Lloyd Catherine May c.lloyd@auckland.ac.nz The University of Auckland The Bioengineering Research Group 2001-10-25 Altered connections after chacking the model with the validator. Lloyd Catherine May 2002-02-25 Updated metadata to conform to the 16/1/02 CellML Metadata 1.0 Specification. Cuellar Autumn A. 2002-01-22 The University of Auckland, Bioengineering Research Group The mitogen-activated protein kinase (MAPK) cascade, 2001 This is the CellML description of Asthagiri and Lauffenburger's mathematical model of the mitogen-activated protein kinase (MAPK) cascade (2001). They examine MAPK pathway dynamics, especially the role of negative feedback mechanisms in generating signal adaptation. Catherine Lloyd 11312698 R free receptor $\frac{d R}{d \mathrm{time}}=\mathrm{delta\_R\_ligand\_receptor\_binding}$ C ligand-bound receptor $\frac{d C}{d \mathrm{time}}=\mathrm{delta\_C\_ligand\_receptor\_binding}+\mathrm{delta\_C\_receptor\_dimerisation}$ C2 ligand-bound and dimerised receptor $\frac{d \mathrm{C2}}{d \mathrm{time}}=\mathrm{delta\_C2\_receptor\_dimerisation}+\mathrm{delta\_C2\_dimerised\_receptor\_activation}$ C_ dimerised and activated receptor $\frac{d \mathrm{C\_}}{d \mathrm{time}}=\mathrm{delta\_C\_\_dimerised\_receptor\_activation}+\mathrm{delta\_C\_\_receptor\_adaptor\_complex\_syn}+\mathrm{delta\_C\_\_receptor\_adaptors\_complex\_syn2}$ L free ligand $\frac{d L}{d \mathrm{time}}=\mathrm{delta\_L\_ligand\_receptor\_binding}$ A2_ non-functional second adaptor $\frac{d \mathrm{A2\_}}{d \mathrm{time}}=\mathrm{delta\_A2\_\_E0\_E4\_\_desyn}$ E4_ 4th activated signaling enzyme $\frac{d \mathrm{E4\_}}{d \mathrm{time}}=\mathrm{delta\_E4\_\_E0\_E4\_\_desyn}+\mathrm{delta\_E4\_\_E2\_E4\_\_desyn}+\mathrm{delta\_E4\_\_E4\_activation}+\mathrm{delta\_E4\_\_E5\_activation}+\mathrm{delta\_E4\_\_E0\_E4\_\_syn}+\mathrm{delta\_E4\_\_E2\_E4\_\_syn}+\mathrm{delta\_E4\_\_E4\_\_P4\_binding}+\mathrm{delta\_E4\_\_E4\_\_E5\_binding}$ E0_E4_ transition complex in feedback, mediated by E4_ $\frac{d \mathrm{E0\_E4\_}}{d \mathrm{time}}=\mathrm{delta\_E0\_E4\_\_E0\_E4\_\_syn}+\mathrm{delta\_E0\_E4\_\_E0\_E4\_\_desyn}$ E1_ 1st activated signaling enzyme $\frac{d \mathrm{E1\_}}{d \mathrm{time}}=\mathrm{delta\_E1\_\_E1\_activation}+\mathrm{delta\_E1\_\_E2\_activation}+\mathrm{delta\_E1\_\_E1\_\_P1\_binding}+\mathrm{delta\_E1\_\_E1\_\_E2\_binding}$ E1 1st inactive signaling enzyme $\frac{d \mathrm{E1}}{d \mathrm{time}}=\mathrm{delta\_E1\_E1\_\_inactivation}+\mathrm{delta\_E1\_E0\_\_E1\_binding}$ A1 free first adaptor $\frac{d \mathrm{A1}}{d \mathrm{time}}=\mathrm{delta\_A1\_adaptor\_heterodimer\_syn}+\mathrm{delta\_A1\_receptor\_adaptor\_complex\_syn}$ A2 free second adaptor $\frac{d \mathrm{A2}}{d \mathrm{time}}=\mathrm{delta\_A2\_adaptor\_heterodimer\_syn}+\mathrm{delta\_A2\_receptor\_adaptors\_complex\_syn1}$ E0_ receptor-ligand dimer adaptors 1 + 2 complex $\frac{d \mathrm{E0\_}}{d \mathrm{time}}=\mathrm{delta\_E0\_\_receptor\_adaptors\_complex\_syn1}+\mathrm{delta\_E0\_\_receptor\_adaptors\_complex\_syn2}+\mathrm{delta\_E0\_\_E1\_activation}+\mathrm{delta\_E0\_\_E0\_E4\_\_syn}+\mathrm{delta\_E0\_\_E0\_\_E1\_binding}$ C_A1 active receptor-ligand dimer adaptor 1 complex $\frac{d \mathrm{C\_A1}}{d \mathrm{time}}=\mathrm{delta\_C\_A1\_receptor\_adaptor\_complex\_syn}+\mathrm{delta\_C\_A1\_E0\_E4\_\_desyn}+\mathrm{delta\_C\_A1\_receptor\_adaptors\_complex\_syn1}$ P1 1st deactivating enzyme $\frac{d \mathrm{P1}}{d \mathrm{time}}=\mathrm{delta\_P1\_E1\_\_inactivation}+\mathrm{delta\_P1\_E1\_\_P1\_binding}$ E2_act 2nd activated signaling enzyme $\frac{d \mathrm{E2\_}}{d \mathrm{time}}=\mathrm{delta\_E2\_\_E2\_activation}+\mathrm{delta\_E2\_\_E3\_activation}+\mathrm{delta\_E2\_\_E2\_\_P2\_binding}+\mathrm{delta\_E2\_\_E2\_E4\_\_syn}+\mathrm{delta\_E2\_\_E2\_E4\_\_desyn}+\mathrm{delta\_E2\_\_E2\_\_E3\_binding}$ E2 2nd inactive signaling enzyme $\frac{d \mathrm{E2}}{d \mathrm{time}}=\mathrm{delta\_E2\_E2\_\_inactivation}+\mathrm{delta\_E2\_E1\_\_E2\_binding}$ P2 2nd deactivating enzyme $\frac{d \mathrm{P2}}{d \mathrm{time}}=\mathrm{delta\_P2\_E2\_\_inactivation}+\mathrm{delta\_P2\_E2\_\_P2\_binding}$ E1_P1 transition complex between an active substrate and its deactivating enzyme $\frac{d \mathrm{E1\_P1}}{d \mathrm{time}}=\mathrm{delta\_E1\_P1\_E1\_\_P1\_binding}+\mathrm{delta\_E1\_P1\_E1\_\_inactivation}$ E2_P2 transition complex between an active substrate and its deactivating enzyme $\frac{d \mathrm{E2\_P2}}{d \mathrm{time}}=\mathrm{delta\_E2\_P2\_E2\_\_P2\_binding}+\mathrm{delta\_E2\_P2\_E2\_\_inactivation}$ E3_ 3rd activated signaling enzyme $\frac{d \mathrm{E3\_}}{d \mathrm{time}}=\mathrm{delta\_E3\_\_E3\_activation}+\mathrm{delta\_E3\_\_E4\_activation}+\mathrm{delta\_E3\_\_E3\_P3\_binding}+\mathrm{delta\_E3\_\_E3\_\_E4\_binding}$ E3 3rd inactive signaling enzyme $\frac{d \mathrm{E3}}{d \mathrm{time}}=\mathrm{delta\_E3\_E3\_\_inactivation}+\mathrm{delta\_E3\_E2\_\_E3\_binding}$ E3_P3 transition complex between an active substrate and its deactivating enzyme $\frac{d \mathrm{E3\_P3}}{d \mathrm{time}}=\mathrm{delta\_E3\_P3\_E3\_P3\_binding}+\mathrm{delta\_E3\_P3\_E3\_\_inactivation}$ P3 3rd deactivating enzyme $\frac{d \mathrm{P3}}{d \mathrm{time}}=\mathrm{delta\_P3\_E3\_\_inactivation}+\mathrm{delta\_P3\_E3\_P3\_binding}$ E4 4th inactive signaling enzyme $\frac{d \mathrm{E4}}{d \mathrm{time}}=\mathrm{delta\_E4\_E4\_\_inactivation}+\mathrm{delta\_E4\_E3\_\_E4\_binding}$ E4_P4 transition complex between an active substrate and its deactivating enzyme $\frac{d \mathrm{E4\_P4}}{d \mathrm{time}}=\mathrm{delta\_E4\_P4\_E4\_\_P4\_binding}+\mathrm{delta\_E4\_P4\_E4\_\_inactivation}$ P4 4th deactivating enzyme $\frac{d \mathrm{P4}}{d \mathrm{time}}=\mathrm{delta\_P4\_E4\_\_inactivation}+\mathrm{delta\_P4\_E4\_\_P4\_binding}$ E5_ 5th activated signaling enzyme $\frac{d \mathrm{E5\_}}{d \mathrm{time}}=\mathrm{delta\_E5\_\_E5\_activation}+\mathrm{delta\_E5\_\_E5\_\_P5\_binding}$ E5 5th inactive signaling enzyme $\frac{d \mathrm{E5}}{d \mathrm{time}}=\mathrm{delta\_E5\_E5\_\_inactivation}+\mathrm{delta\_E5\_E4\_\_E5\_binding}$ P5 5th deactivating enzyme $\frac{d \mathrm{P5}}{d \mathrm{time}}=\mathrm{delta\_P5\_E5\_\_inactivation}+\mathrm{delta\_P5\_E5\_\_P5\_binding}$ E5_P5 transition complex between an active substrate and its deactivating enzyme $\frac{d \mathrm{E5\_P5}}{d \mathrm{time}}=\mathrm{delta\_E5\_P5\_E5\_\_P5\_binding}+\mathrm{delta\_E5\_P5\_E5\_\_inactivation}$ A1A2 adaptor heterodimer $\frac{d \mathrm{A1A2}}{d \mathrm{time}}=\mathrm{delta\_A1A2\_receptor\_adaptors\_complex\_syn2}+\mathrm{delta\_A1A2\_adaptor\_heterodimer\_syn}$ E2_E4_ transition complex in feedback mediated by enzyme E4_ $\frac{d \mathrm{E2\_E4\_}}{d \mathrm{time}}=\mathrm{delta\_E2\_E4\_\_E2\_E4\_\_syn}+\mathrm{delta\_E2\_E4\_\_E2\_E4\_\_desyn}$ E0_E1 transition complex between an inactive substrate and its activator $\frac{d \mathrm{E0\_E1}}{d \mathrm{time}}=\mathrm{delta\_E0\_E1\_E0\_\_E1\_binding}+\mathrm{delta\_E0\_E1\_E1\_activation}$ E1_E2 transition complex between an inactive substrate and its activator $\frac{d \mathrm{E1\_E2}}{d \mathrm{time}}=\mathrm{delta\_E1\_E2\_E1\_\_E2\_binding}+\mathrm{delta\_E1\_E2\_E2\_activation}$ E2_E3 transition complex between an inactive substrate and its activator $\frac{d \mathrm{E2\_E3}}{d \mathrm{time}}=\mathrm{delta\_E2\_E3\_E2\_\_E3\_binding}+\mathrm{delta\_E2\_E3\_E3\_activation}$ E3_E4 transition complex between an inactive substrate and its activator $\frac{d \mathrm{E3\_E4}}{d \mathrm{time}}=\mathrm{delta\_E3\_E4\_E3\_\_E4\_binding}+\mathrm{delta\_E3\_E4\_E4\_activation}$ E4_E5 transition complex between an inactive substrate and its activator $\frac{d \mathrm{E4\_E5}}{d \mathrm{time}}=\mathrm{delta\_E4\_E5\_E4\_\_E5\_binding}+\mathrm{delta\_E4\_E5\_E5\_activation}$ $\mathrm{rate}=\mathrm{k\_forward}LR+-(\mathrm{k\_reverse}C)$ $\mathrm{rate}=\mathrm{k2}\mathrm{C2}+-(\mathrm{k2\_}\mathrm{C\_})$ $\mathrm{rate}=\mathrm{k3}\mathrm{C\_}\mathrm{A1}+-(\mathrm{k3\_}\mathrm{C\_A1})$ $\mathrm{rate}=\mathrm{k4}\mathrm{A2}\mathrm{C\_A1}+-(\mathrm{k4\_}\mathrm{E0\_})$ $\mathrm{rate}=\mathrm{k5}\mathrm{C\_}\mathrm{A1A2}+-(\mathrm{k5\_}\mathrm{E0\_})$ $\mathrm{rate}=\mathrm{k6}\mathrm{A1A2}+-(\mathrm{k6\_}\mathrm{A1}\mathrm{A2})$ $\mathrm{rate}=\mathrm{k7}\mathrm{E0\_}\mathrm{E4\_}+-(\mathrm{k7\_}\mathrm{E0\_E4\_})$ $\mathrm{rate}=\mathrm{k8}\mathrm{E0\_E4\_}$ $\mathrm{rate}=\mathrm{k9}\mathrm{P1}\mathrm{E1\_}+-(\mathrm{k9\_}\mathrm{E1\_P1})$ $\mathrm{rate}=\mathrm{k10}\mathrm{E1\_P1}$ $\mathrm{rate}=\mathrm{k11}\mathrm{E2\_P2}$ $\mathrm{rate}=\mathrm{k12}\mathrm{E2\_}\mathrm{P2}+-(\mathrm{k12\_}\mathrm{E2\_P2})$ $\mathrm{rate}=\mathrm{k13}\mathrm{E2\_}\mathrm{E4\_}+-(\mathrm{k13\_}\mathrm{E2\_E4\_})$ $\mathrm{rate}=\mathrm{k14}\mathrm{E2\_E4\_}$ $\mathrm{rate}=\mathrm{k15}\mathrm{E3\_P3}$ $\mathrm{rate}=\mathrm{k16}\mathrm{E3\_}\mathrm{P3}+-(\mathrm{k16\_}\mathrm{E3\_P3})$ $\mathrm{rate}=\mathrm{k17}\mathrm{E4\_P4}$ $\mathrm{rate}=\mathrm{k18}\mathrm{E4\_}\mathrm{P4}+-(\mathrm{k18\_}\mathrm{E4\_P4})$ $\mathrm{rate}=\mathrm{k19}\mathrm{E5\_P5}$ $\mathrm{rate}=\mathrm{k20}\mathrm{E5\_}\mathrm{P5}+-(\mathrm{k20\_}\mathrm{E5\_P5})$ $\mathrm{rate}=\mathrm{k21}\mathrm{E1}\mathrm{E0\_}+-(\mathrm{k21\_}\mathrm{E0\_E1})$ $\mathrm{rate}=\mathrm{k22}\mathrm{E0\_E1}$ $\mathrm{rate}=\mathrm{k23}\mathrm{E1\_E2}$ $\mathrm{rate}=\mathrm{k24}\mathrm{E3}\mathrm{E2\_}+-(\mathrm{k24\_}\mathrm{E2\_E3})$ $\mathrm{rate}=\mathrm{k25}\mathrm{E2\_E3}$ $\mathrm{rate}=\mathrm{k26}\mathrm{E4}\mathrm{E3\_}+-(\mathrm{k26\_}\mathrm{E3\_E4})$ $\mathrm{rate}=\mathrm{k27}\mathrm{E3\_E4}$ $\mathrm{rate}=\mathrm{k28}\mathrm{E4\_}\mathrm{E5}+-(\mathrm{k28\_}\mathrm{E4\_E5})$ $\mathrm{rate}=\mathrm{k29}\mathrm{E4\_E5}$ $\mathrm{rate}=\mathrm{k30}\mathrm{E1\_}\mathrm{E2}+-(\mathrm{k30\_}\mathrm{E1\_E2})$