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Model Mathematics

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Component: environment

Component: MP

\frac{d}{d time} (MP) = vsP \frac{{BN}^{n}}{{KAP}^{n} + {BN}^{n}} - (vmP \frac{MP}{KmP + MP} + kdmp MP) vsP = vstot

Component: MC

\frac{d}{d time} (MC) = vsC \frac{{BN}^{n}}{{KAC}^{n} + {BN}^{n}} - (vmC \frac{MC}{KmC + MC} + kdmc MC) vsC = 0.8 vstot

Component: MB

\frac{d}{d time} (MB) = vsB \frac{{KIB}^{m}}{{KIB}^{m} + {BN}^{m}} - (vmB \frac{MB}{KmB + MB} + kdmb MB) vsB = 0.7 vstot

Component: PC

\frac{d}{d time} (PC) = ksP MP + V2P \frac{PCP}{Kdp + PCP} + k4 PCC - (V1P \frac{PC}{Kp + PC} + k3 PC CC + kdn PC)

Component: CC

\frac{d}{d time} (CC) = ksC MC + V2C \frac{CCP}{Kdp + CCP} + k4 PCC - (V1C \frac{CC}{Kp + CC} + k3 PC CC + kdnc CC)

Component: PCP

\frac{d}{d time} (PCP) = V1P \frac{PC}{Kp + PC} - (V2P \frac{PCP}{Kdp + PCP} + vdPC \frac{PCP}{Kd + PCP} + kdn PCP)

Component: CCP

\frac{d}{d time} (CCP) = V1C \frac{CC}{Kp + CC} - (V2C \frac{CCP}{Kdp + CCP} + vdCC \frac{CCP}{Kd + CCP} + kdn CCP)

Component: PCC

\frac{d}{d time} (PCC) = V2PC \frac{PCCP}{Kdp + PCCP} + k3 PC CC + k2 PCN - (V1PC \frac{PCC}{Kp + PCC} + k4 PCC + k1 PCC + kdn PCC)

Component: PCN

\frac{d}{d time} (PCN) = V4PC \frac{PCNP}{Kdp + PCNP} + k1 PCC + k8 IN - (V3PC \frac{PCN}{Kp + PCN} + k2 PCN + k7 BN PCN + kdn PCN)

Component: PCCP

\frac{d}{d time} (PCCP) = V1PC \frac{PCC}{Kp + PCC} - (V2PC \frac{PCCP}{Kdp + PCCP} + vdPCC \frac{PCCP}{Kd + PCCP} + kdn PCCP)

Component: PCNP

\frac{d}{d time} (PCNP) = V3PC \frac{PCN}{Kp + PCN} - (V4PC \frac{PCNP}{Kdp + PCNP} + vdPCN \frac{PCNP}{Kd + PCNP} + kdn PCNP)

Component: BC

\frac{d}{d time} (BC) = V2B \frac{BCP}{Kdp + BCP} + k6 BN + ksB MB - (V1B \frac{BC}{Kp + BC} + k5 BC + kdn BC)

Component: BCP

\frac{d}{d time} (BCP) = V1B \frac{BC}{Kp + BC} - (V2B \frac{BCP}{Kdp + BCP} + vdBC \frac{BCP}{Kd + BCP} + kdn BCP)

Component: BN

\frac{d}{d time} (BN) = V4B \frac{BNP}{Kdp + BNP} + k5 BC + k8 IN - (V3B \frac{BN}{Kp + BN} + k6 BN + k7 BN PCN + kdn BN)

Component: BNP

\frac{d}{d time} (BNP) = V3B \frac{BN}{Kp + BN} - (V4B \frac{BNP}{Kdp + BNP} + vdBN \frac{BNP}{Kd + BNP} + kdn BNP)

Component: IN

\frac{d}{d time} (IN) = k7 BN PCN - (k8 IN + vdIN \frac{IN}{Kd + IN} + kdn IN)

Component: model_parameters

ksB = kstot ksC = kstot ksP = 0.5 kstot V1P = Vphos V1PC = Vphos V3PC = Vphos

Source: Derived from workspace Leloup, Goldbeter, 2004 at changeset e12c13b3c70b.

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Modeling the mammalian circadian clock: sensitivity analysis and multiplicity of oscillatory mechanisms