You are here: Home / Exposures / Wolf, Sohn, Heinrich, Kuriyama, 2001 / Mathematical analysis of a mechanism for autonomous metabolic oscillations in continuous culture of Saccharomyces cerevisae

Model Mathematics

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Component: environment

Component: S1

\frac{d}{d time} (S1) = v8 - v9

Component: S

S2 = S - S1

Component: sul

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

Component: aps

\frac{d}{d time} (aps) = v2 - v3

Component: pap

\frac{d}{d time} (pap) = v3 - v4

Component: hyd

\frac{d}{d time} (hyd) = v4 - (v5 + v17)

Component: cys

\frac{d}{d time} (cys) = v5 - v6

Component: eth

\frac{d}{d time} (eth) = v13 - v7

Component: aco

\frac{d}{d time} (aco) = v7 - (v8 + v15)

Component: oxy

\frac{d}{d time} (oxy) = v10 - (v11A + v14)

Component: A3_c

\frac{d}{d time} (A3_c) = v16 - (v2 + v3 + v12)

Component: A3_m

\frac{d}{d time} (A3_m) = v11B - v16

Component: A_c

A2_c = A_c - A3_c

Component: A_m

A2_m = A_m - A3_m

Component: N2

\frac{d}{d time} (N2) = 2 v7 + 4 v9 - (3 v4 + v11A)

Component: N

N1 = N - N2

Component: oah

\frac{d}{d time} (oah) = v15 - (v5 + v18)

Component: v1

v1 = v0 f1 f1 = {(1 + {(\frac{cys}{Kc})}^{n})}^{- 1}

Component: v2

v2 = k2 sul A3_c

Component: v3

v3 = k3 aps A3_c

Component: v4

v4 = k4 pap N2

Component: v5

v5 = k5 hyd oah

Component: v6

v6 = k6 cys

Component: v7

v7 = k7 eth N1

Component: v8

v8 = k8 aco S2

Component: v9

v9 = k9 S1 N1

Component: v10

Component: v11A

v11A = \frac{k11 N2 oxy f2}{alpha N2 + oxy} f2 = {(1 + {(\frac{hyd}{KH})}^{m})}^{- 1}

Component: v11B

v11B = \frac{3 v11A A2_m}{KA + A2_m}

Component: v12

v12 = k12 A3_c

Component: v13

Component: v14

v14 = k14 oxy

Component: v15

v15 = k15 aco

Component: v16

v16 = k16 A3_m A2_c

Component: v17

v17 = k17 hyd

Component: v18

v18 = k18 oah

Source: Derived from workspace Wolf, Sohn, Heinrich, Kuriyama, 2001 at changeset 3a6924b88a89.

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Mathematical analysis of a mechanism for autonomous metabolic oscillations in continuous culture of Saccharomyces cerevisae