- Open Access
BMRF-MI: integrative identification of protein interaction network by modeling the gene dependency
© Shi et al.; licensee BioMed Central Ltd. 2015
Published: 11 June 2015
Identification of protein interaction network is a very important step for understanding the molecular mechanisms in cancer. Several methods have been developed to integrate protein-protein interaction (PPI) data with gene expression data for network identification. However, they often fail to model the dependency between genes in the network, which makes many important genes, especially the upstream genes, unidentified. It is necessary to develop a method to improve the network identification performance by incorporating the dependency between genes.
We proposed an approach for identifying protein interaction network by incorporating mutual information (MI) into a Markov random field (MRF) based framework to model the dependency between genes. MI is widely used in information theory to measure the uncertainty between random variables. Different from traditional Pearson correlation test, MI is capable of capturing both linear and non-linear relationship between random variables. Among all the existing MI estimators, we choose to use k-nearest neighbor MI (kNN-MI) estimator which is proved to have minimum bias. The estimated MI is integrated with an MRF framework to model the gene dependency in the context of network. The maximum a posterior (MAP) estimation is applied on the MRF-based model to estimate the network score. In order to reduce the computational complexity of finding the optimal network, a probabilistic searching algorithm is implemented. We further increase the robustness and reproducibility of the results by applying a non-parametric bootstrapping method to measure the confidence level of the identified genes. To evaluate the performance of the proposed method, we test the method on simulation data under different conditions. The experimental results show an improved accuracy in terms of subnetwork identification compared to existing methods. Furthermore, we applied our method onto real breast cancer patient data; the identified protein interaction network shows a close association with the recurrence of breast cancer, which is supported by functional annotation. We also show that the identified subnetworks can be used to predict the recurrence status of cancer patients by survival analysis.
We have developed an integrated approach for protein interaction network identification, which combines Markov random field framework and mutual information to model the gene dependency in PPI network. Improvements in subnetwork identification have been demonstrated with simulation datasets compared to existing methods. We then apply our method onto breast cancer patient data to identify recurrence related subnetworks. The experiment results show that the identified genes are enriched in the pathway and functional categories relevant to progression and recurrence of breast cancer. Finally, the survival analysis based on identified subnetworks achieves a good result of classifying the recurrence status of cancer patients.
Biological systems in cancer involve multifunctional modules that coordinately regulate complex behavior . Many researches focus on identifying biomarkers on high-throughput data such as DNA microarray data and RNA sequencing data. However, the high complexity of biological systems makes the single molecular approach hard to fully reveal the underlying mechanism. Integrative approaches with different data sources are needed to extract deeper insights in different levels and aspects . Several methods [3–6] have been developed to integrate protein-protein interaction (PPI) data with microarray gene expression data to identify significant protein interaction networks. Chuang et al.  proposed a protein-network based approach to identify the biomarkers of metastasis within gene expression profiles. The biomarkers identified in interconnected subnetworks have shown high reproducibility and accuracy in the classification of metastatic versus non-metastatic tumors. Ideker et al.  introduced an approach to identify active subnetworks, which shows consistent condition-specific gene expression change on PPI network. The change of gene expression is measured by significance value (p-value) and further converted to z-score, then the network score can be aggregated by the z-score of the genes in the subnetwork. A simulated annealing based searching algorithm is implemented to find the maximal-scoring connected network. Chen et al.  point out that these two methods mentioned above define the network score as an aggregation of significance score of genes, which usually leave the less differentially expressed biomarkers unidentified. In order to address the concern of gene interaction, Chen et al. proposed a bagging Markov random field (BMRF) based method to improve the protein interaction subnetwork identification. BMRF employs maximum a posterior (MAP) principle to estimate the differential score of genes or proteins and form a novel network score that considers the pairwise gene interaction in the subnetworks. Although BMRF has achieved success in identifying biologically meaningful subnetworks, there are still some concerns about the method. BMRF treats the PPI connection equally by putting the same weight on the edges of the network, which is not true in the real case. As a cell needs to act differently in response to different stimuli, the regulatory mechanism should have condition specific preference. Accepting all the connections in the PPI database may lead to errors in MAP estimation. Furthermore, it has been proven that there are a lot of false positives in the protein interaction database . Therefore, we need to quantify the dependency between genes to reduce the negative effect of false connections and improve the performance.
In this paper, we proposed an approach, namely BMRF-MI, for identifying protein interaction network by incorporating mutual information (MI) into a Markov random field (MRF) framework to model the dependency of genes. MI is developed in information theory to measure the uncertainty between random variables. As the complexity of the biological system is very high, using MI to estimate the correlation between genes can help us reveal both linear and non-linear relationships. By incorporating the quantification of the dependency between the genes, we are able to minimize the effects of false edges in protein network and identify more accurate subnetworks. We generate synthetic data to show that our method has an improved performance in protein subnetwork identification. Besides, we also apply BMRF-MI to breast cancer patient data to demonstrate the feasibility of the proposed method for real biological studies. Experimental results show that the proposed method is able to identify biologically meaningful subnetworks. Furthermore, we use survival analysis to show that the identified subnetworks can be used to predict the recurrence status of the cancer patients.
Results and discussion
Bagging Markov random field and mutual information (BMRF-MI) based network identification
The simulation PPI network is an estrogen receptor (ER) related PPI network with 376 nodes and 1,825 edges extracted from the HPRD database [6, 8]. The ground truth subnetwork is constructed by the genes in pathways closely related to breast cancer, which has 35 genes and 89 interactions. The dependency between genes can be constructed as a symmetric matrix, and the magnitude of the element indicates the strength of dependency. The genes in the ground truth subnetwork are set to have a higher dependency value, which means that they have stronger mutual dependency than the other genes. We use the Markov random field model developed by Wei et al.  to simulate the differential state of genes. Based on the differential state and gene dependency, the gene expression data is simulated from multivariate Gaussian distribution with 40 samples in each phenotype (80 samples in total), which takes the dependency matrix as the covariance matrix. For differential genes, a random difference will be generated to differentiate the mean level of two phenotypes. For non-differential genes, the gene expression data comes from the same distribution. The differential z-score is calculated by inverse cumulative standard normal distribution of p-value estimated from Student's t-test. The false positive rate (FPR) of the simulation data can be controlled by a weight parameter w in the MRF model introduced by Chen et al. . We simulate the data by varying the FPR ranging from 30% to 85% to evaluate the performance of identifying differential expressed protein interaction networks under different levels.
AUC values for subnetwork identification.
F-scores for subnetwork identification.
Breast cancer microarray data
We further tested our method on one estrogen receptor (ER) related breast cancer patient dataset introduced in Loi et al.  to identify subnetworks related to recurrence of breast cancer. The patients samples are divided into 'early recurrence' group (≤ 5 years) and 'late recurrence' group (> 5 years) based on survival time. We finally got 19 samples in 'early recurrence' group and 28 samples in 'late recurrence' group. The PPI network data is obtained from HPRD database , which contains about 9000 genes and 35000 interactions. We further extracted an ER focused PPI network with 2545 genes and 15094 connections by finding the subnetwork within two jumps from ER. The 199 seed genes are selected from the ER focused network with node degree larger than 10. For the differential score of the genes, we perform Student's t-test on the 2545 genes between two groups of samples to calculate the p-value and convert the p-value to z-score by inverse cumulative standard normal distribution. The gene dependency is estimated by R package 'parmigene', which implements the kNN-MI estimator mentioned in Kraskov et al. . For the bootstrapping process, the confidence level threshold is set to 0.3 to find significant genes in network.
P-values of the enriched pathways of identified subnetworks from functional annotation.
In this paper, we have proposed a new method by incorporating mutual information into a Markov random field based framework to tackle the problem of protein interaction subnetwork identification. The proposed method is tested by simulation data with different experimental conditions. We have observed significant improvements in terms of the accuracy of subnetwork identification. To validate the efficacy of the method in real biomedical applications, a breast cancer patient dataset is used for the identification of protein interaction networks related to recurrence of breast cancer. The identified subnetworks are significantly enriched in pathways related to the progression and recurrence of breast cancer. We further validate the significance of the subnetworks on other dataset by predicting the recurrence status of patients.
Gene dependency estimation
where is the digamma function, averages f(x) all over i and realizations, and N is the number of realizations or samples. Assume and are the distance from point i with coordinate (xi,yi) to its k-th nearest neighbor in subspace × and Y respectively, n x and n y are the number of points in the set . Sales et al.  compare kNN-MI estimator with several other mutual information estimators such as KDEMI , the Miller-Madow  and the Schurmann-Grassberger estimators  and show that the kNN-MI estimator has the minimum bias. In this paper, we use the 'parmigene' , a well-developed R package, to estimate the mutual information between all pair of genes. The mutual information can be represented as a symmetric matrix W, where w(i, j) is the estimated mutual information between the ith and the jth gene.
Markov random field (MRF) based network score
where w(i, j) is the mutual information between ith gene and jth gene and the node degree d i can be calculated as . The weights added in the second term of Equation (7) can guarantee the smoothness of the discriminative scores over genes with strong dependency.
where μ(M) and σ(M) are the mean and standard deviation estimated from the null distribution of the networks with the same size of M.
Simulated annealing searching
Given the network score definition, finding the optimal network with the highest network score is an NP hard problem. Instead of using exhausted searching approach, a probabilistic approach for global optimization, simulated annealing, is applied here. To reduce the computational complexity, we start the simulated annealing searching from 'seed' genes, which are pre-selected from the PPI network. Several constraints are made to further increase the network searching efficiency: (i) the searching space is restricted to a local 2-jump network from 'seed' node and (ii) the searching will be terminated when no significant improvement is observed.
Confidence level measurement
Due to the large noise of data and heterogeneity of samples, the reproducibility of subnetwork identification is usually low. Furthermore, the number of samples is usually limited in biological experiment due to cost and quality issue, which will introduce bias to the results. In order to get more robust results, we applied a non-parametric bootstrapping strategy to measure the confidence level of the genes in the identified network. For each bootstrap, we generate a data set by randomly sampling the samples from the gene expression data with replacement. Applying BMRF-MI on the generated data sets, we can measure the confidence level of genes as the frequency of appearance. We are more confident about the genes with high frequency; then a threshold can be set to generate the final network.
Clustering networks by affinity propagation clustering (APC)
S(i, j) has a value between 0 and 1 and higher value indicates higher similarity between the two networks. The number of exemplars or clusters can be automatically determined without pre-configuration, which is different from traditional clustering methods such as k-means clustering.
This work is supported by National Institutes of Health (NIH) [CA149653, CA149147, CA164384, and NS29525-18A, in part].
The publication costs for this article were funded by National Institutes of Health (NIH) [CA149653].
This article has been published as part of BMC Genomics Volume 16 Supplement 7, 2015: Selected articles from The International Conference on Intelligent Biology and Medicine (ICIBM) 2014: Genomics. The full contents of the supplement are available online at http://www.biomedcentral.com/bmcgenomics/supplements/16/S7.
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