You are here: Home / Exposures / Goldbeter, Pourquie, 2008 / Modeling the segmentation clock as a network of coupled oscillations in the Notch, Wnt and FGF signaling pathways: uncoupled Notch, Wnt and FGF signalling pathways

Model Mathematics

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Component: environment

Component: N

\frac{d}{d time} (N) = epsilon (vsN - (vdN \frac{N}{KdN + N} + kc N \frac{{KIF}^{j}}{{KIF}^{j} + F^{j}}))

Component: Na

\frac{d}{d time} (Na) = epsilon (kc N \frac{{KIF}^{j}}{{KIF}^{j} + F^{j}} - (VdNa \frac{Na}{KdNa + Na} + Vtr))

Vtr = kt1 Na - (kt2 Nan)

Component: Nan

\frac{d}{d time} (Nan) = epsilon (Vtr - (VdNan \frac{Nan}{KdNan + Nan}))

Component: MF

\frac{d}{d time} (MF) = epsilon (vsF \frac{{Nan}^{p}}{{KA}^{p} + {Nan}^{p}} - (vmF \frac{MF}{KdMF + MF}))

Component: F

\frac{d}{d time} (F) = epsilon (ksF MF - (vdF \frac{F}{KdF + F}))

Component: K

\frac{d}{d time} (K) = theta V1

Component: B

\frac{d}{d time} (B) = theta (vsB + VP + V2 - (VK \frac{AK}{Kt} + kd1 B))

Component: Bp

\frac{d}{d time} (Bp) = theta (VK \frac{AK}{Kt} - (VP + kd2 Bp))

Component: BN

\frac{d}{d time} (BN) = - (theta V2)

Component: MAx

\frac{d}{d time} (MAx) = theta (v0 + vMB \frac{{BN}^{n}}{{KaB}^{n} + {BN}^{n}} - (vmd \frac{MAx}{Kmd + MAx}))

Component: A

\frac{d}{d time} (A) = theta (ksAx MAx + V1 - (vdAx \frac{A}{KdAx + A}))

Component: Wnt_parameters

AK = Kt - K

V1 = d1 AK - (a1 A K)

V2 = kt4 BN - (kt3 B)

VK = VMK \frac{KID}{KID + D} \frac{B}{K1 + B}

VP = VMP \frac{Bp}{K2 + Bp}

Component: Rasa

\frac{d}{d time} (Rasa) = eta (VaRas - VdRas)

Component: ERKa

\frac{d}{d time} (ERKa) = eta (VaErk - VdErk)

Component: Xa

\frac{d}{d time} (Xa) = eta (VaX - VdX)

Component: MDusp

\frac{d}{d time} (MDusp) = eta (VsMDusp - VdMDusp)

Component: Dusp

\frac{d}{d time} (Dusp) = eta (ksDusp MDusp - (vdDusp \frac{Dusp}{KdDusp + Dusp}))

Component: FGF_parameters

Rasi = Rast - Rasa

VaRas = VMaRas \frac{{Fgf}^{r}}{{KaFgf}^{r} + {Fgf}^{r}} \frac{Rasi}{KaRas + Rasi}

VdRas = VMdRas \frac{Rasa}{KdRas + Rasa}

ERKi = ERKt - ERKa

VaErk = VMaErk \frac{Rasa}{Rast} \frac{ERKi}{KaErk + ERKi}

VdErk = kcDusp Dusp \frac{ERKa}{KdErk + ERKa}

Xi = Xt - Xa

VaX = VMaX \frac{ERKa}{ERKt} \frac{Xi}{KaX + Xi}

VdX = VMdX \frac{Xa}{KdX + Xa}

VsMDusp = VMsMDusp \frac{{Xa}^{q}}{{KaMDusp}^{q} + {Xa}^{q}}

VdMDusp = VMdMDusp \frac{MDusp}{KdMDusp + MDusp}

Component: model_parameters

Source: Derived from workspace Goldbeter, Pourquie, 2008 at changeset 1de828a08739.

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