2-Compound Loop in E. coli Model iJR904

The Metabolic Network

• From Palsson’s group• 1075 reactions and 7

62 compounds

Reaction type Number of reactions

The BIOMASS reaction (biomass)

1

Exchange reaction (ex_rct)

143

Metabolic reaction (meta_rct)

802

Single-compound transport (trans_1)

16

Facilitated (mixed) transport (trans_n)

113

The Mostly Connected Nodes

Node Degree

co2[c] 60

Nadh[c] 71

ppi[c] 74

nad[c] 76

h[e] 115

adp[c] 142

pi[c] 148

atp[c] 175

h2o[c] 292

h[c] 496

Using the objective function proposed by Palsson’s group: H[c] is the only compound whose free drainage increases biomass production significantly.

Compounds removed are: Atp, adp, nad, nadh, nadp, nadph, ppi, co2, fe2, h, h2o, k, na, nh4, pi, so4, and all other external compounds which have single-transport reaction.

Loop-Finding Algorithm

• Breadth-first search in Matlab

• A 2-compound loop is composed of two metabolites and two reactions, in the form of C1R1C2R2C1.

• A loop has directionality. C1R1C2R2C1 and C1R1C2R2C1 are considered to be two distinct loop.

Loops of Different SizesLoop type Number of this type

2R2C 820

3R3C 340

4R4C 1587

5R5C 5905

6R6C 30281

7R7C 163290

Loop type Number of this type

3R3C 24

4R4C 35

5R5C 29

6R6C 36

7R7C 29

Count of loops increases sharply as more compounds are allowed to be included.

If all connections which make up 2-compound loops are removed, the number of larger loops reduces dramatically.

Most Frequently Observed 2-Compound Pairs

• Many of the 2R2C loops have exactly the same set of 2C. For the 820 2R2C loops, 128 unique compound pairs are identified.

1st compound

2nd compound

Freq Diff

Glu-L[c] Akg[c] 215 H4N1O-1

Coa[c] Accoa[c] 177 C-2H-2O-1

Mqn8[c] Mql8[c] 60 H-2

Q8h2[c] Q8[c] 55 H2

2dmmq8[c]

2dmmql8[c]

25 H-2

Succ[c] Succ[e] 18

Pyr[c] Pep[c] 15 H1O-3P-1

Glu-L[c] Gln-L[c] 12 H-2N-1O1

Gtp[c] Gdp[c] 10 O3P1

Trodx[c] Trdrd[c] 9 H-2

The 2-C

ompound P

airs

Co-activation of Reactions in 2R2C Loop

• The conditions tested are Glc_aer, ac_aer, akg_aer, glyc_aer, lac-D_aer, lac-L_aer, mal-L_aer, pyr_aer, succ_aer, and glc_ana, where aer stands for aerobic and ana for anaerobic.

Type (by reactions activated)

Number of loops

All-0 216

All-2 153

Some 2 and some 0 8

Some 1 443

All the 2R

2C loops and their activation

pattern

Classification of Connectivities of 2R2C Elements

• Order all the loop in the format of CRCR. 1connected; 0not connected to other components in the network.

• The majority (624 out of 820) have all component nodes connected.

Type Number of loops

0101 1 (1)

1000 / 0010 3 (3)

1001 / 0110 2 (2)

1010 39 (34)

1011 / 1110 142 (31)

1100 / 0011 1 (1)

1101 / 0111 8 (8)

1111 624 (65)

4-node: 4-arc 820 8-arc 160

5-node: 6-arc 12860 8-arc 5492

6-node: 7-arc 542

7-node:8-arc 18678

6-node: 8-arc 67400