adlung1

BaF3 model

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Title

Protein abundance of AKT and ERK pathway components governs cell-type- specific regulation of proliferation

Authors

Lorenz Adlung1§, Sandip Kar2,3,4§, Marie-Christine Wagner1§, Bin She1§, Sajib Chakraborty1, Jie Bao5, Susen Lattermann1, Melanie Boerries5,6,7, Hauke Busch5,6,7, Jens Timmer8, Marcel Schilling1, Thomas Höfer2,3*, Ursula Klingmüller1,9*

Affiliations

1 Division of Systems Biology of Signal Transduction, German Cancer Research Center (DKFZ), D-69120 Heidelberg, Germany 2 Division of Theoretical Systems Biology, German Cancer Research Center (DKFZ), D-69120 Heidelberg, Germany 3 BioQuant Center, University of Heidelberg, D-69120 Heidelberg, Germany 4 Department of Chemistry, Indian Institute of Technology, Bombay, Powai, Mumbai 400076, India 5 Systems Biology of the Cellular Microenvironment Group, IMMZ, ALU, D-79104 Freiburg, Germany 6 German Cancer Consortium (DKTK), D-79104 Freiburg, Germany 7 German Cancer Research Center (DKFZ), D-69120 Heidelberg, Germany 8 Center for Biological Signaling Studies (BIOSS), Institute of Physics, University of Freiburg, D-79104 Freiburg, Germany 9 Translational Lung Research Center (TLRC), Member of the German Center for Lung Research (DZL), D-69120 Heidelberg, Germany

Abstract

Signaling through the AKT and ERK pathways controls cell proliferation. However, the integrated regulation of this multistep process, involving signal processing, cell growth and cell-cycle progression, is poorly understood. Here we study different hematopoietic cell types, in which AKT and ERK signaling is triggered by erythropoietin (Epo). Although these cell types share the molecular network topology for pro-proliferative Epo signaling, they exhibit distinct proliferative responses. Iterating quantitative experiments and mathematical modeling, we identify two molecular sources for cell-type-specific proliferation. First, cell- type-specific protein abundance patterns cause differential signal flow along the AKT and ERK pathways. Second, downstream regulators of both pathways have differential effects on proliferation, suggesting that protein synthesis is rate-limiting for faster cycling cells while slower cell cycles are controlled at the G1-S progression. The integrated mathematical model of Epo-driven proliferation explains cell-type-specific effects of targeted AKT and ERK inhibitors and faithfully predicts, based on the protein abundance, anti-proliferative effects of inhibitors in primary human erythroid progenitor cells. Our findings suggest that the effectiveness of targeted cancer therapy might become predictable from protein abundance.

Journal

MSB

Unit definitions have no effect on the numerical analysis of the model. It remains the responsibility of the modeler to ensure the internal numerical consistency of the model. If units are provided, however, the consistency of the model units will be checked.

Name Definition
Id Name Spatial dimensions Size
cyt cyt 3.0 1.0
Id Name Initial quantity Compartment Fixed
AkttBaF3 AkttBaF3 0.51 cyt (cyt)
BaF3Epo BaF3Epo 0.002 cyt (cyt)
EpoRBaF3 EpoRBaF3 0.01862 cyt (cyt)
ErktBaF3 ErktBaF3 2.964 cyt (cyt)
GTPRas 0.0 cyt (cyt)
IntpS6 0.0 cyt (cyt)
Intpakt 0.0 cyt (cyt)
Intperk 0.0 cyt (cyt)
MektBaF3 MektBaF3 4.38 cyt (cyt)
PDK1tBaF3 PDK1tBaF3 0.763 cyt (cyt)
PI3KtBaF3 PI3KtBaF3 0.0124 cyt (cyt)
PI45P2BaF3 PI45P2BaF3 10.0 cyt (cyt)
PIP3 0.0 cyt (cyt)
PIP3Akt 0.0 cyt (cyt)
PIP3PDK1 0.0 cyt (cyt)
PTENBaF3 PTENBaF3 0.1074 cyt (cyt)
PhosphatasetBaF3 PhosphatasetBaF3 0.0415 cyt (cyt)
Proliferation 0.0 cyt (cyt)
RSKa 0.0 cyt (cyt)
RSKtb RSKtb 3.0306 cyt (cyt)
RaftBaF3 RaftBaF3 3.886 cyt (cyt)
Raptorb Raptorb 0.1 cyt (cyt)
RastBaF3 RastBaF3 9.531 cyt (cyt)
Rictorb Rictorb 1.2329 cyt (cyt)
RpSHIP1 0.0 cyt (cyt)
RpSos 0.0 cyt (cyt)
S6tBaF3 S6tBaF3 2.59 cyt (cyt)
SHIP1tBaF3 SHIP1tBaF3 0.0842 cyt (cyt)
TORC1 0.0 cyt (cyt)
TORC2 0.0 cyt (cyt)
actPhosphatase 0.0 cyt (cyt)
mTORa 0.0 cyt (cyt)
mTORt mTORt 0.1 cyt (cyt)
pAkt 0.0 cyt (cyt)
pEpoR 0.0 cyt (cyt)
pErk 0.0 cyt (cyt)
pMek 0.0 cyt (cyt)
pRaf 0.0 cyt (cyt)
pS6 0.0 cyt (cyt)
pS6plot 0.0 cyt (cyt)
pSos 0.0 cyt (cyt)
phos2 0.0 cyt (cyt)
ppErk 0.0 cyt (cyt)
ppMek 0.0 cyt (cyt)

Initial assignments are expressions that are evaluated at time=0. It is not recommended to create initial assignments for all model entities. Restrict the use of initial assignments to cases where a value is expressed in terms of values or sizes of other model entities. Note that it is not permitted to have both an initial assignment and an assignment rule for a single model entity.

Definition
pAkt = -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * initAkttBaF3 * (-(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * initPDK1tBaF3 * kPDK1 / (lPDK1 + -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * kPDK1)) * kAkt * vpAkt / (dpAkt * lAkt + dpAkt * (-(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1))) * kAkt + dpAkt * (-(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * initPDK1tBaF3 * kPDK1 / (lPDK1 + -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * kPDK1)) * vpAkt + -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * (-(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * initPDK1tBaF3 * kPDK1 / (lPDK1 + -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * kPDK1)) * kAkt * vpAkt)
PDK1tBaF3 = initPDK1tBaF3
PIP3PDK1 = -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * initPDK1tBaF3 * kPDK1 / (lPDK1 + -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * kPDK1)
RpSHIP1 = initRpSHIP1
SHIP1tBaF3 = initSHIP1tBaF3
PTENBaF3 = initPTENBaF3
PI3KtBaF3 = initPI3KtBaF3
PI45P2BaF3 = initPI45P2BaF3
PIP3 = -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1))
ErktBaF3 = initErktBaF3
S6tBaF3 = initS6tBaF3
pS6 = initS6tBaF3 * (kbacks6 + initTORC1 * kas6t + -(0.5 * (kdphoss6 + initTORC1 * kas6t - 1 * pow((RSKin * kinrskb + 1) * (Mekin * kmekinb + 1) * (pow(kdphoss6, 2) + pow(initTORC1, 2) * pow(kas6t, 2) + 2 * initTORC1 * kas6t * kdphoss6 + RSKin * pow(kdphoss6, 2) * kinrskb + Mekin * pow(kdphoss6, 2) * kmekinb + 4 * initRSKtb * (initErktBaF3 * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) * kpErk / (kpErk * kppErk * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek, 2) / (bDUSP3 * lppErk) + kpErk * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) + bDUSP3 * lpErk) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) * kppErk / (bDUSP3 * lppErk)) * karsk * kas6r + pow(initTORC1, 2) * RSKin * pow(kas6t, 2) * kinrskb + pow(initTORC1, 2) * Mekin * pow(kas6t, 2) * kmekinb + 2 * initTORC1 * RSKin * kas6t * kdphoss6 * kinrskb + 2 * initTORC1 * Mekin * kas6t * kdphoss6 * kmekinb + RSKin * Mekin * pow(kdphoss6, 2) * kinrskb * kmekinb + pow(initTORC1, 2) * RSKin * Mekin * pow(kas6t, 2) * kinrskb * kmekinb + 2 * initTORC1 * RSKin * Mekin * kas6t * kdphoss6 * kinrskb * kmekinb), (1/2)) + RSKin * kdphoss6 * kinrskb + Mekin * kdphoss6 * kmekinb + initTORC1 * RSKin * kas6t * kinrskb + initTORC1 * Mekin * kas6t * kmekinb + RSKin * Mekin * kdphoss6 * kinrskb * kmekinb + initTORC1 * RSKin * Mekin * kas6t * kinrskb * kmekinb)) / (kas6r * (RSKin * kinrskb + 1) * (Mekin * kmekinb + 1)) * kas6r) / (kbacks6 + kdphoss6 + initTORC1 * kas6t + -(0.5 * (kdphoss6 + initTORC1 * kas6t - 1 * pow((RSKin * kinrskb + 1) * (Mekin * kmekinb + 1) * (pow(kdphoss6, 2) + pow(initTORC1, 2) * pow(kas6t, 2) + 2 * initTORC1 * kas6t * kdphoss6 + RSKin * pow(kdphoss6, 2) * kinrskb + Mekin * pow(kdphoss6, 2) * kmekinb + 4 * initRSKtb * (initErktBaF3 * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) * kpErk / (kpErk * kppErk * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek, 2) / (bDUSP3 * lppErk) + kpErk * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) + bDUSP3 * lpErk) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) * kppErk / (bDUSP3 * lppErk)) * karsk * kas6r + pow(initTORC1, 2) * RSKin * pow(kas6t, 2) * kinrskb + pow(initTORC1, 2) * Mekin * pow(kas6t, 2) * kmekinb + 2 * initTORC1 * RSKin * kas6t * kdphoss6 * kinrskb + 2 * initTORC1 * Mekin * kas6t * kdphoss6 * kmekinb + RSKin * Mekin * pow(kdphoss6, 2) * kinrskb * kmekinb + pow(initTORC1, 2) * RSKin * Mekin * pow(kas6t, 2) * kinrskb * kmekinb + 2 * initTORC1 * RSKin * Mekin * kas6t * kdphoss6 * kinrskb * kmekinb), (1/2)) + RSKin * kdphoss6 * kinrskb + Mekin * kdphoss6 * kmekinb + initTORC1 * RSKin * kas6t * kinrskb + initTORC1 * Mekin * kas6t * kmekinb + RSKin * Mekin * kdphoss6 * kinrskb * kmekinb + initTORC1 * RSKin * Mekin * kas6t * kinrskb * kmekinb)) / (kas6r * (RSKin * kinrskb + 1) * (Mekin * kmekinb + 1)) * kas6r)
TORC1 = initTORC1
RSKtb = initRSKtb
AkttBaF3 = initAkttBaF3
RSKa = -(0.5 * (kdphoss6 + initTORC1 * kas6t - 1 * pow((RSKin * kinrskb + 1) * (Mekin * kmekinb + 1) * (pow(kdphoss6, 2) + pow(initTORC1, 2) * pow(kas6t, 2) + 2 * initTORC1 * kas6t * kdphoss6 + RSKin * pow(kdphoss6, 2) * kinrskb + Mekin * pow(kdphoss6, 2) * kmekinb + 4 * initRSKtb * (initErktBaF3 * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) * kpErk / (kpErk * kppErk * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek, 2) / (bDUSP3 * lppErk) + kpErk * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) + bDUSP3 * lpErk) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) * kppErk / (bDUSP3 * lppErk)) * karsk * kas6r + pow(initTORC1, 2) * RSKin * pow(kas6t, 2) * kinrskb + pow(initTORC1, 2) * Mekin * pow(kas6t, 2) * kmekinb + 2 * initTORC1 * RSKin * kas6t * kdphoss6 * kinrskb + 2 * initTORC1 * Mekin * kas6t * kdphoss6 * kmekinb + RSKin * Mekin * pow(kdphoss6, 2) * kinrskb * kmekinb + pow(initTORC1, 2) * RSKin * Mekin * pow(kas6t, 2) * kinrskb * kmekinb + 2 * initTORC1 * RSKin * Mekin * kas6t * kdphoss6 * kinrskb * kmekinb), (1/2)) + RSKin * kdphoss6 * kinrskb + Mekin * kdphoss6 * kmekinb + initTORC1 * RSKin * kas6t * kinrskb + initTORC1 * Mekin * kas6t * kmekinb + RSKin * Mekin * kdphoss6 * kinrskb * kmekinb + initTORC1 * RSKin * Mekin * kas6t * kinrskb * kmekinb)) / (kas6r * (RSKin * kinrskb + 1) * (Mekin * kmekinb + 1))
ppErk = initErktBaF3 * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) * kpErk / (kpErk * kppErk * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek, 2) / (bDUSP3 * lppErk) + kpErk * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) + bDUSP3 * lpErk) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) * kppErk / (bDUSP3 * lppErk)
GTPRas = initRastBaF3 * kbackRas / (kbackRas + kdRas)
RastBaF3 = initRastBaF3
pRaf = initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)
RaftBaF3 = initRaftBaF3
pMek = initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)
MektBaF3 = initMektBaF3
ppMek = initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek
pErk = initErktBaF3 * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) * kpErk / (kpErk * kppErk * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek, 2) / (bDUSP3 * lppErk) + kpErk * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf) * initMektBaF3 * kpMek / (kpMek * kppMek * pow(initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf), 2) / lppMek + kpMek * (initRaftBaF3 * (initRastBaF3 * kbackRas / (kbackRas + kdRas)) * kpRaf / (kpRaf + lpRaf)) + lpMek)) * kppMek / lppMek) + bDUSP3 * lpErk)
PIP3Akt = dpAkt * (-(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1))) * initAkttBaF3 * kAkt / (dpAkt * lAkt + dpAkt * (-(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1))) * kAkt + dpAkt * (-(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * initPDK1tBaF3 * kPDK1 / (lPDK1 + -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * kPDK1)) * vpAkt + -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * (-(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * initPDK1tBaF3 * kPDK1 / (lPDK1 + -(initPI45P2BaF3 * vPIP3basal * (0 - initPI3KtBaF3 + 0)) / (initPTENBaF3 * vPI45P2 + kshbasal * (initSHIP1tBaF3 - initRpSHIP1)) * kPDK1)) * kAkt * vpAkt)
Id Name Objective coefficient Reaction Equation and Kinetic Law Flux bounds
v1 BaF3Epo = ∅

Epodegradation * BaF3Epo
v18 v18 ∅ = RpSHIP1

kSHIP1 * (SHIP1tBaF3 - RpSHIP1) * (pEpoR - RpSHIP1)
v19 RpSHIP1 = ∅

lSHIP1 * RpSHIP1
v2 v2 ∅ = pEpoR

EpoRactivation1 / (1 + phos2 / Ki1) * (EpoRBaF3 - pEpoR * (1 + kPI3K / ((1 + kPI3K) * 1 + kPI3K * kPI3Kras * 1) + kPI3K * kPI3Kras / ((1 + kPI3K) * 1 + kPI3K * kPI3Kras * 1))) * (pow(BaF3Epo, nb) / (pow(ksatb, nb) + pow(BaF3Epo, nb)))
v20 v20 ∅ = PIP3

vPIP3 * PI45P2BaF3 * kPI3K / ((1 + kPI3K) * 1 + kPI3K * kPI3Kras * 1) * pEpoR
v21 v21 ∅ = PIP3

vPIP3 * main1 * PI45P2BaF3 * kPI3K * kPI3Kras / ((1 + kPI3K) * 1 + kPI3K * kPI3Kras * 1) * pEpoR
v22 v22 PIP3 = ∅

kshbasal * PIP3 * (SHIP1tBaF3 - RpSHIP1)
v23 v23 PIP3 = ∅

vPI45P2 * PIP3 * PTENBaF3
v24 v24 PIP3 = ∅

vPI34P2 * PIP3 * RpSHIP1
v25 v25 PIP3 = PIP3PDK1

kPDK1 * PIP3 * (PDK1tBaF3 - PIP3PDK1)
v26 PIP3PDK1 = PIP3

lPDK1 * PIP3PDK1
v27 v27 PIP3 = PIP3Akt

kAkt * PIP3 * (AkttBaF3 - PIP3Akt - pAkt)
v28 PIP3Akt = PIP3

lAkt * PIP3Akt
v29 v29 PIP3Akt = ∅

vpAkt * PIP3Akt * PIP3PDK1
v3 v3 ∅ = actPhosphatase

Phosphataseactivation1 * (PhosphatasetBaF3 - actPhosphatase) * pEpoR
v30 v30 ∅ = PIP3

vpAkt * PIP3Akt * PIP3PDK1
v31 v31 ∅ = pAkt

vpAkt * PIP3Akt * PIP3PDK1 / (1 + kaktinb * Aktin)
v32 pAkt = ∅

dpAkt * pAkt
v33 v33 ∅ = PIP3

vPIP3basal * PI45P2BaF3 * (PI3KtBaF3 - kPI3K / ((1 + kPI3K) * 1 + kPI3K * kPI3Kras * 1) * pEpoR - kPI3K * kPI3Kras / ((1 + kPI3K) * 1 + kPI3K * kPI3Kras * 1) * pEpoR)
v34 v34 ∅ = PIP3

vPIP3basal * main1 * PI45P2BaF3
v35 v35 ∅ = pSos

kpes * (Sostb - pSos - RpSos) * ppErk
v36 pSos = ∅

kdpes * pSos
v37 v37 ∅ = RpSos

kSos * (Sostb - RpSos - pSos) * (pEpoR - RpSos)
v38 RpSos = ∅

lSos * RpSos
v39 v39 RpSos = pSos

kpes * RpSos * ppErk
v4 actPhosphatase = ∅

Phosphatasedeactivation1 * actPhosphatase
v40 v40 ∅ = GTPRas

kbackRas * (RastBaF3 - GTPRas - kPI3K * kPI3Kras / ((1 + kPI3K) * 1 + kPI3K * kPI3Kras * 1) * pEpoR)
v41 v41 ∅ = GTPRas

kaRas * RpSos * (RastBaF3 - GTPRas - kPI3K * kPI3Kras / ((1 + kPI3K) * 1 + kPI3K * kPI3Kras * 1) * pEpoR)
v42 GTPRas = ∅

kdRas * GTPRas
v43 v43 ∅ = pRaf

kpRaf * (GTPRas + kPI3K * kPI3Kras / ((1 + kPI3K) * 1 + kPI3K * kPI3Kras * 1) * pEpoR) * (RaftBaF3 - pRaf)
v44 pRaf = ∅

lpRaf * pRaf
v45 v45 ∅ = pMek

kpMek * pRaf * (MektBaF3 - pMek - ppMek)
v46 pMek = ∅

lpMek * pMek
v47 v47 pMek = ppMek

kppMek * pRaf * pMek
v48 ppMek = pMek

lppMek * ppMek
v49 v49 ∅ = pErk

kpErk * ppMek * (ErktBaF3 - pErk - ppErk)
v5 v5 pEpoR = ∅

pEpoRdeactivation1 * pEpoR * actPhosphatase
v50 pErk = ∅

lpErk * bDUSP3 * pErk
v51 v51 pErk = ppErk

kppErk * ppMek * pErk / (1 + kmekinb * Mekin)
v52 ppErk = pErk

lppErk * bDUSP3 * ppErk
v53 v53 ∅ = Intperk

ppErk
v54 v54 ∅ = Intpakt

pAkt
v55 v55 ∅ = mTORa

kvpakt * pAkt * (mTORt - mTORa - TORC1 - TORC2)
v56 v56 ∅ = mTORa

kvppErk * RSKa / (1 + kinrskb * RSKin) * (mTORt - mTORa - TORC1 - TORC2)
v57 mTORa = ∅

kdactm * mTORa
v58 v58 mTORa = TORC1

kst1 / (1 + kinrapab * Rapamycin) * (mTORa - TORC1 - TORC2) * (Raptorb - TORC1)
v59 TORC1 = mTORa

kdt1 * TORC1
v6 v6 ∅ = phos2

Phosact1 * pow(pEpoR, n1) / (pow(Ji1, n1) + pow(pEpoR, n1))
v60 TORC1 = ∅

kdactm * TORC1
v61 v61 mTORa = TORC2

kst2 * (mTORa - TORC2 - TORC1) * (Rictorb - TORC2)
v62 TORC2 = mTORa

kdt2 * TORC2
v63 TORC2 = ∅

kdactm * TORC2
v64 v64 ∅ = RSKa

karsk / (1 + kinrskb * RSKin) * (RSKtb - RSKa) * ppErk
v65 RSKa = ∅

kdrsk * RSKa
v66 v66 ∅ = pS6

kas6t * TORC1 * (S6tBaF3 - pS6)
v67 v67 ∅ = pS6

kas6r * RSKa * (S6tBaF3 - pS6)
v68 v68 ∅ = pS6

kbacks6 * (S6tBaF3 - pS6)
v69 pS6 = ∅

kdphoss6 * pS6
v7 phos2 = ∅

Phosdeact1 * phos2
v71 v71 ∅ = IntpS6

pS6
v73 v73 ∅ = Proliferation

pbk2correct * ((cycleaktinb * pAkt + cyclemekinb * ppErk) / maxccb) + pboffcorrect / 60

Global parameters

Id Value
Aktin 0.0
EpoRactivation1 0.140964
Epodegradation 0.0173287
Ji1 0.220505
Ki1 0.0272784
Mekin 0.0
Phosact1 341.317
Phosdeact1 0.00001
Phosphataseactivation1 144.425
Phosphatasedeactivation1 0.00001
RSKin 0.0
Rapamycin 0.0
Sostb 0.0000446181
bDUSP3 96.7699
cycleaktinb 0.967522
cyclemekinb 0.127989
dpAkt 3.4739
initAkttBaF3 0.51
initErktBaF3 2.964
initMektBaF3 4.38
initPDK1tBaF3 0.763
initPI3KtBaF3 0.0124
initPI45P2BaF3 10.0
initPTENBaF3 0.1074
initRSKtb 3.0306
initRaftBaF3 3.886
initRastBaF3 9.531
initRpSHIP1 0.0
initS6tBaF3 2.59
initSHIP1tBaF3 0.0842
initTORC1 0.0
kAkt 9984.96
kPDK1 9439.5
kPI3K 0.000104741
kPI3Kras 10000.0
kSHIP1 0.0745937
kSos 59.4049
kaRas 2981.53
kaktinb 1.866219406
karsk 1.26435
kas6r 0.000533083
kas6t 2180.44
kbackRas 0.0103384
kbacks6 0.0000100003
kdRas 0.540777
kdactm 0.0617342
kdpes 0.0270729
kdphoss6 0.328006
kdrsk 0.677229
kdt1 1588.13
kdt2 0.00001
kinrapab 2.778901656
kinrskb 0.552054462
kmekinb 3.224998336
kpErk 9999.08
kpMek 9774.26
kpRaf 1.17959
kpes 0.583255
kppErk 9999.96
kppMek 9999.77
ksatb 0.0024577
kshbasal 0.00001
kst1 20.0908
kst2 0.0619403
kvpakt 0.000174996
kvppErk 0.000282332
lAkt 10.1007
lPDK1 2355.54
lSHIP1 0.000650697
lSos 0.39616
lpErk 177.216
lpMek 0.0414313
lpRaf 2549.69
lppErk 3.2516
lppMek 1336.21
main1 0.000224787
maxccb 0.99
n1 4.0
nb 2.03939
pEpoRdeactivation1 3.20488
pbk2correct 0.485791
pboffcorrect 0.470245
vPI34P2 9996.96
vPI45P2 84.5564
vPIP3 10000.0
vPIP3basal 0.104429
vpAkt 6.90774

Local parameters

Id Value Reaction

Assignment rules

Definition
pS6plot = 412.8573*pS6

Rate rules

Definition

Algebraic rules

Definition
Trigger Assignments