Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms Catherine Lloyd Auckland Bioengineering Institute, The University of Auckland
Model Status This CellML model runs in OpenCell to recreate the published results (figure 2C from the published paper). The model needs to be run for 160 hours with a step size of 0.1 hours, and MP, MB and MC are plotted. Ignore the first couple of oscillations as the model needs to stabilise. Also please note that in the version of the model presented here, parameter set 4 from the original paper has been used. The units have been checked and they are consistent.
$\frac{d \mathrm{MP}}{d \mathrm{time}}}=\mathrm{vsP}\frac{\mathrm{BN}^{n}}{\mathrm{KAP}^{n}+\mathrm{BN}^{n}}-\mathrm{vmP}\frac{\mathrm{MP}}{\mathrm{KmP}+\mathrm{MP}}+\mathrm{kdmp}\mathrm{MP}\mathrm{vsP}=\mathrm{vstot}$ $\frac{d \mathrm{MC}}{d \mathrm{time}}}=\mathrm{vsC}\frac{\mathrm{BN}^{n}}{\mathrm{KAC}^{n}+\mathrm{BN}^{n}}-\mathrm{vmC}\frac{\mathrm{MC}}{\mathrm{KmC}+\mathrm{MC}}+\mathrm{kdmc}\mathrm{MC}\mathrm{vsC}=0.8\mathrm{vstot}$ $\frac{d \mathrm{MB}}{d \mathrm{time}}}=\mathrm{vsB}\frac{\mathrm{KIB}^{m}}{\mathrm{KIB}^{m}+\mathrm{BN}^{m}}-\mathrm{vmB}\frac{\mathrm{MB}}{\mathrm{KmB}+\mathrm{MB}}+\mathrm{kdmb}\mathrm{MB}\mathrm{vsB}=0.7\mathrm{vstot}$ $\frac{d \mathrm{PC}}{d \mathrm{time}}}=\mathrm{ksP}\mathrm{MP}+\mathrm{V2P}\frac{\mathrm{PCP}}{\mathrm{Kdp}+\mathrm{PCP}}+\mathrm{k4}\mathrm{PCC}-\mathrm{V1P}\frac{\mathrm{PC}}{\mathrm{Kp}+\mathrm{PC}}+\mathrm{k3}\mathrm{PC}\mathrm{CC}+\mathrm{kdn}\mathrm{PC}$ $\frac{d \mathrm{CC}}{d \mathrm{time}}}=\mathrm{ksC}\mathrm{MC}+\mathrm{V2C}\frac{\mathrm{CCP}}{\mathrm{Kdp}+\mathrm{CCP}}+\mathrm{k4}\mathrm{PCC}-\mathrm{V1C}\frac{\mathrm{CC}}{\mathrm{Kp}+\mathrm{CC}}+\mathrm{k3}\mathrm{PC}\mathrm{CC}+\mathrm{kdnc}\mathrm{CC}$ $\frac{d \mathrm{PCP}}{d \mathrm{time}}}=\mathrm{V1P}\frac{\mathrm{PC}}{\mathrm{Kp}+\mathrm{PC}}-\mathrm{V2P}\frac{\mathrm{PCP}}{\mathrm{Kdp}+\mathrm{PCP}}+\mathrm{vdPC}\frac{\mathrm{PCP}}{\mathrm{Kd}+\mathrm{PCP}}+\mathrm{kdn}\mathrm{PCP}$ $\frac{d \mathrm{CCP}}{d \mathrm{time}}}=\mathrm{V1C}\frac{\mathrm{CC}}{\mathrm{Kp}+\mathrm{CC}}-\mathrm{V2C}\frac{\mathrm{CCP}}{\mathrm{Kdp}+\mathrm{CCP}}+\mathrm{vdCC}\frac{\mathrm{CCP}}{\mathrm{Kd}+\mathrm{CCP}}+\mathrm{kdn}\mathrm{CCP}$ $\frac{d \mathrm{PCC}}{d \mathrm{time}}}=\mathrm{V2PC}\frac{\mathrm{PCCP}}{\mathrm{Kdp}+\mathrm{PCCP}}+\mathrm{k3}\mathrm{PC}\mathrm{CC}+\mathrm{k2}\mathrm{PCN}-\mathrm{V1PC}\frac{\mathrm{PCC}}{\mathrm{Kp}+\mathrm{PCC}}+\mathrm{k4}\mathrm{PCC}+\mathrm{k1}\mathrm{PCC}+\mathrm{kdn}\mathrm{PCC}$ $\frac{d \mathrm{PCN}}{d \mathrm{time}}}=\mathrm{V4PC}\frac{\mathrm{PCNP}}{\mathrm{Kdp}+\mathrm{PCNP}}+\mathrm{k1}\mathrm{PCC}+\mathrm{k8}\mathrm{IN}-\mathrm{V3PC}\frac{\mathrm{PCN}}{\mathrm{Kp}+\mathrm{PCN}}+\mathrm{k2}\mathrm{PCN}+\mathrm{k7}\mathrm{BN}\mathrm{PCN}+\mathrm{kdn}\mathrm{PCN}$ $\frac{d \mathrm{PCCP}}{d \mathrm{time}}}=\mathrm{V1PC}\frac{\mathrm{PCC}}{\mathrm{Kp}+\mathrm{PCC}}-\mathrm{V2PC}\frac{\mathrm{PCCP}}{\mathrm{Kdp}+\mathrm{PCCP}}+\mathrm{vdPCC}\frac{\mathrm{PCCP}}{\mathrm{Kd}+\mathrm{PCCP}}+\mathrm{kdn}\mathrm{PCCP}$ $\frac{d \mathrm{PCNP}}{d \mathrm{time}}}=\mathrm{V3PC}\frac{\mathrm{PCN}}{\mathrm{Kp}+\mathrm{PCN}}-\mathrm{V4PC}\frac{\mathrm{PCNP}}{\mathrm{Kdp}+\mathrm{PCNP}}+\mathrm{vdPCN}\frac{\mathrm{PCNP}}{\mathrm{Kd}+\mathrm{PCNP}}+\mathrm{kdn}\mathrm{PCNP}$ $\frac{d \mathrm{BC}}{d \mathrm{time}}}=\mathrm{V2B}\frac{\mathrm{BCP}}{\mathrm{Kdp}+\mathrm{BCP}}+\mathrm{k6}\mathrm{BN}+\mathrm{ksB}\mathrm{MB}-\mathrm{V1B}\frac{\mathrm{BC}}{\mathrm{Kp}+\mathrm{BC}}+\mathrm{k5}\mathrm{BC}+\mathrm{kdn}\mathrm{BC}$ $\frac{d \mathrm{BCP}}{d \mathrm{time}}}=\mathrm{V1B}\frac{\mathrm{BC}}{\mathrm{Kp}+\mathrm{BC}}-\mathrm{V2B}\frac{\mathrm{BCP}}{\mathrm{Kdp}+\mathrm{BCP}}+\mathrm{vdBC}\frac{\mathrm{BCP}}{\mathrm{Kd}+\mathrm{BCP}}+\mathrm{kdn}\mathrm{BCP}$ $\frac{d \mathrm{BN}}{d \mathrm{time}}}=\mathrm{V4B}\frac{\mathrm{BNP}}{\mathrm{Kdp}+\mathrm{BNP}}+\mathrm{k5}\mathrm{BC}+\mathrm{k8}\mathrm{IN}-\mathrm{V3B}\frac{\mathrm{BN}}{\mathrm{Kp}+\mathrm{BN}}+\mathrm{k6}\mathrm{BN}+\mathrm{k7}\mathrm{BN}\mathrm{PCN}+\mathrm{kdn}\mathrm{BN}$ $\frac{d \mathrm{BNP}}{d \mathrm{time}}}=\mathrm{V3B}\frac{\mathrm{BN}}{\mathrm{Kp}+\mathrm{BN}}-\mathrm{V4B}\frac{\mathrm{BNP}}{\mathrm{Kdp}+\mathrm{BNP}}+\mathrm{vdBN}\frac{\mathrm{BNP}}{\mathrm{Kd}+\mathrm{BNP}}+\mathrm{kdn}\mathrm{BNP}$ $\frac{d \mathrm{IN}}{d \mathrm{time}}}=\mathrm{k7}\mathrm{BN}\mathrm{PCN}-\mathrm{k8}\mathrm{IN}+\mathrm{vdIN}\frac{\mathrm{IN}}{\mathrm{Kd}+\mathrm{IN}}+\mathrm{kdn}\mathrm{IN}$ $\mathrm{ksB}=\mathrm{kstot}\mathrm{ksC}=\mathrm{kstot}\mathrm{ksP}=0.5\mathrm{kstot}\mathrm{V1P}=\mathrm{Vphos}\mathrm{V1PC}=\mathrm{Vphos}\mathrm{V3PC}=\mathrm{Vphos}$ MPPer mRNAPCcytosolic non-phosphorylated PER protein2007-08-14T00:00:00+00:00CCcytosolic non-phosphorylated CRY proteinPCNPnuclear phosphorylated PER-CRY protein complexAuckland Bioengineering InstituteThe University of AucklandPCCcytosolic non-phosphorylated PER-CRY protein complexBNPnuclear phosphorylated BMAL1 proteinAlbertGoldbeter2004-10-21CCPcytosolic phosphorylated CRY proteinBCcytosolic non-phosphorylated BMAL1 proteinPCPcytosolic phosphorylated PER proteinModeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms230541562This is a CellML description of Leloup and Goldbeter's 2004 mathematical model of the mammalian circadian clock.c.lloyd@auckland.ac.nzCatherineLloydMayCatherine Lloyd10010000The University of Auckland, Auckland Bioengineering InstituteJean-ChristopheLeloupMCCry mRNAkeywordINnuclear inactive complex between PER-CRY and CLOCK-BMAL1PCCPcytosolic phosphorylated PER-CRY protein complexBCPcytosolic phosphorylated BMAL1 proteinLeloup and Goldbeter's 2004 mathematical model of the mammalian circadian clock.MBBmal1 mRNAJournal of Thoretical BiologyPCNBNnuclear non-phosphorylated PER-CRY protein complexnuclear non-phosphorylated BMAL1 proteincircadian rhythmssignal transductionclock15363675