Drought Stress-Related Gene Identification in Rice by Random Walk with Restart on Multiplex Biological Networks

Abstract

Drought stress-related gene identification is vital in revealing the drought resistance mechanisms underlying rice and for cultivating rice-resistant varieties. Traditional methods, such as Genome-Wide Association Studies (GWAS), usually identify hundreds of candidate stress genes, and further validation by biological experiements is then time-consuming and laborious. However, computational and prioritization methods can effectively reduce the number of candidate stress genes. This study introduces a random walk with restart algorithm (RWR), a state-of-the-art guilt-by-association method, to operate on rice multiplex biological networks. It explores the physical and functional interactions between biological molecules at different levels and prioritizes a set of potential genes. Firstly, we integrated a Protein–Protein Interaction (PPI) network, constructed by multiple protein interaction data, with a gene coexpression network into a multiplex network. Then, we implemented the RWR on multiplex networks (RWR-M) with known drought stress genes as seed nodes to identify potential drought stress-related genes. Finally, we conducted association analysis between the potential genes and the known drought stress genes. Thirteen genes were identified as rice drought stress-related genes, five of which have been reported in the recent literature to be involved in drought stress resistance mechanisms.

1. Introduction

As an essential food crop, rice has a wide cultivation area worldwide. According to data from the Food and Agriculture Organization of the United Nations, the global rice planting area is about 167 million hectares, and the total production is about 750 million tons [1]. Rice demand is expected to increase as the population increases [2]. However, the yield of rice is severely affected by drought stress. Improving the drought stress resistance of rice will expand the planting area and increase rice production. Therefore, growing rice varieties with drought stress resistance is essential to ensure food security.

Usually, rice drought tolerance is affected by multiple genes. With the development of high-throughput sequencing technology, many biological omics data and biomolecular interactions have been explored. Utilizing these technologies sheds light on the drought tolerance mechanism and the development of drought-tolerant varieties. Previous research mainly focused on Genome-Wide Association Studies (GWAS) [3], weighted gene coexpression network analysis (WGCNA) [4], and gene-by-gene association analysis [5,6]. The WGCNA clusters genes with similar expression patterns and analyzes the relationship between modules and specific traits to find hub genes in each module. The GWAS carries out overall association analysis on genetic variation genes within the whole genome, which can provide an overview of abiotic stress and discover new abiotic stress mechanisms [7]. However, GWAS usually generates hundreds of candidate genes, which need a lot of biological experiments for verification. The WGCNA-obtained coexpression module is unstable if the sample data are too small. As a state-of-the-art association-by-guilt algorithm, the random walk with restart algorithm (RWR) [8,9] can quickly and effectively predict the degree of association between nodes and the starting seed points in the network. In this manner, the RWR effectively reduces the number of candidate genes and predicts the candidate genes’ functional role based on the seed nodes. The RWR has become a powerful approach to identify human disease-related genes [10]; however, its ability to identify rice resistance-related genes has rarely been studied. Given its excellent performance in predicting pathogenic genes, we believe that the RWR is promising for rice drought stress-related gene identifications.

In this study, we fused data from multiple rice public PPI databases, which expanded the information in the PPI network and reduced the sample bias and noise. At the same time, the rice coexpression network was constructed using RNA-seq data. With each node corresponding to the genes or the derived proteins, we merged the PPI and coexpression networks into a two-layer network, allowing multiple edges between a pair of nodes. Then, the RWR on multiplex networks (RWR-M) [8] was applied to this multiplex network to identify rice drought stress-related potential genes. Next, potential genes were analyzed in enrichment analysis and association with known drought stress genes to identify stress-related candidate genes. To validate the findings, a support vector machine (SVM) [11] model was constructed using the candidate genes to predict rice phenotypes. As external validation, we reviewed the recent literature to understand the regulatory mechanisms of the candidate genes.

2. Materials and Methods

2.1. Dataset

We extracted the rice protein interaction information from the STRING database (https://cn.string-db.org) [12], RicePPINet (http://netbio.sjtu.edu.cn) [13], and PRIN database (http://bis.zju.edu.cn/prin/) [14]. Then, we matched the protein names to gene names using the RAP-DB [15] database, which provides a comprehensive set of gene annotations for the rice genome sequences. In addition, genes with mismatched names were removed. Finally, the numbers of PPIs obtained from STRING, RicePPINet, and PRIN were 8949049, 673489, and 55211, respectively.

We downloaded the rice RNA-seq data from NCBI’s Sequence Read Archive (SRA) database [16] to construct a gene coexpression network. The data included ten drought stress treatment samples and ten normal samples (SRR7054176-83, SRR3051740-45, and SRR30517527-57), for a total of 20 samples of about 33,688 genes.

The China Rice Data Center (https://www.ricedata.cn) is a rice-themed database sponsored by the China National Rice Research Institute. In total, 218 genes known to be related to drought stress were in the China Rice Data Center as of June 2022, each denoted as $G{K}_i(i=1,2,\dots ,218)$. These 218 known genes were considered as the seed nodes in this study.

2.2. The Networks’ Construction

2.2.1. Protein–Protein Interaction Network

We constructed a rice PPI network based on the STRING database, named SinglePPI. In addition, we obtained the PPI from the PRIN and RicePPINet databases to provide complementary information to the STRING database. Each of the PPIs provides pairwise protein interaction scores. We normalized the interaction scores and then connected a pair of nodes when their interaction score in any database was higher than 0.3. An edge connecting two nodes meant there was an interaction between the corresponding proteins. Finally, a multisource network was constructed by these PPI, named MetaPPI, which consisted of 23,860 nodes and 3,096,015 edges.

2.2.2. Gene Coexpression Network

We constructed rice gene coexpression networks using the RNA-seq data. Differentially expressed genes (DEGs) were identified if padj < 0.05 and $\left|log2FoldChange\right|>1$ [17]. Using the Pearson coefficient [18] between DEGs, we constructed a coexpression network named COEX_DP, which was composed of 8928 nodes and 1,0267,919 edges.

The maximum information coefficient (MIC) [19,20] captures a wide range of correlations, including linear, nonlinear, and nonfunctional correlations [21]. The higher the MIC value, the stronger the correlation between two features. In this study, we calculated the MIC values between each DEG and the phenotype and selected those genes ranked in the top 30% of the MIC values. Then, based on the MIC between any pair of the selected genes, we constructed another coexpression network, named COEX_MM. It consisted of 8949 nodes and 24,352,943 edges.

2.2.3. Multiplex Network

A PPI network and a gene coexpression network were merged into a multiplex network, sharing the same set of nodes and different edges [22]. In this study, the MetaPPI_COEX_DP comprised the MetaPPI and COEX_DP, which consisted of 14972 nodes and 7682248 edges; the MetaPPI_COEX_MM comprised the MetaPPI and COEX_MM, which consisted of 14298 nodes and 16491940 edges. The process of the network construction is illustrated in Figure 1.

2.3. Random Walk with Restart on Multiplex Networks

The random walk is an effective approach to calculate the proximity between nodes and extract the topology structure of the network [23]. It describes a path that involves a series of random steps in a mathematical space. Its extension, random walk with restart (RWR) (Pseudocode is shown in Algorithm 1) [24,25], allows random walk to return to the starting point and continues to execute during the random walk process within a certain probability.

However, the existing algorithm was not applicable to multi-omics data. The RWR with multiplex networks (RWR-M) effectively accommodated multi-omics data and improved the prediction accuracy of a gene’s functional role. The walk traveled between different nodes in the same layer or jumped to a different layer on the same node, which reduced the prediction error caused by the network structure.

Algorithm 1 Random Walk with Restart (RWR).

Input:  a restart probability $\lambda$, a transition matrix M, an initial probability vector ${\overrightarrow{P}}_0^T$, and a threshold $Threshold$ Output:  A vector indicating the importance of nodes in the network: ${\overrightarrow{P}}_{t+1}^T$ 1: function RWR(M,$\lambda$,${\overrightarrow{P}}_0^T$) 2:     $Threshold\leftarrow {10}^{-5}$ 3:     $t\leftarrow 1$ 4:     ${\overrightarrow{P}}_1^T\leftarrow (1-\lambda )M{\overrightarrow{P}}_0^T+\lambda {\overrightarrow{P}}_0^T$ 5:     $Thre\leftarrow \sqrt{\sum {({\overrightarrow{P}}_1^T-{\overrightarrow{P}}_0^T)}^2}$ 6:     while $Thre>=Threshold$ do 7:         ${\overrightarrow{P}}_{t+1}^T\leftarrow (1-\lambda )M{\overrightarrow{P}}_t^T+\lambda {\overrightarrow{P}}_0^T$ 8:         $Thre\leftarrow \sqrt{\sum {({\overrightarrow{P}}_{t+1}^T-{\overrightarrow{P}}_t^T)}^2}$ 9:         $t\leftarrow t+1$ 10:     end while 11:     return ${\overrightarrow{P}}_{t+1}^T$ 12: end function

A multiplex network is an L-layer network. The edges in different layers belong to different categories or represent different properties. Each layer $\alpha =1,\dots ,L.$, is represented by its adjacency matrix, $A^{\left[\alpha \right]}(i,j)=0,\forall i=1,\dots ,n.$; if there is an interaction between nodes i and j in $\alpha$ layer, then $A^{\left[\alpha \right]}(i,j)=1$, otherwise 0. The automatic interactions were not considered in this study; then, $A^{\left[\alpha \right]}(i,i)=0,\forall i=1,\dots ,n$, and a multiplex graph is characterized by its adjacency matrix:

$$A=A^{\left[1\right]},\dots \dots ,A^{\left[L\right]}.$$

(1)

The random walk with restart on a multiplex network randomly walked within the same layers and had a certain probability to jump to another layer on the same node. Each layer of a network is regarded as an $n\ast n$ matrix, and an $nL\ast nL$ transfer matrix was constructed in the multiplex networks:

$$A=\left(\begin{array}{cccc}(1-\delta )A^{\left[1\right]}& \frac{\delta }{L-1}\mathbf{I}& \cdots & \frac{\delta }{(L-1)}\mathbf{I}\\ \frac{\delta }{(L-1)}\mathbf{I}& (1-\delta )A^{\left[2\right]}& \cdots & \frac{\delta }{(L-1)}\mathbf{I}\\ ⋮& ⋮& \ddots & ⋮\\ \frac{\delta }{(L-1)}\mathbf{I}& \frac{\delta }{(L-1)}\mathbf{I}& \cdots & (1-\delta )A^{\left[L\right]}\\ \end{array}\right),$$

(2)

where $\mathbf{I}$ is the $n\ast n$ identity matrix, $A^{\left[\alpha \right]}$ is the adjacency matrix of the $\alpha$th layer, the parameter $\delta \in [0,1]$ quantifies the probability of staying at each layer or jumping to another layer, and $\delta =0$ indicates that the particle always stays in the same layer without switching layers [26].

When using M to represent the column-normalized transition matrix obtained by A, the RWR-M is expressed as:

$${\overrightarrow{P}}_{t+1}^T=(1-\lambda )M{\overrightarrow{P}}_t^T+\lambda {\overrightarrow{P}}_{RS}^T.$$

(3)

The ${\overrightarrow{P}}_{t+1}=[{\overrightarrow{P}}_{t+1}^1,\dots ,{\overrightarrow{P}}_{t+1}^L]$ and ${\overrightarrow{P}}_t=[{\overrightarrow{P}}_t^1,\dots ,{\overrightarrow{P}}_t^L],t\in \mathbb{N}$ are vectors of length $n\ast L$, representing the probability distribution of particles in the multiplex network, and ${\overrightarrow{P}}_{RS}=[{\overrightarrow{P}}_{RS}^1,\dots ,{\overrightarrow{P}}_{RS}^L]$ is the initial probability vector of a restart. ${\overrightarrow{P}}_{RS}=\tau {\overrightarrow{P}}_0$, and the vector parameter $\tau =[{\tau }_1,\dots ,{\tau }_L]$ indicates the restart probability of each layer of the particle in the multiplex network. We can change the weights between different layers by changing the parameter $\tau$ to promote the important layers. In this study, all layers were considered equally important. Finally, the RWR-M outputs a score for each gene, reflecting the global similarity of the gene to the known stress genes. In this study, we chose the top n genes as potential genes for further analysis.

2.4. Leave-One-Out Cross-Validation Strategy

We used the leave-one-out cross-validation (LOOCV) strategy (Pseudocode is shown in Algorithm 2) [5,27] to evaluate the predictive performance of the RWR on the single and multiplex networks. We first created a test set, where the genes were the known drought stress genes from the China Rice Data Center. We removed the genes in the test set one at a time, named the left-out gene, and considered the rest of the genes as seed nodes in the RWR algorithms. According to their proximity to the seeds, the network nodes were scored and ranked. Using the same model, we recorded the rank of the left-out genes.

Algorithm 2 Leave-One-Out Cross-Validation Strategy.

Input:  drought stress-related genes: $test\_set$ Output:  left-out gene rank sets 1: function LOOCV_S($test\_set$) 2:     $left\_out\_gene\_result\leftarrow None$ 3:     for $i=1$ to $length(test\_set)$ do 4:         $left\_out\_gene\leftarrow test\_set\left[i\right]$ 5:         $test\_genes\leftarrow test\_set[1,2,\dots ,i-1,i+1,\dots ,n]$ 6:         $all\_genes\_rank\leftarrow RWR(test\_genes)$ 7:         $left\_out\_gene$ rank 8:         $left\_out\_gene\_result.append(left\_out\_gene$ rank) 9:       end for 10:     return $left\_out\_gene\_result$ 11: end function

2.5. Association Analysis between Potential Genes and Known Drought Stress Genes

Correlated genes are likely to have similar functions [27]. Therefore, a gene interacting with several known drought stress genes was more likely to be a drought stress-related gene. For each potential gene $G{P}_j(j=1,2,3,\dots ,n)$, we obtained its interaction scores with $G{K}_i(i=1,2,3,\dots ,218)$ from the STRING database. We defined it as $S(G{P}_j,G{K}_i)$, with $G{K}_i$ representing the drought stress gene obtained from the China Rice Data Center. Any potential gene with more than one $S(G{P}_j,G{K}_i)\ge 0.9$ was selected as a candidate gene.

3. Results

3.1. Prediction Performance Analysis of the RWR on the PPI Network

We compared the performance of the RWR on the MetaPPI with the SinglePPI by the LOOCV strategy. As shown in Figure 2, The ranking of the RWR on the MetaPPI was more accurate than on the SinglePPI. The result indicated that for the MetaPPI, the relation between proteins from the multisource data was more reliable than that from STRING. Therefore, we used the MetaPPI in the construction of the multiplex network.

3.2. Prediction Performance Analysis of the RWR on the Multiplex Network

In this step, we compared the performance of the RWR on the multiplex network (RWR-M) with the RWR on the PPI network. In the multiplex network, two proteins can be linked by up to two edges, corresponding to the two layers, and the particle chooses between these different edges to move from a node to one of its neighbors. As shown in Figure 3, the RWR on the multiplex network outperformed the PPI networks. Moreover, the prediction performance of the RWR-M on the MetaPPI_COEX_DP and MetaPPI_COEX_MM was similar, and about 50% of the left-out genes were in the top 300 genes. Therefore, we utilized the multiplex networks to predict the drought stress-related genes.

3.3. Obtaining Potential Genes Based on the RWR-M

The RWR-M displayed a remarkable performance in prioritizing genes; over 50% of the left-out genes ranked in the top 300. We screened out the top 300 genes by the RWR on MetaPPI_COEX_DP or MetaPPI_COEX_MM and retained the overlapped findings from the two methods. The consensus hits by both approaches were more likely to be drought stress-related genes, resulting in 174 potential genes for further analysis.

3.4. Enrichment Analysis

AmiGO is a web application that allows users to query and visualize ontologies and their related gene products’ annotations [28]. In this study, we used AmiGO to analyze the 174 potential genes. These potential genes were enriched in multiple related GO pathways in the three categories of Biological Process (BP), Molecular Function (MF), and Cellular Component (CC) (as shown in

Table 1. Results of the enrichment analysis.

GO Term	Number of Genes	Ontology	Description	p-Value
GO:0009266	18	BP	Response to temperature stimulus	$2.25\times {10}^{-17}$
GO:0009628	22	BP	Response to abiotic stimulus	$1.24\times {10}^{-14}$
GO:0009408	11	BP	Response to heat	$2.17\times {10}^{-10}$
GO:0009631	6	BP	Cold acclimation	$2.37\times {10}^{-08}$
GO:0009414	11	BP	Response to water deprivation	$4.27\times {10}^{-12}$
GO:0009719	22	BP	Response to endogenous stimulus	$1.51\times {10}^{-13}$
GO:0019222	44	BP	Regulation of metabolic process	$3.76\times {10}^{-15}$
GO:0031072	5	MF	Heat shock protein binding	$3.27\times {10}^{-03}$
GO:0106307	8	MF	Protein threonine phosphatase activity	$2.08\times {10}^{-05}$
GO:0042578	10	MF	Phosphoric ester hydrolase activity	$2.28\times {10}^{-03}$
GO:0106306	8	MF	Protein serine phosphatase activity	$2.08\times {10}^{-05}$
GO:0017111	11	MF	Nucleoside–triphosphatase activity	$1.68\times {10}^{-04}$
GO:0005737	60	CC	Cytoplasm	$6.59\times {10}^{-11}$
GO:0043231	80	CC	Intracellular membrane-bounded organelle	$2.04\times {10}^{-19}$
GO:0043229	83	CC	Intracellular organelle	$1.08\times {10}^{-19}$

). The GO pathway with a p value less than 0.01 was selected and recorded. The enrichment results showed that the pathways were significantly enriched in biological processes, including the response pathways to stimuli: the response to temperature stimuli, response to endogenous stimuli, and the response to abiotic stimuli; the pathways to metabolic regulation: the regulation of metabolic process; and a pathway that may affect drought tolerance: the response to water deprivation. In molecular functions, the potential genes were significantly enriched in protein threonine phosphatase activity, protein serine phosphatase activity, phosphoric ester hydrolase activity, nucleoside–triphosphatase activity, and heat shock protein binding. In terms of cellular components, the significantly enriched pathways included the cytoplasm and the intracellular membrane-bounded organelle. Therefore, the potential genes were enriched in response to temperature stimulus, heat, water deprivation, and other pathways related to drought stress.

3.5. Obtaining Candidate Genes Based on Association Analysis

The genes $G{P}_j$ with two or more $S(G{P}_j,G{K}_i)\ge 0.9$ were selected as our candidate genes. In our study, 13 related genes were identified. The annotation of the candidate genes in STRING is shown in

Table 2. Annotation of candidate genes related to drought stress.

Candidate Genes	Name in STRING	Annotation	The Chromosome Location
Os10g0564500	SAPK3	Serine/threonine-protein kinase SAPK3; may play a role in the signal transduction of the hyperosmotic response	10
Os02g0281000	OsJ_06259	Os02g0281000 protein	2
Os03g0268600	PP2C30; OsJ_009875	Probable protein phosphatase 2C 30; belongs to the PP2C family	3
Os05g0537400	PP2C50	Probable protein phosphatase 2c 50; protein phosphatase involved in abscisic acid (ABA) signaling. Together with PYL3 and SAPK10, may form an ABA signaling module involved in the stress response	5
Os01g0846300	PP2C09; OsJ_04060	Probable protein phosphatase 2c 9; belongs to the PP2C family	1
Os01g0869900	SAPK4	Serine/threonine-protein kinase sapk4; may play a role in the signal transduction of the hyperosmotic response	1
Os03g0390200	SAPK1	Serine/threonine-protein kinase SAPK1; may play a role in the signal transduction of the hyperosmotic response	3
Os03g0610900	SAPK10	Serine/threonine-protein kinase SAPK10; may play a role in the signal transduction of the hyperosmotic response	3
Os03g0231700	OS03T0231700-02	Os03g0231700 protein; squalene monooxygenase, putative, expressed	3
Os05g0572700	OsJ_19620	Probable protein phosphatase 2C 51; belongs to the PP2C family	5
Os09g0325700	OsJ_027745; PP108	Probable protein phosphatase 2C 68; belongs to the PP2C family	9
Os01g0583100	OS01T0583100-01; PP2C06	Probable protein phosphatase 2C 6; belongs to the PP2C family	1
Os09g0440300	OS09T0440300-01	Aldehyde dehydrogenase-like protein; belongs to the aldehyde dehydrogenase family	9

. Cytoscape [29] was used to map the connection between the potential genes and the known drought stress-related genes (as shown in Figure 4).

3.6. Receiver Operating Characteristic Curve Analysis

Support vector machines (SVM) is a powerful method to classify two or more classes of data. The candidate genes were subsequently utilized to construct the SVM classifier. The RNA-seq data was used to validate the classifier model. We created the receiver operating characteristic curve (ROC) [30] using pROC tools [31]. The area under the curve (AUC) value was 1. An area under the curve (AUC) value ranges from 0 to 1, with 1 indicating the candidate genes could distinguish the phenotypes of samples.

4. Discussion

When rice suffers from drought stress, its drought stress response genes’ expression level changes rapidly and releases rice stress signal molecules to regulate rice plant resistance [32,33]. Often, the resistance is regulated by multiple genes. In this article, we introduced the RWR-M to predict rice drought stress genes, which outperformed the existing methods. To our knowledge, this was the first study in rice that applied the RWR with integrative genomics. To construct the rice biological network, we compared our methods against several methods applied to a platform. Extensive data analyses suggested that multisource data fusion reduced the noise of the single-source data and improved the prediction performance of the algorithm. In addition, we incorporated various similarity matrices in the network construction, such as Pearson’s correlation coefficient and the MIC, to capture different aspects of associations. We expected the consensus findings across different similarity matrices to be more reliable. We identified 13 genes, of which five were reported in previous studies. This confirmed the utility of our approach.

Among the candidate genes, SAPK10 [34], OsPP108 [35], PP2C06, OsJ_009875(PP2C30) [36], and OsJ_04060(PP2C09) [36,37] have been reported to be related to drought stress; the other eight genes were likely to regulate drought resistance in rice. SnRK2s (SAPK1-10) are released by ABA-PYR/PYL/RCAR complexes, competitively interacting with the PP2C family [38]. SAPK1 and SAPK3 are activated by osmotic stress [39,40]. SAPK4 is weakly activated by ABA and osmotic stress, and SAPK10 is strongly activated by ABA and osmotic stress [41]. Abscisic acid (ABA) plays an important role in the drought resistance of plants. In addition, a new "SAPK10-WRKY87-ABF1" module revealed that SAPK10 participated in rice’s drought and salt tolerance [34]. Moreover, the type 2C protein phosphate (PP2C) regulates the ABA response [42,43]. Similarly, OsPP108 [35] is involved in the regulation of ABA, and its overexpression enhances drought resistance and salt tolerance. PP2C06, PP2C09, and PP2C30 can be used as positive regulatory factors of stress signals; PP2C09 regulates the drought response regulators and activates the ABA-independent signaling pathways by activating the DRE promoters [36,37]. Liu et al. [16] predicted six genes (HSF11, HSF5, HSFB2C, PP2C06, OS03T0231700-02, and OS03T0376100-01) to be associated with drought stress using the WGCNA with multiplatform genomic data. PP2C06 and OS03T0231700-02 were also identified in our study.

In sum, the RWR on the multiplex network has the potential to identify key genes related to drought stress. Our findings were consistent with previous studies. This has value as a reference for the gene mining of a crop’s abiotic stress response. In associate analysis, the number of candidate genes obtained will vary with the setting of the parameter thresholds. In this study, we selected $S(G{P}_j,G{K}_i)\ge$ 0.9, and the threshold can be adjusted appropriately according to the actual situation.

5. Conclusions

In this article, we constructed a rice multiplex biological network; the RWR was applied to this multiplex network to predict genes that were highly related to drought stress, and we conducted a series of analyses to further screen the genes. This approach yielded 13 candidates, five of which were involved in drought stress resistance mechanisms, according to the supporting experimental evidence available, and the other eight candidate genes may be involved in the drought stress regulation of rice.

The construction of multiplex molecular networks of other abiotic stresses in rice is similar to drought stress, so this method can be extended to other abiotic stress-related gene mining. This study provides a new idea for fully utilizing multisource data to mine abiotic stress-related genes in rice and also provides a reference for further research on stress-resistant rice varieties.