Similar bowtie structures and distinct largest strong components are identified in the transcriptional regulatory networks of Arabidopsis thaliana during photomorphogenesis and heat shock

Abstract

Photomorphogenesis and heat shock are critical biological processes of plants. A recent research constructed the transcriptional regulatory networks (TRNs) of Arabidopsis thaliana during these processes using DNase-seq. In this study, by strong decomposition, we revealed that each of these TRNs can be represented as a similar bowtie structure with only one non-trivial and distinct strong component. We further identified distinct patterns of variation of a few light-related genes in these bowtie structures during photomorphogenesis. These results suggest that bowtie structure may be a common property of TRNs of plants, and distinct variation patterns of genes in bowtie structures of TRNs during biological processes may reflect distinct functions. Overall, our study provides an insight into the molecular mechanisms underlying photomorphogenesis and heat shock, and emphasizes the necessity to investigate the strong connectivity structures while studying TRNs.

Introduction

In natural habitats, Arabidopsis thaliana (A. thaliana) confronts a variety of stimuli and stresses, nevertheless succeeds to thrive. When exposed to light, A. thaliana seedlings undergo photomorphogenesis, which is a developmental program essential for photosynthesis (Wu, 2014). In contrast, skotomorphogenesis is a developmental program of plants that takes place in dark (Wu, 2014). Heat stress occurs when temperature rises above the normal range and results in dehydration of plants (Jacob et al., 2017). Increasing numbers of studies identified the critical genes related to photomorphogenesis and heat stress; moreover, some of these efforts were spent to discover the regulatory relations among these genes and to elucidate the underlying mechanisms (Castillon et al., 2007; Barah et al., 2016). Sullivan et al. (2014) established large-scale transcriptional regulatory networks consisting of 251 transcription factor genes for A. thaliana seedlings before and after exposure to light and heat by mapping DNase I hypersensitivity sites and genomic footprinting (Vierstra et al., 2015; Sullivan et al., 2015).

Transcriptional regulatory networks (TRNs) are collections of regulatory relations between transcription factor (TF) genes and their target genes (He and Tan, 2016; Gaudinier and Brady, 2016; Muhammad et al., 2017). TRNs are directed networks, also called directed graphs; therefore, many graph-theoretical methods have been applied to discover the global and local properties of TRNs (Barabási and Oltvai, 2004; Barabási et al., 2011; Milo et al., 2004; Cheng et al., 2015). A directed network consists of a set of vertices, e.g. the genes in TRNs, and a set of edges, each of which represents a relation between two vertices (possibly the same) and is endowed with a direction, e.g. the regulatory relations in TRNs. A path from vertex i to vertex j is a finite sequence of vertices (v₁, v₂, v₃, …, v_n-1, v_n), such that v₁ = i, v_n = j and the edges from v₁ to v₂, from v₂ to v₃, …, and from v_n-1 to v_n exist in the network; if such a path exists, j is said to be reachable from i. Trivially, any vertex is considered reachable from itself. A binary relation of two vertices reachable from each other defined on the vertex set is an equivalence relation; hence, the vertex set can be partitioned into distinct equivalence classes, i.e. strong components or strongly connected components (Cormen et al., 2009). Such a partition is called the strong decomposition of a directed network (Fig. 1), which uncovers its strong connectivity structures (the word “strong” emphasizes the fact that these structures cannot be revealed by analyzing a directed network as an undirected one). It has the properties that between any two vertices of the same strong component, there are paths in either direction; however, between two vertices of different strong components, there are only paths in one direction or none at all. Strong component SC₁ is said to have a path to strong component SC₂ if there is a path from any vertex in SC₁ to any vertex in SC₂. By strong decomposition, many important structural properties of a directed network can be revealed. The strong components (or the vertices in them) other than the largest strong component (LSC) can be categorized according to whether they have paths from or to LSC: IN, the strong components that have paths to LSC; OUT, the strong components that have paths from LSC; Other, all the other strong components (Newman et al., 2002; Ma and Zeng, 2003). IN and OUT don’t intersect due to the properties of strong decomposition. If LSC contains a significant amount of vertices, this representation of a directed network is called a bowtie structure due to its apparent visual resemblance (Fig. 1). Broder et al. (2000) investigated the strong connectivity structure of the World Wide Web. Newman et al. (2002) showed that an email network could be represented as a bowtie diagram with a large strong component situated at the core. Ma and Zeng (2003) identified similar bowtie structures decomposing metabolic networks, and reasoned it could be used to explain the metabolic phenomena of growth and development. Rodríguez-Caso et al. (2009) uncovered only small dynamical modules within a top-down hierarchy in the TRN of E. coli or B. subtilis, whereas a large dynamical module in a bowtie structure in the TRN of S. cerevisiae. Whether the A. thaliana TRNs harbor similar structural properties and how these properties are correlated with the biological functions require detailed investigation.

In this study, by decomposing the A. thaliana TRNs under six conditions into strong components (Sullivan et al., 2014), we aimed to identify the potential bowtie structures of the TRNs; in turn, to test whether the sizes of the LSCs of the TRNs are statistically significant or not; to quantify how much the gene sets of the LSCs varies among the conditions; and to find the genes with specific patterns of variation in the bowtie structures.