Construction and analysis of microRNA‐transcription factor regulation network in arabidopsis

Abstract

Transcription factors (TFs) and microRNAs (miRNAs) are two major types of regulators of gene expression, at transcriptional and post‐transcriptional levels, respectively. By gathering their gene regulatory relationships, gene regulatory networks (GRNs) could be formed. A network motif is a type of connection pattern among a set of nodes which appears significantly more frequently than in random networks. Investigations of the network motifs often yield biological insights into the nature of the network. The previous study on miRNA–TF regulation networks concentrated on animals, and relied heavily on computational predictions. The authors collected data concerning miRNA regulation and transcriptional regulation relationships in Arabidopsis from publicly available databases, and further incorporated them with the protein–protein interaction data. All the data in the author's collection are supported by experiments. They screened the network motifs, whose size ranges between 1 and 4. The biological implications of the motifs were further analysed, and a flower development related network was constructed as an example. In this example, they illustrated the relevance of the network with the given process, and proposed the association of several genes with flowers by a network cluster identification. In this study, they analysed the properties of the GRN in Arabidopsis, and discussed their biological implications, as well as their potential applications.

1 Introduction

Transcription factors (TFs) and microRNAs (miRNAs) are the major regulators of gene expression. TFs control gene expression by binding to their promoter regions and initiating transcription. MiRNAs serve to finetune gene expression by inhibiting translation or degrading their target mRNAs [1]. There are ∼ 22 nt non‐coding RNAs which bind to the mRNAs by a sequence complementarity and degrade their target mRNAs by recruiting the Argonaute protein complex. The TFs and the miRNAs control gene expression on transcriptional and post‐transcriptional levels, respectively, but they often interact to achieve effective control of gene expression. For instance, it has been pointed out in the previous paper that among the target genes of the miRNAs, the TFs are significantly enriched [2]. One generally accepted explanation of this phenomenon is that by suppressing the expression of the TFs, a miRNA could effectively down‐regulate the expression of a number of genes (targets of the miRNA‐regulated TFs). The previous paper of the gene regulatory networks (GRNs) involving both miRNA and TF is mainly about animals [3]. This may not be surprising because of the relative lack of gene regulation data in plants. With the recent development of plant TF and miRNA regulation databases such as AtRegnet [4] and PmiRKB [5], it has become possible to make initial attempts to analyse certain aspects of the miRNA‐TF joint regulation network in plants. A network motif is a pattern of node interconnection which appears significantly more often than expected by chance. Evidence suggesting these motifs may perform certain biological functions has been accumulating. For example, the simple three‐node feed‐forward loops (FFLs) are common motifs in GRNs [6], and they may be related to transport, signalling or organ identity maintenance [7–9]. In this paper, we established a GRN in Arabidopsis by using the miRNA knowledgebase recently published by our lab and a public transcription regulation database. In addition, we further incorporated protein–protein interaction (PPI) and gene co‐expression data. After the data collection, the network motifs were screened and subjected to further analysis of their potential biological implications. Finally, we analysed the network related to a certain process, and proposed a method of inferring the functional association of certain genes with this process.

2 Results and discussions

A flowchart of our entire network analysis framework is shown in Supplementary Figure S1. Firstly, we collected the gene regulation data, and merged them into a comprehensive network. The properties of the genes in our network were analysed, and the motifs were screened. Based on the results of motif identification, we investigated the relevance of these motifs with a given biological process (flower development) by analysing gene ontology (GO) enrichment, pathway enrichment and the hub nodes. Finally, we proposed a method of inferring the functions of certain genes by cluster identification in networks.

2.1 Data collection

PmiRKB [5] and plant microRNA database (PMRD) [10] are two databases concerning plant miRNAs and their targets. As the PMRD relies on prediction tools in determining regulation relationships, we chose PmiRKB whose regulation data were obtained by degradome sequencing. According to miRBase [11], some of the miRNAs in PmiRKB may not be true miRNAs because of their lack of conservation, poor hairpin structure, low northern blot signals and so on. Therefore we discarded the regulation relationships involving these miRNAs. Since most of the data in the protein interaction and transcription regulation databases only records the gene loci, we ignored the transcripts a miRNA actually targets and only maintained their target gene loci in the data integration process. As a result, 4448 miRNA‐target gene relationships involving 256 miRNAs and 2718 targets were integrated into the GRN.

The transcription regulation data were gathered from the publicly available database AtRegnet, which consists of about 11 500 targets of 60 TFs.

The currently available PPI databases such as BioGrid [12], MINT [13], IntAct [14] and DIP [15] contain a large number of PPIs in Arabidopsis. Apart from these comprehensive databases, we also collected data from the Arabidopsis‐specific PPI databases including AtPID [16], AtPIN [17] and TAIR [18]. Among the above‐mentioned databases, AtPID and AtPIN contain computationally predicted interactions, whereas the others focus on curating experimentally obtained data.

To ensure the quality of our interaction dataset, we integrated the experimentally verified interactions and discarded the predicted ones. About 18 000 PPIs among 6770 genes were gathered in this step. To access the functional linkage between a pair of genes from another aspect, we collected the gene coexpression data in Arabidopsis from ATTED_II [19]. It contains a large number (∼ 2 400 000) of coexpressed gene pairs with their Pearson correlation coefficients (PCC scores). We used the coexpression data of this database, and set 0.5 as the cutoff for the PCC scores.

2.2 Analysis of the miRNA and the TF target genes

As mentioned above, the miRNA target genes in our collection amount to 2718. GO analysis was performed for this set of genes, as this may provide hints for the potential functions of the miRNAs in our network. The result indicates that these genes are enriched in F‐box associated proteins (1.7 × 10⁻⁴³), transcription regulator (1.1 × 10⁻¹¹) and gene silencing by miRNA (2.5 × 10⁻¹⁰). This is what was expected, as the previous evidence has shown that the miRNAs bind preferentially to the F‐box proteins in cell cycle regulation and signal transduction [20], to the TFs to effectively affect gene expression [21] and to the miRNAs themselves because of the sequence similarity between the mature miRNAs and their precursors [22]. In addition, the miRNA targets are also enriched in meristem development (2.6 × 10⁻⁷), post‐embryonic development (4.4 × 10⁻⁵) and organ development such as shoot (2.8 × 10⁻⁴), leaf (4.0 × 10⁻⁴) and flower (4.5 × 10⁻⁴), respectively. This is also consistent with the earlier findings that the miRNAs participate in a variety of developmental processes [20]. The top ten enriched biological processes are shown in Fig. 1, in which the terms ‘post‐transcriptional gene silencing by RNA’ and ‘regulation of transcription’ can be observed.

Fig. 1.

–log(P) value of the top enriched biological processes among the miRNA targets

The same analysis was also performed for the TF target genes in our network. As a result, we found that the target genes are highly enriched in the TFs themselves (2.0 × 10⁻⁴⁵). This implies the prevalence of transcriptional cascades which are capable of resisting the expression level fluctuations [23]. Apart from the TFs, we also found that the TF target genes are enriched in response to the organic substance (2.9 × 10⁻⁵⁰), response to hormone stimulus (3.6 × 10⁻³⁸), alternative splicing (1.7 × 10⁻¹⁷) and so on. The MiRNAs, however, are not significantly overrepresented in these target genes. In Fig. 2, the top enriched biological processes of the TF targets are shown. The full list of the enriched GO terms of the miRNA and the TF targets are shown in supplementary Tables S1 and S2.

Fig. 2.

–log(P) value of the top enriched biological processes among the TF targets

For the 60 TFs included in this network, most of their targets were identified by the high‐throughput experimental approaches which are capable of detecting the binding sites on a genome‐wide level. For instance, the regulatory relationships determined by the methods including ‘ChIP−Chip + CisGenome’, ‘ChIP‐seq’, ‘ChIP−Chip + Parks’ and ‘ChIP−Chip’ make up 90% of all the relationships. Thus, it is not likely that the statistical significance of a certain biological process results from the intense studies focusing specifically on it.

After integrating the PPI data, we found that the TFs have a very strong affinity of physically interacting with their target genes: we identified 59 such PPI pairs in our network, whereas in a randomised network, only 2.88 PPIs are expected to be found (P < 2.2 × 10⁻¹⁶). The SEP3–AP1 interaction is an example. SEP3 and AP1 are both members of the MADS family TFs, and they interact to promote normal flower development [24]. In addition, SEP3 regulates AP1 expression by binding to its promoter region. This suggests that SEP3 promotes flower development not only by transcriptionally regulating its target AP1, but also by forming a PPI with it. Examples of this kind are prevalent in our network.

On analysing the overlap between the miRNA and the TF target genes, we found that they have a high PPI enrichment (6.8 × 10⁻¹⁶). This suggests that the genes targeted by both the miRNA and the TF tend to interact with each other, and may jointly participate in certain biological processes. By using the union of the miRNA and the TF target genes as a background, we performed a GO analysis for the genes involved in these PPIs. The result shows that the TFs are strongly overrepresented (3.1 × 10⁻¹⁰) inspite of being compared with the entire genome; the TFs are already enriched in the background. Similarly, by selecting the hub genes (degree cutoff = 6) in the miRNA regulation network and by analysing their GO in the background of all the miRNA target genes, we found that the TFs are also enriched (3.2 × 10⁻²⁴). To test the robustness of our result, we enhanced the cutoff to 8, which includes only 12.9% of all the PPI‐participating genes. The same GO analysis was performed and the P ‐value for the term ‘transcription regulation’ is 1.4 × 10⁻⁴. These findings imply that the TFs may play pivotal roles in our GRN. It is believed that coexpression serves as a strong indicator of the PPI, thus we calculated the coexpression enrichment in the intersection of the miRNA and the TF target genes. Reassuringly, the coexpression is also highly enriched (P < 2.2 × 10⁻¹⁶) in the given set of genes, confirming the notion that these genes tend to interact with each other.

2.3 Network motifs

Network motifs are overrepresented node connection patterns that may have certain functions. Here, we screen motifs by using the miRNA regulation, the TF regulation and the PPI data collected above. Judging from the number of the participating nodes, we classified our motifs into four types: from one‐ node to four‐node motifs.

2.4 One‐node

The auto‐regulatory loop is the simplest motif, which consists of a single node, which regulates itself. As expected, we found 45 miRNA self‐regulations (P < 2.2 × 10⁻¹⁶) (Fig. 3). In addition, only 8 among the 329 miRNA–miRNA regulations occur between the miRNAs in different families. These findings confirm our previous speculation that the enrichment of the miRNAs in the miRNA targets is largely caused by their self‐regulation. According to the previous paper, this kind of auto‐regulatory loop serves as a buffering system for the expression level of the miRNAs [22]. As for the TFs, we detected ten auto‐regulatory loops (8.4 × 10⁻⁹), indicating a tendency of the TFs to transcriptionally regulate themselves. The auto‐regulatory loops for the TFs may shorten the response time and reduce variation, or slow response and enhance variation, depending on whether it suppresses or promotes its own expression [25]. These simple motifs have been discovered in other organisms including human [26] and Escherichia coli (E. coli) [27]. As expected, they were found in Arabidopsis as well.

Fig. 3.

Summary of the network motifs (size‐1 and 2)

2.5 Two‐node

The feedback loop is a motif which consists of two nodes regulating each other. In our network, there are three possible types of feedback loops: miRNA–miRNA, TF–TF and miRNA–TF loops, respectively. Fourty‐six miRNA–miRNA feedback loops were found all of which involve the miRNAs in the same family. As expected, this result is also very significant (P < 2.2 × 10⁻¹⁶) (Fig. 3). Five TF–TF feedback loops were detected, which is also statistically significant (1.3 × 10⁻⁵). Although feedback loops are abundant in the post‐transcriptional level for E. coli, the abundance of the TF–TF feedback loops in E. coli failed to reach a statistical significance [23]. As for the miRNA–TF loop, only one exists in our network: the miR166 g‐ATHB8 loop. These two nodes control the development of the leaf vasculature together [28].

2.6 Three‐node

In case of the three‐node motifs, myriads of possibilities exist. Thus, it would be far too time consuming if we extract every possible motif manually. Fortunately, software designed for network motif detection is available. FANMOD [29] was chosen because of its ability to handle networks with different kinds of nodes and edges, and the relatively low time‐complexity of its algorithm. We imported our miRNA regulation, transcription regulation and PPI data, and chose to detect the size‐three motifs. The results showed that the following motifs (Fig. 4) are significant.

Fig. 4.

Overrepresented three‐node motifs

The three types of nodes represent miRNAs, TFs and proteins (apart from TFs) respectively

arrows represent regulatory relationships

Fig. 4 a illustrates that the two miRNAs in a miRNA–miRNA regulation relationship tend to have the same target genes, and the one miRNAs tend to regulate the other. This is what was expected, because according to our previous analysis, the two miRNAs in this motif tend to have a very high sequence similarity. Thus, they are likely to regulate the same gene, or regulate each other. Fig. 4 B demonstrates that the TFs regulating the same target gene tend to form PPIs, no matter whether the target encodes a miRNA, a TF or a common gene. This statistically confirms the notion that the TFs often function in complexes, as is previously reported in yeast [30]. Fig. 4 c is the incoherent FFL in which a miRNA and a TF jointly regulate the target. There are 12 such loops in our network. The miR172‐AP2‐TOE1 FFL is an example of this kind. MiR172 is a miRNA which controls the patterning and the timing of Arabidopsis by targeting AP2 and other AP2‐like genes including TOE1 [31]. AP2 is a floral homoeotic gene. It disrupts the miR172 base‐pairing resulting in enhanced AP2 levels and defects in flower patterning [32]. TOE1 is an AP2‐like gene targeted by both miR172 and AP2 whose overexpression causes late flowering [33]. The above evidence suggests that miR172 represses TOE1 by two possible ways: directly targeting TOE1, and repress TOE1 transcription by targeting AP2. By controlling the TOE1 expression at both the transcriptional and the post‐transcriptional level, miR172 effectively represses TOE1 and thus influences the flowering time. In an alternative form of the miRNA‐TF composite FFL, the TF transcripts the pre‐miRNA and targets a gene together with the mature miRNA. We failed to detect any of this kind of FFLs, because the TFs in our network do not have an affinity for the miRNAs. Interestingly, for mammalians, the statistical significance of the former form of FFL depends on the target prediction tool, whereas the latter form is always significant [2]. Figs. 4 d and e indicate the tendency of the proteins regulated by the same TF or miRNA to form PPIs. It is previously reported that in C. elegans, a pair of proteins in a PPI tend to be regulated by the same miRNA [34]. We observed a similar phenomenon in Arabidopsis. As for the proteins regulated by the same TF, they also tend to form PPIs. These forms have been discovered in other organisms including C. elegans [35] and yeast [30]. Considering whether the protein is a TF, and whether the two miRNAs in Fig. 3 a regulate each other, these motifs can be classified into different types. FANMOD calculated their Z scores, respectively, and the results are shown in supplementary Table S3.

2.7 Four‐node

For detection of the four‐node motifs in our network, we calculated the P ‐value of each motif by examining the PPI enrichment score (see Section 4). We looked for three kinds of motifs in our network: miRNA–miRNA‐PPI, miRNA–TF‐PPI, TF–TF‐PPI, respectively (Fig. 5).

Fig. 5.

Four‐node motifs

a miRNA–miRNA‐PPI

b miRNA–TF‐PPI

c TF–TF‐PPI

As shown in the graph, the miRNA–miRNA‐PPI motif consists of two miRNAs, each regulating one of the two proteins in a PPI. In the miRNA–TF‐PPI motif, one of the regulators is TF and the other is a miRNA. In the TF–TF‐PPI motif, both the regulators are TFs. For each possible pair of miRNAs in the miRNA–miRNA‐PPI motif, we calculated the PPI enrichment score for their targets. The same process of calculation was also performed for the miRNA–TF‐PPI and the TF–TF‐PPI motifs. The results are shown in Fig. 6.

Fig. 6.

Pairwise PPI enrichment of the three motifs

The X ‐axis represents all the pairs, and the Y ‐axis is the Z ‐score

a miRNA–miRNA‐PPI

b TF–TF‐PPI

c miRNA–TF‐PPI

The red line is Z = 2, the cutoff for significance

2.7.1 miRNA–miRNA‐PPI

For the miRNA–miRNA‐PPI motif, almost a half of the regulator pairs are enriched in PPI, reflecting the prevalence of this motif. Considering the scarcity of the targets for a miRNA, it is not surprising that for most pairs of miRNAs, we cannot detect PPI between their targets in our dataset. Thus, only a fraction of all THE miRNA pairs, which are capable of forming this motif, are included in the chart above.

To evaluate the overall enrichment of this miRNA–miRNA‐PPI motif, we pooled all the miRNA targets and calculated their PPI enrichment score. The result (1.496 × 10⁻⁰⁷) indicates that the PPIs are significantly enriched in the miRNA targets, suggesting functional associations among all the miRNA target genes in our network. Previous analysis suggests that the PPI enrichment may be explained by the existence of many TF complexes and F‐box protein complexes. For instance, EGL‐3 is a bHLH TF which interacts with five other TFs. The five TFs are MYB, MYB75, MYB113, MYB66 and MYB123. Together with EGL3, the MYB family TFs are regulated by different miRNAs, and they are likely to form protein complexes.

For the miRNA pairs in this motif, we checked if they have an affinity to regulate each other. As expected, the P ‐value is less than 2.2 × 10⁻¹⁶, and the possibility that one regulator miRNA targets the other is ten times higher than the possibility of regulation between two randomly selected miRNAs. Consider the fact that in our network, most miRNA–miRNA occurs within the same family, it is clear that in the miRNA–miRNA‐PPI motif, the two miRNAs are very likely to belong to the same family. As a result of their sequence similarity, their targets tend to have a high homology. For instance, JAZ4 and JAZ9 are two JAZ‐domain proteins involved in jasmonate signalling [36]. Their homology leads to the interaction, as well as being targeted by two miRNAs in the same family (miR169n and miR169d), respectively.

2.7.2 TF–TF‐PPI

Next, we discussed the potential implications of the TF–TF‐PPI motif. Similarly, only TF pairs with at least one PPI between their targets are included. Similar to the miRNA–miRNA‐PPI motif, most TF–TF pairs are excluded because of the lack of PPI. The overall PPI enrichment was also calculated, with the p ‐value less than 2.2 × 10⁻¹⁶. This is highly significant, thus it suggests that the TFs in our dataset may be functionally associated.

PIF1 encodes a Myc‐related bHLH TF whose targets form extensive PPI with the targets of SEP3, a TF with a homoeotic domain. The PPIs between their targets amount to 539, with a P ‐value less than 2.2 × 10⁻¹⁶. GO analysis about genes forming these PPIs indicates that they are involved in transcriptional regulation, response to stimulus, flower development etc. This is what was expected,because the TFs are enriched in the TF target genes, and PIF1 and SEP3 are involved in reproductive structure development and flower development, respectively. This example illustrates that the GO of the target genes participating in the PPIs may serve as an indicator of the regulators’ function.

For the pair of the regulators, we examined whether they tend to physically interact. By using all the TFs whose target information is available as the background, we calculated the PPI enrichment score for the TFs that appear in this motif. The resulting P ‐value is 1.39 × 10⁻¹², demonstrating their strong affinity for physical interaction. It indicates that if two TFs interact, their targets also tend to form a PPI. The GL1 and GL3 are two TFs which interact with each other in trichome development and epidermal cell differentiation [37, 38]. Among their 19 285 target gene pairs, 29 are capable of forming a PPI and this yields a P ‐value of 0.002. By analysing the GO enrichment for the PPI‐participating genes, we found that trichome development and epidermal cell differentiation are overrepresented with the P ‐values of 1.2 × 10⁻⁴ and 3.2 × 10⁻⁵, respectively. This example again bolsters the notion that the proteins in the TF–TF‐PPI motif are functionally related to the two regulator TFs.

2.7.3 miRNA–TF‐PPI

After investigating the miRNA–miRNA‐PPI and the TF–TF‐PPI motifs, we finally investigated if the miRNA–TF‐PPI regulation relationship is also significantly overrepresented. The result is also positive, with a P ‐value of 8.8 × 10⁻⁵. This indicates that in our dataset, a protein regulated by one or more miRNAs and another regulated by at least one TF is likely to form a PPI. Next, we extracted all the miRNA–TF pairs whose targets form this kind of PPI. 1051 pairs were identified, among which most of the pairs show a significant PPI enrichment (P < 0.05) (Fig. 6). The results indicate that apart from regulating the same target gene, this motif may serve as an alternative form of the miRNA–TF cooperation, because their targets tend to physically interact and may jointly perform certain functions.

To illustrate the function of this motif more clearly, we take miR172‐SEP3 as an example. miR172 promotes flowering when overexpressed [39], and SEP3 is a homoeotic gene indispensable for flowering. We examined the PPIs between their targets and detected 27 PPIs (2.7 × 10⁻¹¹). According to the recent literature, many genes in these PPIs are related to flowering. For instance, the above‐mentioned AP2 is a homoeotic gene which functions in flower development. It suppresses several floral organ identity genes in Arabidopsis by physically interacting with the corepressor TOPLESS [40]. In this PPI, AP2 is targeted by miR172, whereas SEP3 transcriptionally regulates TOPLESS. LSU1, a protein which was considered to be involved in the response of low sulphur, was recently discovered to play an essential role in flower patterning [41]. LSU1 interacts with TOE2, a MADS domain TF which suppresses flowering. In this case, LSU1 is regulated by SEP3 whereas TOE2 is a target of miR172. TOE2 also interacts with FIN4, a SEP3 target and an l ‐aspartate oxidase. The l ‐aspartate has an inhibitory effect on flowering [42], thus FIN4 may be linked with flowering as well. TOE1, a homologue of TOE2, forms a PPI with KAN1, a regulator of organ polarity which is required for the abaxial identity of carpels [43]. Similar to TOE2, TOE1 is also a miR172 target, whereas KAN1 is targeted by SEP3.

MiR167d is another flower‐related miRNA which controls the fertility of anthers and ovules via the patterning of the ARF6 and the ARF8 expressions [44]. Its targets also tend to form PPIs with the targets of SEP3 (7.5 × 10⁻¹⁶). For example, ARF6 and ARF8 form several PPIs with the IAA family proteins (including IAA 1, 2, 4, 7, 13, 17 and 24, respectively), which are targeted by SEP3. The IAA family proteins are transcription regulators acting as the repressors of an auxin‐inducible gene expression. Auxin has been implicated to play a role in the development of flowers. For instance, the paper by Cheng et al. [45] pointed out that ‘auxin is necessary for the initiation of floral primordia, and the disruption of auxin biosynthesis, polar auxin transport or auxin signalling leads to the failure of flower formation. Auxin also plays an essential role in specifying the number and identity of floral organs’. Therefore it is highly likely that the proteins in these PPIs participate in flowering by regulating the auxin‐mediated pathways.

A previous paper by Lin et al. [46] screened the four‐node motifs in a human GRN. The results showed that these motifs exist in the human GRNs well, but their P ‐values vary. The median Z score for the miRNA–TF‐PPI is above the cutoff for significance (2.16), but the scores for the miRNA–miRNA‐PPI and the TF–TF‐PPI motifs are not significant (1.86 and 0.74, respectively).

2.8 Flower development related network

In the previous section, we identified the network motifs in the Arabidopsis GRN. In this section, we narrow down our scope to a certain biological process to examine the potential implication of our motifs. We chose the miRNAs and the TFs involved in a given process: flower development. This process was chosen because it is one of the best understood biological processes in plants, and the known TFs and miRNAs participating in it are relatively abundant. We manually collected the miRNAs related to flowering from recent publication [47], and the TFs whose GO terms contain ‘flower development’. We then calculated the overall PPI enrichment for the miRNA–miRNA‐PPI, the miRNA–TF‐PPI and the TF–TF‐PPI motifs, the resulting P ‐values being 1.64 × 10⁻⁵, 4.30 × 10⁻³ and less than 2.2 × 10^−16, respectively. These results indicate that in the flower development related network, these motifs also exist. By using all the genes regulated by the flower related miRNAs and TFs as a background, we performed a GO enrichment analysis for the genes in the PPIs regulated by the flower related miRNAs and TFs. The results indicate that these genes are enriched in flower development (1.2 × 10⁻¹⁰), reproductive structure development (1.3 × 10⁻⁹) and reproductive developmental process (2.9 × 10⁻⁸). These results illustrate that the PPIs in the flower development network are relevant to this process.

We tested whether the flower development related genes play important roles in our network. The hub genes are the nodes in the gene network which possess relatively high degrees. They are usually biologically important because the hub nodes in a network are critical for the overall connectivity of the network. By choosing ten as the cutoff for connectivity, we defined a set of hub genes in our network. The degree cutoff of the hub nodes can be selected arbitrarily, but conventionally, the standard is that the hubs should make up about 10% of all the nodes. For the flower development network, the 66 hubs make up 8%. Then, these genes were subjected to a GO analysis in the background of all the PPI participating genes in the flower development network. In the results, ‘flower development’ is again enriched (9.1 × 10⁻⁴), which is also the case for ‘reproductive structure development’ (6.1 × 10⁻⁴) and ‘reproductive process’ (9.1 × 10⁻⁴). This substantiates the notion that the flower development related genes in this network tend to play pivotal roles. Pathway enrichment analysis was performed for this network by using database for anotation, visualisation and integrated discovery (DAVID). As a result, two Kyoto Encyclopedia of Genes and Genomes (KEGG) pathways are significantly enriched: ‘circadian rhythm’ (7.1 × 10⁻⁴) and ‘cysteine and methionine metabolism’ (5.9 × 10⁻³). Arabidopsis is a long day plant, which flowers early in long days and later in short days [48]. The response of the plant to day lengths is caused by the circadian clock, which measures the duration of day and night [49]. Thus, the circadian rhythm is of vital importance for the regulation of Arabidopsis flowering.

There are nine genes in our network which take part in the ‘circadian rhythm’ pathway. By selecting their PPI partners, we obtained 31 genes. By performing a GO analysis with the background of the entire network, we found that the term ‘flower development’ appears with a P ‐value of 6.7 × 10⁻⁶. For ‘reproductive structure development’ and ‘reproductive developmental process’, their P ‐values are 7.5 × 10⁻⁴ and 1.3 × 10⁻³, respectively. This is what was expected, because it supports the idea that the ‘circadian rhythm’ pathway is associated with flower development.

In the network (Fig. 7), we saw several clusters formed by extensive PPIs among a subset of genes. To identify these tightly connected subnetworks, we used the subnetwork identification software Cfinder. The result shows that there are 30 tightly connected subnetworks with a minimum size of 3. In some of these clusters, the flower development related genes are overrepresented. In one of the clusters, 16 of its 25 genes have the GO term ‘flower development’. We reckoned that the other nine genes may also be relevant to flower development, as the majority of the genes in their cluster are involved in this process. Among the nine genes, there are four MADS domain proteins: AGL15, AGL19, AGL21 and AGL44, respectively. In plants, the MADS proteins participate in many major developmental processes, among which flower development is included [50, 51]. Although the four MADS genes do not have the GO term ‘flower development’, there is evidence showing their relevance to this process. For example, AGL15 act as a repressor of floral transition in Arabidopsis [52], whereas the overexpression of AGL19 accelerates flowering [53]. Apart from the MADS domain proteins, there are three calmodulin‐like calcium‐binding proteins. The previous literature discovered that the endogenous level of the Ca²⁺ functions in the inhibition of floral induction and the calmodulin antagonists reduced the flowering response [54]. After considering their topological linkage with the flower development related genes and the evidence cited above, we propose that the other genes in the cluster may also be related to flowers. This example demonstrates that by collecting the miRNAs and the TFs related to a given process and gathering the PPIs from their targets, a PPI network consisting of multiple miRNA–miRNA‐PPI, miRNA–TF‐PPI and TF–TF‐PPI regulation relationships could be constructed. This PPI network would be relevant to the given process, and the novel genes associated with this process could be identified by examining the tightly connected subnetworks.

Fig. 7.

Flower development related PPI network

Light grey nodes are the genes involved in flower development

The graph in the lower right corner is the cluster in which the flower development related genes are overrepresented

In the overview graph, it is located in the black rectangle

The network was visualised with Cytoscape [56]

3 Conclusions

In this paper, we collected an Arabidopsis miRNA regulation, a TF regulation and the PPI data. Then, these data were integrated to construct a comprehensive Arabidopsis GRN. After analysing the functions of the genes in this network, we screened the network motifs. The results contain a one‐node self‐regulation, a two‐node feedback loop, a three‐node coregulation and FFLs and the four‐node crosstalk motifs. We discussed their biological meanings and chose to focus on the four‐node motifs, which are classified into three categories: miRNA–miRNA‐PPI, miRNA–TF‐PPI and TF–TF‐PPI, respectively. The PPI enrichment scores were calculated for the three motifs and a few examples were examined to study their biological implications. By filtering the flower development related miRNAs and TFs, we concentrated on a given process (flower development) to investigate the relevance of these motifs to a certain biological phenomenon. The results indicate that the PPIs in this specific network have an extensive functional linkage with this flower development. Finally, we illustrated the potential application of our network analysis. By identifying the clusters in the flower development related PPI network, the association of a few genes with this process was proposed, and the previous publications were consulted to bolster our notion.

Although the previous studies on the miRNA–TF regulatory networks mainly concentrate on animals, we chose to analyse the miRNA−TF network in plants. As the earlier studies rely heavily on the computational predictions of the miRNA and the TF targets, we based our research on experimentally verified data. Apart from the functional analysis of the network components and the network motif detection, we utilised our results to propose the potential functions of certain genes. As the literature evidence on the gene regulatory data in plants proceeds to accumulate, our method may serve to predict the associations of an increasing number of genes with various biological phenomena.

4 Methods

4.1 PPI enrichment score

For a given set of genes, we calculated the PPI enrichment by using the method proposed by Lin et al. [55]. That is, we define the possibility for an interaction between a randomly selected pair of genes in the PPI network as

$$p=\frac{{\text{PPI}}_{\text{all}}}{N},0<p<1$$

Here, p denotes the possibility for an interaction, N is the total number of the gene pairs involved in the entire PPI network and PPI_all represents the total number of the PPIs. Then, we assume that the number of the PPIs among a given set of genes follows a binomial distribution. That is, the possibility of forming a PPI between a pair of randomly given genes is p ₀, and the presence/absence of the PPIs between different pairs of genes is independent. Thus, the null hypothesis for the statistic test can be defined as

$$p_0=p$$

This means that in our set of genes, the possibility of an interaction for two genes which are also in the PPI network is equivalent to p. In that case, this set of genes would have no PPI enrichment compared with the random gene sets.

By conducting a binomial test, the P ‐value could be calculated. The parameters should be set as follows

$$\begin{array}{rl}\text{Number}\text{of}\text{success}& ={\text{PPI}}_{\text{set}}\\ \text{Total}\text{number}\text{of}\text{trials}& =N_{\text{set}}\\ \text{Possibility}& =p\end{array}$$

where PPI_set denotes the total number of the PPIs in the gene set, and N _set represents the total number of the genes which are also in the PPI network.

The P ‐values are normalised to the Z scores, which is defined as

$$z=\frac{{\text{PPI}}_{\text{set}}-p\ast N_{\text{set}}}{\sqrt{p(1-p)N_{\text{set}}}}$$

4.2 GO analysis and pathway enrichment analysis

We simply used DAVID to perform the analysis. For the GO term ‘flower development’ in the flower development related network, we reported the P ‐value of the hypergeometric distribution; otherwise, the family‐wise error rate (FWER) was taken into account, and the Bonferroni procedure was employed. For the pathway enrichment analysis, we controlled the FWER and selected only the KEGG‐registered pathways. P < 0.01 was selected as the cutoff, although most results are far more significant.

4.3 Motif discovery

4.3.1 One‐node motif

There are two kinds of one‐node motifs: miRNA self‐regulation and TF self‐regulation. We first defined the possibility for regulation between two random miRNAs as the following

$$P_{\text{miR}}=\frac{N_{\text{miRmiR}}}{{\sum }_{i=1}^{N_{\text{miR}}}i}$$

p _miR is the possibility, N _miRmiR represents the number of the miRNA–miRNA regulation relationships and N _miR denotes the number of the total miRNAs in our network.

Then, we used a binomial test to calculate the significance of the miRNA self‐regulation motif with the following parameters

$$\begin{array}{rl}\text{Number}\text{of}\text{success}& :N_{\text{miRloop}}\\ \text{Number}\text{of}\text{trials}& :N_{\text{miRmiR}}\\ \text{Possibility}& :p_{\text{miR}}\end{array}$$

where N _miRloop represents the number of the miRNA self‐regulation loops.

Similarly, we defined the possibility for regulation between two TFs as

$$p_{\text{TF}}=\frac{N_{\text{TFTF}}}{{\sum }_{i=1}^{N_{\text{TF}}}i}$$

The significance of the TF self‐regulation loops can be calculated by the following binomial distribution:

$$\begin{array}{rl}\text{Number}\text{of}\text{success}& :N_{\text{TFloop}}\\ \text{Number}\text{of}\text{trials}& :N_{\text{TFTF}}\\ \text{Possibility}& :p_{\text{TF}}\end{array}$$

4.3.2 Two‐node motif

Given a miRNA–miRNA regulation relationship, there is a possibility that the target also regulates the regulator. Here, we calculate the P ‐value of this motif by examining whether this possibility is significantly higher than the possibility for a random pair of miRNAs. The binomial test was again employed by using the following parameters

$$\begin{array}{rl}\text{Number}\text{of}\text{success}& :2\ast N_{\text{miRFL}}\\ \text{Number}\text{of}\text{trials}& :N_{\text{miRmiR}}\\ \text{Possibility}& :p_{\text{miR}}\end{array}$$

where N _miRFL denotes the number of the miRNA feedback loops.

The same method was applied to the TF–TF feedback loops with the following parameters

$$\begin{array}{rl}\text{Number}\text{of}\text{success}& :2\ast N_{\text{TFFL}}\\ \text{Number}\text{of}\text{trials}& :N_{\text{TFTF}}\\ \text{Possibility}& :p_{\text{TF}}\end{array}$$

4.3.3 Three‐node motif

As mentioned in the results section, we used FANMOD as the motif discovery software. The parameters are chosen as follows:

Algorithm options:

• Subgraph size: 3

• Samples to estimate the number of subgraphs: 100 000

• Full enumeration: yes

Random networks:

• Number of bidirectional edges: local const

• Number of networks: 50

• Regard vertex colours: yes

• Regard edge colours: yes

• Exchange edges: yes

• Exchange per edge: 3

• Exchange attempts: 3

• Re‐estimate subgraph number: yes

Input graph:

• Directed: yes

• Coloured vertices: yes

• Coloured edges: yes

4.3.4 Four‐node motif

We evaluated their significance by calculating the PPI enrichment score (see ‘PPI enrichment score in this section).

4.4 Cluster identification

CFinder was employed to do this. We loaded all the PPIs in the network, ran the program and chose k = 3 from the output. The k value is the clique size parameter in the algorithm. A lower k means a lower link density in the cluster, but more and larger clusters would be identified. On the contrary, a higher k value results in a smaller number but stronger clusters.