.2e-06 40 PIP2_PLC-Ca -> PLC-Ca +DAG + IP3 :: 10 PIP2 + PLC-Ca-Gq <> PIP2_PLC-Ca-Gq :: 8e-05 192PIP2_PLC-Ca-Gq -> PLC-Ca-Gq +DAG + IP3 :: 48 PIP2 + Ca.PLC_g <> PIP2_Ca.PLC_g :: 1.2e-06 56PIP2_Ca.PLC_g -> Ca.PLC_g +DAG + IP3 :: 14 PIP2 + Ca.PLC_g* <> PIP2_Ca.PLC_g* :: 2.4e-05 228PIP2_Ca.PLC_g* -> Ca.PLC_g* +DAG + IP3 :: 57 GDP-Ras + GEF-Gprot-bg <> GDP-Ras_GEF-Gprot-bg :: 3.3e-07 0.08GDP-Ras_GEF-Gprot-bg -> GEF-Gprot-bg +GTP-Ras :: 0.02 GDP-Ras + GEF* <> GDP-Ras_GEF* :: 3.3e-07 0.08GDP-Ras_GEF* -> GEF* +GTP-Ras :: 0.02 GTP-Ras + GAP <> GTP-Ras_GAP :: 0.001666 1000GTP-Ras_GAP -> GAP +GDP-Ras :: 10 GDP-Ras + CaM-GEF <> GDP-Ras_CaM-GEF :: 3.3e-07 0.08GDP-Ras_CaM-GEF -> CaM-GEF +GTP-Ras :: 0.02 CaTransp-2Ca -> CaTransp + Ca-sequester + Ca-sequester :: 25
Ca +CaTransp +Ca <> CaTransp-2Ca :: 1e-08 144 IP3R +IP3 +IP3 +IP3 <> IP3R* :: 1e-20 1 Ca-sequester +Ca-sequester +capacitive_Ca_entry* <> inact_cap_entry :: 1.2e-11 1 EGFR +EGF <> L.EGFR :: 7e-06 0.25 SHC* -> SHC :: 0.0016667 L.EGFR <> Internal_L.EGFR :: 0.002 0.00033 mGluR +Glu <> Rec-Glu :: 2.8e-05 10 G-GDP -> G*GTP + BetaGamma :: 0.0001 G*GDP +BetaGamma -> G-GDP :: 1e-05 G*GTP -> G*GDP :: 0.0133 G-GDP +Rec-Glu <> Rec-Glu-Gq :: 1e-08 0.0001 Glu +Rec-Gq <> Rec-Glu-Gq :: 2.8e-05 0.1 Rec-Glu-Gq -> G*GTP + BetaGamma + Rec-Glu :: 0.01 G-GDP +mGluR <> Rec-Gq :: 1e-06 1 Rec-Gq +mGluRAntag <> Blocked-rec-Gq :: 0.0001 0.01 craf-1* +GTP-Ras <> Raf-GTP-Ras* :: 4e-05 0.5 PKC-cytosolic +Ca <> PKC-Ca :: 1e-06 0.5 DAG +PKC-Ca <> PKC-Ca-DAG :: 1.3333e-08 8.6348 PKC-Ca <> PKC-Ca-memb* :: 1.2705 3.5026 PKC-Ca-DAG <> PKC-DAG-memb* :: 1 0.1 PKC-Ca +AA <> PKC-Ca-AA* :: 2e-09 0.1 PKC-DAG-AA <> PKC-DAG-AA* :: 2 0.2 PKC-cytosolic <> PKC-basal* :: 1 50 AA +PKC-cytosolic <> PKC-AA* :: 2e-10 0.1 PKC-cytosolic +DAG <> PKC-DAG :: 1e-09 0.1 PKC-DAG +AA <> PKC-DAG-AA :: 3e-08 2 PLA2-cytosolic +Ca <> PLA2-Ca* :: 1.6667e-06 0.1 temp-PIP2 +PLA2-cytosolic <> PIP2-PLA2* :: 2e-09 0.5 temp-PIP2 +PLA2-Ca* <> PIP2-Ca-PLA2* :: 2e-08 0.1 DAG +PLA2-Ca* <> DAG-Ca-PLA2* :: 5e-09 4 AA -> APC :: 0.4 PLA2* +Ca <> PLA2*-Ca :: 1e-05 0.1 PLA2* -> PLA2-cytosolic :: 0.17 Ca +PLC <> PLC-Ca :: 5e-06 1 IP3 -> Inositol :: 2.5 DAG -> PC :: 0.15 G*GTP +PLC-Ca <> PLC-Ca-Gq :: 4.2e-05 1 PLC-Ca-Gq -> G*GDP + PLC-Ca :: 0.0133 PLC +G*GTP <> PLC-Gq :: 4.2e-06 1 Ca +PLC-Gq <> PLC-Ca-Gq :: 5e-05 1 PLC_g +Ca <> Ca.PLC_g :: 0.0003 10 Ca +PLC_G* <> Ca.PLC_g* :: 2e-05 10 Ca.PLC_g* -> Ca.PLC_g :: 0.05 BetaGamma +inact-GEF <> GEF-Gprot-bg :: 1e-05 1 GEF* -> inact-GEF :: 1 GTP-Ras -> GDP-Ras :: 0.0001 GAP* -> GAP :: 0.1 inact-GEF +CaM-Ca4 <> CaM-GEF :: 0.0001 1 inact-GEF* -> inact-GEF :: 1 Sos.Grb2 +SHC* <> Shc*.Sos.Grb2 :: 8.333e-07 0.1 Sos* +Grb2 <> Sos*.Grb2 :: 4.1667e-08 0.0168 Sos* -> Sos :: 0.001 Grb2 +Sos <> Sos.Grb2 :: 4.1667e-08 0.0168
Special topics on Electrical and Systems Engineering 2007Systems Biology
Leads to..d[capacitive_ca_entry*]/dt = 1[inact_cap_entry] - 1.2e-11[ca-sequester][ca-sequester][capacitive_ca_entry*]d[ca]/dt = 288[ca_caepump] + 144[catransp-2ca] + 144[catransp-2ca] + 0.5[pkc-ca] + 0.1[pla2-ca*] + 0.1[pla2*-ca] + 1[plc-ca] + 1[plc-ca-gq] + 10[ca.plc_g] + 10[ca.plc_g*] - 0.003[ca][caepump] - 1e-08[ca][catransp][ca] - 1e-08[ca][catransp][ca] - 1e-06[pkc-cytosolic][ca] - 1.6667e-06[pla2-cytosolic][ca] - 1e-05[pla2*][ca] - 5e-06[ca][plc] - 5e-05[ca][plc-gq] - 0.0003[plc_g][ca] - 2e-05[ca][plc_g*] + 0.005 * [capacitive_ca_entry*] * ( [ca-ext] - [ca] ) + 0.004 * [ca-leak-from-extracell] * ( [ca-ext] - [ca] ) + 8 * [ca-leak-to-cytoplasm] * ( [ca-sequester] - [ca] ) + 19.2 * [ip3r*] * ( [ca-sequester] - [ca] ) d[ca-leak-from-extracell]/dt = d[ca-leak-to-cytoplasm]/dt = d[ip3r*]/dt = 1e-20[ip3r][ip3][ip3][ip3] - 1[ip3r*]d[caepump]/dt = 288[ca_caepump] + 72[ca_caepump] - 0.003[ca][caepump]d[ca_caepump]/dt = 0.003[ca][caepump] - 288[ca_caepump] - 72[ca_caepump]d[ca.plc_g]/dt = 0.8[ca.plc_g_l.egfr] + 56[pip2_ca.plc_g] + 14[pip2_ca.plc_g] + 0.0003[plc_g][ca] + 0.05[ca.plc_g*] - 5e-06[ca.plc_g][l.egfr] - 1.2e-06[pip2][ca.plc_g] - 10[ca.plc_g]d[l.egfr]/dt = 0.8[ca.plc_g_l.egfr] + 0.2[ca.plc_g_l.egfr] + 0.8[shc_l.egfr] + 0.2[shc_l.egfr] + 7e-06[egfr][egf] + 0.00033[internal_l.egfr] - 5e-06[ca.plc_g][l.egfr] - 2e-06[shc][l.egfr] - 0.25[l.egfr] - 0.002[l.egfr]d[ca.plc_g_l.egfr]/dt = 5e-06[ca.plc_g][l.egfr] - 0.8[ca.plc_g_l.egfr] - 0.2[ca.plc_g_l.egfr]d[ca.plc_g*]/dt = 0.2[ca.plc_g_l.egfr] + 228[pip2_ca.plc_g*] + 57[pip2_ca.plc_g*] + 2e-05[ca][plc_g*] - 2.4e-05[pip2][ca.plc_g*] - 10[ca.plc_g*] - 0.05[ca.plc_g*]d[shc]/dt = 0.8[shc_l.egfr] + 0.0016667[shc*] - 2e-06[shc][l.egfr]d[shc_l.egfr]/dt = 2e-06[shc][l.egfr] - 0.8[shc_l.egfr] - 0.2[shc_l.egfr]d[shc*]/dt = 0.2[shc_l.egfr] + 0.1[shc*.sos.grb2] - 0.0016667[shc*] - 8.333e-07[sos.grb2][shc*]d[mapk]/dt = 0.6[mapk_mapkk*] + 1[mapk-tyr_mkp-1] - 2.7e-05[mapk][mapkk*]d[mapkk*]/dt = 0.6[mapk_mapkk*] + 0.15[mapk_mapkk*] + 0.6[mapk-tyr_mapkk*] + 0.15[mapk-tyr_mapkk*] + 0.105[mapkk-ser_raf-gtp-ras*] + 25[mapkk*_pphosphatase2a] - 2.7e-05[mapk][mapkk*] - 2.7e-05[mapk-tyr][mapkk*] - 3.3e-06[mapkk*][pphosphatase2a]d[mapk_mapkk*]/dt = 2.7e-05[mapk][mapkk*] - 0.6[mapk_mapkk*] - 0.15[mapk_mapkk*]d[mapk-tyr]/dt = 0.15[mapk_mapkk*] + 0.6[mapk-tyr_mapkk*] + 4[mapk-tyr_mkp-1] + 1[mapk*_mkp-1] - 2.7e-05[mapk-tyr][mapkk*] - 0.000125[mapk-tyr][mkp-1]d[mapk-tyr_mapkk*]/dt = 2.7e-05[mapk-tyr][mapkk*] - 0.6[mapk-tyr_mapkk*] - 0.15[mapk-tyr_mapkk*]d[mapk*]/dt = 0.15[mapk-tyr_mapkk*] + 80[pla2-cytosolic_mapk*] + 20[pla2-cytosolic_mapk*] + 40[craf-1*_mapk*] + 10[craf-1*_mapk*] + 40[sos_mapk*] + 10[sos_mapk*] + 4[mapk*_mkp-1] - 6.5e-06[pla2-cytosolic][mapk*] - 3.25e-06[craf-1*][mapk*] - 3.25e-05[sos][mapk*] - 0.000125[mapk*][mkp-1]d[mapkk]/dt = 0.42[mapkk_raf-gtp-ras*] + 6[mapkk-ser_pphosphatase2a] - 5.5e-06[mapkk][raf-gtp-ras*]d[raf-gtp-ras*]/dt = 0.42[mapkk_raf-gtp-ras*] + 0.105[mapkk_raf-gtp-ras*] + 0.42[mapkk-ser_raf-gtp-ras*] + 0.105[mapkk-ser_raf-gtp-ras*] + 4e-05[craf-1*][gtp-ras] - 5.5e-06[mapkk][raf-gtp-ras*] - 5.5e-06[mapkk-ser][raf-gtp-ras*] - 0.5[raf-gtp-ras*]d[mapkk_raf-gtp-ras*]/dt = 5.5e-06[mapkk][raf-gtp-ras*] - 0.42[mapkk_raf-gtp-ras*] - 0.105[mapkk_raf-gtp-ras*]d[mapkk-ser]/dt = 0.105[mapkk_raf-gtp-ras*] + 0.42[mapkk-ser_raf-gtp-ras*] + 6[mapkk*_pphosphatase2a] + 25[mapkk-ser_pphosphatase2a] - 5.5e-06[mapkk-ser][raf-gtp-ras*] - 3.3e-06[mapkk-ser][pphosphatase2a]d[mapkk-ser_raf-gtp-ras*]/dt = 5.5e-06[mapkk-ser][raf-gtp-ras*] - 0.42[mapkk-ser_raf-gtp-ras*] - 0.105[mapkk-ser_raf-gtp-ras*]d[craf-1]/dt = 16[craf-1_pkc-dag-aa*] + 16[craf-1_pkc-ca-memb*] + 16[craf-1_pkc-ca-aa*] + 16[craf-1_pkc-dag-memb*] + 16[craf-1_pkc-basal*] + 16[craf-1_pkc-aa*] + 6[craf-1*_pphosphatase2a] - 5e-07[craf-1][pkc-dag-aa*] - 5e-07[craf-1][pkc-ca-memb*] - 5e-07[craf-1][pkc-ca-aa*] - 5e-07[craf-1][pkc-dag-memb*] - 5e-07[craf-1][pkc-basal*] - 5e-07[craf-1][pkc-aa*]d[pkc-dag-aa*]/dt = 16[craf-1_pkc-dag-aa*] + 4[craf-1_pkc-dag-aa*] + 16[gap_pkc-dag-aa*] + 4[gap_pkc-dag-aa*] + 16[inact-gef_pkc-dag-aa*] + 4[inact-gef_pkc-dag-aa*] + 2[pkc-dag-aa] - 5e-07[craf-1][pkc-dag-aa*] - 1e-05[gap][pkc-dag-aa*] - 1e-05[inact-gef][pkc-dag-aa*] - 0.2[pkc-dag-aa*]d[craf-1_pkc-dag-aa*]/dt = 5e-07[craf-1][pkc-dag-aa*] - 16[craf-1_pkc-dag-aa*] - 4[craf-1_pkc-dag-aa*]d[craf-1*]/dt = 4[craf-1_pkc-dag-aa*] + 4[craf-1_pkc-ca-memb*] + 4[craf-1_pkc-ca-aa*] + 4[craf-1_pkc-dag-memb*] + 4[craf-1_pkc-basal*] + 4[craf-1_pkc-aa*] + 40[craf-1*_mapk*] + 25[craf-1*_pphosphatase2a] + 6[craf-1**_pphosphatase2a] + 0.5[raf-gtp-ras*] - 3.25e-06[craf-1*][mapk*] - 3.3e-06[craf-1*][pphosphatase2a] - 4e-05[craf-1*][gtp-ras]d[gap]/dt = 16[gap_pkc-dag-aa*] + 16[gap_pkc-ca-memb*] + 16[gap_pkc-ca-aa*] + 16[gap_pkc-dag-memb*] + 16[gap_pkc-basal*] + 16[gap_pkc-aa*] + 1000[gtp-ras_gap] + 10[gtp-ras_gap] + 0.1[gap*] - 1e-05[gap][pkc-dag-aa*] - 1e-05[gap][pkc-ca-memb*] - 1e-05[gap][pkc-ca-aa*] - 1e-05[gap][pkc-dag-memb*] - 1e-05[gap][pkc-basal*] - 1e-05[gap][pkc-aa*] - 0.001666[gtp-ras][gap]d[gap_pkc-dag-aa*]/dt = 1e-05[gap][pkc-dag-aa*] - 16[gap_pkc-dag-aa*] - 4[gap_pkc-dag-aa*]d[gap*]/dt = 4[gap_pkc-dag-aa*] + 4[gap_pkc-ca-memb*] + 4[gap_pkc-ca-aa*] + 4[gap_pkc-dag-memb*] + 4[gap_pkc-basal*] + 4[gap_pkc-aa*] - 0.1[gap*]d[inact-gef]/dt = 16[inact-gef_pkc-dag-aa*] + 16[inact-gef_pkc-ca-memb*] + 16[inact-gef_pkc-ca-aa*] + 16[inact-gef_pkc-dag-memb*] + 16[inact-gef_pkc-basal*] + 16[inact-gef_pkc-aa*] + 36[inact-gef_pka-active] + 1[gef-gprot-bg] + 1[gef*] + 1[cam-gef] + 1[inact-gef*] - 1e-05[inact-gef][pkc-dag-aa*] - 1e-05[inact-gef][pkc-ca-memb*] - 1e-05[inact-gef][pkc-ca-aa*] - 1e-05[inact-gef][pkc-dag-memb*] - 1e-05[inact-gef][pkc-basal*] - 1e-05[inact-gef][pkc-aa*] - 1e-05[inact-gef][pka-active] - 1e-05[betagamma][inact-gef] - 0.0001[inact-gef][cam-ca4]d[inact-gef_pkc-dag-aa*]/dt = 1e-05[inact-gef][pkc-dag-aa*] - 16[inact-gef_pkc-dag-aa*] - 4[inact-gef_pkc-dag-aa*]d[gef*]/dt = 4[inact-gef_pkc-dag-aa*] + 4[inact-gef_pkc-ca-memb*] + 4[inact-gef_pkc-ca-aa*] + 4[inact-gef_pkc-dag-memb*] + 4[inact-gef_pkc-basal*] + 4[inact-gef_pkc-aa*] + 0.08[gdp-ras_gef*] + 0.02[gdp-ras_gef*] - 3.3e-07[gdp-ras][gef*] - 1[gef*]d[pkc-ca-memb*]/dt = 16[craf-1_pkc-ca-memb*] + 4[craf-1_pkc-ca-memb*] + 16[gap_pkc-ca-memb*] + 4[gap_pkc-ca-memb*] + 16[inact-gef_pkc-ca-memb*] + 4[inact-gef_pkc-ca-memb*] + 1.2705[pkc-ca] - 5e-07[craf-1][pkc-ca-memb*] - 1e-05[gap][pkc-ca-memb*] - 1e-05[inact-gef][pkc-ca-memb*] - 3.5026[pkc-ca-memb*]d[craf-1_pkc-ca-memb*]/dt = 5e-07[craf-1][pkc-ca-memb*] - 16[craf-1_pkc-ca-memb*] - 4[craf-1_pkc-ca-memb*]d[gap_pkc-ca-memb*]/dt = 1e-05[gap][pkc-ca-memb*] - 16[gap_pkc-ca-memb*] - 4[gap_pkc-ca-memb*]d[inact-gef_pkc-ca-memb*]/dt = 1e-05[inact-gef][pkc-ca-memb*] - 16[inact-gef_pkc-ca-memb*] - 4[inact-gef_pkc-ca-memb*]d[pkc-ca-aa*]/dt = 16[craf-1_pkc-ca-aa*] + 4[craf-1_pkc-ca-aa*] + 16[gap_pkc-ca-aa*] + 4[gap_pkc-ca-aa*] + 16[inact-gef_pkc-ca-aa*] + 4[inact-gef_pkc-ca-aa*] + 2e-09[pkc-ca][aa] - 5e-07[craf-1][pkc-ca-aa*] - 1e-05[gap][pkc-ca-aa*] - 1e-05[inact-gef][pkc-ca-aa*] - 0.1[pkc-ca-aa*]d[craf-1_pkc-ca-aa*]/dt = 5e-07[craf-1][pkc-ca-aa*] - 16[craf-1_pkc-ca-aa*] - 4[craf-1_pkc-ca-aa*]d[gap_pkc-ca-aa*]/dt = 1e-05[gap][pkc-ca-aa*] - 16[gap_pkc-ca-aa*] - 4[gap_pkc-ca-aa*]d[glu]/dt = 10[rec-glu] + 0.1[rec-glu-gq] - 2.8e-05[mglur][glu] - 2.8e-05[glu][rec-gq]d[rec-glu]/dt = 2.8e-05[mglur][glu] + 0.0001[rec-glu-gq] + 0.01[rec-glu-gq] - 10[rec-glu] - 1e-08[g-gdp][rec-glu]d[g-gdp]/dt = 1e-05[g*gdp][betagamma] + 0.0001[rec-glu-gq] + 1[rec-gq] - 0.0001[g-gdp] - 1e-08[g-gdp][rec-glu] - 1e-06[g-gdp][mglur]d[g*gtp]/dt = 0.0001[g-gdp] + 0.01[rec-glu-gq] + 1[plc-ca-gq] + 1[plc-gq] - 0.0133[g*gtp] - 4.2e-05[g*gtp][plc-ca] - 4.2e-06[plc][g*gtp]d[betagamma]/dt = 0.0001[g-gdp] + 0.01[rec-glu-gq] + 1[gef-gprot-bg] - 1e-05[g*gdp][betagamma] - 1e-05[betagamma][inact-gef]d[g*gdp]/dt = 0.0133[g*gtp] + 0.0133[plc-ca-gq] - 1e-05[g*gdp][betagamma]d[rec-glu-gq]/dt = 1e-08[g-gdp][rec-glu] + 2.8e-05[glu][rec-gq] - 0.0001[rec-glu-gq] - 0.1[rec-glu-gq] - 0.01[rec-glu-gq]d[rec-gq]/dt = 0.1[rec-glu-gq] + 1e-06[g-gdp][mglur] + 0.01[blocked-rec-gq] - 2.8e-05[glu][rec-gq] - 1[rec-gq] - 0.0001[rec-gq][mglurantag]d[mglurantag]/dt = 0.01[blocked-rec-gq] - 0.0001[rec-gq][mglurantag]d[blocked-rec-gq]/dt = 0.0001[rec-gq][mglurantag] - 0.01[blocked-rec-gq]d[pkc-cytosolic]/dt = 0.5[pkc-ca] + 50[pkc-basal*] + 0.1[pkc-aa*] + 0.1[pkc-dag] - 1e-06[pkc-cytosolic][ca] - 1[pkc-cytosolic] - 2e-10[aa][pkc-cytosolic] - 1e-09[pkc-cytosolic][dag]d[pkc-ca]/dt = 1e-06[pkc-cytosolic][ca] + 8.6348[pkc-ca-dag] + 3.5026[pkc-ca-memb*] + 0.1[pkc-ca-aa*] - 0.5[pkc-ca] - 1.3333e-08[dag][pkc-ca] - 1.2705[pkc-ca] - 2e-09[pkc-ca][aa]d[pkc-ca-dag]/dt = 1.3333e-08[dag][pkc-ca] + 0.1[pkc-dag-memb*] - 8.6348[pkc-ca-dag] - 1[pkc-ca-dag]d[pkc-dag-aa]/dt = 0.2[pkc-dag-aa*] + 3e-08[pkc-dag][aa] - 2[pkc-dag-aa] - 2[pkc-dag-aa]d[pkc-dag]/dt = 1e-09[pkc-cytosolic][dag] + 2[pkc-dag-aa] - 0.1[pkc-dag] - 3e-08[pkc-dag][aa]d[temp-pip2]/dt = 0.5[pip2-pla2*] + 0.1[pip2-ca-pla2*] - 2e-09[temp-pip2][pla2-cytosolic] - 2e-08[temp-pip2][pla2-ca*]d[plc]/dt = 1[plc-ca] + 1[plc-gq] - 5e-06[ca][plc] - 4.2e-06[plc][g*gtp]d[inositol]/dt = 2.5[ip3]d[pc]/dt = 0.15[dag]d[plc-gq]/dt = 4.2e-06[plc][g*gtp] + 1[plc-ca-gq] - 1[plc-gq] - 5e-05[ca][plc-gq]d[plc_g]/dt = 10[ca.plc_g] - 0.0003[plc_g][ca]d[plc_g*]/dt = 10[ca.plc_g*] - 2e-05[ca][plc_g*]d[cam-ca4]/dt = 1[cam-gef] - 0.0001[inact-gef][cam-ca4]d[sos.grb2]/dt = 0.1[shc*.sos.grb2] + 4.1667e-08[grb2][sos] - 8.333e-07[sos.grb2][shc*] - 0.0168[sos.grb2]d[grb2]/dt = 0.0168[sos*.grb2] + 0.0168[sos.grb2] - 4.1667e-08[sos*][grb2] - 4.1667e-08[grb2][sos]d[sos*.grb2]/dt = 4.1667e-08[sos*][grb2] - 0.0168[sos*.grb2]d[ca-ext]/dt = 72[ca_caepump] - 0.005 * [capacitive_ca_entry*] * ( [ca-ext] - [ca] ) - 0.004 * [ca-leak-from-extracell] * ( [ca-ext] - [ca] ) d[ca-sequester]/dt = 25[catransp-2ca] + 25[catransp-2ca] + 1[inact_cap_entry] + 1[inact_cap_entry] - 1.2e-11[ca-sequester][ca-sequester][capacitive_ca_entry*] - 1.2e-11[ca-sequester][ca-sequester]
[capacitive_ca_entry*] - 8 * [ca-leak-to-cytoplasm] * ( [ca-sequester] - [ca] ) - 19.2 * [ip3r*] * ( [ca-sequester] - [ca] )
d[inact-gef_pkc-ca-aa*]/dt = 1e-05[inact-gef][pkc-ca-aa*] - 16[inact-gef_pkc-ca-aa*] - 4[inact-gef_pkc-ca-aa*]d[pkc-dag-memb*]/dt = 16[craf-1_pkc-dag-memb*] + 4[craf-1_pkc-dag-memb*] + 16[gap_pkc-dag-memb*] + 4[gap_pkc-dag-memb*] + 16[inact-gef_pkc-dag-memb*] + 4[inact-gef_pkc-dag-memb*] + 1[pkc-ca-dag] - 5e-07[craf-1][pkc-dag-memb*] - 1e-05[gap][pkc-dag-memb*] - 1e-05[inact-gef][pkc-dag-memb*] - 0.1[pkc-dag-memb*]d[craf-1_pkc-dag-memb*]/dt = 5e-07[craf-1][pkc-dag-memb*] - 16[craf-1_pkc-dag-memb*] - 4[craf-1_pkc-dag-memb*]d[gap_pkc-dag-memb*]/dt = 1e-05[gap][pkc-dag-memb*] - 16[gap_pkc-dag-memb*] - 4[gap_pkc-dag-memb*]d[inact-gef_pkc-dag-memb*]/dt = 1e-05[inact-gef][pkc-dag-memb*] - 16[inact-gef_pkc-dag-memb*] - 4[inact-gef_pkc-dag-memb*]d[pkc-basal*]/dt = 16[craf-1_pkc-basal*] + 4[craf-1_pkc-basal*] + 16[gap_pkc-basal*] + 4[gap_pkc-basal*] + 16[inact-gef_pkc-basal*] + 4[inact-gef_pkc-basal*] + 1[pkc-cytosolic] - 5e-07[craf-1][pkc-basal*] - 1e-05[gap][pkc-basal*] - 1e-05[inact-gef][pkc-basal*] - 50[pkc-basal*]d[craf-1_pkc-basal*]/dt = 5e-07[craf-1][pkc-basal*] - 16[craf-1_pkc-basal*] - 4[craf-1_pkc-basal*]d[gap_pkc-basal*]/dt = 1e-05[gap][pkc-basal*] - 16[gap_pkc-basal*] - 4[gap_pkc-basal*]d[inact-gef_pkc-basal*]/dt = 1e-05[inact-gef][pkc-basal*] - 16[inact-gef_pkc-basal*] - 4[inact-gef_pkc-basal*]d[pkc-aa*]/dt = 16[craf-1_pkc-aa*] + 4[craf-1_pkc-aa*] + 16[gap_pkc-aa*] + 4[gap_pkc-aa*] + 16[inact-gef_pkc-aa*] + 4[inact-gef_pkc-aa*] + 2e-10[aa][pkc-cytosolic] - 5e-07[craf-1][pkc-aa*] - 1e-05[gap][pkc-aa*] - 1e-05[inact-gef][pkc-aa*] - 0.1[pkc-aa*]d[craf-1_pkc-aa*]/dt = 5e-07[craf-1][pkc-aa*] - 16[craf-1_pkc-aa*] - 4[craf-1_pkc-aa*]d[gap_pkc-aa*]/dt = 1e-05[gap][pkc-aa*] - 16[gap_pkc-aa*] - 4[gap_pkc-aa*]d[inact-gef_pkc-aa*]/dt = 1e-05[inact-gef][pkc-aa*] - 16[inact-gef_pkc-aa*] - 4[inact-gef_pkc-aa*]d[apc]/dt = 21.6[apc_pla2-ca*] + 44.16[apc_pip2-pla2*] + 144[apc_pip2-ca-pla2*] + 240[apc_dag-ca-pla2*] + 480[apc_pla2*-ca] + 0.4[aa] - 2.25e-06[apc][pla2-ca*] - 4.6e-06[apc][pip2-pla2*] - 1.5e-05[apc][pip2-ca-pla2*] - 2.5e-05[apc][dag-ca-pla2*] - 5e-05[apc][pla2*-ca]d[pla2-ca*]/dt = 21.6[apc_pla2-ca*] + 5.4[apc_pla2-ca*] + 1.6667e-06[pla2-cytosolic][ca] + 0.1[pip2-ca-pla2*] + 4[dag-ca-pla2*] - 2.25e-06[apc][pla2-ca*] - 0.1[pla2-ca*] - 2e-08[temp-pip2][pla2-ca*] - 5e-09[dag][pla2-ca*]d[apc_pla2-ca*]/dt = 2.25e-06[apc][pla2-ca*] - 21.6[apc_pla2-ca*] - 5.4[apc_pla2-ca*]d[aa]/dt = 5.4[apc_pla2-ca*] + 11.04[apc_pip2-pla2*] + 36[apc_pip2-ca-pla2*] + 60[apc_dag-ca-pla2*] + 120[apc_pla2*-ca] + 0.1[pkc-ca-aa*] + 0.1[pkc-aa*] + 2[pkc-dag-aa] - 2e-09[pkc-ca][aa] - 2e-10[aa][pkc-cytosolic] - 3e-08[pkc-dag][aa] - 0.4[aa]d[pip2-pla2*]/dt = 44.16[apc_pip2-pla2*] + 11.04[apc_pip2-pla2*] + 2e-09[temp-pip2][pla2-cytosolic] - 4.6e-06[apc][pip2-pla2*] - 0.5[pip2-pla2*]d[apc_pip2-pla2*]/dt = 4.6e-06[apc][pip2-pla2*] - 44.16[apc_pip2-pla2*] - 11.04[apc_pip2-pla2*]d[pip2-ca-pla2*]/dt = 144[apc_pip2-ca-pla2*] + 36[apc_pip2-ca-pla2*] + 2e-08[temp-pip2][pla2-ca*] - 1.5e-05[apc][pip2-ca-pla2*] - 0.1[pip2-ca-pla2*]d[apc_pip2-ca-pla2*]/dt = 1.5e-05[apc][pip2-ca-pla2*] - 144[apc_pip2-ca-pla2*] - 36[apc_pip2-ca-pla2*]d[dag-ca-pla2*]/dt = 240[apc_dag-ca-pla2*] + 60[apc_dag-ca-pla2*] + 5e-09[dag][pla2-ca*] - 2.5e-05[apc][dag-ca-pla2*] - 4[dag-ca-pla2*]d[apc_dag-ca-pla2*]/dt = 2.5e-05[apc][dag-ca-pla2*] - 240[apc_dag-ca-pla2*] - 60[apc_dag-ca-pla2*]d[pla2*-ca]/dt = 480[apc_pla2*-ca] + 120[apc_pla2*-ca] + 1e-05[pla2*][ca] - 5e-05[apc][pla2*-ca] - 0.1[pla2*-ca]d[apc_pla2*-ca]/dt = 5e-05[apc][pla2*-ca] - 480[apc_pla2*-ca] - 120[apc_pla2*-ca]d[pla2-cytosolic]/dt = 80[pla2-cytosolic_mapk*] + 0.1[pla2-ca*] + 0.5[pip2-pla2*] + 0.17[pla2*] - 6.5e-06[pla2-cytosolic][mapk*] - 1.6667e-06[pla2-cytosolic][ca] - 2e-09[temp-pip2][pla2-cytosolic]d[pla2-cytosolic_mapk*]/dt = 6.5e-06[pla2-cytosolic][mapk*] - 80[pla2-cytosolic_mapk*] - 20[pla2-cytosolic_mapk*]d[pla2*]/dt = 20[pla2-cytosolic_mapk*] + 0.1[pla2*-ca] - 1e-05[pla2*][ca] - 0.17[pla2*]d[craf-1*_mapk*]/dt = 3.25e-06[craf-1*][mapk*] - 40[craf-1*_mapk*] - 10[craf-1*_mapk*]d[craf-1**]/dt = 10[craf-1*_mapk*] + 25[craf-1**_pphosphatase2a] - 3.3e-06[craf-1**][pphosphatase2a]d[sos]/dt = 40[sos_mapk*] + 0.001[sos*] + 0.0168[sos.grb2] - 3.25e-05[sos][mapk*] - 4.1667e-08[grb2][sos]d[sos_mapk*]/dt = 3.25e-05[sos][mapk*] - 40[sos_mapk*] - 10[sos_mapk*]d[sos*]/dt = 10[sos_mapk*] + 0.0168[sos*.grb2] - 4.1667e-08[sos*][grb2] - 0.001[sos*]d[mkp-1]/dt = 4[mapk-tyr_mkp-1] + 1[mapk-tyr_mkp-1] + 4[mapk*_mkp-1] + 1[mapk*_mkp-1] - 0.000125[mapk-tyr][mkp-1] - 0.000125[mapk*][mkp-1]d[mapk-tyr_mkp-1]/dt = 0.000125[mapk-tyr][mkp-1] - 4[mapk-tyr_mkp-1] - 1[mapk-tyr_mkp-1]d[mapk*_mkp-1]/dt = 0.000125[mapk*][mkp-1] - 4[mapk*_mkp-1] - 1[mapk*_mkp-1]d[pphosphatase2a]/dt = 25[craf-1*_pphosphatase2a] + 6[craf-1*_pphosphatase2a] + 25[mapkk*_pphosphatase2a] + 6[mapkk*_pphosphatase2a] + 25[mapkk-ser_pphosphatase2a] + 6[mapkk-ser_pphosphatase2a] + 25[craf-1**_pphosphatase2a] + 6[craf-1**_pphosphatase2a] - 3.3e-06[craf-1*][pphosphatase2a] - 3.3e-06[mapkk*][pphosphatase2a] - 3.3e-06[mapkk-ser][pphosphatase2a] - 3.3e-06[craf-1**][pphosphatase2a]d[craf-1*_pphosphatase2a]/dt = 3.3e-06[craf-1*][pphosphatase2a] - 25[craf-1*_pphosphatase2a] - 6[craf-1*_pphosphatase2a]d[mapkk*_pphosphatase2a]/dt = 3.3e-06[mapkk*][pphosphatase2a] - 25[mapkk*_pphosphatase2a] - 6[mapkk*_pphosphatase2a]d[mapkk-ser_pphosphatase2a]/dt = 3.3e-06[mapkk-ser][pphosphatase2a] - 25[mapkk-ser_pphosphatase2a] - 6[mapkk-ser_pphosphatase2a]d[craf-1**_pphosphatase2a]/dt = 3.3e-06[craf-1**][pphosphatase2a] - 25[craf-1**_pphosphatase2a] - 6[craf-1**_pphosphatase2a]d[pka-active]/dt = 36[inact-gef_pka-active] + 9[inact-gef_pka-active] - 1e-05[inact-gef][pka-active]d[inact-gef_pka-active]/dt = 1e-05[inact-gef][pka-active] - 36[inact-gef_pka-active] - 9[inact-gef_pka-active]d[inact-gef*]/dt = 9[inact-gef_pka-active] - 1[inact-gef*]d[gdp-ras]/dt = 0.08[gdp-ras_shc*.sos.grb2] + 0.08[gdp-ras_gef-gprot-bg] + 0.08[gdp-ras_gef*] + 10[gtp-ras_gap] + 0.08[gdp-ras_cam-gef] + 0.0001[gtp-ras] - 3.3e-07[gdp-ras][shc*.sos.grb2] - 3.3e-07[gdp-ras][gef-gprot-bg] - 3.3e-07[gdp-ras][gef*] - 3.3e-07[gdp-ras][cam-gef]d[shc*.sos.grb2]/dt = 0.08[gdp-ras_shc*.sos.grb2] + 0.02[gdp-ras_shc*.sos.grb2] + 8.333e-07[sos.grb2][shc*] - 3.3e-07[gdp-ras][shc*.sos.grb2] - 0.1[shc*.sos.grb2]d[gdp-ras_shc*.sos.grb2]/dt = 3.3e-07[gdp-ras][shc*.sos.grb2] - 0.08[gdp-ras_shc*.sos.grb2] - 0.02[gdp-ras_shc*.sos.grb2]d[gtp-ras]/dt = 0.02[gdp-ras_shc*.sos.grb2] + 0.02[gdp-ras_gef-gprot-bg] + 0.02[gdp-ras_gef*] + 1000[gtp-ras_gap] + 0.02[gdp-ras_cam-gef] + 0.5[raf-gtp-ras*] - 0.001666[gtp-ras][gap] - 4e-05[craf-1*][gtp-ras] - 0.0001[gtp-ras]d[pip2]/dt = 40[pip2_plc-ca] + 192[pip2_plc-ca-gq] + 56[pip2_ca.plc_g] + 228[pip2_ca.plc_g*] - 4.2e-06[pip2][plc-ca] - 8e-05[pip2][plc-ca-gq] - 1.2e-06[pip2][ca.plc_g] - 2.4e-05[pip2][ca.plc_g*]d[plc-ca]/dt = 40[pip2_plc-ca] + 10[pip2_plc-ca] + 5e-06[ca][plc] + 1[plc-ca-gq] + 0.0133[plc-ca-gq] - 4.2e-06[pip2][plc-ca] - 1[plc-ca] - 4.2e-05[g*gtp][plc-ca]d[pip2_plc-ca]/dt = 4.2e-06[pip2][plc-ca] - 40[pip2_plc-ca] - 10[pip2_plc-ca]d[dag]/dt = 10[pip2_plc-ca] + 48[pip2_plc-ca-gq] + 14[pip2_ca.plc_g] + 57[pip2_ca.plc_g*] + 8.6348[pkc-ca-dag] + 0.1[pkc-dag] + 4[dag-ca-pla2*] - 1.3333e-08[dag][pkc-ca] - 1e-09[pkc-cytosolic][dag] - 5e-09[dag][pla2-ca*] - 0.15[dag]d[ip3]/dt = 10[pip2_plc-ca] + 48[pip2_plc-ca-gq] + 14[pip2_ca.plc_g] + 57[pip2_ca.plc_g*] + 1[ip3r*] + 1[ip3r*] + 1[ip3r*] - 1e-20[ip3r][ip3][ip3][ip3] - 1e-20[ip3r][ip3][ip3][ip3] - 1e-20[ip3r][ip3][ip3][ip3] - 2.5[ip3]d[plc-ca-gq]/dt = 192[pip2_plc-ca-gq] + 48[pip2_plc-ca-gq] + 4.2e-05[g*gtp][plc-ca] + 5e-05[ca][plc-gq] - 8e-05[pip2][plc-ca-gq] - 1[plc-ca-gq] - 0.0133[plc-ca-gq] - 1[plc-ca-gq]d[pip2_plc-ca-gq]/dt = 8e-05[pip2][plc-ca-gq] - 192[pip2_plc-ca-gq] - 48[pip2_plc-ca-gq]d[pip2_ca.plc_g]/dt = 1.2e-06[pip2][ca.plc_g] - 56[pip2_ca.plc_g] - 14[pip2_ca.plc_g]d[pip2_ca.plc_g*]/dt = 2.4e-05[pip2][ca.plc_g*] - 228[pip2_ca.plc_g*] - 57[pip2_ca.plc_g*]d[gef-gprot-bg]/dt = 0.08[gdp-ras_gef-gprot-bg] + 0.02[gdp-ras_gef-gprot-bg] + 1e-05[betagamma][inact-gef] - 3.3e-07[gdp-ras][gef-gprot-bg] - 1[gef-gprot-bg]d[gdp-ras_gef-gprot-bg]/dt = 3.3e-07[gdp-ras][gef-gprot-bg] - 0.08[gdp-ras_gef-gprot-bg] - 0.02[gdp-ras_gef-gprot-bg]d[gdp-ras_gef*]/dt = 3.3e-07[gdp-ras][gef*] - 0.08[gdp-ras_gef*] - 0.02[gdp-ras_gef*]d[gtp-ras_gap]/dt = 0.001666[gtp-ras][gap] - 1000[gtp-ras_gap] - 10[gtp-ras_gap]d[cam-gef]/dt = 0.08[gdp-ras_cam-gef] + 0.02[gdp-ras_cam-gef] + 0.0001[inact-gef][cam-ca4] - 3.3e-07[gdp-ras][cam-gef] - 1[cam-gef]d[gdp-ras_cam-gef]/dt = 3.3e-07[gdp-ras][cam-gef] - 0.08[gdp-ras_cam-gef] - 0.02[gdp-ras_cam-gef]d[catransp-2ca]/dt = 1e-08[ca][catransp][ca] - 25[catransp-2ca] - 144[catransp-2ca]d[catransp]/dt = 25[catransp-2ca] + 144[catransp-2ca] - 1e-08[ca][catransp][ca]d[ip3r]/dt = 1[ip3r*] - 1e-20[ip3r][ip3][ip3][ip3]d[inact_cap_entry]/dt = 1.2e-11[ca-sequester][ca-sequester][capacitive_ca_entry*] - 1[inact_cap_entry]d[egfr]/dt = 0.25[l.egfr] - 7e-06[egfr][egf]d[egf]/dt = 0.25[l.egfr] - 7e-06[egfr][egf]d[internal_l.egfr]/dt = 0.002[l.egfr] - 0.00033[internal_l.egfr]d[mglur]/dt = 10[rec-glu] + 1[rec-gq] - 2.8e-05[mglur][glu] - 1e-06[g-gdp][mglur]
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Parameters
1: Science. 1999 Jan 15;283(5400):381-7.
Emergent properties of networks of biological signaling pathways.
Bhalla US, Iyengar R.
Special topics on Electrical and Systems Engineering 2007Systems Biology
How may a mutation affect kinetics?
1
1
2
2
/
/
b
b
G k Tf
G k Tf
k Ae
k Ae
−Δ
−Δ
=
=
1 2
1 2
/f f b
f f
k k k Tk k e δ′ ′ −= =
δ
δ =−kbT log
′kf1
kf1( )
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Effects on signaling
A mutation between two unique species
Affects Reactant State
Affects Product State
Affects Transition State
′kf =e−δ /kTkf
′kb =e−δ /kTkb
′kf =e−δ /kTkf
′kb =e−δ /kTkb
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Cancer as a cumulative process
Multiple Mutations at different sites contribute to tumor transformation
Tumor may exist as “families” of differentially mutated cells
Overrides resistance of tumor to treatment
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“In Silico” Interaction Knockout experiments
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Single Site Transformations(kf’/kf)
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Top Ranked Mutations
X* + pp2a X*.pp2a 0.75
X*.pp2a X + pp2a 0.75
raf* + gtp-ras raf*.gtp.ras 0.60
Gtp-ras.gap gap + gdp-ras 0.55
raf* + pp2a raf*.pp2a 0.55
gtp-ras + gap gtp.ras_gap 0.55
AA apc 0.55
Ca.CaPump capump + ca-ext 0.55
X + Raf.GTP.Ras X.Raf.GTP.Ras 0.50
PKC.DAG + AA PKC.DAG.AA* 0.50
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Top Ranked expression level mutations
0.4 MKP-1
0.5 GAP
0.7 PP2-A
1.4 PKC-I
1.6 Raf
1.7 Ras
Species
1.9 GEF
2.8 MEK
3.0 PLC
3.4 PLC-g
3.6 ERK
k'
k
k'
k Species
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Advantages of In Silico Pathway Analysis
Using experimentally validated models of a working signal pathway and a simple kinetic view of mutations
One can: Quantify (and rank)
Single Interaction Mutations Multiple Interaction Mutations Initial State Mutations
Many results are validated in the literature
Several new and non-obvious predictions
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In Silico Cancer Cells
We have developed a family of “in silico” cancer cells as models of pathways
What is this good for?
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The effect of Drugs on Signaling in mutated cells
E + Sà Üàá àà ES⏐ →⏐ E + P
E + I à Üàá àà EI
E + Sà Üàá àà E.S⏐ →⏐ E + P
E + I à Üàá àà EI + Sà Üàá àà EISà Üàá àà ES+ I
Competitive Binding
Noncompetitive binding
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ERK Target
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MEK Target
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Calciumblockers
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Threshold “Ranking”
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Experimental Assays PLC- - peptide based inhibitors PLC - U73122 PKC - Tamoxifen , Go6976, SPC-100221 PLA-2 - Quinacrine (anti-inflammatory) ERK - MEK - AZD6244/ARRY-142886, CI-1040 , PD98059 Ras - R115577, BMS-214462 SCH-66336 Raf - Bay43-9006 ISIS-5132 GEF - Calcium Blockers Verapamil , Nicardipine
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Overview
Ras/Gap mutations predicted PP2A mutations predicted Ras/Raf interaction “importance” predicted Much of the overexpression/underexpression
mutations predicted Drug targets are for the most part have experimental counter
parts.
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Transport?
?=
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How to treat real cells?
d[S*]
dt=k2, f [E.S] + Ds∇
2[S* ] + vg∇[S* ]
d[E]
dt=−k1, f [E][S] + k1,b[E.S] + k2, f [E.S] + DE∇
2[E]
d[S]
dt=−k1, f [E][S] + k1,b[E.S] + DS∇
2[S]
d[E.S]
dt=k1, f [E][S] −k1,b[E.S] + k2, f [E.S] + DE.S∇
2[E.S]
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Confocal Imaging and Quantum Dots
(Andres Kriete)
QDots
Tunable
Photostable
Narrow Emission Spectra
Broad Absorption Spectrum
Confocal Imaging Live Cells and fixed cells sub micron imaging
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Quantitative Signaling Analysis
Data from Confocal Imaging
- derivation of “in vivo” rate constants through global analysis
Given time sliced images and model
Derived rate constants will “fit” experimental images best (global optimization problem) with confidence intervals
- wealth of data helps prevent over fitting C(x,y,z,t) - “Automated” Sensitivity Analysis will be used for fitting
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Cell(ular)Sim(ulator)
•Cross Platform (Linux, Windows, MacOS X, Solaris) •Multiprocessor (MPI) (linear scaling)•Freely Available (GPL) •Pseudo-C Scripting Language
Adaptive Integrators (Reaction Diffusion) with Sensitivity Analysis - (Adaptive 2nd and 4th order Rosenbrock, Euler RK2,RK4,ARK4) - Strang Split RDR Coupled Diffusion
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Analysis Optimization Tools
Sensitivity Analysis Module (Automatic generation of Jacobian, Hessian)
MCA Module (Conservation Relationships) Global Optimization Tools - Use tools derived by the Protein Folding
Community (and elsewhere) - Simulated Annealing - Monte Carlo + Minimization - GA / Evolutionary Programming
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Numerical Methods
Reaction - DiffusionReaction - Advection
RADAR
Must ||’ize well and must be accurate
Equations are stiff, Jacobian is Sparse
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Reaction Operator :: Rosenbrock
drC
dt= f (
rC,
rk,t)
y(t+ h) =y(t) + piuii∑
(1−hJ )⋅ui =hf (y+ α ijuj ) + hJ ⋅ ijujj
i−1
∑j∑
We have this for solving
d
dt
drC
drk
Inherently || for our distribution scheme
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Diffusion Operator
Simple || algorithm based on explicit (FTCS) method
Simple single processor method based on Crank-Nicolson
|| Crank-Nicolson method based on the fact that you are solving a slew of independent 1D tri-diagonal solves
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Advection Operator
Based on Lax (explicit, inherently || )
Nonlinear part of advection operator moved to reactionOperator
dC / dt =∇⋅rvC + R(C,t)
dC / dt =rv⋅∇C +C(∇⋅
rv) + R(C,t)
dC / dt =rv⋅∇C + R'(C,t)
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Time Step Adaptability
Calculate the splitting error (and local errors) : use total error for estimating time step
Currently we have this for Reaction-Diffusion
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Visualization
Cross Platform QT/OpenGL Code Base
Client / Server (Socket Based) GUI“Live” Interaction with Numerical Code 1D/2D/3D time lapse contour plots Mouse-based interactive manipulation
Flexible Modular Design
To Be Implemented Point and Click graphical Entry of Biological Pathways, Grid Geometry, Initial Parameters and Control
Special topics on Electrical and Systems Engineering 2007Systems Biology
Who did the real work? Dhruv Pant Ph.D.
Dave Miller Ray Zou Yihua Wang Hanbing Lin Tom Shortell Travis Hoppe Aparna Kumar
Email : [email protected]
http://bio.physics.drexel.eduhttp://bio.physics.drexel.edu/systemsBiology