Figure 1

S-matrix and S-graphs of the two reactions shown among four carriers ATP, ADP, NADH, and NAD and four other metabolites $S_1$, $S_2$, $S_3$, and $S_4$, with enzymes hidden. The S-matrix has a color-code that helps visualize larger S-matrices. Red and blue correspond to positive and negative elements, respectively, for irreversible reactions, and pink and green correspond to positive and negative elements, respectively, for reversible reactions. An S-graph consists of reaction nodes (black diamond), noncarrier metabolite nodes (orange square), and carrier metabolite nodes (light blue square). Edges are color coded as in the S-matrix, so all the information in the S-matrix appears schematically in the S-graph. Carriers which always occur in pairs (ATP/ADP, NAD/NADH, etc.) are grouped into a single node.Reuse & Permissions

Figure 2

S-matrix for H. Pylori metabolism with 325 metabolites and 315 reactions. Reactions (columns) are decomposed into standard functional modules of catabolism, amino acid biosynthesis, nucleotide biosynthesis, lipid biosynthesis, and vitamin biosynthesis. The rows (metabolites) are arranged by their role in reaction modules to clarify the sparsity pattern of long chains of successive reactions from inputs to outputs in each module. The bottom rows are precursor metabolites and carrier metabolites, which appear throughout different reaction modules. The 12 precursor metabolites are outputs of catabolism and are the starting points for biosynthesis. Carrier metabolites correspond to conserved quantities, are activated in catabolism, and act as carriers to transfer energy and phosphate groups (ATP/ADP/AMP), hydrogen/redox (NADH/NAD), amino groups (AKG/GLU), acetyl groups (ACCOA/COA), and one carbon units (THF/METHF) throughout all modules. The other (than carriers and precursors) metabolites occur primarily in separate reaction modules.Reuse & Permissions

Figure 3

An S-graph for the amino acid biosynthesis module of the H. Pylori S-matrix. The conventions are the same as those in Fig. 1. This illustrates that long biosynthetic pathways build complex building blocks (in yellow on the right) from precursors (in orange on the left) in a series of simple reactions (in the middle). Each biosynthetic module has a qualitatively similar structure.Reuse & Permissions

Figure 4

Rank (cumulative distribution) of metabolite node degree ($=\mathrm{\text{number of reactions}}=\mathrm{\text{number of links}}$) for metabolic networks of H. Pylori. Degrees of (a) carrier, (b) precursor, and (c) other metabolites in the whole network [large marker with (a) blue, (b) red, and (c) dark green] and in each reaction module (small markers with pink, dark red, brown, orange, and light green colors). Each module shows exponential distribution. (d) Metabolite node degrees of the whole network (black $+$) resulting from the mixture of carrier (○), precursor (◇), and other metabolites (*), for which the plot is the same as for (a), (b), and (c), respectively. (e) Log-log plot of (d) indicates total degrees are approximately power laws. (f) The total metabolites in each reaction module with exponential distribution sums up to create the power-law distribution in the whole network.Reuse & Permissions

Figure 5

Reaction node degree ($=\mathrm{\text{number}}$ of substrates) distribution for metabolic networks of H. Pylori. $\mathrm{CV}=0.30$. The contributions of carrier metabolites to degrees is also indicated.Reuse & Permissions