Incorporating prior biological knowledge for networkbased differential gene expression analysis using differentially weighted graphical LASSO
 Yiming Zuo^{1, 2, 3},
 Yi Cui^{2},
 Guoqiang Yu^{1},
 Ruijiang Li^{2} and
 Habtom W. Ressom^{3}Email authorView ORCID ID profile
DOI: 10.1186/s1285901715151
© The Author(s) 2017
Received: 18 February 2016
Accepted: 31 January 2017
Published: 10 February 2017
Abstract
Background
Conventional differential gene expression analysis by methods such as student’s ttest, SAM, and Empirical Bayes often searches for statistically significant genes without considering the interactions among them. Networkbased approaches provide a natural way to study these interactions and to investigate the rewiring interactions in disease versus control groups. In this paper, we apply weighted graphical LASSO (wgLASSO) algorithm to integrate a datadriven network model with prior biological knowledge (i.e., proteinprotein interactions) for biological network inference. We propose a novel differentially weighted graphical LASSO (dwgLASSO) algorithm that builds groupspecific networks and perform networkbased differential gene expression analysis to select biomarker candidates by considering their topological differences between the groups.
Results
Through simulation, we showed that wgLASSO can achieve better performance in building biologically relevant networks than purely datadriven models (e.g., neighbor selection, graphical LASSO), even when only a moderate level of information is available as prior biological knowledge. We evaluated the performance of dwgLASSO for survival time prediction using two microarray breast cancer datasets previously reported by Bild et al. and van de Vijver et al. Compared with the top 10 significant genes selected by conventional differential gene expression analysis method, the top 10 significant genes selected by dwgLASSO in the dataset from Bild et al. led to a significantly improved survival time prediction in the independent dataset from van de Vijver et al. Among the 10 genes selected by dwgLASSO, UBE2S, SALL2, XBP1 and KIAA0922 have been confirmed by literature survey to be highly relevant in breast cancer biomarker discovery study. Additionally, we tested dwgLASSO on TCGA RNAseq data acquired from patients with hepatocellular carcinoma (HCC) on tumors samples and their corresponding nontumorous liver tissues. Improved sensitivity, specificity and area under curve (AUC) were observed when comparing dwgLASSO with conventional differential gene expression analysis method.
Conclusions
The proposed networkbased differential gene expression analysis algorithm dwgLASSO can achieve better performance than conventional differential gene expression analysis methods by integrating information at both gene expression and network topology levels. The incorporation of prior biological knowledge can lead to the identification of biologically meaningful genes in cancer biomarker studies.
Keywords
Prior biological knowledge Gaussian graphical model Weighted graphical LASSO Networkbased differential gene expression analysisBackground
Typically, a differential gene expression analysis (e.g., student’s ttest, SAM, Empirical Bayes, etc.) is performed to identify genes with significant changes between biologically disparate groups [1–3]. However, independent studies for the same clinical types of patients often lead to different sets of significant genes and had only few in common [4]. This may be attributed to the fact that genes are members of strongly intertwined biological pathways and are highly interactive with each other. Without considering these interactions, differential gene expression analysis will easily yield biased result and lead to a fragmented picture.
Networkbased methods provide a natural framework to study the interactions among genes [5]. Datadriven network model reconstructs biological networks solely based on statistical evidence. Relevance network is one common datadriven network model [6, 7]. It uses correlation or mutual information to measure the “relevance” between genes and sets a hard threshold to connect high relevant pairs. Relevance network has extensive application due to its simplicity and easy implementation. However, its drawback becomes significant when the variable number increases: it confounds direct and indirect associations [8]. For example, a strong correlation for gene pair XY and XZ will introduce a less strong but probably still statistically significant correlation for gene pair YZ. As a result, when the number of genes is large, relevance network tends to generate overcomplicated networks that contain overwhelming false positives. Bayesian network is another classic datadriven network model [9]. Unlike undirected graphs such as relevance networks, Bayesian networks generate directed acyclic graphs, in which each edge indicates a conditional dependence relationship between two genes given their parents. The benefits of using Bayesian networks are: 1) By modeling conditional dependence relationship, Bayesian networks only identify direct associations; 2) With directions in the graph, Bayesian networks allow to infer causal relationship. However, it’s challenging to apply Bayesian networks on highthroughput omic data since learning the structure of Bayesian networks for high dimensional data is timeconsuming and can be statistically unreliable. Additionally, Bayesian network cannot model cyclic structures, such as feedback loops, which are common in biological networks.
Recently, Gaussian graphical models (GGMs) have been increasingly applied on biological network inference [10–12]. Similar to Bayesian network, GGMs can remove the effect of indirect associations through estimation of the conditional dependence relationship. At the same time, they generate undirected graphs and have no limitation on modeling only acyclic structures. In GGMs, a connection between two nodes corresponds to a nonzero entry in the inverse covariance matrix (i.e., precision matrix), which indicates a conditional dependency between these two nodes given the others. GGMs dates back to early 1970s when Dempster introduced “covariance selection” problem [13]. The conventional approach to solve this problem relies on statistical test (e.g., deviation tests) and forward/backward selection procedure [14]. This is not feasible for highthroughput omic data when the number of genes is ranging from several hundred to thousands while the number of samples are only tens to hundreds. In addition, the “small n, large p” scenario for omic data (i.e., sample size is far less than the variable number), makes maximum likelihood estimation (MLE) of precision matrix not to exist because the sample covariance matrix is rank deficient. To deal with these issues, Schäfer et al. proposed to combine MoorePenrose pseudoinverse and bootstrapping technique to approximate the precision matrix [15]. Others applied ℓ _{1} regularization to get a sparse network [16–18]. Taking into account of the sparsity property of biological networks and the computational burden of bootstrapping, ℓ _{1} regularization methods are preferred. Among various ℓ _{1} regularization methods, Meinshausen et al. performed ℓ _{1} regularized linear regression (i.e., LASSO) for each node to select its “neighbors” [16]. Given all its neighbors, one node is conditionally independent with the remaining ones. Since LASSO is performed for each node, this ‘neighbor selection’ approach may face a consistency problem. For example, while gene X is selected as Y’s neighbor, gene Y may not be selected as X’s neighbor when performing LASSO for gene X and gene Y separately. Compared with neighbor selection method, a more reasonable approach is graphical LASSO, which directly estimates precision matrix by applying ℓ _{1} regulation on the elements of the precision matrix to obtain a sparse estimated precision matrix [17, 18]. We will pursuit the extension of graphical LASSO in this paper.
In additional to datadriven network models, there are many publicly available databases such as STRING (http://stringdb.org), KEGG (http://www.genome.jp/kegg), BioGRID(http://thebiogrid.org/), and ConsensusPathDB (http://consensuspathdb.org/), where one can extract various types of interactions including proteinprotein, signaling, and gene regulatory interactions [19–22]. Biological networks reconstructed from these databases have been reported useful. For example, Chuang et al. reconstructed proteinprotein interaction (PPI) network from multiple databases to help identify markers of metastasis for breast cancer studies using gene expression data [23]. They overlaid the gene expression value on its corresponding protein in the network and searched for subnetworks whose activities across all patients were highly discriminative of metastasis. By doing this, they found several hub genes related to known breast cancer mutations, while these genes were not found significant by conventional differential gene expression analysis. They also reported that the identified subnetworks are more reproducible between different breast cancer cohorts than individual gene markers. However, databases are far from being complete. Networks constructed purely based on the databases have a large number of false negatives. In addition, databases are seldom specific to a certain disease, so the interactions that exist in the databases may not be reflective of the patient population under study. In contrast, datadriven models are likely to have a large number of false positives due to background noise. Considering this, an appropriate approach to integrate the prior biological knowledge from databases and datadriven network model is desirable for more robust and biologically relevant network reconstruction [24].
The rest of the paper is organized as follows. “Methods” section introduces the extended wgLASSO algorithm and the proposed dwgLASSO for networkbased differential gene expression analysis. “Results and discussion” section presents the results of wgLASSO and dwgLASSO based on simulation, microarray and RNAseq data. Finally, “Conclusion” section summarizes our work and discusses possible future extensions.
Methods
Network inference using wgLASSO
where Θ is the precision matrix, Θ≻0 is the constraint that Θ has to be positive definite, S is the sample covariance matrix, tr denotes the trace, the sum of the diagonal elements in a matrix, ‖Θ‖_{1} represents the ℓ _{1} norm of Θ, the sum of the absolute values of all the elements in Θ, and λ is the tuning parameter controlling the sparsity of Θ.
where 1 is all 1 matrix, W is the weight matrix containing the confidence score for each gene pair and ∗ represents the elementwise multiplication between two matrices.
For LASSO based optimization problem as shown in Eq. (4), tuning the parameter λ is crucial since it controls the sparsity of the output \(\hat {\boldsymbol {\Theta }}\). Typically, λ is tuned by crossvalidation, Akaike information criterion (AIC), Bayesian information criterion (BIC), or stability selection [36]. Considering that AIC and BIC often lead to data underfitting (i.e., oversparse network) and stability selection requires extensive computational time, we prefer to use cross validation with one standard error rule to select the optimal tuning parameter λ ^{ o p t }. By using one standard error rule, we can achieve the simplest (most regularized) model whose error is within one standard deviation of the minimal error. Our wgLASSO algorithm is shown below.
Networkbased differential gene expression analysis using dwgLASSO
Results and discussion
Simulation data
Biological networks are reported to be scalefree, which means the degree distribution of the network follows a power law [37]. We considered this scalefree property of biological network in generating simulation data using R package huge [38]. Using huge, a scalefree network was built by inputting the node number p. The sparsity of the network s is fixed, depending on p. For example, when the node number is 100, the sparsity of the network is 0.02, indicating only 2% of all possible connections (i.e., \(\frac {p\times (p1)}{2}\)) exist in the scalefree network. Once the scalefree network is built, huge creates the true precision matrix Θ _{ true } based on the network topology and the positive definite constraint Θ _{ true }≻0 so that Σ _{ true }=(Θ _{ true })^{−1} exists. At last, simulation data \(\mathbf {X}_{n\times p} \sim \mathcal {N}(\mathbf {0},\mathbf {\Sigma }_{true})\) was generated.
The mean and standard deviation (in parenthesis) of false positives (FP) and false negatives (FN) for connections from neighbor selection (NS), graphical LASSO (gLASSO) and weighted graphical LASSO (wgLASSO) methods under different node number (p) and sample size (n) scenarios
p  n  NS (or)  NS (and)  gLASSO  wgLASSO (a c c=60%)  wgLASSO (a c c=40%)  

FP  FN  FP  FN  FP  FN  FP  FN  FP  FN  
100  50  150 (17)  151 (10)  166 (15)  157 (10)  154 (23)  148 (11)  1 1 2 ( 1 7 )  1 0 4 ( 1 1 )  129 (18)  122 (11) 
100  113 (16)  111 (15)  132 (17)  122 (16)  114 (20)  112 (15)  8 2 ( 1 5 )  7 4 ( 1 3 )  93 (16)  87 (12)  
200  69 (13)  59 (18)  78 (15)  72 (21)  79 (17)  63 (19)  5 1 ( 1 1 )  3 9 ( 1 4 )  58 (13)  50 (15)  
500  250  707 (42)  679 (77)  758 (43)  738 (82)  710 (48)  681 (77)  4 8 0 ( 3 6 )  4 5 1 ( 6 6 )  549 (39)  526 (60) 
500  425 (30)  453 (129)  473 (42)  493 (134)  431 (40)  468 (129)  2 7 7 ( 2 6 )  2 9 0 ( 8 7 )  330 (31)  313 (106)  
1000  175 (22)  164 (117)  189 (27)  177 (118)  199 (28)  186 (126)  1 0 9 ( 1 8 )  1 1 0 ( 7 6 )  130 (21)  135 (88) 
We estimated the true network topology by using neighbor selection, graphical LASSO, and the proposed wgLASSO methods. For neighbor selection method, two strategies were applied to deal with the inconsistency problem. Neighbor selection with “or” operator accepted inconsistent connections while neighbor selection with “and” operator rejected them. To make a fair comparison, we tuned the regularization parameter in each method to ensure the output network has the same sparsity as the true network (i.e., s=0.02 for p=100, s=0.004 for p=500). For each n and p scenario, we regenerated X _{ n×p } 100 times, calculated the false positives and false negatives of connections for each method, and listed their means and standard deviations in Table 1. To evaluate how the incorrect connections in W would impact the performance of wgLASSO, we randomly reassigned 40% (a c c=60%) and 60% (a c c=40%) incorrect prior biological knowledge in W. From Table 1, we can conclude that the estimated network from wgLASSO has much less false positives and false negatives, compared with those from neighbor selection and graphical LASSO methods. A decrease of acc in W would lead to more false positives and false negatives from wgLASSO, but it still outperforms neighbor selection and graphical LASSO methods when the acc in W is only as moderate as 40%.
Microarray data
We applied the proposed dwgLASSO algorithm on two breast cancer microarray datasets: Bild et al. and van de Vijver et al. datasets [39, 40]. The former includes 158 patients with all their survival records, and was used for training. We excluded patients with less than 5year followup time. Among the remaining patients, 42 with less than 5year survival during the followup time were considered to form high risk group while the other 60 formed the low risk group. van de Vijver et al. dataset contains 295 breast cancer patients, together with their survival records, and was used for independent testing. Both datasets are available at PRECOG website (https://precog.stanford.edu), an online repository for querying cancer gene expression and clinical data, and have been preprocessed for subsequent statistical analysis [41]. The raw Bild et al. and van de Vijver et al. datasets are also available at Gene Expression Omnibus (GSE3143) and R package seventyGeneData, respectively [42].
The top 10 significant genes based on conventional differential gene expression analysis (i.e., concordance index) and dwgLASSO with prior biological knowledge incorporated, along with their adjusted pvalue
Top 10 significant genes based on concordance index  Top 10 significant genes based on dwgLASSO  

Gene symbol  Adjusted pvalue  Gene symbol  Adjusted pvalue 
BTD  0.000167029  SALL2  0.018149333 
FKTN  0.000424976  UBE2S  0.015577505 
LRRC17  0.000424976  R A B 1 1 F I P 5  0.001638818 
R A B 1 1 F I P 5  0.001638818  KIAA1467  0.005012636 
E M X 2  0.002384716  XBP1  0.005019825 
HNRNPAB  0.002384716  KIAA0922  0.021163875 
TKT  0.002805234  E M X 2  0.002384716 
LANCL1  0.003481701  OAZ2  0.040090787 
TFF3  0.003481701  NDC80  0.030630047 
USF2  0.004094746  CCT5  0.048116117 
Among the top 10 significant genes based on dwgLASSO in Table 2, UBE2S has been reported to be overexpressed in breast cancer [44]. The authors showed UBE2S knockdown suppressed the malignant characteristics of breast cancer cells, such as migration, invasion, and anchorageindependent growth. SALL2 has also been reported as a predictor of lymph node metastasis in breast cancer [45]. Unlike UBE2S, SALL2 was identified as a tumor suppressor gene that can suppress cell growth when overexpressed [46]. Additionally, XBP1 has been reported to be activated in triplenegative breast cancer and has a pivotal role in the tumorigenicity and progression of this breast cancer subtype [47]. KIAA0922 has also been reported as a novel inhibitor of Wnt signaling pathway, which is closely related to breast cancer [48]. None of UBE2S, SALL2, XBP1 and KIAA0922 is among the top 10 significant genes based on concordance index according to Table 2.
The survival time prediction performance (pvalue and hazard ratio) for the top 5, top 10 and top 15 significant genes based on concordance index: DEA, dwgLASSO with no prior biological knowledge incorporated: dwgLASSO (no prior), KDDN, and dwgLASSO with prior biological knowledge incorporated: dwgLASSO (prior)
Methods  Top 5 significant genes  Top 10 significant genes  Top 15 significant genes  

pvalue  Hazard ratio  pvalue  Hazard ratio  pvalue  Hazard ratio  
DEA  0.0073  1.851  2.00E03  2.037  4.00E04  2.274 
dwgLASSO (no prior)  0.0066  1.864  3.10E04  2.316  4.60E06  2.969 
KDDN  0.0022  2.028  7.46E07  3.304  8.04E06  2.889 
dwgLASSO (prior)  0 . 0 0 1 3  2 . 1 0 4  7 . 0 1 E − 0 7  3 . 3 2 5  9 . 3 7 E − 0 7  3 . 2 5 
RNAseq data
The mean and standard deviation (in parenthesis) of sensitivity, specificity and area under curve (AUC) calculated for conventional differential gene expression analysis: DEA, dwgLASSO with no prior biological knowledge incorporated: dwgLASSO (no prior), KDDN, and dwgLASSO with prior biological knowledge incorporated: dwgLASSO (prior)
Methods  Testing dataset 1  Testing dataset 2  

Specificity  Sensitivity  AUC  Specificity  Sensitivity  AUC  
DEA  0.950 (0.07)  0.913 (0.06)  0.951 (0.04)  0.950 (0.07)  0.941 (0.04)  0.983 (0.01) 
dwgLASSO (no prior)  0 . 9 8 8 ( 0 . 0 3 )  0.888 (0.11)  0.972 (0.02)  0 . 9 8 8 ( 0 . 0 3 )  0.956 (0.05)  0.990 (0.01) 
KDDN  0.963 (0.08)  0 . 9 5 0 ( 0 . 0 4 )  0.980 (0.02)  0.963 (0.08)  0.939 (0.03)  0.989 (0.01) 
dwgLASSO (prior)  0 . 9 8 8 ( 0 . 0 3 )  0.950 (0.07)  0 . 9 8 2 ( 0 . 0 3 )  0 . 9 8 8 ( 0 . 0 3 )  0 . 9 6 5 ( 0 . 0 3 )  0 . 9 9 4 ( 0 . 0 1 ) 
Conclusion
In this paper, we apply a novel network inference method, wgLASSO to integrate prior biological knowledge into a datadriven model. We also propose a new networkbased differential gene expression analysis method dwgLASSO for better identification of genes associated with biologically disparate groups. Simulation results show that wgLASSO can achieve better performance in building biologically relevant networks than purely datadriven models (e.g., neighbor selection and graphical LASSO) even when only a moderate level of information is available as prior biological knowledge. We demonstrate the performance of dwgLASSO in survival time prediction using two independent microarray breast cancer datasets previously published by Bild et al. and van de Vijver et al. The top 10 genes selected by dwgLASSO based on the dataset from Bild et al. dataset lead to a significantly improved survival time prediction on the dataset from van de Vijver et al., compared with the top 10 significant genes obtained by conventional differential gene expression analysis. Among the top 10 genes selected by dwgLASSO, UBE2S, SALL2, XBP1 and KIAA0922 have been previously reported to be relevant in breast cancer biomarker discovery study. We also tested dwgLASSO using TCGA RNAseq data acquired from patients with HCC on tumors samples and their corresponding nontumorous liver tissues. Improved sensitivity, specificity and AUC were observed when comparing dwgLASSO with conventional differential gene expression analysis method. Future research work will focus on applying dwgLASSO on other omic studies such as proteomics and metabolomics.
Abbreviations
 AIC:

Akaike information criterion
 AUC:

area under curve
 BIC:

Bayesian information criterion
 DEA:

differential gene expression analysis
 DN:

differential network
 dwgLASSO:

differentially weighted graphical LASSO
 FDR:

false discovery rate
 FP:

false positives
 FN:

false negatives
 GGMs:

Gaussian graphical models
 HCC:

hepatocellular carcinoma
 KDDN:

Knowledgefused differential dependency network
 LASSO:

least absolute shrinkage and selectioin operator
 MAP:

maximum a posteriori
 MLE:

maximum likelihood estimation
 PPI:

proteinprotein interaction
 wgLASSO:

weighted graphical LASSO
Declarations
Acknowledgements
None.
Funding
This work is in part supported by the National Institutes of Health Grants U01CA185188, R01CA143420 and R01GM086746 awarded to HWR.
Availability of supporting data
The datasets supporting the results of this article are included within the article and its additional files, or from referenced sources.
Authors’ contributions
YZ designed and implemented the algorithms, conducted the synthetic simulation and real data application, and drafted the paper. YC collected the two microarray datasets and participated in generating the results for the synthetic simulation and real data application. GY and RL provided expertise in differential expression analysis. HWR directed the project and completed the paper. All authors reviewed and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
Consent for publication
Not applicable.
Ethics approval and consent to participate
Not applicable.
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
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