Cell-specific gene association network construction from single-cell RNA sequence

ABSTRACT

The recent development of a high throughput single-cell RNA sequence devises the opportunity to study entire transcriptomes in the smallest detail. It also leads to the characterization of molecules and subtypes of a cell. Cancer epigenetics induced not only from individual molecules but also from the dysfunction of the system and the coupling effect of genes. While rapid advances are being made in the development of tools for single-cell RNA-seq data analysis, few slants are noticed in the potential advantages of single-cell network construction.

Here, we used network perturbation theory with significant analysis to develop a cell-specific network that provides an insight into gene–gene association based on molecular expressions in a single-cell resolution. Besides, using this method, we can characterize each cell by inspecting how genes are connected and can identify the hub genes using network degree theory. Pathway & Gene enrichment analysis of the identified cell-specific high network degree genes supported the effectiveness of this method. This method could be beneficial for personalized drug design and even therapeutics.

1. Introduction

High throughput Single-cell RNA sequence analysis enables the potentiality to study gene expression, transcriptional heterogeneity, and molecular process on a cell level [1,2]. Recent studies suggest that gene expressions are heterogeneous even if collected from the same tissue or the same group of cells [3]. According to the heterogeneous nature of gene expression, cell to cell gene expression variability provides precise knowledge of transcriptome and molecular functions. Identification of highly variable genes at the network-level allows the detection of genes that differ from cell to cell while also offering a way to identify subcellular populations.

Since bulk RNA sequence is the average of gene expression underlying limitation of heterogeneity analysis and higher noise ratio in some extinct [4], Single-cell RNA sequencing (scRNA seq) becomes a groundbreaking method because of its unparallel possibilities in inspecting gene expression and cell heterogeneity at the single-cell level.

Molecular components such as genes contain functional interdependencies in human cells. Rarely, a single gene gets involved in decaying the biological process; perhaps it’s the reason for the perturbation of inner and intercellular networks [5]. Phenotypic variability toward abnormality of cells cannot be described by analyzing only single molecules because such anomaly is the consequence of several events generated by a group of molecules [6]. A molecular-level network can provide a complete picturization to understand the inner mechanism using the high throughput single-cell RNA sequence [7]. Most of the methods concentrate on gene expression level analysis, while gene association involves the innumerable biological processes such as DNA modification-expression, regulation, and disease progression. Although gene association networks are based on similarity measure or correlation, they can give a proper insight into the biological and molecular process, which is rarely introduced in single-cell RNA analysis studies.

Network-based methods can be integral to identify the molecular mechanism and progression of genetic changes toward dysfunctionality [8]. The components of a network are edge, node, and network. The network data structure can accurately represent the functional interaction and association of cell components. Network representation of a specific cell can be used to identify biomarkers and dysregulation of gene–gene interaction.

Other traditional biological networks [9–11], such as protein–protein interaction network, disease-miRNA, phenotype-gene network, all are based on similarity, correlation probabilistic attributes, but those network construction methods ignored the possibilities of a single sample or cell-specific network. Identifying network; for a single cell can be crucial for drug design and drug response specialization, which can mitigate the complexity. Those advantages have not been noticed in traditional association network methods. Recently proposed method “network embedding-based representation learning for single-cell RNA-seq” explicitly constructed a bipartite graph based on gene–gene interaction according to prior knowledge where edge width was either 1 or 0 depending on the level of interaction. Mainly this method reduces the dimensionality and calculates similarity measurement [10].

CSN is one of the new approaches to network construction; its gene–gene association determines the statistical independence of two genes [12]. Here Gene-Gene Association has been represented as edge and edges either 1 or 0. The most significant advancement and weakness of this approach are that it does not need any prior knowledge of the reference sample. It is comparatively complex to identify which genes lead that cell to dysfunctional behavior. Another limitation of CSN is, it cannot exhibit whether the association is negative or positive

This paper introduces a computational approach to construct a cell-specific network, solely based on single-cell RNA sequence data, which contains gene expression data rather aggregated network from a group of samples. Cell-specific networks elaborated as one network for one cell. Here the nodes of the network are gene, and edges of the network are based on inner relation or association between nodes. The input of the method is gene expression data, and the output is a network of each cell.

This method presents a new approach to investigate scRNA sequence data by identifying the latent knowledge of the biological system and molecular interaction in the ground of the gene association network. In contrast to traditional methods that emphasize differential gene expression of cells, this method identified such genes that don’t have high variability on gene expression but have an immense effect on interaction perspective. Besides, such genes are missed by conventional methods but can be identified through network degree analysis of the single-cell network.

2. Materials and method

2.1. Data

The human embryonic stem cell-derived lineage-specific progenitor cells were collected from the chu type dataset used in our experiment [13]. Cells were distinguished by fluorescence-activated cell sorting (FACS) based on their corresponding markers.

Cells having fewer than 5000 were removed in quality control. A total of 1018 cells passed the quality control. This dataset contained seven types of cells and 1018 cells containing 19,098 genes. In detail, there are 212 H1 embryonic stem cells, 169 H9 embryonic stem cells, 159 human foreskin fibroblasts, 173 neuronal progenitor cells, 138 definitive endoderm cells, 105 endothelial cells, and 69 trophoblast-like cells. Cells having less than 5000 genes with TPM >1 were removed from the dataset. Genes, which may have had a potential ordering effect, were also removed from the dataset.

A comparative statistical analysis is done to understand the properties of the chu-type single-cell RNA-seq data. Figure 1(a) shows the distribution of the genes in the cell. For visualizing high dimensional data in 2-dimension, t-distributed stochastic neighbor embedding (t-SNE) is used (Figure 1(b)). To find the optimal number of clusters elbow method is applied (Figure 1(c)). The k-means algorithm is used on principal components without any quality control and preprocessing of the chu-type dataset, which is shown in Figure 1(d).

Figure 1.

(a) Distribution of row sum of the gene expression matrix of genes. (b) The 2-dimensional plot of principal components after dimensionality reduction using t-sne (c) the number of clusters identification using elbow method (d) K means clustering of cells on t-sne components.

2.2. Preprocessing

The usual preprocessing methods to initial data matrix include gene selection and imputation. A distinctive feature of scRNA-seq data is the presence of zero-inflated counts, which is caused due to reasons such as dropout or transient gene expression [14]. To minimize the technology bias and a large number of zero counts, the genes with all zero-expression values have been removed from all the human embryonic stem cells.

In this work, the initial gene expression matrix transformed into the logarithm log(1 + x), which is used in almost all scRNA-seq data [15,16],, and the genes expressed in less than 10 cells are discarded [12]. We also removed the genes which have higher gene expression than 99% quantiles and less than 1% quantile. It provides a smooth density of gene expression and the remaining genes are considered for further analysis.

At the end of the preprocessing process, we obtained 15,298 genes from 19,097 genes. Figure 2 describes the properties such as gene distribution (Figure 2(a)), principal components (Figure 2(b)), optimal cluster numbers (Figure 2(c)), and clusters of preprocessed datasets (Figure 2(d)); this filtered dataset was used for all subsequent analyses. The performance comparison of the component analysis(T-SNE) & clustering (K-Means) on the unprocessed and normalized preprocessed data presented in Table 1. The adjusted rand index shows that after the normalization and preprocessing process clustering performance improved significantly.

Figure 2.

After log transformation and preprocessing of the gene expression matrix: (a) Distribution of row sum of the gene expression matrix of genes. (b) The 2-dimensional plot of principal components after dimensionality reduction using t-sne (c) the number of cluster identification using elbow method (d) K means clustering of cells on t-sne components.

Table 1.

The clustering performance of t-sne, k-means on original and normalized preprocessed data, evaluated by adjusted random index (ARI)

	Before Preprocessing	After Preprocessing
Adjusted Rand Index	0.58	0.98

3. Methodology

3.1. Single sample network construction

In this paper, we propose a new method using perturbation statistics that constructs a cell-specific network against a group of reference cells from single-cell RNA sequence data. The reference samples are used here are either from the same group of cells or from a different group of cells or a mixture of the same group and different groups of the cell. If there are m genes n cells under consideration, a total n cell network will be constructed.Figure 3

Figure 3.

Overview of cell-specific gene association network model from single-cell RNA sequence. By integrating the correlation coefficient between genes and sample-specific network theory, a single cell network is constructed by network perturbation from the reference network. Significant genes and their association are identified by z-test where p-value < 0.05 and network degree analysis.

In each cell network, there are m nodes, and edges are gene associations. The value of each gene association is in a range of −1 to +1 due to positive and negative associations among each pair of genes. In our proposed method, each cell entirely relies on the gene association network, which is based on differential correlation. The data structure that is used here is the adjacency matrix [17]. Given a network graph G = (V, E) the adjacency matrix representation consists of a $\left|\mathit{V}\right|\times \left|\mathit{V}\right|=\mathit{m}$ where matrix $\mathrm{A}={\mathrm{a}}_{\mathrm{ij}}$. For its undirected characteristics, the matrix is symmetric because ${\mathrm{a}}_{\mathrm{ij}}={\mathrm{a}}_{\mathrm{ji}}$. so, the network contains $\frac{\mathit{m}\left(\mathit{m}-1\right)}{2}$ edges, where m is a number of genes, and each edge represents association between genes which are either weak or strong.

The conceptual design of the methodology presented in Figure 3.The concept of single-cell network construction mainly stands on three networks: perturbed network, reference network, and differential network. From the group of reference cells, the reference network is constructed using the Pearson correlation coefficient of each pair of the gene. If the reference network is constructed from the same cluster element, cells would have common attributes and a similar pattern of gene expression so that the gene-gene correlation coefficient can provide precise insights into a specific cell. As the reference network is constructed from different cluster members or all cluster members, that particular single cell network describes the attributes of respect to the reference network. The correlation coefficient is calculated from equation 1 [18]. In a reference network, genes are represented as a node, and the correlation coefficient served as an edge.

$$\mathit{corr}=\frac{{\sum }_{i=1}^n\left(x_i-\bar{x}\right)\left(y_i-\bar{y}\right)}{\sqrt{{\sum }_i^n{\left(x_i-\bar{x}\right)}^2{\sum }_i^n{\left(y_i-\bar{y}\right)}^2}}$$ (1)

By combining the specific cell with the reference cells, subsequently, the Pearson correlation coefficient applied to each pair of genes. The new network is called the perturbed network. A differential network composed of the difference between the reference network and perturbed network; can adequately describe the features of a specific single-cell relative to a reference group.

If the reference cell group and specific cell are elements of the same cluster, it’s obvious, similar in terms of RNA gene expression. Consequently, a perturbated network with the addition of cell α would not show a significant difference but can preserve that cell’s identical nature. If they are from a different cluster, the difference between the reference network and perturbated network will be compelling, and the differential network will show significant changes on some edges.

3.2. Aggregation interference

A differential network is quantified from the difference between the network from a set of n samples, which is called reference network, and network constructed with the addition of a specific cell α from a set of (n + α) samples which is called perturbed network. It can be described as the contribution of that α cell to the overall association.

$$\mathrm{\Delta PCN}=\mathit{PC}{N}_{\mathit{n}+\mathit{\alpha }}-\mathit{PC}{N}_n$$ (2)

In Equation 2, $\mathit{PC}{N}_n$ represented as the reference network and perturbed network defined as $\mathit{PC}{N}_{\mathit{n}+\mathit{\alpha }}$. $\mathrm{\Delta PCN}$ derived from the difference between the reference and perturbed networks. In other words, $\mathrm{\Delta PCN}$ is the aggregate interference of the cell α.

3.3. Significance analysis

The ΔPCN is the difference between two consecutive PCN_n+1 and PCN_n on the condition of core n samples. The distribution follows the difference between the two consecutive t distributions on the condition that both of the two groups have the core n samples. All of these n samples are assumed to be in a group with the same phenotype, attribute, or probability distribution. The additional sample may or may not have a similar attribute, phenotype, or probability distribution as the core n samples.

Distribution of the $\mathit{PC}{N}_n$ tend to be closer to the normal distribution when $\mathrm{n}\to \mathrm{\infty }$. In equation 3 & equation 4 ${\mu }_{\mathit{PCN}}$ and ${\sigma }_{\mathit{PCN}}$ are the mean and standard deviation of PCN_n for the samples, then

$${\mu }_{\mathit{PCN}}=\mathit{E}\left(\mathit{PC}{N}_n\right)=0$$ (3)

$${\sigma }_{\mathit{PCN}}=\sqrt{\mathit{E}\left(\mathit{PC}{N}_n^2\right)}=\sqrt{\left(1-\mathit{PC}{N}_n^2\right)}$$ (4)

ΔPCN follows a new type of distribution, which is symmetric. The distribution of ∆PCN or the volcano distribution cannot be obtained simply by evaluating the difference between two PCN in two random groups. This volcano distribution follows the distribution of the ∆PCN with two groups containing n and n + 1 samples, which only differ by one sample. In other words, these two groups are not two random n samples and n + 1 samples, but they are subjected to a condition in which both groups differ by only one sample.

It refers to the multivariate normal distribution for the detailed derivation. Thus, In equation 5 & equation 6 the mean and standard deviation of the differential $\mathit{PCN}\left(\mathrm{\Delta PC}{N}_n\right)$, for n samples are [19]

$${\mu }_{\mathrm{\Delta PCN}}=\mathit{E}\left(\mathrm{\Delta PCN}\right)=0$$ (5)

$${\sigma }_{\mathrm{\Delta PCN}}=\sqrt{\mathit{E}\left(\mathrm{\Delta PC}{N}^2\right)}=\frac{1}{\mathit{n}-1}\left(1-\mathit{PC}{N}_n^2\right)$$ (6)

A probability-based z score inference technique is used to identify the effect of the specific cell. z-score indicates which edges are significantly changed. As defined in equation 7, the z score is a dimensionless quantity obtained by dividing the deviation from the mean of the observation divided by the standard deviation of the distribution.

$$\mathit{Z}\left(\mathit{C}\right)=\frac{\mathit{x}-\mathit{\mu }}{\sigma }$$ (7)

The statistical hypothesis test of the Z-test is used to evaluate the significance level of ΔPCN by the central limit theorem [20] in equation 8, which is derived from equation 7.

$$\mathit{Z}=\frac{\mathrm{\Delta PCN}-{\mathit{\mu }}_{\mathrm{\Delta PCN}}}{{\sigma }_{\mathrm{\Delta }\mathit{PCC}}}$$ (8)

Using mean and standard deviation from equation (5) and equation (6) on equation (8) the p-value of the Z-test of the differential network’s edges as follows:

$$\mathit{Z}\left(\mathit{x},\mathit{y}\right)=\frac{\mathrm{\Delta }\mathrm{PCN}\left(x,y\right)}{\frac{\left(1-PC{N}_n^2\left(\mathit{x},\mathit{y}\right)\right)}{\mathit{n}-1}}$$ (9)

Equation 9 is used to evaluate the significance of two genes interaction. the z-score inference is used to identify the important edges. P-value is used for hypothesis tests and to rank edges based on their statistical significance [21]. If the p-value of an edge between gene x and gene y is less than 0.05 (p-value <0.05), the edge is statistically significant. Here z-test p-value expresses the deviation caused by the perturbation from the mean measurement [22].

Based on the difference between PCN and reference network, three types of edges can be induced, such as correlation-increased edge, correlation-decreased edge, correlation-unchanged edge.

3.4. Network degree analysis

Based on the analysis of computational networks, a high degree hub gene can have significant consequences on the network [23–25]. In numerous studies, the correlation between gene degree and essentiality was confirmed [26,27]. To identify the degree of a specific gene network degree equation is applied. As equation 10, a node degree is the total number of edges incident on a given node. Whereas, A network degree is a centrality measure where a node is connected with the number of nodes. As previously mentioned, nodes are genes, and edges are an association between genes. Network degree analysis is crucial in this context because it helps to determine the number of connected neighboring nodes. It also determines how that particular gene is associated with other genes on a network.

If there are n genes in the network of the cell c, the network degree of gene x can calculate from equation 10 as follows

$$\mathit{NetworkDegre}{e}_{\mathit{xc}}=\sum _{\mathit{y}=1,\mathit{x}\ne \mathit{y}}^n\mathit{edg}{{\mathit{e}}_{\mathit{xy}}}^{\mathit{c}}$$ (10)

For further analysis, a network degree can be used for its robustness feature, such as subpopulation identification, finding the significance of a specific gene. If there are n genes and m cells after finding a perturbated network in a structure of an adjacency matrix, the data structure is $\mathit{n}\times \mathit{n}$ which is completely different from the original gene expression matrix and is not suitable for cell-based analysis. The network degree matrix provides a similar data structure as the original gene expression matrix. By columns as cells and rows as gene expression, the output matrix is in the form of $\mathit{m}\times \mathit{n}$. The traditional dimensionality reduction, clustering can be applied to this output matrix.

4. Result analysis

In this paper, we applied our method on the Chu-type dataset [13]. This dataset was obtained from a study of developmental biology, which contains seven cell types, including H1 embryonic stem cells (H1), H9 embryonic stem cells (H9), human foreskin fibroblasts (HFF), neuronal progenitor cells (NPC), definitive endoderm cells (DEC), endothelial cells (E.C.) and trophoblast-like cells (T.B.).

The clustering performance of PCA is not satisfactory, however, Chu-type cells can be clearly distinguished by t-SNE. The k-means cluster plot of the preprocessed dataset is shown in Figure 4(a). Figure 4(c) presents the gene expression plot of 2 H1 embryonic stem cells. To understand the similarity between the cells, similarity-based hierarchical clustering (Figure 4(b)) is used on the whole dataset. Negative distance matrix-based similarity between 2 H1 embryonic stem cells shows satisfactory evidence of gene expression similarity (Figure 4(d)) of the same type of cell.

Figure 4.

Illustration of the chu-type dataset (a)PCA and K-means implementation on the dataset (b) Similarity-based hierarchical clustering on the chu-type dataset (c) Gene Expression plot between two H1 embryonic stem cells after log2 transformation (d) Similarity plot between two H1 embryonic stem cells using negative distance matrix.

4.1. Network analysis

This method is solely responsible for constructing a network of a single-cell. It offers a way to understand the personalized network and gene-gene interaction using perturbed network theory on a single-cell resolution. z-Scores are inferred by comparing the probability distribution for each gene-gene interaction with its background distribution [28].

The single-cell network is constructed based on perturbation statistics against the reference sample. A single-cell RNA sequence of a group of samples is used as a reference sample. Reference samples or reference networks have an influential effect on the process of network construction because background distribution completely relies on the reference network. Three types of reference samples are used to evaluate the intra- cell type and inter-cell type characteristics of genes and interaction between genes. First, cells from the same cell cluster as a reference network. Second, cells from different cell clusters as a reference network, and third, cells from the same and different cluster as the reference network.

Despite some structural differences of each cell network, there are some common structural similarities. Most of the constructed single-cell network consists of three modules. Usually, the same cluster member cells show a similar pattern of networks where most genes are connected in a similar fashion, and it solely depends on the reference network. Figure 5 illustrates each cell network’s common structure pattern where genes with a higher network degree located in the center module act as a connector between the left and right modules. The P-value lower than 0.05 is considered a threshold to select significant gene–gene associations. Those edges are interpreted as a strong association between two specific genes. Using significant analysis, we have identified several gene pair association restricted by p-value.

Figure 5.

Cell-specific network from scRNA sequence consist of 3 modules where nodes are gene and edges are the association between genes (z test p-value<0.05).

Figure 6(a) illustrates the single-cell network of an H1 cell. Here only significant edges are presented in particular where the p-value is less than 0.05 (p-value < 0.05). In this cell network, distinct network topologies were identified which can indicate some interesting hints about the inner mechanism of genes in a single cell. Figure 6(b) is extracted from Figure 6(a) by increasing the significant level (p-value < 0.001) and higher network degree genes. This change of p-value threshold can allow having a closer look at significant interaction between genes.

Figure 6.

Illustration of network analyses of Chu-type dataset based on our cell-specific network construction method where reference is different group cells (a) Single-cell network of cell H1_Batch1.001 (b)High degree and significant paths of Single-cell network of cell H1_Batch1.001 derived from Figure 6(a).

In most of the H1 cells, edges between genes such as POU5F1, GATA6, DNMT3B, ZFP42, NANOG show a higher significance than other edges. A strong association between POU5F1 and GATA6 is also found in H9 cells. The top gene-gene associations are listed in Table 2. Common edges are enlisted in Table 2, but only if those edges are identified using all 3 types of reference networks. POU5F1 is one of the molecular markers of embryonic stem cells, and it plays an important role in the regulation of pluripotency [29,30]. Significance edges connected with POU5F1 is found in almost all cells. GATA6 is a member of the family of transcription factors that play an important role in the regulation of cellular differentiation [31]. A previous study described that NANOG, SOX2, and OCT4 are transcription factors essential to maintain the pluripotent embryonic stem cell phenotype [13,32]. It is important to mention that those genes may have a lower network degree, but some of the edges are significantly enriched. Those associations have also been found in the previous study of single-cell network construction [12].

Table 2.

Top edges between two genes identified from z test p-value

Gene	Gene	p-value	Cell Type	Sample Id
POU5F1	GATA6	3.15 e-8	H1 embryonic stem cells (H1)	H1_Exp1.001
DNMT3B	ZFP42	4.57 e-7	H1 embryonic stem cells (H1)	H1_Exp1.001
POU5F1	NANOG	1.97 e-3	H1 embryonic stem cells (H1)	H1_Exp1.001
POU5F1	GATA6	1.37 e-7	H9 embryonic stem cells (H9)	H9_Batch1.001
DPPA4	L1TD1	1.3 e-4	H9 embryonic stem cells (H9)	H9_Batch1.001
PHC1	TERF1	5.95 e-3	H9 embryonic stem cells (H9)	H9_Batch1.001
FBX033	KDR	1.61 e-8	human foreskin fibroblasts (HFF)	HFF_Batch1.001
LIN28A	B2M	1.59 e-5	human foreskin fibroblasts (HFF)	HFF_Batch1.001
AXL	LGALS1	7.61 e-3	human foreskin fibroblasts (HFF)	HFF_Batch1.001
SOX2	PAX6	1.32 e-7	neuronal progenitor cells (NPC)	NPC_Batch1.001
PAX6	MAP2	5.28 e-4	neuronal progenitor cells (NPC)	NPC_Batch1.001
PAX6	OCT4	5.28 e-4	neuronal progenitor cells (NPC)	NPC_Batch1.001
CDH6	LIX1	4.46 e-3	neuronal progenitor cells (NPC)	NPC_Batch1.001
POU5F1	GATA6	6.65 e-6	definitive endoderm cells (DEC)	DEC_Batch1.001
ZHX2	PECAM1	1.77 e-3	definitive endoderm cells (DEC)	DEC_Batch1.001
CER1	EOMES	1.05 e-2	definitive endoderm cells (DEC)	DEC_Batch1.001
FBX033	KDR	2.2 e-6	endothelial cells (EC)	EC_Batch1.001
PECAM1	CD34	1.81 e-4	endothelial cells (EC)	EC_Batch1.001
CXorf36	MMRN2	1.32 e-2	endothelial cells (EC)	EC_Batch1.001
GATA3	HAND1	2.85 e-9	trophoblast-like cells (TB)	TB_Batch2.073
ITGB6	VGLL1	1.04 e-7	trophoblast-like cells (TB)	TB_Batch2.073
PLSCR5	GABRP	5.78 e-4	trophoblast-like cells (TB)	TB_Batch2.073

Derived from the perturbed network theory, significant analysis of the gene-gene association represented as the edge can provide substantial insight into hub genes and their interaction. Highly connected hub genes in a module play an essential role in biological processes. The functional analysis of the hub genes revealed that they are significantly enriched in cell cycle regulation and cell division [33]. The connecting edges of hub genes may be induced gene regulation, alternative splicing, gene expression, including other gene functions. Several studies indicate that hub genes have significant predictive value for the prognosis and progression of the disease [34–36]. Though this method cannot deduct a specific effect of gene functions based on gene association statistics, it introduced some critical questions and hints for the concerned researchers.

To illustrate the network topology and association between genes, Cytoscape is used which allows the basic functionality to layout and query the network [37]. Figure 7(a) demonstrates the connected edges of high network degree gene POU5F1 in H1 embryonic stem cells. A simplified network structure of PAX6 is shown in Figure 7(b). A perturbation network of an endothelial cell (EC_Batch1.001) is shown in Figure 7(c). More detailed network illustrations are available in the supplementary document.

Figure 7.

(a) POU5F1 as hub gene and its significant edges in H1 embryonic stem cells. (b) A simplified network structure of neuronal progenitor cells (NPC) where protein-coding gene PAX6 is considered as a hub gene. (c) Single-cell network of an endothelial cell (EC_Batch1.001).

Key regulatory genes regulate the expression of other associated genes; it is obvious that those regulatory genes are connected with more genes in the single-cell network. Those regulatory hub genes have comparatively higher connecting edges. By applying network degree theory, this method also provides a way to identify key genes that impact the expression of other genes. From each single cell network, we have identified genes that have a higher network degree from a network perspective.

Interaction in a means of association of protein-encoding genes with high network degree, are more likely connected with important genes and plays an essential in the biological processes [38]. From the network viewpoint, the centrality-lethality rule proclaims that high degree genes can provide the basic structure of the network [39,40]. To evaluate and identify essential genes, top genes are ordered by the gene degree of one cell per cell type, which has been shown in the supplementary document.

4.2. Gene analysis from literature

The sole purpose of this method is to identify statistically significant gene–gene associations, important genes, and network topology. Since node, path, and network topology are interrelated, the validation process of the correctness of our constructed biological network is achievable through the validation of identified genes and their association.

Here several transcription factors are found as a form of interaction in the constructed network. DNMT3B, POU5F1, GATA, SOX2, NANOG are few of the crucial genes which are significantly expressed in H1 and H9 embryonic stem cell. They are involved in differentiation, proliferation, forming the tissue of the heart, blood vessels, retina. DNMT3B proteins are expressed in different stages of embryogenesis, specifically in embryonic ectoderm cells. It also contributes to specify the methylation patterns [41]. POU5F1/OCT-4 promotes differentiation, also shows a critical role in the self-renewal of undifferentiated human embryonic stem cells. OCT-4 is capable of forming a heterodimer with SOX2. In numerous studies, NANOG, SOX2, and OCT4 are found as a transcription factor which maintains the pluripotent phenotype by interacting with each other [32].In our analysis, a significant association between those three genes are identified. The GATA3 and GATA6 transcription factors are key to the development of various tissue. GATA3 is responsible for the functioning of endothelium and GATA6 plays an influential role in the proliferation of endodermal embryonic stem cells by involving in the production of LIF [42,43].

Multiple growth factor receptors and genes that are expressed in early neuronal progenitor and definitive endoderm cells are found. Those genes such as KDR, PAX6, DPPA participated in a lot of crucial biological processes. KDR bind with vascular endothelial growth factor receptor 2, It is involved in blood cell formation that takes place within the embryo and differentiation process of endothelial cells [44]. During embryological development, the PAX6 gene, found on chromosome 2, can be seen expressed in multiple early structures such as the spinal cord, hindbrain, forebrain, and eyes [45]. Developmental Pluripotency-Associated-4 (DPPA4) is one of the core genes which have significant implications for pluripotent stem cell biology and potentially cancer stem cells [46].

In particular, statistically significant edges between genes ITGB6, VGLL1, PLSCR5, GABRP, ZHX2, MMRN2, CD34, KDR, HAND1 identified in endothelial and trophoblast cells. In both trophoblast giant cell differentiation and cardiac morphogenesis HAND1 contributed directly. It is also involved in biological processes like embryonic heart tube development, embryonic heart tube formation [47]. ZHX2 is one of the genes which is responsible for retinal development. It promotes maintenance and suppresses differentiation in the developing cortex, often found in neural progenitor cells [48]. MMRN2 acts as a negative regulator of angiogenesis; it downregulates KDR activation by binding VEGFA. This gene contributes to the negative regulation of vascular endothelial growth factor receptor signaling pathway [49]. CD34 plays an important role in the biological process such as endothelial cell proliferation, endothelium development, glomerular endothelium development, and hematopoietic stem cell proliferation [50]. It functions in the trophoblast differentiation process which is required for the specification and proliferation of the intermediate progenitor cells [51].

A high percentile gene similarity is found between available literature assays and our proposed method which verifies the soundness of this network construction approach. A large number of pathway genes are also found in our analysis which is discussed below.

4.3. Gene set enrichment analysis

Knowledge-based methods such as Gene Set Enrichment Analysis can be performed to extract and investigate the biological and molecular function of a particular group of genes. Also, gene overlap and enrichment analysis can provide insight into biochemical pathways using the KEGG pathway and gene ontology (GO.) terms [52–54].

Identification of molecular and biological pathways of high ranked gene sets can be achieved using Gene Set Enrichment analysis against the molecular signature database, which is available through Broad Institute (www.broadinstitute.org/gsea/) [55].

Here we performed GSEA on the top-ranked genes according to high network degree genes of specific cells, combined gene set of all seven types of cell-based on different reference types. Specifically, we have taken the top 2000 genes under consideration based on the reference network. To evaluate the significance, we only considered the false detection rate less than 0.05 (FDR<0.5) for the enrichment analysis. The enrichment analysis of one cell per cell type is available in the Supplementary document. Our results clearly state that the corresponding genes are significantly enriched in most cells.

The primary aim of gene set analysis of high degree genes is to find their membership in specific biological pathways under certain criteria. Here we include the genes into the gene set which have high network degree identified using all three types of reference network. The biological function or molecular profile of a specific cell can vary even they are members of the same cell family because each cell is different in some extinct. The gene set enrichment analysis of each cell can allow analyzing the activity, regulation, and biological knowledge of genes of interest.

To validate the constructed network, we create a gene set where we include

• Genes identified from seven cell types using three types of reference network.

• Genes involved in significant paths of seven cell types identified using three types of reference network.

All genes are selected based on their p-value of z score. After that, we performed GSEA on this gene set. The investigation of human embryonic stem cells may provide critical insight into the development process. Previous studies showed that lineage-related differentiation reflects the development progression of the cell type [56,57]. From the Gene set enrichment analysis of the curated gene set, we found significant overlap with the pathways related to response to an external stimulus, cell differentiation, cellular developmental process, cell surface receptor linked signal transduction, positive regulation of the biological process, regulation of cell proliferation, cell-cell signaling. Top KEGG pathways associated with identified genes related to identified genes and paths are presented in Table 3.

Table 3.

KEGG enriched pathways

Pathways	P-Value	Pathways	P-Value
Multicellular organismal process	4.36 e-23	Immune system process	6.90 e-26
System development	8.95 e-19	Anatomical structure morphogenesis	5.18 e-27
Multicellular organismal development	9.37 e-19	Immune response	1.20 e-21
Anatomical structure development	1.69 e-18	Response to wounding	2.59 e-21
Sensory perception of chemical stimtimulus	9.21 e-18	Defense response	3.01 e-21
Developmental process	1.35 e-33	Inflammatory response	4.37 e-35
Cell surface receptor linked signal transduction	5.28 e-23	Response to stimulus	7.32 e-24
Nervous system development	1.22 e-25	Positive regulation of immune system process	5.36 e-12
Neurological system process	3.22 e-24	Molecular transducer activity	4.25 e-11
G-protein coupled receptor protein signaling pathway	1.17 e-23	Regulation of response to stimulus	2.89 e-11
Neuron projection morphogenesis	4.58 e-21	Regulation of immune system process	3.16 e-24
Organ development	6.61 e-19	Response to external stimulus	7.22 e-31
Cellular developmental process	9.50 e-19	Positive regulation of biological process	1.83 e-30
Cell differentiation	5.11 e-38	Organ morphogenesis	7.75 e-30
Cognition	5.38 e-36	Cell-cell signaling	5.42 e-27
Central nervous system development	7.73 e-33	Regulation of cell proliferation	3.16 e-26
Neurogenesis	2.55 e-30	Cell communication	5.76 e-24
Reactome signaling by gpcr	5.36 e-20	Positive regulation of cellular process	9.76 e-22
cell morphogenesis involved in neuron differentiation	4.25 e-28	immune system process	5.74 e-21
generation of neurons	2.89 e-26	cell projection	6.07 e-21

5. Conclusion

Gene regulation is involved in many biological processes such as transcriptional regulation, co-expression, alternative splicing, DNA modification, and functions of non-coding RNA. This method provides a technique to analyze the gene association at a single-cell resolution. It describes those biological processes as a form of dependency and independence of a pair of genes in scRNA sequence data. One of the important features of our approach is that the network is constructed from the gene expression data without the knowledge of the cell type from the data source. Nevertheless, cell clusters are generated using t-sne and k-means that makes the algorithm free from the data source technology bias.

Due to the unstable nature of gene expression through the gene association, it is more convenient to characterize the biological process and interconnection between genes. Changes of association of two genes perturbing the reference cells express the divergence as a cell network. scRNA sequence can represent the heterogeneity and functionality of each cell, which is unique. Our method allows us to capture the difference between different cells on a network viewpoint by the association of genes.

Generally, in differential expression analysis, some of the critical genes are ignored because small changes cannot be captured using differential statistics. However, our method allows us to understand that each gene has a biological effect and association from network-level resolution. Though some genes have a similar level of gene expression, they have different network degrees.

However, it is not an original molecular network; In this approach, we constructed a cell-specific network based on correlation statistics and perturbation network theory against the reference network. The reference network encapsulates the effect of direct and indirect regulation between two genes. There are a few statistical and bioinformatics tools are available to identify the cell-specific network and key genes. By addressing the challenges, we have accorded an adequate and straightforward technique to construct a cell-specific network using perturbation statistics, which provides an insight into how genes are directly or indirectly associated with each other.

Funding Statement

This work was supported by the National Natural Science Foundation of China [61672011, 61474267, and 60973153]; Natural Science Foundation of Hunan Province [2018JJ2461]; National Key Research and Development Program [2017YFC1311003].

Supplementary material

Supplemental data for this article can be accessed here.