/* * Decoupling of receptor and downstream signals in the Akt pathway * by its low-pass filter characteristics * * Model Status * * This CellML represents the EGFR-inhibited Akt Pathway model * from the original publication (EGF has been set to 30 and the * inhibitor to 15). 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_2010c.png]] * * Schematic diagram of the simple simulation model of the EGFR-inhibited * 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 EGF dimensionless; EGF=30.0; real inhibitor dimensionless; inhibitor=15.0; real pro_EGFR dimensionless; pro_EGFR=6.81902e-4; real EGFR(time) dimensionless; when(time=time.min) EGFR=68190.000000002; real EGF_EGFR(time) dimensionless; when(time=time.min) EGF_EGFR=0.0; real EGFR_i(time) dimensionless; when(time=time.min) EGFR_i=0.0; real EGF_binding_kb first_order_rate_constant; EGF_binding_kb=4.07490e-2; real EGF_binding_kf first_order_rate_constant; EGF_binding_kf=6.73816e-3; real inhibitor_binding_kb first_order_rate_constant; inhibitor_binding_kb=5.25097e-5; real inhibitor_binding_kf first_order_rate_constant; inhibitor_binding_kf=2.434663e-5; real EGFR_turnover first_order_rate_constant; EGFR_turnover=1.06386129269658e-4; real EGF_EGFR_i(time) dimensionless; when(time=time.min) EGF_EGFR_i=0.0; real k1_EGFR_phosphorylation first_order_rate_constant; k1_EGFR_phosphorylation=1.92391e-2; real pEGFR(time) dimensionless; when(time=time.min) pEGFR=0.0; real pEGFR_Akt(time) dimensionless; when(time=time.min) pEGFR_Akt=0.0; real Akt(time) dimensionless; when(time=time.min) Akt=4.33090e-2; real k1_pEGFR_degradation first_order_rate_constant; k1_pEGFR_degradation=9.97194e-2; real k1_Akt_phosphorylation first_order_rate_constant; k1_Akt_phosphorylation=3.05684e-2; real k1_pEGFR_Akt first_order_rate_constant; k1_pEGFR_Akt=1.55430e-5; real k2_pEGFR_Akt first_order_rate_constant; k2_pEGFR_Akt=5.17473e-3; real pAkt(time) dimensionless; when(time=time.min) pAkt=0.0; real k1_pAkt_dephosphorylation first_order_rate_constant; k1_pAkt_dephosphorylation=3.27962e-2; real S6(time) dimensionless; when(time=time.min) S6=3.54317e0; real pAkt_S6(time) dimensionless; when(time=time.min) pAkt_S6=0.0; real k1_pAkt_S6 first_order_rate_constant; k1_pAkt_S6=2.10189e-6; real k2_pAkt_S6 first_order_rate_constant; k2_pAkt_S6=5.17940e-15; real k1_S6_phosphorylation first_order_rate_constant; k1_S6_phosphorylation=1.21498e-3; real pS6(time) dimensionless; when(time=time.min) pS6=0.0; real k1_pS6_dephosphorylation first_order_rate_constant; k1_pS6_dephosphorylation=1.13102e-3; real pEGFR_total(time) dimensionless; real pEGFR_scalefactor dimensionless; pEGFR_scalefactor=1.81735e-4; real pAkt_total(time) dimensionless; real pAkt_scalefactor dimensionless; pAkt_scalefactor=6.00588e1; real pS6_total(time) dimensionless; real pS6_scalefactor dimensionless; pS6_scalefactor=4.98862e4; // // // // // EGFR:time=(EGF_binding_kb*EGF_EGFR+inhibitor_binding_kb*EGFR_i+EGFR_turnover*(pro_EGFR-EGFR)-(EGF_binding_kf*EGF*EGFR+inhibitor_binding_kf*inhibitor*EGFR)); // EGF_EGFR:time=(EGF_binding_kf*EGF*EGFR+inhibitor_binding_kb*EGF_EGFR_i-(EGF_binding_kb*EGF_EGFR+inhibitor_binding_kf*inhibitor*EGF_EGFR+k1_EGFR_phosphorylation*EGF_EGFR)); // EGFR_i:time=(EGF_binding_kb*EGF_EGFR_i+inhibitor_binding_kf*inhibitor*EGFR-(EGF_binding_kf*EGF*EGFR_i+inhibitor_binding_kb*EGFR_i+EGFR_turnover*EGFR_i)); // EGF_EGFR_i:time=(EGF_binding_kf*EGF*EGFR_i+inhibitor_binding_kf*inhibitor*EGF_EGFR-(EGF_binding_kb*EGF_EGFR_i+inhibitor_binding_kb*EGF_EGFR_i)); // pEGFR:time=(k1_EGFR_phosphorylation*EGF_EGFR+k1_Akt_phosphorylation*pEGFR_Akt+k2_pEGFR_Akt*pEGFR_Akt-(k1_pEGFR_degradation*pEGFR+k1_pEGFR_Akt*pEGFR*Akt)); // pEGFR_Akt:time=(k1_pEGFR_Akt*pEGFR*Akt-(k2_pEGFR_Akt*pEGFR_Akt+k1_Akt_phosphorylation*pEGFR_Akt)); // Akt:time=(k2_pEGFR_Akt*pEGFR_Akt+k1_pAkt_dephosphorylation*pAkt-k1_pEGFR_Akt*pEGFR*Akt); // pAkt:time=(k1_Akt_phosphorylation*pEGFR_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); // pEGFR_total=((pEGFR+pEGFR_Akt)*pEGFR_scalefactor); // pAkt_total=((pAkt+pAkt_S6)*pAkt_scalefactor); // pS6_total=(pS6*pS6_scalefactor); // }