Revealing Tumor Heterogeneity Based On Gaussian Graphical Models

Tumor is a complex heterogeneous disease.The tumor heterogeneity is not only reflected in the differences of pathological characteristics between different patients of the same type of tumor(inter-tumor heterogeneity),but also reflected in the dif-ferences between different regions of the same tumor tissue(intra-tumor heterogene-ity).The analysis of tumor heterogeneity is of great significance for the diagnosis,treatment and prognosis of cancer.Tumor heterogeneity is not only caused by gene mutation or gene differential expression,but also related to the change of gene in-teractions.The analysis of tumor heterogeneity can provide a theoretical basis for revealing the pathogenesis of cancer.Based on Gaussian graphical models which can learn the direct relationship between genes,we study the following two aspects in this dissertation:1.The tumor tissue samples for a single cancer type can be divided into multiple distinct subtypes,and are composed of non-cancerous and cancerous cells.At present,the bulk gene expression data is the average expression values of tumor tissue mixed cells.If tumor heterogeneity is ignored when inferring gene net-works,the edges specific to individual cancer subtypes and cell types cannot be characterized.However,most existing network reconstruction methods do not simultaneously take inter-tumor and intra-tumor heterogeneity into account.In this paper,we propose a new Gaussian graphical model based method for jointly estimating multiple cancer gene networks by simultaneously capturing inter-tumor and intra-tumor heterogeneity.For an observed gene expression data,we use a latent variable model to divide tumor samples into tumor cell components and non-cancer cell components.Then,a non-cancerous network shared across different cancer subtypes and multiple subtype specific cancer-ous networks are estimated jointly by Gaussian graphical models.Finally,we propose an Expectation Maximization algorithm to optimization model.The performance of our method is first evaluated using simulated data,and the results indicate that our method outperforms other state-of-the-art methods.We also apply our method to The Cancer Genome Atlas breast cancer data to reconstruct non-cancerous and subtype specific cancerous gene networks.The similarities and differences of gene network among different subtypes are analyzed,and hub nodes in the networks estimated by our method perfor-m important biological functions associated with breast cancer development and subtype classification.Our method provides a tool for analyzing tumor heterogeneity at the network level.2.Differential network analysis is an important tool to analyze the heterogeneity between tumors.A differential edge should be driven by at least one of the two involved genes,and a reasonable differential network should satisfy the hierarchical constraint that a differential edge is considered only if at least one of the two involved genes is differentially expressed.Several computation-al methods have been developed to estimate differential networks from gene expression data,but most do not consider that gene network rewiring may be driven by the differential expression of individual genes and not satisfy hierarchical constraints.In this paper,we propose a hierarchical differential network analysis method that considers the differential expression of individ-ual genes when identifying differential edges.Firstly,based on the properties of Gaussian graphical model,a differential network is defined as the differ-ence of partial correlations,and a new test statistic to quantify the change of partial correlations between gene pairs is developed.Student's t-test statistic is used to identify significant changes in the expression levels of genes.An optimization model combines the two(network and gene level)test statistic-s to give estimated differential networks that exhibit hierarchical structures.A closed-formed solution is derived to solve the optimization model.Sim-ulation experiments to assess the empirical performance of our model show that it outperform current state-of-the-art methods.Our method is applied to gene expression data from breast cancer and acute myeloid leukemia samples and shows that hub nodes,including both differentially and non-differentially expressed genes in the inferred differential networks,play critical roles the mechanism of these cancers.The method of this paper provides a method and tool for identifying network markers related to tumor heterogeneity.