Fig 1.
Schematic representation of the involved processes and biological elements in the integrative metabolic-regulatory E. coli network.
Gene regulatory processes primarily comprise genes (yellow circles) and several proteins (monomers (brown triangles) as well as complexes (gray triangles)), mainly transcription factors. In contrast, metabolic processes are predominantly defined by small molecules (blue squares) and the catalyzing biochemical reactions (green hexagons). The interactions between regulatory and metabolic processes can be mainly characterized by proteins (also modified proteins (purple triangles)) serving as enzymes and regulators, respectively. The symbols are also explained in Fig 2. While regulatory links are represented as dashed lines, the encoding and reaction-associated links are shown as solid lines. Note that this scheme does not cover all aspects of the biological categories and their classification (see Methods for details).
Fig 2.
Spring-block graph representation and vertex composition of the integrative E. coli network.
A scalable force directed placement algorithm has been used. The coverage of the pioneer model from [11] is provided in column iMC1010.
Fig 3.
Graph snapshots of the four partitions.
The functional three-domain partition into metabolic and regulatory domains and protein interface (MD—PI—RD) (A), the functional two-domain partition into metabolic and regulatory domains (MD—RD) (B), vertex-driven three-domain partition into compounds/reactions, proteins and genes (C), vertex-driven two-domain partition into compounds/reactions, and proteins/genes (D). Vertices are colored according to their domain-affiliation: yellow–(pseudo) regulatory and gene-focused domain, respectively, and blue—(pseudo) metabolic and compound-focused domain, respectively. The interface domain in the three-domain partitions are drawn in red. The diagrams in the top right corners of each panel show the edge composition of the system in terms of intra-domain and inter-domain edges.
Fig 4.
Topological properties of the functional and vertex type-driven network partitions.
The functional partitions are denoted by the respective modules, metabolic domain (MD), regulatory domain (RD) and protein interface (PI). The vertex type-driven partitions are represented by the comprising vertex types, reaction (green hexagon), compound (blue square), gene (yellow circle), and protein (brown triangle). For each property, the module-specific coefficients and contributions (I, II, III) are presented, respectively. For the modularity, M, the overall network coefficient (Total) is shown as well as the best coefficient is underlined, the module-specific values correspond to the terms in the sum of Eq (1).
Fig 5.
Schematic overview of the components and connections of the integrative E. coli network, especially those involved in the protein interface.
The information about edges are presented in gray and about traversing paths are shown in gold while the number of vertices are shown in dark blue and the traversing paths-related ones are given in dark brown, in addition. The solid lines denote direct link connections while the dashed lines the traversing paths connections. In the regulatory domain, for example, 274 vertices are directly linked to 283 vertices in the metabolic domain via 283 edges. Also, 806 vertices have a directed edge to 812 vertices in the protein interface (summing up to 813 edges). Similarly, the regulatory domain has 3210 edges residing in this domain. The total number of vertices in the regulatory domain that exchange an incoming or outgoing link with one of the other domains are 1533. The number of edges displayed on the right-hand side of the figure is the total count of edges between two domains or within a single domain. The number 385, for example, is the total count of edges between the regulatory domain and the metabolic domain. The number 1854 is the total count of edges within the interface domain. In gold (as numbers and dashed lines) the information about traversing paths is given. The total number of downwards traversing paths (18904) and of upwards traversing paths (4070) is indicated in gold along these dashed lines.
Fig 6.
Distribution of the path lengths.
Lengths are provided for the downwards (RD → MD) and upwards traversing paths (MD → RD), respectively (dark blue). The golden bars represent the fraction of downwards and upwards traversing paths comprising the PTS and RNR, and the NtrBC system associated vertices.
Fig 7.
Classical representation of the three major interface systems of the integrative E. coli network.
The systems shown here are the phosphoenolpyruvate-dependent sugar phosphotransferase system (PTS, A), the ribonucleotide reducing system (RNR system, B) and the nitrogen regulation two-component signal transduction system (NtrBC system, C). The edges represent biochemical reactions and the vertices denote the involved compounds and proteins. The reactions and proteins highlighted in dark blue are the most abundant vertices determining nearly half of the traversing paths (Table E in S1 Text).
Fig 8.
Key elements of the integrative E. coli network.
Key elements with respect to degree (DC) and betweenness centrality (BC) are listed according to their rank as well as their functional characteristic and cross-systemic property, respectively. Open squares denote trivial compounds and filled squares indicate currency metabolites. The colored arrows depict the cross-systemic contribution—downwards interface-related (▼), upwards interface-related (▲). The orange arrows emphasize the cross-systemic components with significant low intra-domain degree fraction and the golden ones point out elements indirectly linking to one of the major traversing paths systems.
Fig 9.
Extraction of database information (EcoCyc, release 20.0) on regulatory and metabolic processes.
Table 1.
Comparison of vertex composition and the coverage to the model from [11] of the integrative E. coli network (Largest WCC), the underlying full graph and the EcoCyc database (release 20.0).
Fig 10.
Network affiliation compilation based on vertex type, and the vertex neighbors types and affiliations. Affiliation assignment for non-ambiguous reactions, compounds and proteins. Continued in Algorithm 2B in Fig 11.
Fig 11.
Network affiliation compilation based on vertex type, and the vertex neighbors types and affiliations. Affiliation assignment for non-ambiguous genes and vertices assigned as ambiguous.
Fig 12.
Recursive algorithm for the determination of the, so-termed, domain-traversing paths from regulatory to metabolic domain and vice versa truly passing the interface domain.