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Table 7 Reduced networks

From: The topology of metabolic isotope labeling networks

pool

atoms

essential cumomer nodes

percentage

Leu

6

297

2.9 %

Gly

2

488

4.7 %

Val

5

649

6.3 %

Arg

6

649

6.3 %

Glu

5

650

6.3 %

Ser

3

652

6.3 %

Ala

3

659

6.4 %

Cys

3

659

6.4 %

Gln

5

681

6.6 %

Pro

5

681

6.6 %

Lys

6

736

7.1 %

Ile

6

739

7.2 %

Met

5

741

7.2 %

Asp

4

742

7.2 %

Thr

4

742

7.2 %

His

6

983

9.5 %

Trp

11

1106

10.7 %

Phe

9

1802

17.5 %

Tyr

9

2313

22.4 %

  1. In case only a small subset of cumomers needs to be simulated, e.g. all cumomers of a single amino acid pool, a reduced network can be extracted from the full cumomer network. The reduced network provides a significant dimensional reduction and is minimal in the sense that it consists of the smallest subset of cumomers necessary to describe the desired set of cumomers subject to simulation. As an example the sizes of the reduced networks for all nineteen amino acid pools in the E. coli network are shown. Note that if the network size reduces to p percent, then also the running time of the simulation algorithm reduces to O MathType@MTEF@5@5@+=feaafiart1ev1aaatCvAUfKttLearuWrP9MDH5MBPbIqV92AaeXatLxBI9gBaebbnrfifHhDYfgasaacH8akY=wiFfYdH8Gipec8Eeeu0xXdbba9frFj0=OqFfea0dXdd9vqai=hGuQ8kuc9pgc9s8qqaq=dirpe0xb9q8qiLsFr0=vr0=vr0dc8meaabaqaciaacaGaaeqabaqabeGadaaakeaat0uy0HwzTfgDPnwy1egaryqtHrhAL1wy0L2yHvdaiqaacqWFoe=taaa@383C@ (p3) percent.