You are here: Home / Exposures / Brightman, Fell, 2000 / Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells.

Model Mathematics

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Component: environment

Component: Rs

\frac{d}{d time} (Rs) = v3 - v1

Component: RL

\frac{d}{d time} (RL) = v1 - v2 - v4

Component: Ri

\frac{d}{d time} (Ri) = v2 + v3 + v6

Component: L

\frac{d}{d time} (L) = - v1

Component: R2L2

\frac{d}{d time} (R2L2) = v4 - v5 - v7

Component: R2_CPP

\frac{d}{d time} (R2_CPP) = v7 - v8

Component: Li

\frac{d}{d time} (Li) = v2 + v6

Component: R2i

\frac{d}{d time} (R2i) = v5 + v8 - v6

Component: Shc

\frac{d}{d time} (Shc) = v10 - v9

Component: ShcP

\frac{d}{d time} (ShcP) = v27 - v10 - v11

Component: ShcGS

\frac{d}{d time} (ShcGS) = v13 + v11 - v27 - v12

Component: GS

\frac{d}{d time} (GS) = v28 - v11

Component: GSP

\frac{d}{d time} (GSP) = v27 - v28

Component: RasGDP

\frac{d}{d time} (RasGDP) = v15 - v12

Component: Ras_ShcGS

\frac{d}{d time} (Ras_ShcGS) = v12 - v13

Component: RasGTP

\frac{d}{d time} (RasGTP) = v13 + v17 - v14 - v16

Component: GAP

\frac{d}{d time} (GAP) = v15 - v14

Component: Ras_GAP

\frac{d}{d time} (Ras_GAP) = v14 - v15

Component: Raf

\frac{d}{d time} (Raf) = v18 - v16

Component: Ras_Raf

\frac{d}{d time} (Ras_Raf) = v16 - v17

Component: Rafa

\frac{d}{d time} (Rafa) = v17 - v19 - v21 - v18

Component: MEK

\frac{d}{d time} (MEK) = v20 - v19

Component: MEKP

\frac{d}{d time} (MEKP) = v19 + v22 - v20 - v21

Component: MEKPP

\frac{d}{d time} (MEKPP) = v21 - v22

Component: ERK

\frac{d}{d time} (ERK) = v24 - v23

Component: ERKP

\frac{d}{d time} (ERKP) = v23 + v26 - v24 - v25

Component: ERKPP

\frac{d}{d time} (ERKPP) = v25 - v26

Component: t

\frac{d}{d time} (t) = v29

Component: X

\frac{d}{d time} (X) = v30

Component: v1

v1 = k1 Rs L - (kn1 RL)

Component: v2

v2 = f k2 (E + (1 - E) (1 - (ⅇ^{- ({(\frac{t}{DT})}^{3})}))) RL

Component: v3

v3 = k3 Ri - (f kn3 (E + (1 - E) (1 - (ⅇ^{- ({(\frac{t}{DT})}^{3})}))) Rs)

Component: v4

v4 = k4 RL RL - (k2_4 R2L2)

Component: v5

v5 = f k5 (E + (1 - E) (1 - (ⅇ^{- ({(\frac{t}{DT})}^{3})}))) R2L2

Component: v6

v6 = k6 (E + (1 - E) (1 - (ⅇ^{- ({(\frac{t}{DT})}^{3})}))) R2i

Component: v7

v7 = k7 f R2L2 - (kn7 R2_CPP)

Component: v8

v8 = k8 (E + (1 - E) (1 - (ⅇ^{- ({(\frac{t}{DT})}^{3})}))) R2_CPP

Component: v9

v9 = \frac{k9 2 (R2L2 + R2i + R2_CPP) Shc}{K_9 + Shc}

Component: v10

v10 = \frac{V_10 ShcP}{K_10 + ShcP}

Component: v11

v11 = k11 ShcP GS - (kn11 ShcGS)

Component: v12

v12 = k12 RasGDP ShcGS - (kn12 Ras_ShcGS)

Component: v13

v13 = k_13 Ras_ShcGS

Component: v14

v14 = k14 RasGTP GAP - (kn14 Ras_GAP)

Component: v15

v15 = k15 Ras_GAP

Component: v16

v16 = k16 RasGTP Raf - (kn16 Ras_Raf)

Component: v17

v17 = k17 Ras_Raf

Component: v18

v18 = \frac{V_18 Rafa}{K_18 + Rafa}

Component: v19

v19 = \frac{Rafa MEK k19}{K_19 + MEK}

Component: v20

v20 = \frac{V_20 MEKP}{K_20 + MEKP}

Component: v21

v21 = \frac{Rafa MEKP k21}{K_21 + MEKP}

Component: v22

v22 = \frac{V_22 MEKPP}{K_22 + MEKPP}

Component: v23

v23 = \frac{k23 ERK (MEKP + MEKPP)}{K_23 + ERK}

Component: v24

v24 = \frac{V_24 ERKP}{K_24 + ERKP}

Component: v25

v25 = \frac{k25 ERKP (MEKP + MEKPP)}{K_25 + ERKP}

Component: v26

v26 = \frac{V_26 ERKPP}{K_26 + ERKPP}

Component: v27

v27 = \frac{ERKPP ShcGS k27}{K_27 + ShcGS}

Component: v28

v28 = \frac{V_28 GSP}{K_28 + GSP}

Component: v29

v29 = v_1

Component: v30

v30 = k_11 t

Source: Derived from workspace Brightman, Fell, 2000 at changeset f8341eba65d2.

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Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells.