Table S1 Mathematical equations of the artificial network.10.1007/s00449-012-0789... · Table S1...

14
Table S1 Mathematical equations of the artificial network. Binding Phase total [E] [E] [E:ATP:P:R] total [R] [R] [P:R] [E:ATP:P:R] [E-AMP:R] [R:Pr] total [Pr] [Pr] [R:Pr] total [E-AMP] [E-AMP] [E-AMP:R] 1 [P:R] Kb [P][R] 2 [E:ATP:P:R] Kb [E][ATP][P:R] 3 [E-AMP:R] Kb [E-AMP][R] 4 [R:Pr] Kb [R][Pr] Reaction Phase 1 total 2 1 2 d[P] [S] [P] =Q [E] Q dt Kmich +[S] Kmich +[P] 1 1 total d[mRNA(E)] [R:Pr] km [Gene(E)] kmd [mRNA(E)] dt [Pr] total 1 2 1 1 total d[E] =kp [mRNA(E)] kx [E-AMP:R] kx [E:ATP:P:R] kpd [E] dt total 1 2 2 total d[E-AMP] kx [E:ATP:P:R] kx [E-AMP:R] kpd [E-AMP] dt

Transcript of Table S1 Mathematical equations of the artificial network.10.1007/s00449-012-0789... · Table S1...

Page 1: Table S1 Mathematical equations of the artificial network.10.1007/s00449-012-0789... · Table S1 Mathematical equations of the artificial network. ... Reaction rate constant for E:

Table S1 Mathematical equations of the artificial network.

Binding Phase

total[E] [E] [E:ATP:P:R]

total[R] [R] [P:R] [E:ATP:P:R] [E-AMP:R] [R:Pr]

total[Pr] [Pr] [R:Pr]

total[E-AMP] [E-AMP] [E-AMP:R]

1[P:R] Kb [P][R]

2[E:ATP:P:R] Kb [E][ATP][P:R]

3[E-AMP:R] Kb [E-AMP][R]

4[R:Pr] Kb [R][Pr]

Reaction Phase

1 total 2

1 2

d[P] [S] [P]=Q [E] Q

dt Kmich +[S] Kmich +[P]

1 1

total

d[mRNA(E)] [R:Pr]km [Gene(E)] kmd [mRNA(E)]

dt [Pr]

total1 2 1 1 total

d[E]=kp [mRNA(E)] kx [E-AMP:R] kx [E:ATP:P:R] kpd [E]

dt

total1 2 2 total

d[E-AMP]kx [E:ATP:P:R] kx [E-AMP:R] kpd [E-AMP]

dt

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Table S2 Component list for the mathematical model of the artificial network.

Component Definition Concentration [M]

[E] Enzyme 3.373704x10-7

[R] Regulator protein 4.731668x10-8

[Pr] Promoter 1.324335x10-9

[E-AMP] Adenylylated enzyme 6.237807x10-8

[P:R] Product-regulator complex 1.265995x10-6

[E:ATP:P:R] Product-regulator complex-bound E 1.990329x10-9

[E-AMP:R] Regulator-bound E-AMP 3.482797x10-9

[R:Pr] Regulator-bound promoter 1.215665x10-9

[P] Product 9.872980x10-4

[mRNA(E)] mRNA of enzyme 1.215665x10-8

[E]total Total enzyme 3.393608x10-7

[E-AMP]total Total adenylylated enzyme 6.586087x10-8

[Gene(E)] Gene of enzyme 2.540000x10-9

(constant)

[ATP] Adenosine triphosphate 1.000000x10-3

(constant)

[R]total Total regulator 10-7

- 10-5

(constant)

[Pr]total Total promoter 2.540000x10-9

(constant)

[S] Substrate 1.000000x10-3

(constant)

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Table S3 Parameter list for the mathematical model of the artificial network.

Parameter Definition Value

Kb1 Binding constant between P and R 104 - 10

8 [M

-1]

Kb2 Binding constant between P:R, ATP and E 104 - 10

8 [M

-2]

Kb3 Binding constant between R and E-AMP 104 - 10

8 [M

-1]

Kb4 Binding constant between Pr and R 104 - 10

8 [M

-1]

kx1 Reaction rate constant for E:ATP:P:R 10-1

- 101 [min

-1]

kx2 Reaction rate constant for E-AMP:R 10-1

- 101 [min

-1]

kp1 Translation rate constant for mRNA(E) 1.000000 [min-1

]

kpd1 Degradation rate constant for Total E 3.000000x10-2

[min-1

]

kpd2 Degradation rate constant for Total E-AMP 3.000000x10-2

[min-1

]

km1 Transcription rate constant for Gene(E) by Pr 1.000000 [min-1

]

kmd1 Degradation rate constant for mRNA(E) 1.000000x10-1

[min-1

]

Q1 Reaction rate constant for the conversion from S to P 1.000000x104 [min

-1]

Q2 Reaction rate constant for efflux of P 5.950000x10-3

[min-1

]

Kmich1 Michaelis constant for the conversion from S toP 4.600000x10-4

[M]

Kmich2 Michaelis constant for efflux of P 1.540000x10-3

[M]

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Table S4 Mathematical equations of the E. coli ammonia assimilation system.

Binding Phase

total[ ] [ ] [NRI: ]glnAp1 glnAp1 glnAp1

total[ ] [ ] [NRI: ]glnLp glnLp glnLp

total 4[ ] [ ] [(NRI-P) : ]glnAp2 glnAp2 glnAp2

total[ ] [ ] [NR1-P: ]governor governor governor

total[ ] [ ] [NR1-P: ]glnKp glnKp glnKp

total[ ] [ ] [NR1-P: ]nacp nacp nacp

total[UTUR] [UTUR] [UTUR:Gln] [UTUR:αKG] [P2:UMP:UTUR:aKG]

[UTUR:Gln:P2-UMP] [GlnK:UMP:aKG:UTUR] [GlnK-UMP:Gln:UTUR]

[aKG:P2-UMP:Gln:UTUR] [αKG:P2:UMP:aKG:UTUR]

total[P1] [P1] [P1:P2] [P1:P2-UMP] [GS:AMP:P1:P2] [GS-AMP:P1:P2-UMP]

[GS-AMP:P1:GlnK-UMP] [GS:AMP:P1:GlnK] [GlnK-UMP:P1] [GlnK:P1]

[aKG:P2-UMP:P1] [GS-AMP:aKG:P2-UMP:P1]

total[P2] [P2] [P2:UMP:UTUR:aKG] [P1:P2] [GS:AMP:P1:P2] [NR2:P2]

[NR2-P:P2:ADP] [NR1-P:NR2:P2] [aKG:P2] [aKG:P2:UMP:aKG:UTUR]

total[P2-UMP] [P2-UMP] [UTUR:Gln:P2-UMP] [P1:P2-UMP] [GS-AMP:P1:P2-UMP]

[aKG:P2-UMP:P1] [aKG:P2-UMP:Gln:UTUR] [GS-AMP:aKG:P2-UMP:P1]

[aKG:P2-UMP]

total[GlnK] [GlnK] [GlnK:P1] [NR2:GlnK] [GS:AMP:P1:GlnK] [GlnK:UMP:aKG:UTUR]

[NR2-P:ADP:GlnK] [NR1-P:NR2:GlnK]

total[GlnK-UMP] [GlnK-UMP] [GlnK-UMP:P1] [GS-AMP:P1:GlnK-UMP]

[GlnK-UMP:Gln:UTUR]

total[NR2] [NR2] [NR2:P2] [NR2:ATP] [NR1-P:NR2:P2] [NR2:GlnK]

[NR1-P:NR2:GlnK]

total[NR2-P] [NR2-P] [NR2-P:P2:ADP] [NR1:NR2-P] [NR2-P:ADP:GlnK]

total[NR1] [NR1] [NR1:NR2-P] [NR1:AceP] [NR1: ] [NR1: ]glnAp1 glnLp

total 4[NR1-P] [NR1-P] [NR1-P:NR2:P2] 4 [(NR1-P) : ] [NR1-P:NR2:GlnK]

[NR1-P: ] [NR1-P: ] [NR1-P: ]

glnAp2

glnKp governor nacp

total[GS] [GS] [GS:AMP:PI:PII] [GS:AMP:PI:GlnK]

total[GS-AMP] [GS-AMP] [GS-AMP:P1:P2-UMP] [GS-AMP:P1:GlnK-UMP]

[GS-AMP:aKG:P2-UMP:P1]

1[UTUR:Gln] Kb [UTUR][Gln]

2[UTUR:aKG] Kb [UTUR][aKG]

3[P2:UMP:UTUR:aKG] Kb [UTUR:aKG][P2][UMP]

4[UTUR:Gln:P2-UMP] Kb [UTUR:Gln][P2-UMP]

5[P1:P2] Kb [P1][P2]

6[P1:P2-UMP] Kb [P1][P2-UMP]

7[GS:AMP:P1:P2] Kb [P1:P2][GS][AMP]

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8[GS-AMP:P1:P2-UMP] Kb [P1:P2-UMP][GS-AMP]

9[NR2:P2] Kb [NR2][P2]

10[NR2:ATP] Kb [NR2][ATP]

11[NR2-P:P2:ADP] Kb [P2][NR2-P][ADP]

12[NR1:NR2-P] Kb [NR1][NR2-P]

13[NR1:AceP] Kb [NR1][AceP]

14[NR1-P:NR2:P2] Kb [NR2:P2][NR1-P]

15[NR1: ] Kb [NR1][ ]glnAp1 glnAp1

16[NR1: ] Kb [NR1][ ]glnLp glnLp

4 4

4 17[(NR1-P) : ] Kb [NR1-P] [ ]glnAp2 glnAp2

18[GS-AMP:P1:GlnK-UMP] Kb [GlnK-UMP:P1][GS-AMP]

19[GS:AMP:P1:GlnK] Kb [GS][GlnK:P1][AMP]

20[NR2-P:ADP:GlnK] Kb [NR2-P][GlnK][ADP]

21[NR1-P:NR2:GlnK] Kb [NR1-P][NR2:GlnK]

22[GlnK:UMP:aKG:UTUR] Kb [GlnK][UTUR:aKG][UMP]

23[GlnK-UMP:Gln:UTUR] Kb [GlnK-UMP][UTUR:Gln]

24[GlnK-UMP:P1] Kb [GlnK-UMP][P1]

25[GlnK:P1] Kb [GlnK][P1]

26[NR1-P: ] Kb [NR1-P][ ]glnKp glnKp

27[NR1-P: ] Kb [NR1-P][ ]governor governor

28[NR2:GlnK] Kb [GlnK][NR2]

29[NR1-P: ] Kb [ ][NR1-P]nacp nacp

3 3

30[aKG:P2] Kb [aKG] [P2]

31[aKG:P2-UMP:P1] Kb [aKG:P2-UMP][P1]

32[GS-AMP:aKG:P2-UMP:P1] Kb [aKG:P2-UMP:P1][GS-AMP]

33[aKG:P2-UMP:Gln:UTUR]=Kb [aKG:P2-UMP][UTUR:Gln]

34[aKG:P2:UMP:aKG:UTUR] Kb [aKG:P2][UTUR:aKG][UMP]

3 3

35[aKG:P2-UMP] Kb [aKG] [P2-UMP]

Reaction Phase

41

total total

2 1

total

d[mRNA( )] [(NR1-P) : ] [NR1-P: ]km [ ] 1.3

dt [ ] [ ]

[NR1: ]km 1.0 [ ] kmd [mRNA( )]

[ ]

glnA glnAp2 governorglnA

glnAp2 governor

glnAp1glnA glnA

glnAp1

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3

total

44

total total

2

d[mRNA( )] [NR1: ]km 1.0 [ ]

dt [ ]

[(NR1-P) : ] [NR1-P: ]km [ ] 1.3

[ ] [ ]

kmd [mRNA( )]

glnG glnLpglnG

glnLp

glnAp2 governorglnG

glnAp2 governor

glnG

5

total

46

total total

3

d[mRNA( )] [NRI: ]km 1.0 [ ]

dt [ ]

[(NRI-P) : ] [NRI-P: ]km [ ] 1.3

[ ] [ ]

kmd [mRNA( )]

glnL glnLpglnL

glnLp

glnAp2 governorglnL

glnAp2 governor

glnL

7 4

total

d[mRNA( )] [NR1-P: ]km [ ] kmd [mRNA( )]

dt [ ]

glnK glnKpglnK glnK

glnKp

8 5

total

d[mRNA( )] [NR1-P: ]km [ ] kmd [mRNA( )]

dt [ ]

nac nacpnac nac

nacp

total1 2

17 18

d[P2]kx [P2:UMP:UTUR:aKG] kx [UTUR:Gln:P2-UMP]

dt

kx [aKG:P2:UMP:aKG:UTUR] kx [aKG:P2-UMP:Gln:UTUR]

total2 1

17 18

d[P2-UMP]kx [UTUR:Gln:P2-UMP] kx [P2:UMP:UTUR:aKG]

dt

kx [aKG:P2:UMP:aKG:UTUR] kx [aKG:P2-UMP:Gln:UTUR]

total4 19 30 31

32 16 33

34 35

36

d[GlnK]kp [mRNA( )] kx [GlnK-UMP:Gln:UTUR] kpd [GlnK] kpd [GlnK:P1]

dt

kpd [NR2:GlnK] kx [GlnK:UMP:aKG:UTUR] kpd [NR1-P:NR2:GlnK]

kpd [NR2-P:ADP:GlnK] kpd [GS:AMP:P1:GlnK]

kpd [GlnK:U

glnK

MP:aKG:UTUR]

total16 37 38

19 39

40

d[GlnK-UMP]kx [GlnK:UMP:aKG:UTUR] kpd [GlnK-UMP] kpd [GlnK-UMP:P1]

dt

kx [GlnK-UMP:Gln:UTUR] kpd [GS-AMP:P1:GlnK-UMP]

kpd [GlnK-UMP:Gln:UTUR]

total1 3 2 4

5 1 3 4

6 5 6

d[NR2]kpd [NR2:P2] kx [NR2:ATP] kpd [NR2:ATP] kx [NR2-P:P2:ADP]

dt

kx [NR1:NR2-P] kp [mRNA( )] kpd [NR2] kpd [NR1-P:NR2:P2]

kx [NR2-P:ADP:GlnK] kpd [NR2:GlnK] kpd [NR1-P:NR2:GlnK]

glnL

total4 7 5

8 3 9 6

10

d[NR2-P]kx [NR2-P:P2:ADP] kpd [NR2-P:P2:ADP] kx [NR1:NR2-P]

dt

kpd [NR1:NR2-P] kx [NR2:ATP] kpd [NR2-P] kx [NR2-P:ADP:GlnK]

kpd [NR2-P:ADP:GlnK]

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total7 11 8 12

13 14 9 2

15 10

d[NR1]kx [NR1:NR2-P] kpd [NR1:NR2-P] kx [NR1:AceP] kpd [NR1:AceP]

dt

kpd [NR1: ] kpd [NR1: ] kx [NR1-P:NR2:P2] kp [mRNA( )]

kpd [NR1] kx [NR1-P:NR2:GlnK]

glnAp1 glnLp glnG

total9 16 7

8 17 4 18

19 20 10

21

d[NR1-P]kx [NR1-P:NR2:P2] kpd [NR1-P:NR2:P2] kx [NR1:NR2-P]

dt

kx [NR1:AceP] kpd 4 [(NR1-P) : ] kpd [NR1-P]

kpd [NR1-P: ] kpd [NR1-P: ] kx [NR1-P:NR2:GlnK]

kpd [NR1-P:NR2

glnAp2

governor glnKp

22:GlnK] kpd [NR1-P: ]nacp

total11 23 12

3 24 13

14 25

15

d[GS]= kx [GS:AMP:P1:P2] kpd [GS:AMP:P1:P2] kx [GS-AMP:P1:P2-UMP]

dt

kp [mRNA( )] kpd [GS] kx [GS-AMP:P1:GlnK-UMP]

kx [GS:AMP:P1:GlnK] kpd [GS:AMP:P1:GlnK]

kx [GS-AMP:aKG:P2-UMP:P1]

glnA

total12 26

11 27 14

13 28

29

d[GS-AMP]kx [GS-AMP:P1:P2-UMP] kpd [GS-AMP:P1:P2-UMP]

dt

kx [GS:AMP:P1:P2] kpd [GS-AMP] kx [GS:AMP:P1:GlnK]

kx [GS-AMP:P1:GlnK-UMP] kpd [GS-AMP:P1:GlnK-UMP]

kpd [GS-AMP:aKG:P2-UMP:P1] kx

15[GS-AMP:aKG:P2-UMP:P1]

total5 41

d[Nac]kp [mRNA( )] kpd [Nac]

dtnac

6

7 6

37

9 8 3

35 total 2

5 4 3 2

d[Glu] [aKG] [Gln]Q [GOGAT]

dt Kmich [aKG] Kmich [Gln]

[aKG] [NH ]Q [GDH]

Kmich [aKG] Kmich [NH ]

[Glu] [NH ] [Glu]Q [GS] Q

Kmich [Glu] Kmich [NH ] Kmich [Glu]

3 6

10 7 6

37 4

9 8 3 3

d[aKG] [Dummy] [aKG] [Gln]Q 0.5 Q [GOGAT]

dt Kmich [Dummy] Kmich [aKG] Kmich [Gln]

[aKG] [NH ] [aKG]Q [GDH] Q

Kmich [aKG] Kmich [NH ] Kmich [aKG]

6

7 6

35 total 1

5 4 3 1

d[Gln] [aKG] [Gln]0.5 Q [GOGAT]

dt Kmich [aKG] Kmich [Gln]

[Glu] [NH ] [Gln]+Q [GS] Q

Kmich [Glu] Kmich [NH ] Kmich [Gln]

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Table S5 Component list for the mathematical model of the E. coli ammonia assimilation system.

Component Definition Concentration [M]

[UTUR] UTase/UR 4.298863x10-13

[P2] PII 7.436169x10-9

[P2-UMP] Uridylylated PII 4.568248x10-16

[P1] PI 3.280442x10-9

[NR2] NRII 9.155574x10-10

[NR2-P] Phosphorylated NRII 8.934311x10-8

[NR1] NRI 3.660916x10-9

[NR1-P] Phosphorylated NRI 2.609817x10-8

[glnAp1] glnAp1 8.002873x10-10

[glnLp] glnLp 9.286833x10-10

[glnAp2] glnAp2 9.337829x10-10

[UTUR:Gln] Glutamine-bound UTase/UR 3.111439x10-8

[UTUR:aKG] -ketoglutarate-bound UTase/UR 6.825852x10-8

[P2:UMP:UTUR:aKG] PII:UMP:UTase/UR:-ketoglutarate 3.056244x10-10

[UTUR:Gln:P2-UMP] UTase/UR:glutamine:PII-UMP 1.956248x10-16

[P1:P2] PI:PII 2.660901x10-11

[P1:P2-UMP] PI:PII-UMP 1.950173x10-16

[NR2:P2] NRII:PII 1.182268x10-9

[NR2:ATP] NRII:ATP 7.351696x10-10

[NR2-P:P2:ADP] NRII-P:PII:ADP 2.816750x10-10

[NR1:NR2-P] NRI:NRII-P 4.913781x10-12

[NR1:AceP] Acetyl phosphate-bound NRI 6.359951x10-8

[NR1-P:NR2:P2] NRI-P:NRII:PII 4.954421x10-8

[NR1:glnAp1] NRI-bound glnAp1 1.997127x10-10

[NR1:glnLp] NRI-bound glnLp 7.131672x10-11

[(NR1-P)4:glnAp2] 4 NRI-bound glnAp2 6.621714x10-11

[GS] Glutamine synthetase 1.159221x10-7

[GS-AMP] Adenylylated GS 1.515874x10-9

[GS:AMP:P1:P2] GS:AMP:PI:PII 7.503657x10-12

[GS-AMP:P1:P2-UMP] GS-AMP:PI:PII-UMP 1.626804x10-17

[GlnK] GlnK 2.269222x10-9

[NR2:GlnK] NRII:GlnK 1.620226x10-9

[GlnK-UMP] GlnK-UMP 9.009511x10-14

[glnKp] glnKp 8.774398x10-10

[governor] governor 9.987750x10-10

[GS-AMP:P1:GlnK-UMP] GS-AMP:PI:GlnK-UMP 1.039781x10-15

[GS:AMP:P1:GlnK] GS:AMP:PI:GlnK 1.852779x10-13

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[NR2-P:ADP:GlnK] NRII-P:ADP:GlnK 4.515086x10-13

[NR1-P:NR2:GlnK] NRI-P:NRII:GlnK 1.361171x10-8

[GlnK:UMP:aKG:UTUR] GlnK:UMP:-ketoglutarate:UTase/UR 8.127890x10-13

[GlnK-UMP:Gln:UTUR] GlnK-UMP:glutamine:UTase/UR 8.024843x10-13

[GlnK-UMP:P1] GlnK-UMP:PI 1.167067x10-12

[GlnK:P1] GlnK:PI 3.686332x10-12

[NR1-P:glnKp] NRI-P-bound glnKp 1.225602x10-10

[NR1-P:governor] NRI-P-bound governor 1.224974x10-12

[nacp] nacp 9.398270x10-10

[NR1-P:nacp] NRI-P-bound nacp 6.017305x10-11

[aKG:P2] -ketoglutarate-bound PII 2.811104x10-8

[aKG:P2-UMP:P1] -ketoglutarate:PII-UMP:PI 6.680297x10-9

[GS-AMP:aKG:P2-UMP:P1] GS-AMP:-ketoglutarate:PII-UMP:PI 1.079230x10-13

[aKG:P2-UMP:Gln:UTUR] -ketoglutarate:PII-UMP:glutamine:UTase/UR 3.125199x10-10

[aKG:P2:UMP:aKG:UTUR] -ketoglutarate:PII:UMP:-ketoglutarate:UTase/

UR

6.900344x10-12

[aKG:P2-UMP] -ketoglutarate:PII-UMP 6.105052x10-9

[Nac] Nac 8.596020x10-9

[mRNA(glnA)] Transcript of glnA 2.055295x10-10

[mRNA(glnG)] Transcript of glnG 2.751685x10-10

[mRNA(glnL)] Transcript of glnL 2.751685x10-10

[GlnK]total Total amount of GlnK 1.750629x10-8

[GlnK-UMP]total Total amount of uridylylated GlnK 2.060686x10-12

[governor]total Total amount of governor 1.000000x10-9

(constant)

[glnKp]total Total amount of glnKp 1.000000x10-9

(constant)

[UTUR]total Total amount of UTase/UR 1.000000x10-7

(constant)

[P2]total Total amount of PII 8.690200x10-8

[P2-UMP]total Total amount of uridylylated PII 1.309798x10-8

[P1]total Total amount of PI 1.000000x10-8

(constant)

[NR2]total Total amount of NRII 6.760914x10-8

[NR2-P]total Total amount of phosphorylated NRII 8.963015x10-8

[NR1]total Total amount of NRI 6.753637x10-8

[NR1-P]total Total amount of phosphorylated NRI 8.970292x10-8

[glnAp1]total Total amount of glnAp1 1.000000x10-9

(constant)

[glnLp]total Total amount of glnLp 1.000000x10-9

(constant)

[glnAp2]total Total amount of glnAp2 1.000000x10-9

(constant)

[glnA] glnA gene 1.000000x10-9

(constant)

[glnG] glnG gene 1.000000x10-9

(constant)

[glnL] glnL gene 1.000000x10-9

(constant)

[GS]total Total amount of GS 1.159298x10-7

Page 10: Table S1 Mathematical equations of the artificial network.10.1007/s00449-012-0789... · Table S1 Mathematical equations of the artificial network. ... Reaction rate constant for E:

[GS-AMP]total Total amount of adenylylated GS 1.515983x10-9

[NH3] Ammonia 1.000000x10-4

(constant)

[mRNA(glnK)] Transcript of glnK 3.063958x10-11

[aKG] -ketoglutarate 1.902870x10-3

[Gln] Glutamine 2.118692x10-3

[Glu] Glutamate 2.611788x10-3

[GOGAT] Glutamate synthase 6.000000x10-7

(constant)

[GDH] Glutamate dehydrogenase 1.000000x10-7

(constant)

[glnK] glnK gene 1.000000x10-9

(constant)

[mRNA(nac)] Transcript of nac 1.504301x10-11

[nac] nac gene 1.000000x10-9

(constant)

[nacp]total Total amount of nacp 1.000000x10-9

(constant)

[AceP] Acetyl phosphate 1.000000x10-3

(constant)

[AMP] AMP 1.000000x10-3

(constant)

[ADP] ADP 1.000000x10-3

(constant)

[ATP] ATP 1.000000x10-3

(constant)

[UMP] UMP 1.000000x10-3

(constant)

[Dummy] Dummy metabolite from TCA cycle 1.000000x10-3

(constant)

Page 11: Table S1 Mathematical equations of the artificial network.10.1007/s00449-012-0789... · Table S1 Mathematical equations of the artificial network. ... Reaction rate constant for E:

Table S6 Parameter list for the mathematical model of the E. coli ammonia assimilation system.

Parameter Definition Value

Kb1 Binding constant between UTUR and glutamine 102 - 10

10 [M

-1]

Kb2 Binding constant between UTUR and -ketoglutarate 102 - 10

10 [M

-1]

Kb3 Binding constant between UTUR:-ketoglutarate, PII and UMP 102 - 10

10 [M

-2]

Kb4 Binding constant between UTUR:glutamine and PII-UMP 102 - 10

10 [M

-1]

Kb5 Binding constant between PI and PII 102 - 10

10 [M

-1]

Kb6 Binding constant between PI and PII-UMP 102 - 10

10 [M

-1]

Kb7 Binding constant between PI:PII, AMP and GS 102 - 10

10 [M

-2]

Kb8 Binding constant between PI:PII-UMP and GS-AMP 102 - 10

10 [M

-1]

Kb9 Binding constant between NRII and PII 102 - 10

10 [M

-1]

Kb10 Binding constant between ATP and NRII 102 - 10

10 [M

-1]

Kb11 Binding constant between PII and ADP and NRII-P 102 - 10

10 [M

-2]

Kb12 Binding constant between NRI and NRII-P 102 - 10

10 [M

-1]

Kb13 Binding constant between NRI and acetyl phosphate 102 - 10

10 [M

-1]

Kb14 Binding constant between NRII:PII and NRI-P 102 - 10

10 [M

-1]

Kb15 Binding constant between glnAp1 and NRI 102 - 10

10 [M

-1]

Kb16 Binding constant between glnLp and NRI 102 - 10

10 [M

-1]

Kb17 Binding constant between glnAp2 and NRI-P 102 - 10

10 [M

-1]

Kb18 Binding constant between PI:GlnK-UMP and GS-AMP 102 - 10

10 [M

-1]

Kb19 Binding constant between PI:GlnK, AMP and GS 102 - 10

10 [M

-2]

Kb20 Binding constant between GlnK, ADP and NRII-P 102 - 10

10 [M

-2]

Kb21 Binding constant between NRII:GlnK and NRI-P 102 - 10

10 [M

-1]

Kb22 Binding constant between UTUR:-ketoglutarate, GlnK and UMP 102 - 10

10 [M

-2]

Kb23 Binding constant between UTUR:glutamine and GlnK-UMP 102 - 10

10 [M

-1]

Kb24 Binding constant between GlnK-UMP and PI 102 - 10

10 [M

-1]

Kb25 Binding constant between GlnK and PI 102 - 10

10 [M

-1]

Kb26 Binding constant between glnKp and NRI-P 102 - 10

10 [M

-1]

Kb27 Binding constant between NRI-P and governor 102 - 10

10 [M

-1]

Kb28 Binding constant between GlnK and NRII 102 - 10

10 [M

-1]

Kb29 Binding constant between NRI-P and nacp 102 - 10

10 [M

-1]

Kb30 Binding constant between -ketoglutarate and PII 102 - 10

10 [M

-1]

Kb31 Binding constant between -ketoglutarate:PII-UMP and PI 102 - 10

10 [M

-1]

Kb32 Binding constant between GS-AMP and -ketoglutarate:PII-UMP:PI 102 - 10

10 [M

-1]

Kb33 Binding constant between -ketoglutarate:PII-UMP and

glutamine :UTUR

102 - 10

10 [M

-1]

Kb34 Binding constant between -ketoglutarate:PII and

-ketoglutarate:UTUR and UMP

102 - 10

10 [M

-2]

Kb35 Binding constant between -ketoglutarate and PII-UMP 102 - 10

10 [M

-1]

Page 12: Table S1 Mathematical equations of the artificial network.10.1007/s00449-012-0789... · Table S1 Mathematical equations of the artificial network. ... Reaction rate constant for E:

kx1 Reaction rate constant for PII:UMP:UTUR:-ketoglutarate 7.00 [min-1

]

kx2 Reaction rate constant for UTUR:glutamine:PII-UMP 7.00 [min-1

]

kx3 Reaction rate constant for NRII:ATP 7.00 [min-1

]

kx4 Reaction rate constant for NRII-P:PII:ADP 7.00 [min-1

]

kx5 Reaction rate constant for NRI:NRII-P 7.00 [min-1

]

kx6 Reaction rate constant for NRII-P:ADP:GlnK 7.00 [min-1

]

kx7 Reaction rate constant for NRI:NRII-P 7.00 [min-1

]

kx8 Reaction rate constant for NRI:acetyl phosphate 7.00 [min-1

]

kx9 Reaction rate constant for NRI-P:NRII:PII 7.00 [min-1

]

kx10 Reaction rate constant for NRI-P:NRII:GlnK 7.00 [min-1

]

kx11 Reaction rate constant for GS:AMP:PI:PII 7.00 [min-1

]

kx12 Reaction rate constant for GS-AMP:PI:PII-UMP 7.00 [min-1

]

kx13 Reaction rate constant for GS-AMP:PI:GlnK-UMP 7.00 [min-1

]

kx14 Reaction rate constant for GS:AMP:PI:GlnK 7.00 [min-1

]

kx15 Reaction rate constant for GS-AMP:-ketoglutarate:PII-UMP:PI 7.00 [min-1

]

kx16 Reaction rate constant for GlnK:UMP:-ketoglutarate:UTUR 7.00 [min-1

]

kx17 Reaction rate constant for

-ketoglutarate:PII:UMP:-ketoglutarate:UTUR

7.00 [min-1

]

kx18 Reaction rate constant for -ketoglutarate:PII-UMP:glutamine:UTUR 7.00 [min-1

]

kx19 Reaction rate constant for GlnK-UMP:glutamine:UTUR 7.00 [min-1

]

kp1 Translation rate constant for mRNA(glnL) 2.00x101 [min

-1]

kp2 Translation rate constant for mRNA(glnG) 2.00x101 [min

-1]

kp3 Translation rate constant for mRNA(glnA) 2.00x101 [min

-1]

kp4 Translation rate constant for mRNA(glnK) 2.00x101 [min

-1]

kp5 Translation rate constant for mRNA(nac) 2.00x101 [min

-1]

kpd1 Degradation rate constant for NRII:PII 3.50x10-2

[min-1

]

kpd2 Degradation rate constant for NRII:ATP 3.50x10-2

[min-1

]

kpd3 Degradation rate constant for NRII 3.50x10-2

[min-1

]

kpd4 Degradation rate constant for NRI-P:NRII:PII 3.50x10-2

[min-1

]

kpd5 Degradation rate constant for NRII:GlnK 3.50x10-2

[min-1

]

kpd6 Degradation rate constant for NRI-P:NRII:GlnK 3.50x10-2

[min-1

]

kpd7 Degradation rate constant for NRII-P:PII:ADP 3.50x10-2

[min-1

]

kpd8 Degradation rate constant for NRI:NRII-P 3.50x10-2

[min-1

]

kpd9 Degradation rate constant for NRII-P 3.50x10-2

[min-1

]

kpd10 Degradation rate constant for NRII-P:ADP:GlnK 3.50x10-2

[min-1

]

kpd11 Degradation rate constant for NRI:NRII-P 3.50x10-2

[min-1

]

kpd12 Degradation rate constant for NRI:acetyl phosphate 3.50x10-2

[min-1

]

kpd13 Degradation rate constant for NRI:glnAp1 3.50x10-2

[min-1

]

kpd14 Degradation rate constant for NRI:glnLp 3.50x10-2

[min-1

]

kpd15 Degradation rate constant for NRI 3.50x10-2

[min-1

]

Page 13: Table S1 Mathematical equations of the artificial network.10.1007/s00449-012-0789... · Table S1 Mathematical equations of the artificial network. ... Reaction rate constant for E:

kpd16 Degradation rate constant for NRI-P:NRII:PII 3.50x10-2

[min-1

]

kpd17 Degradation rate constant for (NRI-P)4:glnAp2 3.50x10-2

[min-1

]

kpd18 Degradation rate constant for NRI-P 3.50x10-2

[min-1

]

kpd19 Degradation rate constant for NRI-P:governor 3.50x10-2

[min-1

]

kpd20 Degradation rate constant for NRI-P:glnKp 3.50x10-2

[min-1

]

kpd21 Degradation rate constant for NRI-P:NRII:GlnK 3.50x10-2

[min-1

]

kpd22 Degradation rate constant for NRI-P:nacp 3.50x10-2

[min-1

]

kpd23 Degradation rate constant for GS:AMP:PI:PII 3.50x10-2

[min-1

]

kpd24 Degradation rate constant for GS 3.50x10-2

[min-1

]

kpd25 Degradation rate constant for GS:AMP:PI:GlnK 3.50x10-2

[min-1

]

kpd26 Degradation rate constant for GS-AMP:PI:PII-UMP 3.50x10-2

[min-1

]

kpd27 Degradation rate constant for GS-AMP 3.50x10-2

[min-1

]

kpd28 Degradation rate constant for GS-AMP:PI:GlnK-UMP 3.50x10-2

[min-1

]

kpd29 Degradation rate constant for GS-AMP:-ketoglutarate:PII-UMP:PI 3.50x10-2

[min-1

]

kpd30 Degradation rate constant for GlnK 3.50x10-2

[min-1

]

kpd31 Degradation rate constant for GlnK:PI 3.50x10-2

[min-1

]

kpd32 Degradation rate constant for NRII:GlnK 3.50x10-2

[min-1

]

kpd33 Degradation rate constant for NRI-P:NRII:GlnK 3.50x10-2

[min-1

]

kpd34 Degradation rate constant for NRII-P:ADP:GlnK 3.50x10-2

[min-1

]

kpd35 Degradation rate constant for GS:AMP:PI:GlnK 3.50x10-2

[min-1

]

kpd36 Degradation rate constant for GlnK:UMP:-ketoglutarate:UTUR 3.50x10-2

[min-1

]

kpd37 Degradation rate constant for GlnK-UMP 3.50x10-2

[min-1

]

kpd38 Degradation rate constant for GlnK-UMP:PI 3.50x10-2

[min-1

]

kpd39 Degradation rate constant for GS-AMP:PI:GlnK-UMP 3.50x10-2

[min-1

]

kpd40 Degradation rate constant for GlnK-UMP:glutamine:UTUR 3.50x10-2

[min-1

]

kpd41 Degradation rate constant for Nac 3.50x10-2

[min-1

]

km1 Transcription rate constant for glnA by glnAp2 1.50x10-1

[min-1

]

km2 Transcription rate constant for glnA by glnAp1 1.47x10-2

[min-1

]

km3 Transcription rate constant for glnG by glnLp 3.00x10-2

[min-1

]

km4 Transcription rate constant for glnG by glnAp2 6.00x10-2

[min-1

]

km5 Transcription rate constant for glnL by glnLp 3.00x10-2

[min-1

]

km6 Transcription rate constant for glnL by glnAp2 6.00x10-2

[min-1

]

km7 Transcription rate constant for glnK by glnKp 3.00x10-2

[min-1

]

km8 Transcription rate constant for nac by nacp 3.00x10-2

[min-1

]

kmd1 Degradation rate constant for mRNA(glnA) 1.20x10-1

[min-1

]

kmd2 Degradation rate constant for mRNA(glnG) 1.20x10-1

[min-1

]

kmd3 Degradation rate constant for mRNA(glnL) 1.20x10-1

[min-1

]

kmd4 Degradation rate constant for mRNA(glnK) 1.20x10-1

[min-1

]

kmd5 Degradation rate constant for mRNA(nac) 1.20x10-1

[min-1

]

Q1 Reaction rate constant for efflux of glutamine 2.60x10-2

[M min-1

]

Page 14: Table S1 Mathematical equations of the artificial network.10.1007/s00449-012-0789... · Table S1 Mathematical equations of the artificial network. ... Reaction rate constant for E:

Q2 Reaction rate constant for efflux of glutamate 2.20x10-1

[M min-1

]

Q3 Reaction rate constant for influx of -ketoglutarate 1.00 [M min-1

]

Q4 Reaction rate constant for efflux of -ketoglutarate 1.20 [M min-1

]

Q5 Reaction rate constant for GS 4.00x108 [min

-1]

Q6 Reaction rate constant for GOGAT 9.00x106 [min

-1]

Q7 Reaction rate constant for GDH 4.00x107 [min

-1]

Kmich1 Michaelis constant for efflux of glutamine 3.00x10-2

[M]

Kmich2 Michaelis constant for efflux of glutamate 3.00x10-2

[M]

Kmich3 Michaelis constant for efflux of -ketoglutarate 3.00x10-2

[M]

Kmich4 Michaelis constant of GS for ammonia 3.00x10-2

[M]

Kmich5 Michaelis constant of GS for glutamate 3.00x10-2

[M]

Kmich6 Michaelis constant of GOGAT for glutamine 3.00x10-2

[M]

Kmich7 Michaelis constant of GOGAT for -ketoglutarate 3.00x10-2

[M]

Kmich8 Michaelis constant of GDH for ammonia 3.00x10-2

[M]

Kmich9 Michaelis constant of GDH for -ketoglutarate 1.00x10-3

[M]

Kmich10 Michaelis constant for influx of -ketoglutarate 1.00x10-2

[M]