Probabilistic Random Walk Models for Comparative Network Analysis

Graph-based systems and data analysis methods have become critical tools in many fields as they can provide an intuitive way of representing and analyzing interactions between variables. Due to the advances in measurement techniques, a massive amount of labeled data that can be represented as nodes on a graph (or network) have been archived in databases. Additionally, novel data without label information have been gradually generated and archived. Labeling and identifying characteristics of novel data is an important first step in utilizing the valuable data in an effective and meaningful way. Comparative network analysis is an effective computational means to identify and predict the properties of the unlabeled data by comparing the similarities and differences between well-studied and less-studied networks. Comparative network analysis aims to identify the matching nodes and conserved subnetworks across multiple networks to enable a prediction of the properties of the nodes in the less-studied networks based on the properties of the matching nodes in the well-studied networks (i.e., transferring knowledge between networks). One of the fundamental and important questions in comparative network analysis is how to accurately estimate node-to-node correspondence as it can be a critical clue in analyzing the similarities and differences between networks. Node correspondence is a comprehensive similarity that integrates various types of similarity measurements in a balanced manner. However, there are several challenges in accurately estimating the node correspondence for large-scale networks. First, the scale of the networks is a critical issue. As networks generally include a large number of nodes, we have to examine an extremely large space and it can pose a computational challenge due to the combinatorial nature of the problem. Furthermore, although there are matching nodes and conserved subnetworks in different networks, structural variations such as node insertions and deletions make it difficult to integrate a topological similarity. In this dissertation, novel probabilistic random walk models are proposed to accurately estimate node-to-node correspondence between networks. First, we propose a context-sensitive random walk (CSRW) model. In the CSRW model, the random walker analyzes the context of the current position of the random walker and it can switch the random movement to either a simultaneous walk on both networks or an individual walk on one of the networks. The context-sensitive nature of the random walker enables the method to effectively integrate different types of similarities by dealing with structural variations. Second, we propose the CUFID (Comparative network analysis Using the steady-state network Flow to IDentify orthologous proteins) model. In the CUFID model, we construct an integrated network by inserting pseudo edges between potential matching nodes in different networks. Then, we design the random walk protocol to transit more frequently between potential matching nodes as their node similarity increases and they have more matching neighboring nodes. We apply the proposed random walk models to comparative network analysis problems: global network alignment and network querying. Through extensive performance evaluations, we demonstrate that the proposed random walk models can accurately estimate node correspondence and these can lead to improved and reliable network comparison results

Probabilistic Random Walk Models for Comparative Network Analysis

Graph-based systems and data analysis methods have become critical tools in many fields as they can provide an intuitive way of representing and analyzing interactions between variables. Due to the advances in measurement techniques, a massive amount of labeled data that can be represented as nodes on a graph (or network) have been archived in databases. Additionally, novel data without label information have been gradually generated and archived. Labeling and identifying characteristics of novel data is an important first step in utilizing the valuable data in an effective and meaningful way. Comparative network analysis is an effective computational means to identify and predict the properties of the unlabeled data by comparing the similarities and differences between well-studied and less-studied networks. Comparative network analysis aims to identify the matching nodes and conserved subnetworks across multiple networks to enable a prediction of the properties of the nodes in the less-studied networks based on the properties of the matching nodes in the well-studied networks (i.e., transferring knowledge between networks). One of the fundamental and important questions in comparative network analysis is how to accurately estimate node-to-node correspondence as it can be a critical clue in analyzing the similarities and differences between networks. Node correspondence is a comprehensive similarity that integrates various types of similarity measurements in a balanced manner. However, there are several challenges in accurately estimating the node correspondence for large-scale networks. First, the scale of the networks is a critical issue. As networks generally include a large number of nodes, we have to examine an extremely large space and it can pose a computational challenge due to the combinatorial nature of the problem. Furthermore, although there are matching nodes and conserved subnetworks in different networks, structural variations such as node insertions and deletions make it difficult to integrate a topological similarity. In this dissertation, novel probabilistic random walk models are proposed to accurately estimate node-to-node correspondence between networks. First, we propose a context-sensitive random walk (CSRW) model. In the CSRW model, the random walker analyzes the context of the current position of the random walker and it can switch the random movement to either a simultaneous walk on both networks or an individual walk on one of the networks. The context-sensitive nature of the random walker enables the method to effectively integrate different types of similarities by dealing with structural variations. Second, we propose the CUFID (Comparative network analysis Using the steady-state network Flow to IDentify orthologous proteins) model. In the CUFID model, we construct an integrated network by inserting pseudo edges between potential matching nodes in different networks. Then, we design the random walk protocol to transit more frequently between potential matching nodes as their node similarity increases and they have more matching neighboring nodes. We apply the proposed random walk models to comparative network analysis problems: global network alignment and network querying. Through extensive performance evaluations, we demonstrate that the proposed random walk models can accurately estimate node correspondence and these can lead to improved and reliable network comparison results

A Novel Framework for the Comparative Analysis of Biological Networks

Genome sequencing projects provide nearly complete lists of the individual components present in an organism, but reveal little about how they work together. Follow-up initiatives have deciphered thousands of dynamic and context-dependent interrelationships between gene products that need to be analyzed with novel bioinformatics approaches able to capture their complex emerging properties. Here, we present a novel framework for the alignment and comparative analysis of biological networks of arbitrary topology. Our strategy includes the prediction of likely conserved interactions, based on evolutionary distances, to counter the high number of missing interactions in the current interactome networks, and a fast assessment of the statistical significance of individual alignment solutions, which vastly increases its performance with respect to existing tools. Finally, we illustrate the biological significance of the results through the identification of novel complex components and potential cases of cross-talk between pathways and alternative signaling routes

Finding conserved patterns in biological sequences, networks and genomes

Biological patterns are widely used for identifying biologically interesting regions within macromolecules, classifying biological objects, predicting functions and studying evolution. Good pattern finding algorithms will help biologists to formulate and validate hypotheses in an attempt to obtain important insights into the complex mechanisms of living things. In this dissertation, we aim to improve and develop algorithms for five biological pattern finding problems. For the multiple sequence alignment problem, we propose an alternative formulation in which a final alignment is obtained by preserving pairwise alignments specified by edges of a given tree. In contrast with traditional NPhard formulations, our preserving alignment formulation can be solved in polynomial time without using a heuristic, while having very good accuracy. For the path matching problem, we take advantage of the linearity of the query path to reduce the problem to finding a longest weighted path in a directed acyclic graph. We can find k paths with top scores in a network from the query path in polynomial time. As many biological pathways are not linear, our graph matching approach allows a non-linear graph query to be given. Our graph matching formulation overcomes the common weakness of previous approaches that there is no guarantee on the quality of the results. For the gene cluster finding problem, we investigate a formulation based on constraining the overall size of a cluster and develop statistical significance estimates that allow direct comparisons of clusters of different sizes. We explore both a restricted version which requires that orthologous genes are strictly ordered within each cluster, and the unrestricted problem that allows paralogous genes within a genome and clusters that may not appear in every genome. We solve the first problem in polynomial time and develop practical exact algorithms for the second one. In the gene cluster querying problem, based on a querying strategy, we propose an efficient approach for investigating clustering of related genes across multiple genomes for a given gene cluster. By analyzing gene clustering in 400 bacterial genomes, we show that our algorithm is efficient enough to study gene clusters across hundreds of genomes

Utilizing gene co-expression networks for comparative transcriptomic analyses

The development of high-throughput technologies such as microarray and next-generation RNA sequencing (RNA-seq) has generated numerous transcriptomic data that can be used for comparative transcriptomics studies. Transcriptomes obtained from different species can reveal differentially expressed genes that underlie species-specific traits. It also has the potential to identify genes that have conserved gene expression patterns. However, differential expression alone does not provide information about how the genes relate to each other in terms of gene expression or if groups of genes are correlated in similar ways across species, tissues, etc. This makes gene expression networks, such as co-expression networks, valuable in terms of finding similarities or differences between genes based on their relationships with other genes. The desired outcome of this research was to develop methods for comparative transcriptomics, specifically for comparing gene co-expression networks (GCNs), either within or between any set of organisms. These networks represent genes as nodes in the network, and pairs of genes may be connected by an edge representing the strength of the relationship between the pairs. We begin with a review of currently utilized techniques available that can be used or adapted to compare gene co-expression networks. We also work to systematically determine the appropriate number of samples needed to construct reproducible gene co-expression networks for comparison purposes. In order to systematically compare these replicate networks, software to visualize the relationship between replicate networks was created to determine when the consistency of the networks begins to plateau and if this is affected by factors such as tissue type and sample size. Finally, we developed a tool called Juxtapose that utilizes gene embedding to functionally interpret the commonalities and differences between a given set of co-expression networks constructed using transcriptome datasets from various organisms. A set of transcriptome datasets were utilized from publicly available sources as well as from collaborators. GTEx and Gene Expression Omnibus (GEO) RNA-seq datasets were used for the evaluation of the techniques proposed in this research. Skeletal cell datasets of closely related species and more evolutionarily distant organisms were also analyzed to investigate the evolutionary relationships of several skeletal cell types. We found evidence that data characteristics such as tissue origin, as well as the method used to construct gene co-expression networks, can substantially impact the number of samples required to generate reproducible networks. In particular, if a threshold is used to construct a gene co-expression network for downstream analyses, the number of samples used to construct the networks is an important consideration as many samples may be required to generate networks that have a reproducible edge order when sorted by edge weight. We also demonstrated the capabilities of our proposed method for comparing GCNs, Juxtapose, showing that it is capable of consistently matching up genes in identical networks, and it also reflects the similarity between different networks using cosine distance as a measure of gene similarity. Finally, we applied our proposed method to skeletal cell networks and find evidence of conserved gene relationships within skeletal GCNs from the same species and identify modules of genes with similar embeddings across species that are enriched for biological processes involved in cartilage and osteoblast development. Furthermore, smaller sub-networks of genes reflect the phylogenetic relationships of the species analyzed using our gene embedding strategy to compare the GCNs. This research has produced methodologies and tools that can be used for evolutionary studies and generalizable to scenarios other than cross-species comparisons, including co-expression network comparisons across tissues or conditions within the same species

Modular Algorithms for Biomolecular Network Alignment

Comparative analysis of biomolecular networks constructed using measurements from different conditions, tissues, and organisms offer a powerful approach to understanding the structure, function, dynamics, and evolution of complex biological systems. The rapidly advancing field of systems biology aims to understand the structure, function, dynamics, and evolution of complex biological systems in terms of the underlying networks of interactions among the large number of molecular participants involved including genes, proteins, and metabolites. In particular, the comparative analysis of network models representing biomolecular interactions in different species or tissues offers an important tool for identifying conserved modules, predicting functions of specific genes or proteins and studying the evolution of biological processes, among other applications. The primary focus of this dissertation is on the biomolecular network alignment problem: Given two or more network models, the problem is to optimally match the nodes and links in one network with the nodes and links of the other. The Biomolecular Network Alignment (BiNA) Toolkit developed as part of this dissertation provides a set of efficient (in terms of the running time complexity) and accurate (in terms of various evaluation criteria discussed in the literature) network alignment algorithms for biomolecular networks. BiNA is scalable, user-friendly, modular, and extensible for performing alignments on diverse types of biomolecular networks. The algorithm is applicable to (1) undirected graphs in their weighted and unweighted variations (2) undirected graphs in their labeled and unlabeled variations (3) and has been applied to align multiple networks from hundreds of nodes with a few thousand edges to networks with tens of thousands of nodes with millions of edges. The dissertation provides various applications of network comparison tools including how results from such alignments have been utilized to (1) construct phylogenetic trees based on protein-protein interaction networks, and (2) find biochemical pathways involved in ligand recognition in B cells