Figure 1.
An example of organism-specific metabolic network and the corresponding universal network.
The organism-specific metabolic network (filled circles and thick edges) is always a subset of the universal network (the entire tree). Nodes are divided into layers based on their distance from the root of the tree. Variables
,
,
for the universal network and
,
,
for species-specific network are illustrated using the layer
as an example.
Figure 2.
is the number of leaves in an organism-specific metabolic network and equal to the number of transcriptional regulators of corresponding nutrient-utilizing pathways, while
is the total number of nodes/metabolites in this netowrk. The data are generated by the toolbox model on critical universal network with sizes around 2000. Solid line
, where the exponent
and the prefactor
, are the best fits to the binned data.
Figure 3.
vs.
for KEGG-based universal network with linearized pathways.
(the ratio of the number of metabolites at two consecutive layers) plotted as a function of
(the layer number) for KEGG-based universal network with linearized pathways. Solid line: measurement, dotted line: its expected profile,
, in a critical branching tree. The error bars reflect standard deviation in different spanning trees used to linearize the KEGG network.
Table 1.
The distribution of irreversible reactions classified by their numbers of substrates and products.
Table 2.
The distribution of reversible reactions classified by their numbers substrates/products.
Figure 4.
Diagram of a new pathway added to the metabolic network of the organism.
The diagram explains different types of metabolites and reactions. Reactions (squares) in the added pathway use base substrates (yellow circles with horizontal shading) from the metabolic core of the organism (light blue area) to produce the target metabolite (the red circle). Added pathway generates intermediate products (green circles) as well as byproducts that are not further converted to the target (blue circles). Products of some reactions feed back into the metabolic core (yellow circles with vertical shading). Reactions are labeled with expansion steps at which they were added to the pathway.
Figure 5.
vs.
of toolbox model with branched pathways and multi-substrate reactions.
The scaling between the number of regulated pathways (leaves), and the number of metabolites,
, in metabolic networks generated by the toolbox model with branched pathways and multi-substrate reactions. Solid line with slope 2.0+/−0.1 is the best fit to the data. Error bars reflect the standard deviation of
at a given value of
in 9 realizations of the model (see he section “Error analysis of the toolbox model” of Text S1 for our estimation methods and error analysis).
Figure 6.
vs.
for the universal network consisting of all KEGG reactions.
The ratio of the number of metabolites at two consecutive layers of the scope expansion process plotted versus the layer number
. Scope expansion was performed for the universal network consisting of all KEGG reactions. The dashed line is the mathematical expectation of the same curve in a critical branching process.
Figure 7.
Faster-than-linear scaling of the number of byproducts, nbyproduct, and the total number of metabolites, , in individual branched pathways illustrated in Figure 4. Data for individual pathways were logarithmically binned along the x-axis. Hence y-axis can be and are below 1 due to pathways with 0 byproducts. The solid line with exponent 1.7+/−0.1 is the best fit to the logarithmically-binned data shown in this plot. Readers can refer to the section “Analysis of number of by-product of the pathways of the toolbox model on the metabolic network with branched pathways and multi-substrates reactions” of Text S1 for our estimation methods and error analysis.
Figure 8.
Various linear relationships on the individual pathways.
Approximately linear relationship between a) pathway's length and its number of reactions , ) b) the number of border reactions, nborder rxn, and the total number of reactions,
, c) the number of base metabolites, nbase, and the total number of metabolites,
, d) the number of metabolites receiving feedback, nfeedback, and the total number of metabolites,
. These different geometrical properties of individual pathways are illustrated in Figure 4. Sizes of circles are proportional to the logarithm of the number of discrete (x, y) pairs contributing to this point.
Figure 9.
Comparison of lengths of the pathways and shortest distances of the targets from the core.
The lengths of the pathways are represented by circles and solid line, while the shortest distances of the targets from the core are represented by crosses and dotted line.