A human omics network is a directed graph comprising Protein-Protein Interactions (PPIs) and Protein-DNA (PD) interactions. The interactions were collected from three types of data: PPI, PD, and KEGG database. Firstly, PPI data were from four public databases; BioGRID version 2.0.26 13 , IntAct 14 , HPRD Release 7 15 , and MINT 16 . Secondly, the PD interaction data were from three public data; the results of ORFeome-based analysis 17 , bZIPDB 18 , and MSigDB 19 . Thirdly, we added the PPI and PD interaction data of KEGG 20 into the above integrated PPI and PD data, because they missed many signaling PPI interactions in the KEGG database (Figure S1). Even though adding KEGG interactions into the omics network can cause a circularity problem of the results, we proved that it is a useful and necessary method to find new pathways that do not exist in KEGG pathways from searching the omics network (Figure 1). These interaction data, collected from the eight databases, were integrated based on the Entrez gene information at NCBI providing abundant external references to other databases 21 . The integrated omics network comprises 10,960 nodes and 113,220 edges. Since PPI interactions from four public PPI database have no directional information, one PPI was transformed into two PPIs having opposite directions.

Because finding the highest-scoring connected sub-networks like TRS Pathways in the entire interaction network is a NP-hard problem 8 , we adopted two strategies. The first strategy is to reduce the search space for TRS Pathways by three constraints. The second is to find the pathways only with top scores by defining the scoring function for a TRS Pathway.

The first strategy for identifying TRS Pathways is to reduce the search space of the entire network for TRS Pathways by three constraints. The three constraints are based on three previous approaches mining candidate signaling pathways from PPI data, given a pair of starting and ending proteins 12 22 23 . Firstly, we search for TRS Pathways relaying a signal from 1,728 start proteins to 479 end proteins. According to the definition of signaling pathways by which cells convert extracellular signals into cellular responses 1 , start proteins are defined as ligand or transmembrane proteins; end proteins as transcription factor proteins or some proteins whose roles are clearly known in cells. 1,728 Start proteins and 479 end proteins were found by searching three databases: 1,310 trans-membrane proteins as start proteins from the Locate database 24 ; 236 transcription factors as end proteins from the PD interaction data; 418 start (e.g. ligand proteins) and 243 end proteins (roles are clearly known in cells, e.g. caspase8) from the KEGG database 20 . These 243 end proteins are terminal nodes of KEGG signaling pathways linked to other signaling pathways or biological processes such as apoptosis.

Secondly, because signals are transmitted from an extracellular region into a nucleus, we defined the right orders of pathways as the following: from an extracellular region to a plasma membrane, from a plasma membrane to cytoplasm and from cytoplasm to a nucleus. When we search for TRS Pathways, we remove edges whose directions are opposite to the right orders such as from a plasma membrane to an extracellular region. Removing the opposite edges can lead to the loss of some feedback regulation processes between PPIs, but is an indispensible step to make the complex PPI data into a simple signaling pathway model to deal with. Moreover, since we can identify the transcriptional feedback regulation processes from the PD interaction data, the processes can compensate the loss defect. The sub-cellular localization data were from Locate database 24 . Lastly, we search for TRS Pathways whose path lengths are less than or equal to 10, since the path lengths of all signaling paths in the KEGG database 20 are distributed from 1 to 10 (Figure S2). We search the KEGG database for all signaling paths with the found start and end proteins, then count their path lengths.

The other strategy is to find the pathways only with the top scores by defining the scoring function for a TRS Pathway. Let N and E represent a set of nodes and edges of a TRS Pathway respectively. The scoring function P(N,E) is the sum of the two functions T(N) and R(E);

T(N) measures how many nodes in a TRS Pathway are regulated by transcription. This measure is based on the method of Ideker et al. 8 .

Z _start and Z _end represent the Z score values of the start and end nodes of a TRS Pathway. Z score Z _i = Φ^-1(1-p _i ) is converted from the p value p _i of a gene i to a significance level, where Φ^-1is the inverse normal cumulative density function. The p _i value is acquired from the results of the expression data analysis.

We sum the Z _i over all |N| genes in a TRS Pathway to produce an aggregate Z score (Z _N ) for a TRS Pathway. Then, in order to properly capture the connection between expression and network topology, we investigate whether the score Z _N of a TRS Pathway in Eq. (3) is higher than expected relative to a random set of genes. We randomly take 100,000 samples from all gene sets of size k using a Monte Carlo approach and calculate their scores Z _N . The mean μ _k and standard deviation (SD) σ _k for each k are estimated and the noise in the estimates is reduced using a sliding window average. Using these estimates, the corrected score S(N) is calculated. The corrected score of random TRS Pathways is guaranteed to have a mean of μ = 0 and SD σ = 1.

R(E) estimates how reliable PPIs in a TRS Pathway are. Estimating the PPI reliability R(E) of a TRS Pathway is absolutely necessary to indentify the signaling pathways consisting of PPIs 12 , because the PPI data are noisy 11 . In this study, we adopt Bebek and Yang's method based on a logistic regression model 25 . The model represents the probability of a true interaction as a function of four observed random variables on a pair of proteins: (1) the observed number of papers in which the interaction between two proteins was observed, (2) the Pearson correlation coefficient of expression measurements of the corresponding genes, (3) the proteins' small world clustering coefficient 26 , and (4) the binary (0/1) protein subcellular localization data of interacting proteins 27 . When interacting proteins co-localize in the same subcellular location, we give 1 to the interacting protein pair.

Given positive and negative training data sets, one can optimize the parameters (β₀,..., β₄) to maximize the likelihood of the data. To optimize the parameters, we use the lrm function of the Design R package. We randomly select 5,000 PPIs from 12,363 determined by coimmunoprecipitation as our positive training data set 28 . For the negative training data set, we also randomly select 5,000 PPIs that are not in the interactions. Firstly, we selected 1,000 PPIs for each positive and negative training data as carried out by Bebek and Yang 12 . However, since the number of the entire PPIs was higher than that of Bebek and Yang, we had to increase the training data set to 5,000 PPIs. We repeat these experiments 1,000 times and estimate the mean reliability of each PPI. To calculate a reliability score R(E) of a TRS Pathway, we take the same procedure of estimating the corrected expression score S(N) from the Z _N scores of a TRS Pathway. For an edge of TRS Pathways, we did not use PPIs which reliability scores were less than 0.6 (about 85 quantile) (Figure S3).

To search for the top path score TRS Pathways, we used Dijkstra's algorithm 29 . Although we reduce the search space for TRS Pathways by three constraints, it is still impossible to search for all possible TRS Pathways in a few days. Also, we do not have to find them all. However, other alternative pathways of the same start and end nodes may also be important, just as the highest-scoring path in cell biology. Therefore, we slightly modified Dijkstra's algorithm, which searches for only the smallest-scoring path, to identify TRS Pathways with several top path scores. The statistical significance of TRS Pathways is measured by randomly permutating the expression of individual genes and performing the same search for TRS Pathways 1,000 times.

The following is the pseudo code of a search algorithm for a TRS Network. Input: an entire omics network G, all TRS Pathways relevant to the context, and a start gene. If the start gene is not given, the start gene is determined as the start node of the highest scoring TRS Pathway.

Output: a sub-network G_p of G

(1) Initialize G_p by the top ranked TRS Pathway whose start node is the start gene

(2) Add the end node of the initial TRS Pathway into Queue;

(3) WHILE end nodes exist in Queue

(4)  POLL an end node e,

(5)   FOR i = 1 to n of outgoing edges of e;

(6)    IF a target node t_i of e_i is a DEG (Differentially Expressed Gene) or exists in G_p, add t_i and e_i into G_p;

(7)    IF added t_i is a start node, a DEG, and positively regulated, add the top ranked TRS Pathways of t_i into G_p and add the end node of the top ranked TRS Pathways into Queue;

(8)    IF added t_i is an end and DEG, add t_i into Queue;

(9) Output G _p and its score.

The above search algorithm represents the following; by the top ranked TRS Pathway, the signal is transmitted into the end nodes. The activated end nodes carry out their own roles in cells; transcription feedback regulation, enzyme activity or inducing the expression of new start proteins. The newly activated start proteins can send signals to other end nodes, thus we added the TRS Pathways activated by start proteins of a positively regulated DEG into the TRS Network. Since there are so many TRS Pathways at context, we have to select only the highly significant TRS Pathways for adding a TRS Network. The newly added end nodes also carry out their own roles in cells. Therefore, we repeat this process until there is no protein in the Queue.

The scoring function for a TRS Network SF comprises three parts: how much its nodes are differentially expressed S , how many significant TRS Pathways P it includes, and how many edges | | it has.

here .

In order to calculate S , we use the same function for the expression score of a TRS Pathway (See Eq. (3)). P _i is the score value (See Eq. (1)) of the i ^th TRS Pathway in a TRS Network. N _i and E _i also represent nodes and edges of i ^th TRS Pathway. N ₀ and E ₀ represent a set of nodes and a set of edges which do not belong to any TRS Pathway, respectively. They have a role to inter-connect TRS Pathways. To assess the statistical significance of TRS Networks, we take the same procedure in estimating the TRS Pathways by randomly permutating the expression of individual genes and performing the same search for TRS Networks 1,000 times.

We investigated dendritic cells treated with lipopolysaccharide (LPS), one of the TLR agonists. TLRs are very important innate receptors that sense microbial products and trigger dendritic cell maturation and cytokine production, effectively bridging innate and adaptive immunity 30 . We downloaded GSE2706 data from the GEO database 31 and analyzed the data with limma 32 . The limma results were used in three different ways. Firstly, we used the probability values (p values) of genes for the scoring function. Secondly, we selected genes for which the probability value was p < 0.05 as differential expressed genes for the identification of TRS Networks by a search algorithm. When we compared the performance of the TRS Network identification according to several DEG cut-off p values, p < 0.05 was one of the best performances (Figure S4). Lastly, we used fold changes of gene expression for the color of protein nodes in the networks.

Since phosphorylation is one of the most important and critical processes in the signal transduction pathway, we annotate TRS Networks with the relationships between kinases and their substrates 33 34 . We believe that the kinase reaction annotation makes the TRS Networks more reliable and more meaningful for a biological understanding.

To find which signaling paths are regulated by transcription in our known knowledge, we searched the KEGG pathways 20 for TRS Pathways in dendritic cells 2h after the LPS treatment. The top TRS Pathways can be ranked by the two scores: the expression score and the path score (Additional file 1: Table S1). The expression score is an aggregated expression score S(N) (Eq. (3)) and the path score is our own path scoring function (Eq. (1)). Among all in the expression score, the path from TNF to MAPK12 (p38) was the highest-scoring and among all in the path score, the path from TNF to NFKB1 (p50) was the highest-scoring.

From the viewpoint of understanding the underlying biological phenomena of cellular contexts, the path from TNF to NFKB1 found by our path scoring function is more helpful, though it is difficult to determine which is more significant than the other. Let us suppose that intermediate signaling proteins exist to some extent in a cell to quickly respond to an environmental signal. Then, when the mRNA expression level of the start node of a path increases, we expect that the signal starting from the start node would be transmitted to the end protein of the path. Likewise if the mRNA expression level of the end node of a path increases, we also expect that the biological process of the end node would occur. In the path from TNF to NFKB, both the mRNA expression levels of the start node TNF and the end node NFKB1 were increased. The signal starting from TNF would be transmitted to NFKB1 and NFKB1 would activate the mRNA expression levels of its target genes as a transcription factor. Therefore, we can identify more explicable paths by using our path scoring function, adding the expression scores of the start and end node of a path (Z _start and Z _end of Eq. (2)) into the aggregated expression score, than by using just the aggregated score.

A TRS Pathway from TNF to NFKB1 was the highest-scoring when we searched the omics network with our path scoring function (See Eq. (1) and Methods). We compared it with the highest-scoring TRS Pathway of KEGG, since both pathways have the same start and end nodes (Figure 1). However, their intermediate nodes were shown to be quite different. Unless we thought of the actual biological system where a protein complex is usually used rather than a single protein for sending a signal, we could not recognize that the TRS Pathway of the omics network is also correct. The TRS Pathway of the omics network (Figure 1C) seems to be constructed by selecting each protein from its corresponding protein complex of Figure 1A to make a linear path.

The signaling pathway of Figure 1A has not been included in KEGG pathways, but it was already known in a paper 35 . This shows that our TRS Pathway method suggests highly reliable TRS Pathway candidates by searching the omics network. Moreover, we also confirmed that our analysis can search not only highly reliable but also significantly regulated TRS Pathways from the omics network by assessing their significances quantitatively (See Methods). The TRS Pathway score (13.635) of the omics network (Figure 1C) was higher than that (11.936) of KEGG (Figure 1B), and the TRS Pathway p value (2.428e-4) of the omics network was lower than that (1.476e-3) of KEGG (Additional file 1: Table S2).

The first pathway sending a signal from LPS to the nuclear factor of kappa light polypeptide gene enhancer in B-cells (NFKB) was unfortunately hardly regulated by transcription. Not only was the path score low, but so was its expression score that we could not identify this pathway as a TRS Pathway. It was the correct result because the first pathway was not a TRS Pathway but a relevant signaling pathway in this context. These results shows that our TRS Pathway analysis can search highly reliable TRS Pathway candidates regulated by transcription according to cellular contexts well, even though it cannot guarantee to find all the relevant signaling pathways to the contexts. In our analysis, we fortunately knew that TLR4 senses LPS as the start protein that initiates all relevant signaling pathways. Therefore, we could identify transcriptional regulations between the first pathway and other signaling pathways in TRS Networks, though not when searching for TRS Pathways.

We found that the TLR signaling pathway and Apoptosis are the most relevant and known pathways among all the KEGG pathways 2h after the LPS treatment, by Impact analysis 36 . Impact analysis is one of the best methods ordering known pathways by estimating how each pathway is over-represented in a specific context. However, a major drawback to analyses using known pathways is that the large number of genes are uninvolved in pathways or have no functional classification 37 . Even though we discovered the over-represented pathways in the context of expression data, we could not sometimes find out the new understanding of the biological phenomenon. Therefore, these two pathways are not the TRS Networks we wanted to discover but the most relevant and known pathways in this context.

We used two pathways, the TLR signaling pathway and Apoptosis, to prove that our TRS Network approach finds more known nodes and edges than other previous approaches. The larger the overlap of a network with the two known pathways, the more known nodes and edges the approach constructing the network finds. To compare, two previous methods inferring sub-networks from omics networks were used: a jActiveModule network and a D2D network. A D2D network is constructed by linking DEGs with their corresponding PPIs 7 . A jActiveModule network is inferred from the omics network using Cytoscape 38 . The jActiveModule analysis infers sub-networks perturbed at the condition with thousands of PPI data by devising an adequate scoring function on PPI networks based on the significant changes of expression data 8 . The overlaps of two TRS Networks (TLR4 TRS Network and TNF TRS Network) were superior to those of other two networks: the D2D network and the jActiveModule network (Figure 2 and Additional file 1: Table S3). It shows that our TRS Network approach finds more known nodes and edges than the previous approaches do.

The TLR4 TRS Network and TNF TRS Network were named by the start node used to search for TRS Networks (See Methods). To estimate the performance of our TRS Network analysis without knowing the start node, we searched for the two TRS Networks and compared their overlaps. In this context, TLR4 senses LPS as the start protein. If, however, we did not know the start protein, TNF, the start protein of the highest-scoring TRS Pathway would be selected as the start node of the search step. The TLR4 TRS Network was found by the actual start node and the TNF TRS Network was found by the inferred start node. The overall propensity of the overlaps of two networks looked very similar, though the performance by the actual start node was slightly better than by the inferred start node (Figure 2 and Additional file 1: Table S3). Therefore, this result shows that our TRS Network analysis works quite well on searching for TRS Networks without a known start protein.

By our TRS Network scoring function (Eq. (5)), we ordered 70 KEGG signaling pathways and four sub-networks: the TLR4 TRS Network, the TNF TRS Network, the jActiveModule network, and the D2D Network (Table 1). We compared the orders of KEGG pathways by our scoring function to those by Impact analysis. We obtained the same results in the top ranked KEGG pathways. By both analyses, the TLR pathway and Apoptosis were the most relevant to this context and highly regulated by transcription. However, the network scores (p values) of the two KEGG pathways were much lower (more significant) than those of the two TRS Networks. It shows that the two KEGG pathways are not good TRS Networks, though they are the most relevant to the context among the known pathways.

Among 70 KEGG pathways and the four sub-networks, the highest-scoring pathway or sub-network was the TLR4 TRS Network (Table 1). It includes more significant TRS Pathways (P : 942.988) than the TNF TRS Network (P : 698.589) and the TLR signaling pathway (P : 32.789), though the number of its edges (| |: 218) is similar to that of the TNF TRS Network (| |: 214) and to that of the TLR signaling pathway (| |: 213). This suggests that edges of the TLR4 TRS Network have a higher probability in being the components of significant TRS Pathways than those of other networks. Thus, the TLR4 TRS Network is more explicable and the edges may be more important. The D2D network and jActiveModule network did not obtain high network scores despite their high expression scores (S : 41.025 and 29.244). The networks comprise many edges (| |: 834 and 970) but do not include a lot of TRS Pathways (P : 19.484 and 32.089). This shows that most edges are not components of TRS Pathways. The two sub-networks are inexplicable and do not provide many clues to understand biological phenomenon of the context. Therefore, the orders of the network scores (Table 1) shows that our TRS Network analysis efficiently finds more TRS Pathways and TRS Networks than other approaches (including canonical pathway analyses).

Dendritic cells sense the presence of LPS and are matured by presenting LPS as an antigen-presenting cell to initiate adaptive immune responses through T cell activation 1 . Our TRS Network analysis found that NFKB activated by the signal starting from LPS induces biological process related to the maturation of dendritic cells. We discovered four biological processes related to dendritic cell maturation and among those processes, two processes showed inter-pathway cross-communication of transcriptional regulations between signaling pathways (Figure 3).

Firstly, NFKB has gotten a positive feedback by inducing TNF, which in turn reinforces the activation of NFKB (Figure 3A). When the dendritic cells are treated with LPS, LPS activates TLR4 which recruits adaptor proteins and sends a signal to NFKB to release NFKB into the nucleus (a TLR4-NFKB pathway). NFKB in the nucleus induces the transcription of genes that promote immune and inflammatory responses 1 . TNF, one of the target genes increased by NFKB, has the possibility to activate NFKB as a positive feedback by sending a signal to NFKB through a TNF-NFKB pathway. A positive feedback is possible because the TLR4-NFKB pathway and the TNF-NFKB pathway have a common downstream activating NFKB.

Secondly, NFKB activated by the TNF-NFKB pathway induces inflammatory responses by increasing the mRNA expression levels of inflammatory cytokines (e.g. IL6 and IL12B) (Figure 3B and Figure S5). The inflammatory cytokines IL6 and IL2B stimulates the JAK-STAT signaling pathway. The JAK-STAT signaling pathway provides one of the most direct routes to the nucleus in which transcriptional activation is initiated by each particular member of the STAT family 1 . In spite of the simple pathway that consists of four JAKs and seven STATs, the pathway translates more than 30 cytokines into cell-type specific or context-dependent patterns of cytokine responsiveness and gene expression 39 . In this context, cytokine IL6, IL12B, and OSM were activated by the TNF-NFKB pathway and the cytokines increased the mRNA expression levels of the interferon regulatory transcription factor family genes, such as IRF1 and IRF7 by the JAK-STAT signaling pathway. The chosen genes were transcription factors involved in inflammation and apoptosis 40 . This inter-pathway cross-communication is a good example of transcriptional regulations between signaling pathways.

Thirdly, NFKB elevated the mRNA expression levels of necessary genes for T cell stimulation: CD40, CD80, ICAM1, CD83, CXCL10, CCL5, and CXCL11 (Figure S5). CD40 and CD80 are co-stimulatory molecules that bind to complementary receptors on the T cell surface, in activating a T cell 1 . ICAM1 enables a T cell to remain bound to an antigen-presenting cell long enough for the T cell to become activated by binding lfa-1 on the T cell surface 41 . Moreover, it was reported that the mature dendritic cells expressed CD83 and high levels of CD40, CD80, and CD86 42 . CXCL10, CXCL11, and CCL5 are chemoattractants that guide the migrations of leukocytes such as T cells to induce a suitable immune response 43 44 45 .

Lastly, NFKB increases the mRNA expression levels of genes related to apoptosis, especially inhibitors of apoptosis (IAPs) such as BIRC2 and BIRC3 suppressing caspases (Figure S5) 35 . At 2h after the LPS treatment, mRNA expression levels of IAPs were only increased. However, at 8h after the treatment, those of other genes inhibiting apoptosis (IL15, NFKB1) were also increased. This result shows that apoptosis would be repressed in dendritic cells and it agrees with this context of the dendritic cell maturation. If apoptosis occurred in matured dendritic cells, they could not perform their roles initiating adaptive immune responses as an antigen-presenting cell.