Analysis of the hierarchical structure of the B. subtilis transcriptional regulatory network

Kumar, Santhust; Vendruscolo, Michele; Singh, Amit; Kumar, Dhiraj; Samal, Areejit

doi:10.1039/c4mb00298a

Cited by 13 publications

(13 citation statements)

References 45 publications

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“…Interestingly, the observed distribution of In Forman curvature is very different from that of Out Forman curvature in the E. coli TRN (Supplementary Figure S2(a)). Bacterial transcriptional regulatory networks (TRNs) display an inherently hierarchical architecture [45,[51][52][53] where few transcriptional factors at the top of the hierarchy have no incoming links (i.e., their in-degree is zero), while a large number of target genes at the bottom of the hierarchy have no outgoing links (i.e., their out-degree is zero). Moreover, the out-degree distribution of E. coli TRN is broad with many global transcription factors regulating several target genes, while the in-degree distribution is narrow due to constraints on size of promoter regions in the bacterial genome [54].…”

Section: Resultsmentioning

confidence: 99%

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Forman curvature for complex networks

et al. 2016

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A goal in network science is the geometrical characterization of complex networks. In this direction, we have recently introduced the Forman's discretization of Ricci curvature to the realm of undirected networks. Investigation of this edge-centric network measure, Forman curvature, in diverse model and real-world undirected networks revealed that the curvature measure captures several aspects of the organization of complex undirected networks. However, many important realworld networks are inherently directed in nature, and the definition of the Forman curvature for undirected networks is unsuitable for the analysis of such directed networks. Hence, we here extend the Forman curvature for undirected networks to the case of directed networks. The simple mathematical formula for the Forman curvature of a directed edge elegantly incorporates node weights, edge weights and edge direction. By applying the Forman curvature for directed networks to a variety of model and real-world directed networks, we show that the measure can be used to characterize the structure of complex directed networks. Furthermore, our results also hold in real directed networks which are weighted or spatial in nature. These results in combination with our previous results suggest that the Forman curvature can be readily employed to study the organization of both directed and undirected complex networks. * jost@mis.mpg.de † this also makes the measure suitable for analysis of both unweighted and weighted networks [21]. Since Forman curvature represents a discretization of the classical Ricci curvature which is intrinsically associated with edges of a network, this notion of curvature does not necessitate the technical artifice of extending a measure for the curvature of nodes to the edges [21]. Thus, Forman curvature can be exploited for edge-based analysis of complex networks. Given the definition of the Forman curvature of an edge, one can easily define the Forman curvature of a node in the network by summing or averaging the curvatures of its adjacent edges, somewhat analogous to the concept of scalar curvature in Riemannian geometry [23]. We remark that the Forman curvature for an edge is a local measure dependent on weights of adjacent nodes and edges in the network [21]. Still Forman curvature, a local geometric characteristic, can provide deep insights on the global topology of the network [30]. Moreover, two networks with the same degree distribution can have very different distributions of Forman curvature (Fig. 1).Although, we have successfully introduced Forman curvature to undirected networks [21], several important real networks in nature and society are inherently directed in nature. These include the metabolic networks [7,33,34], gene regulatory networks [35], signaling networks [36], neural networks [37], the world wide web (WWW) [38], online social networks [10] and transportation networks [39,40]. However, the two different discretizations of the Ricci curvature, Ollivier-Ricci curvature and Forman-Ricci curvature, have been...

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Section: Resultsmentioning

confidence: 99%

“…• E. coli TRN [44,45] gives the transcriptional regulatory network in the bacterium Escherichia coli. In this network of 3072 nodes and 7853 edges, nodes corresponds to genes and directed edges represent control of target gene expression through transcription factors.…”

Section: Introductionmentioning

confidence: 99%

Forman curvature for complex networks

et al. 2016

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“…However, B. subtilis is known for its property of sporulation, which imposes constraints on the organization of the genome and chromosome segregation [ 35 ]. Also, it uses different replication factories and possesses different and much more numerous sigma factors [ 36 ]. Thus, we assume that the observed anti-correlation (Fig.…”

Section: Resultsmentioning

confidence: 99%

Relationship between digital information and thermodynamic stability in bacterial genomes

Nigatu

Henkel

Sobetzko

et al. 2016

J Bioinform Sys Biology

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Ever since the introduction of the Watson-Crick model, numerous efforts have been made to fully characterize the digital information content of the DNA. However, it became increasingly evident that variations of DNA configuration also provide an “analog” type of information related to the physicochemical properties of the DNA, such as thermodynamic stability and supercoiling. Hence, the parallel investigation of the digital information contained in the base sequence with associated analog parameters is very important for understanding the coding capacity of the DNA. In this paper, we represented analog information by its thermodynamic stability and compare it with digital information using Shannon and Gibbs entropy measures on the complete genome sequences of several bacteria, including Escherichia coli (E. coli), Bacillus subtilis (B. subtilis), Streptomyces coelicolor (S. coelicolor), and Salmonella typhimurium (S. typhimurium). Furthermore, the link to the broader classes of functional gene groups (anabolic and catabolic) is examined. Obtained results demonstrate the couplings between thermodynamic stability and digital sequence organization in the bacterial genomes. In addition, our data suggest a determinative role of the genome-wide distribution of DNA thermodynamic stability in the spatial organization of functional gene groups.

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“…We divided the yeast TRN into four hierarchical levels using the method adopted by Kumar et al [20]. Firstly, genes without outgoing edges in the directed graph were classified as target genes (TGs) which comprise the lowest level in the hierarchy: Target level.…”

Section: Determining the Hierarchical Levels Of The Yeast Trnmentioning

confidence: 99%

Spatial organization of the transcriptional regulatory network of Saccharomyces cerevisiae

Sun

Liang

2019

Preprint

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Transcriptional regulatory network (TRN) is a directed complex network composed of all regulatory interactions between transcription factors and corresponding target genes. Recently, the three-dimensional (3D) genomics studies have shown that the 3D structure of the genome makes a difference to the regulation of gene transcription, which provides us with a novel perspective. In this study, we constructed the TRN of the budding yeast Saccharomyces cerevisiae and placed it in the context of 3D genome model. We analyzed the spatial organization of the yeast TRN on four levels: global feature, central nodes, hierarchical structure and network motifs. Our results suggested that the TRN of S. cerevisiae presents an optimized structure in space to adapt to functional requirement.

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Analysis of the hierarchical structure of the B. subtilis transcriptional regulatory network

Cited by 13 publications

References 45 publications

Forman curvature for complex networks

Forman curvature for complex networks

Relationship between digital information and thermodynamic stability in bacterial genomes

Spatial organization of the transcriptional regulatory network of Saccharomyces cerevisiae

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