/* * Decoupling of receptor and downstream signals in the Akt pathway * by its low-pass filter characteristics * * Model Status * * This CellML represents the NGF-dependent Akt Pathway model from * the original publication (NGF has been set to 30). The model * runs in both COR and OpenCell to replicate the published results. * The units have been checked and they are consistent. * * Model Structure * * ABSTRACT: In cellular signal transduction, the information in * an external stimulus is encoded in temporal patterns in the * activities of signaling molecules; for example, pulses of a * stimulus may produce an increasing response or may produce pulsatile * responses in the signaling molecules. Here, we show how the * Akt pathway, which is involved in cell growth, specifically * transmits temporal information contained in upstream signals * to downstream effectors. We modeled the epidermal growth factor * (EGF)-dependent Akt pathway in PC12 cells on the basis of experimental * results. We obtained counterintuitive results indicating that * the sizes of the peak amplitudes of receptor and downstream * effector phosphorylation were decoupled; weak, sustained EGF * receptor (EGFR) phosphorylation, rather than strong, transient * phosphorylation, strongly induced phosphorylation of the ribosomal * protein S6, a molecule downstream of Akt. Using frequency response * analysis, we found that a three-component Akt pathway exhibited * the property of a low-pass filter and that this property could * explain decoupling of the peak amplitudes of receptor phosphorylation * and that of downstream effectors. Furthermore, we found that * lapatinib, an EGFR inhibitor used as an anticancer drug, converted * strong, transient Akt phosphorylation into weak, sustained Akt * phosphorylation, and, because of the low-pass filter characteristics * of the Akt pathway, this led to stronger S6 phosphorylation * than occurred in the absence of the inhibitor. Thus, an EGFR * inhibitor can potentially act as a downstream activator of some * effectors. * * model diagram * * [[Image file: fujita_2010b.png]] * * Schematic diagram of the simple simulation model of the NGF-dependent * Akt pathway. * * The original paper reference is cited below: * * Decoupling of receptor and downstream signals in the Akt pathway * by its low-pass filter characteristics, Fujita KA, Toyoshima * Y, Uda S, Ozaki Y, Kubota H, and Kuroda S, 2009, Science Signaling, * 3, issue 132. PubMed ID: 20664065 */ import nsrunit; unit conversion on; unit first_order_rate_constant=1 second^(-1); math main { realDomain time second; time.min=0; extern time.max; extern time.delta; real NGF dimensionless; NGF=30.0; real pro_TrkA dimensionless; pro_TrkA=8.52065e0; real TrkA(time) dimensionless; when(time=time.min) TrkA=8.52065e0; real NGF_TrkA(time) dimensionless; when(time=time.min) NGF_TrkA=0.0; real k2_NGF_TrkA first_order_rate_constant; k2_NGF_TrkA=1.33747e-2; real k1_NGF_TrkA first_order_rate_constant; k1_NGF_TrkA=2.69408e-3; real TrkA_turnover first_order_rate_constant; TrkA_turnover=0.0011032440769796; real k1_TrkA_phosphorylation first_order_rate_constant; k1_TrkA_phosphorylation=8.33178e-3; real pTrkA(time) dimensionless; when(time=time.min) pTrkA=0.0; real pTrkA_Akt(time) dimensionless; when(time=time.min) pTrkA_Akt=0.0; real Akt(time) dimensionless; when(time=time.min) Akt=1.15595e0; real k1_pTrkA_degradation first_order_rate_constant; k1_pTrkA_degradation=6.8084e-2; real k1_Akt_phosphorylation first_order_rate_constant; k1_Akt_phosphorylation=2.02517e-2; real k1_pTrkA_Akt first_order_rate_constant; k1_pTrkA_Akt=8.82701e-2; real k2_pTrkA_Akt first_order_rate_constant; k2_pTrkA_Akt=1.47518e-10; real pAkt(time) dimensionless; when(time=time.min) pAkt=0.0; real k1_pAkt_dephosphorylation first_order_rate_constant; k1_pAkt_dephosphorylation=1.28135e0; real S6(time) dimensionless; when(time=time.min) S6=3.55234e0; real pAkt_S6(time) dimensionless; when(time=time.min) pAkt_S6=0.0; real k1_pAkt_S6 first_order_rate_constant; k1_pAkt_S6=6.83666e1; real k2_pAkt_S6 first_order_rate_constant; k2_pAkt_S6=5.23519e-00; real k1_S6_phosphorylation first_order_rate_constant; k1_S6_phosphorylation=5.65150e-3; real pS6(time) dimensionless; when(time=time.min) pS6=0.0; real k1_pS6_dephosphorylation first_order_rate_constant; k1_pS6_dephosphorylation=2.93167e-4; real pTrkA_total(time) dimensionless; real pTrkA_scalefactor dimensionless; pTrkA_scalefactor=8.48783e-1; real pAkt_total(time) dimensionless; real pAkt_scalefactor dimensionless; pAkt_scalefactor=2.42381e0; real pS6_total(time) dimensionless; real pS6_scalefactor dimensionless; pS6_scalefactor=5.25843e-1; // // // // TrkA:time=(k2_NGF_TrkA*NGF_TrkA+TrkA_turnover*(pro_TrkA-TrkA)-k1_NGF_TrkA*NGF*TrkA); // NGF_TrkA:time=(k1_NGF_TrkA*NGF*TrkA-(k2_NGF_TrkA*NGF_TrkA+k1_TrkA_phosphorylation*NGF_TrkA)); // pTrkA:time=(k1_TrkA_phosphorylation*NGF_TrkA+k1_Akt_phosphorylation*pTrkA_Akt+k2_pTrkA_Akt*pTrkA_Akt-(k1_pTrkA_degradation*pTrkA+k1_pTrkA_Akt*pTrkA*Akt)); // pTrkA_Akt:time=(k1_pTrkA_Akt*pTrkA*Akt-(k2_pTrkA_Akt*pTrkA_Akt+k1_Akt_phosphorylation*pTrkA_Akt)); // Akt:time=(k2_pTrkA_Akt*pTrkA_Akt+k1_pAkt_dephosphorylation*pAkt-k1_pTrkA_Akt*pTrkA*Akt); // pAkt:time=(k1_Akt_phosphorylation*pTrkA_Akt+k2_pAkt_S6*pAkt_S6+k1_S6_phosphorylation*pAkt_S6-(k1_pAkt_dephosphorylation*pAkt+k1_pAkt_S6*pAkt*S6)); // pAkt_S6:time=(k1_pAkt_S6*pAkt*S6-(k2_pAkt_S6*pAkt_S6+k1_S6_phosphorylation*pAkt_S6)); // S6:time=(k2_pAkt_S6*pAkt_S6+k1_pS6_dephosphorylation*pS6-k1_pAkt_S6*pAkt*S6); // pS6:time=(k1_S6_phosphorylation*pAkt_S6-k1_pS6_dephosphorylation*pS6); // pTrkA_total=((pTrkA+pTrkA_Akt)*pTrkA_scalefactor); // pAkt_total=((pAkt+pAkt_S6)*pAkt_scalefactor); // pS6_total=(pS6*pS6_scalefactor); // }