Figure 1.
Hierarchical structure clarifies regulatory interdependencies.
An abstract example of a directed regulatory network is shown (A) unstructured and (B) hierarchically structured. We schematically show in (C) and (D) that for master regulators like HOXA10 significant downstream effects in postnatal hematopoietic development depending on different concentrations can be observed. In contrast to master regulators so called mid-level regulators can not only be mediators of different incoming regulatory signals but also influence multiple downstream components or pathways. We schematically display that TP53 is influenced by various upstream signals such as (E) DNA damage or (F) oncogenes leading to different downstream effects such as apoptosis or development of cancer. The detailed understanding of the hierarchical topology is necessary to comprehend the dynamic behavior and the possible malfunction of regulatory networks.
Table 1.
Regulatory networks.
Table 2.
Transcriptional regulatory networks.
Figure 2.
Illustration of the hierarchy extraction approach.
We illustrate the approach of hierarchy extraction from directed networks. In the first step, the original network (grey) is traversed into a shortest path-tree (step1) with an initial hierarchical organization consisting of three layers. As this alone does not capture all feasible solutions we introduce two correction steps to resolve conflicts in the level assignments (e.g. node 1 is located in level 2, but it is regulating node 4 that is located in level 3). First, in the “downgrade” step each vertex is placed on the lowest level that this vertex and its regulating vertices are assigned to (step2). Thereby it is assured that each regulator has at least the same level assignment as its targets. Here, node 4 and node 5 are downgraded from level 3 to level 2 as its regulators - node 1 and node 3- are assigned to level 2. Second, vertices are “upgraded” if they have successors with the same level assignment and have no regulators themselves. Here, node 1 has no predecessor and targets on the same level (level 2). Consequently it is upgraded from level 2 to level 3 (step3). In the end HiNO determined a three layered hierarchical structure of the directed network without conflicts in the level assignment.
Figure 3.
Pseudocode for extracting the hierarchical organization of directed networks.
Figure 4.
An illustration of the user-friendly web-interface for HiNO is shown. The user can upload (A) a text file containing the representation of any directed network. Afterwards (B) the user retrieves information about node and edge types within the uploaded network and can decide which types should be used for the hierarchy extraction. Additionally, TF annotation can be added for human or mouse networks. (C) Information about the extracted hierarchical structure can be downloaded either as text file or in a graphical representation.
Figure 5.
From the gene regulatory network (GRN) to the hierarchical structure.
Illustration of (A) the GRN of E. coli with 1095 nodes and 2044 edges and (D) the GRN of S. cerevisiae with 3458 nodes and 8371 edges. Red nodes indicate transcription factors, green nodes genes. For extracting the hierarchical structure we deduced transcriptional regulation only. The transcriptional regulatory networks (TRNs) are shown in (B) for E. coli and (E) S. cerevisiae only. A snapshot of the hierarchical structure of the TRNs is shown for E. coli in (C) and for S. cerevisiae in (F). The TRN of E. coli has a four-layered pyramidal-shaped hierarchical structure, whereas the TRN of S. cerevisiae consists only of three layers. The different colors represent the distinct hierarchical levels: level 4– yellow; level 3– red; level 2– green; level 1– blue.
Table 3.
Level distribution of the TRN in E. coli.
Table 4.
Level distribution of the TRN in S. cerevisiae.
Figure 6.
Comparison BFS-method vs. HiNO using the TRN of E. coli.
A snapshot of the results (the comparison of the BFS-method and HiNO) using the TRN of E. coli is shown. Node colors indicate the level assignment in HiNO: blue - level 1; green - level 2; red - level 3; yellow - level 4. Dashed edges represent additional regulatory interdependencies (further up- and/or down-stream factors) that are not shown. The results of the BFS method are shown in (A). The node coloring indicates conflicts in level assignments. In (B) the result of the “downgrade” step of HiNO is shown. In (C) the result of the “upgrade” step is shown. This is also the final hierarchical assignment of the elements by HiNO.
Figure 7.
Comparison BFS-method vs. HiNO using the TRN of S. cerevisiae.
A snapshot of the results (the comparison of the BFS-approach and HiNO) using the TRN of S. cerevisiae is shown. Node colors indicate the level assignment in HiNO: blue - level 1; green - level 2; red - level 3; yellow - level 4. Dashed edges represent additional regulatory interdependencies (further up- and/or down-stream factors) that are not shown. The results of the BFS method are shown in (A). The node coloring indicates conflicts in level assignment. In (B) the result of the “downgrade” step of HiNO is shown. In (C) the result of the “upgrade” step is shown. This is also the final hierarchical assignment of the elements by HiNO.