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Model Mathematics

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Component: environment

Component: differentials

\frac{d}{d time} (A) = - (A2 + A3 + A5) \frac{d}{d time} (G) = D1 - T1 \frac{d}{d time} (GA) = D2 - R4 \frac{d}{d time} (T) = - (T1 + T3 + T4) \frac{d}{d time} (R) = - (R2 + R3 + R4) \frac{d}{d time} (GT) = T1 - P1 - R2 - A2 \frac{d}{d time} (GD) = P1 - D1 - A3 - R3 \frac{d}{d time} (Pi_) = P1 + P3 + P2 + P4 \frac{d}{d time} (D) = D1 + D3 + D2 + D4 \frac{d}{d time} (RG) = (- T3) + D3 \frac{d}{d time} (RGT) = T3 + R2 - P3 - A5 \frac{d}{d time} (GAT) = A2 - P2 \frac{d}{d time} (GAD) = A3 + P2 - D2 \frac{d}{d time} (RGD) = R3 + P3 - D3 \frac{d}{d time} (RGA) = (R4 - T4) + D4 \frac{d}{d time} (RGAT) = T4 + A5 - P4 \frac{d}{d time} (RGAD) = P4 - D4

Component: output

Z = \frac{GT + RGT + RGAT + GAT}{G_tot} v = \frac{P_minus4 RGAT + P_minus2 GAT + P_minus3 RGT + P_minus1 GT}{G_tot}

Component: T1

T1 = k1 G T

Component: P1

P1 = k1 GT

Component: D1

D1 = k1 GD

Component: T3

T3 = k1 RG T

Component: R2

R2 = (- k2) RGT

Component: A2

A2 = k1 GT A

Component: A3

A3 = (- k2) GAD

Component: R3

R3 = k1 GD R

Component: P3

P3 = k1 RGT

Component: D3

D3 = k1 RGD

Component: P2

P2 = k1 GAT

Component: D2

D2 = k1 GAD

Component: R4

R4 = k1 GA R

Component: T4

T4 = k1 RGA T

Component: A5

A5 = k1 RGT A

Component: P4

P4 = k1 RGAT

Component: D4

D4 = k1 RGAD

Source: Derived from workspace Maurya et al. 2005 at changeset ef66087f6377.

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Reduced-order modelling of biochemical networks: application to the GTPase-cycle signalling module