A Systems Biology Approach to Cancer Therapy and Early Detection Avijit Ghosh Dhruv Pant, Rui Zou,...

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

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.

The Normal Functioning MAPK Signal Cascade

Signaling and Cell Growth

Input : EGF – Epidermal Growth

Factor Output:

Signal for gene transcription :: ERK

Activation: Phosphorylation GTP/GDP binding

EGF stimulation and ERK response

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

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

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= − +

[ ][ ][ ] [ . ]f b

d Sk E S k E S

dt=− +

[ *][ . ]f

d Sk E S

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

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]

Parameters

1: Science. 1999 Jan 15;283(5400):381-7.

Emergent properties of networks of biological signaling pathways.

Bhalla US, Iyengar R.

How may a mutation affect kinetics?

G k Tf

/f f b

k k k Tk k e δ′ ′ −= =

δ =−kbT log

′kf1

kf1( )

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

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

“In Silico” Interaction Knockout experiments

Single Site Transformations(kf’/kf)

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

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 Species

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

In Silico Cancer Cells

We have developed a family of “in silico” cancer cells as models of pathways

What is this good for?

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

ERK Target

MEK Target

Calciumblockers

Threshold “Ranking”

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

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.

Transport?

How to treat real cells?

dt=k2, f [E.S] + Ds∇

2[S* ] + vg∇[S* ]

dt=−k1, f [E][S] + k1,b[E.S] + k2, f [E.S] + DE∇

dt=−k1, f [E][S] + k1,b[E.S] + DS∇

d[E.S]

dt=k1, f [E][S] −k1,b[E.S] + k2, f [E.S] + DE.S∇

2[E.S]

Confocal Imaging and Quantum Dots

(Andres Kriete)

Tunable

Photostable

Narrow Emission Spectra

Broad Absorption Spectrum

Confocal Imaging Live Cells and fixed cells sub micron imaging

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

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

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

Numerical Methods

Reaction - DiffusionReaction - Advection

Must ||’ize well and must be accurate

Equations are stiff, Jacobian is Sparse

Reaction Operator :: Rosenbrock

dt= f (

y(t+ h) =y(t) + piuii∑

(1−hJ )⋅ui =hf (y+ α ijuj ) + hJ ⋅ ijujj

∑j∑

We have this for solving

Inherently || for our distribution scheme

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

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)

Time Step Adaptability

Calculate the splitting error (and local errors) : use total error for estimating time step

Currently we have this for Reaction-Diffusion

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

Who did the real work? Dhruv Pant Ph.D.

Dave Miller Ray Zou Yihua Wang Hanbing Lin Tom Shortell Travis Hoppe Aparna Kumar

Email : avijit@physics.drexel.edu

http://bio.physics.drexel.eduhttp://bio.physics.drexel.edu/systemsBiology

A Systems Biology Approach to Cancer Therapy and Early Detection Avijit Ghosh Dhruv Pant, Rui Zou,...

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