- Research
- Open Access
Identifying drug-pathway association pairs based on L_{2,1}-integrative penalized matrix decomposition
- Jin-Xing Liu^{1},
- Dong-Qin Wang^{1},
- Chun-Hou Zheng^{1}Email author,
- Ying-Lian Gao^{2}Email author,
- Sha-Sha Wu^{1} and
- Jun-Liang Shang^{1}
https://doi.org/10.1186/s12918-017-0480-7
© The Author(s). 2017
- Published: 14 December 2017
Abstract
Background
Traditional drug identification methods follow the “one drug-one target” thought. But those methods ignore the natural characters of human diseases. To overcome this limitation, many identification methods of drug-pathway association pairs have been developed, such as the integrative penalized matrix decomposition (iPaD) method. The iPaD method imposes the L_{1}-norm penalty on the regularization term. However, lasso-type penalties have an obvious disadvantage, that is, the sparsity produced by them is too dispersive.
Results
Therefore, to improve the performance of the iPaD method, we propose a novel method named L_{2,1}-iPaD to identify paired drug-pathway associations. In the L_{2,1}-iPaD model, we use the L_{2,1}-norm penalty to replace the L_{1}-norm penalty since the L_{2,1}-norm penalty can produce row sparsity.
Conclusions
By applying the L_{2,1}-iPaD method to the CCLE and NCI-60 datasets, we demonstrate that the performance of L_{2,1}-iPaD method is superior to existing methods. And the proposed method can achieve better enrichment in terms of discovering validated drug-pathway association pairs than the iPaD method by performing permutation test. The results on the two real datasets prove that our method is effective.
Keywords
- Drug discovery
- Sparse method
- Integrative penalized matrix decomposition
- L_{2,1}-norm penalty
Background
Studies of the mechanism of carcinogenesis have led to the implementation that cancer is radically a disease of a variety of genetic aberrations [1]. And at present, the main method to treat cancer is drug therapy. New drug research is an important topic of the drug discovery. And one of the basic research concept of these new drugs is to determine the interaction between drugs and targets. And it can be used to predict candidate drugs, which may act on targets [2]. Besides under the guidance of the concept of pharmacology research and development for new drugs, it can also be used for the relocation of existing drugs, and to forecast the new targets for known drugs [3]. Drug discovery technology is in primary stage, but many related algorithms have been developed to find drug targets. In general, original drug target identification algorithms follow the “one drug-one target” line [4]. The purpose of those methods is to discover the effective drugs, which act on individual targets. It is obvious that those methods do not take into consideration of the relations among genes. Thus, “one drug-one target” algorithms ignore related pathways [5]. Generally, many complex diseases are resulted from unique pathway functions rather than individual genes. And the function of drugs is not just aiming at single proteins, but rather affecting the complex interaction of some associated biological pathways [6]. Therefore, identifying drug-pathway associations is a momentous task for quickening the development of drug discovery.
With the rapid development of high-throughput drugs and pathways related data, it is feasible for researchers to infer drug-pathway interactions. A large amount of studies have utilized the drug related data to obtain insights on drug-pathway modes of action [7]. Gene Set Enrichment Analysis (GSEA) is a traditional method to identify drug-pathway associations. GSEA is proposed by Harvard University and MIT’s broad institute research group. It is utilized to analyze genome-wide expression microarray and drug related data. You can download it after free register [8], whose website is http://software.broadinstitute.org/gsea/index.jsp. Based on known gene-pathway association information, the GSEA method can forecast responsiveness of pathways. But the GSEA method does not consider the known pathway information, its identification precision is poor [9]. In order to improve the identification precision and use the prior information, the FacPad method is proposed to predict drug-pathway associations, and it build a sparse Bayesian factor analysis model to infer pathway responsive for drug treatments [6]. In order to further improve the performance of the FacPad method, another Bayesian model named “iFad” is developed to discover the novel drug-pathway associations [10]. And Ma et al. apply the iFad method to analyze gene expression and drug related data from the NCI-60 cell lines. The NCI-60 cell lines is from the NCI-60 project, which provides useful information for various types of “Omics” characterization of 60 human cancer cell lines with nine different cancer types. The iFad method can discover effective drug-pathway associations. However, its computational costing is expensive since this method applies the Markov Chain Monte Carlo (MCMC) algorithm [11] to perform statistical inferences. At the same time, some prior parameters in the iFad model require to be specified in advance by the investigators. With the rapid development of modern genomics and pharmacology technologies, the dimensionality of the raw data becomes larger and larger, that is, these data have a large number of variables [12]. Thus, the size of sample is also becoming larger and larger. And the computational expense of dealing with the high-dimensional data becomes more expensive. Based on the above problems, an efficient method named “iPaD” is proposed to analyze drug related data [13]. Li et al. use integrative penalized matrix decomposition (iPaD) method to jointly analyze drug expression and drug sensitivity data. And Li et al. apply the iPaD method to the Cancer Cell Line Encyclopedia (CCLE) and NCI-60 datasets. Compared with the NCI-60 data set, the CCLE data set has the larger sample size. At the moment, the CCLE project has more than 1000 cell lines. Compared with the iFad method, the iPaD method has obvious superiority in computational efficiency. And the iPaD method only has one parameter required to be turned. In addition, the iPaD method applies the L _{1}-norm penalty to obtain sparse solutions. However, the sparsity produced byL _{1}-norm penalty is too dispersive [14].
In this paper, we impose the L _{2, 1}-norm penalty to replace the L _{1}-norm penalty on the drug-pathway association matrix. The L _{2, 1}-norm regularization penalty can make each row of the drug-pathway association matrix as a whole and produce row sparsity solutions [15, 16]. Besides, the L _{2, 1}-norm penalty can select the most prominent morphometric variables [17]. In this paper, compared with the iPaD method, our new proposed method has two outstanding advantages: firstly, the L _{2, 1}-iPaD method can achieve better performance in identifying validated drug-pathway associations by applying our proposed method to the CCLE and NCI-60 datasets; secondly, in this paper, we also perform permutation test to evaluate the significance of the identified drug-pathway associations, the experimental results demonstrate that our proposed method can gain the smaller P-values. Thus, we can obtain that our proposed method can achieve better overall enrichment in terms of identifying drug-pathway association pairs.
In the next subsection, at first, we will describe a novel algorithm named L _{2, 1}-iPaD to identify drug-pathway associations. And then we will apply the L _{2, 1}-iPaD method on two real datasets (the CCLE and NCI-60 datasets) and give the results of our proposed and iPaD methods. Finally, we will give the conclusions and future work.
Method
Model description
Optimization algorithm
In this paper, the optimization model (3) is convex, that is, when X is fixed, optimizing gene-pathway association matrix B ^{(1)} and drug-pathway association matrix B ^{(2)} are both convex optimization problems. And when gene-pathway association matrix B ^{(1)} and drug-pathway association matrix B ^{(2)} are fixed, optimizing X is also a convex optimization problem. Thus, in this paper, we optimize X by fixing gene-pathway association matrix B ^{(1)} and drug-pathway association matrix B ^{(2)}, and optimize gene-pathway association matrix B ^{(1)} and drug-pathway association matrix B ^{(2)} by fixing X.
Updating X
Updating B ^{(1)}
Updating B ^{(2)}
Dealing with missing values
The gene expression data matrix Y ^{(1)} and drug related data matrix Y ^{(2)} in original data set have a few missing values. In order to strengthen the performance of our proposed method, we need to deal with missing values. Since each column of the gene-pathway association matrix B ^{(1)} and drug-pathway interaction matrix B ^{(2)} can be solved separately, the missing values in original data set can be removed in the process of updating matrix B ^{(1)} and B ^{(2)}. However, we treat X as a whole matrix in updating matrix X. It is not easy to handle missing values, directly. Similar to [13], we use the soft-impute algorithm to handle the missing values during the process of updating X. The soft-impute algorithm can solve the incomplete matrix learning problem [27, 28]. Following, we will introduce the detailed process for handling missing values in the L _{2, 1}-iPaD method.
The detailed proving process can be found in [13, 27]. The problem (23) means that at every iteration, they will plug into \( {\mathrm{H}}_{\varOmega_1}\left(\mathbf{XB}\right) \) for the next iteration. And this is exactly the main thought of the soft-impute method [27].
Parameters selection and significance test
Results and discussion
In this section, we will show the experimental results on the real datasets, including the CCLE and NCI-60 datasets. And, in order to present the performance of our proposed method, we compare our proposed method with the iPaD algorithm.
Results on the CCLE data set
The top 15 identified drug-pathway association pairs on CCLE data set to L_{2,1}-iPaD and iPaD methods
Drug | KEGG pathway | L _{2, 1}-iPaD | iPaD | Validated? |
---|---|---|---|---|
Sorafenib | Calcium signaling pathway | 0 | 5.79E-04 | Yes |
Panobinostat | Pancreatic cancer | 0 | 6.07E-04 | No |
LBW242 | Chronic myeloid leukemia | 2.80E-44 | 1.34E-10 | No |
Nutlin-3 | Chronic myeloid leukemia | 1.74E-43 | 4.82E-16 | Yes |
L-685458 | Chronic myeloid leukemia | 4.33E-43 | 3.20E-31 | No |
17-AAG | Chronic myeloid leukemia | 9.46E-43 | 2.79E-20 | No |
AZD0530 | Colorectal cancer | 1.62E-41 | 3.05E-07 | No |
PD-0332991 | Chronic myeloid leukemia | 6.93E-41 | 1.38E-09 | Yes |
PHA-665752 | Chronic myeloid leukemia | 1.09E-40 | 1.97E-20 | No |
Paclitaxel | Chronic myeloid leukemia | 2.14E-38 | 2.52E-16 | No |
AZD0530 | Chronic myeloid leukemia | 7.12E-38 | 5.12E-13 | Yes |
ZD-6474 | Chronic myeloid leukemia | 1.62E-21 | 1.23E-11 | No |
AZD0530 | ErbB signaling pathway | 4.41E-16 | 2.81E-05 | Yes |
RAF265 | ECM-receptor interaction | 1.26E-15 | 0 | No |
Erlotinib | Chronic myeloid leukemia | 5.69E-15 | 1.98E-11 | Yes |
The identification and verification rates on CCLE data set with the P-values < 0.05
Method | Number of identification | Number of verification | Verification rate | Identification rate |
---|---|---|---|---|
L _{2, 1}-iPaD | 368 | 66 | 0.0517 | 0.2884 |
iPaD | 88 | 25 | 0.0196 | 0.0689 |
iFad^{a} | 39.4 | 4.8 | 0.0038 | 0.0309 |
The identification and verification rates on CCLE data set with the P-values < 0.005
Method | Number of identification | Number of verification | Verification rate | Identification rate |
---|---|---|---|---|
L _{2, 1}-iPaD | 53 | 16 | 0.0125 | 0.0415 |
iPaD | 51 | 16 | 0.0125 | 0.0399 |
The identification and verification rates on CCLE lung cancer data set with the P-values < 0.05
Method | Number of identification | Number of verification | Verification rate | Identification rate |
---|---|---|---|---|
L _{2, 1}-iPaD | 95 | 12 | 0.0094 | 0.0745 |
iPaD | 57 | 8 | 0.0063 | 0.0447 |
Results on the NCI-60 data set
The top 20 identified drug-pathway association pairs on NCI-60 data set to L_{2,1}-iPaD and iPaD methods
Drug | KEGG pathway | L _{2, 1}-iPaD | iPaD | Validated? |
---|---|---|---|---|
Hydroxyurea | Neuroactive ligand-receptor interation | 0 | NAN | No |
Rebeccamycin | T cell receptor signaling pathway | 4.12E-16 | 4.65E-10 | Yes |
Tiazofurin | Cell cycle | 8.19E-11 | 7.54E-07 | Yes |
Selenazofurin | Cell cycle | 1.75E-10 | 2.78E-07 | Yes |
Mycophenolic Acid | Cell cycle | 2.61E-10 | 2.52E-06 | No |
Lucanthone | Tight junction | 1.04E-08 | 4.31E-06 | Yes |
Tanespimycin | Jak-STAT signaling pathway | 9.95E-07 | 2.67E-04 | No |
Primaquine | Natural killer cell mediated cytotoxicity | 1.14E-06 | 2.69E-04 | No |
Aminoglutethi-mide | Primary immunodeficiency | 1.30E-06 | 1.16E-04 | No |
Geldanamycin | Gap junction | 7.89E-06 | 1.87E-04 | No |
Diallyl Disulfide | Acute myeloid leukemia | 8.13E-06 | 8.41E-05 | No |
Carmustine | Cell cycle | 8.68E-06 | 4.58E-04 | No |
Lomustine | Tight junction | 1.06E-05 | 2.64E-04 | Yes |
Bleomycin | Focal adhesion | 1.17E-05 | 4.56E-04 | No |
Vitamin K 3 | Metabolism of xenobiotics by cytochrome P450 | 2.22E-05 | 2.71E-04 | No |
Melphalan | T cell receptor signaling pathway | 2.64E-05 | 6.16E-04 | Yes |
Tegafur | Gap junction | 6.73E-05 | 5.60E-04 | No |
Chloroquine Phosphate | Tight junction | 7.12E-05 | 8.76E-04 | Yes |
Aclacinomyci- ns | One carbon pool by folate | 1.03E-04 | 5.41E-04 | No |
Tamoxifen | Pyrimidine metabolism | 1.12E-04 | 1.92E-03 | No |
The identification and verification rates on NCI-60 data set with the P-values < 0.05
Method | Number of identification | Number of verification | Verification rate | Identification rate |
---|---|---|---|---|
L _{2, 1}-iPaD | 562 | 163 | 0.0278 | 0.0959 |
iPaD | 247 | 74 | 0.0126 | 0.0422 |
iFad^{a} | 123 | 25.2 | 0.0043 | 0.0210 |
The identification and verification rates on NCI-60 data set with the P-values < 0.005
Method | Number of identification | Number of verification | Verification rate | Identification rate |
---|---|---|---|---|
L _{2, 1}-iPaD | 89 | 33 | 0.0056 | 0.0152 |
iPaD | 72 | 26 | 0.0044 | 0.0122 |
Conclusions
Drug-pathway association identification is an important issue in pharmacology. In this paper, we develop an effective algorithm named “L _{2, 1}-iPaD” to discover novel drug-pathway associations. In the optimization model, the objective function has only one turning parameter λ. Thus, our proposed method is nearly turning-free. To find the best performance of our method, we apply ten-fold cross-validation to discover an appropriate λ value. And to estimate the significance of the identified drug-pathway association pairs, we perform permutation test to calculate the P-values. For the purpose of assessing the performance of the L _{2, 1}-iPaD method, we apply this method in the CCLE and NCI-60 datasets. The experimental results in the CCLE and NCI-60 datasets demonstrate that our proposed method can discover more drug-pathway association pairs than the iPaD method. And the L _{2, 1}-iPaD method can identify more validated associations.
With the development of genomics and pharmacology, dealing with transcription and drug sensitivity data has become feasible. Our proposed method has tremendously improved the performance of the original algorithm. In the future, we are ready to propose more efficient and robust algorithms to handle the high-throughput drug related data. And the rapid growth of the high-throughput gene expression and drug related data is calling for more effective algorithms to solve the computational problems.
Declarations
Acknowledgments
Not applicable.
Funding
Publication costs were funded by the grants of the National Science Foundation of China, Nos. 61,572,284 and 61,502,272.
Availability of data and materials
The datasets are available from the reference [13], which is an open resource.
About this supplement
This article has been published as part of BMC Systems Biology Volume 11 Supplement 6, 2017: Selected articles from the IEEE BIBM International Conference on Bioinformatics & Biomedicine (BIBM) 2016: systems biology. The full contents of the supplement are available online at https://bmcsystbiol.biomedcentral.com/articles/supplements/volume-11-supplement-6.
Authors’ contributions
JXL and DQW created the L_{2,1}-iPaD model. DQW completed the Optimization algorithm, experimental result analysis and drafted the written work. CHZ, YLG, SSW and SJL contributed to the revision of the written work. All authors read and approved the final manuscript.
Ethics approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Competing interests
The authors declare that they have no competing interests.
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Authors’ Affiliations
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