adlung1
BaF3 model
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Protein abundance of AKT and ERK pathway components governs cell-type- specific regulation of proliferation
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*
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
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.
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 |
| 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 |
| Id | Value | Reaction |
|---|
| Definition | |
|---|---|
| pS6plot = 412.8573*pS6 |
| Definition |
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| Definition |
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| Definition |
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| Trigger | Assignments |
|---|