CAMPways: constrained alignment framework for the comparative analysis of a pair of metabolic pathways

Exploring the expressiveness of abstract metabolic networks

Metabolism is characterised by chemical reactions linked to each other, creating a complex network structure. The whole metabolic network is divided into pathways of chemical reactions, such that every pathway is a metabolic function. A simplified representation of metabolism, which we call an abstract metabolic network, is a graph in which metabolic pathways are nodes and there is an edge between two nodes if their corresponding pathways share one or more compounds. The abstract metabolic network of a given organism results in a small network that requires low computational power to be analysed and makes it a suitable model to perform a large-scale comparison of organisms' metabolism. To explore the potentials and limits of such a basic representation, we considered a comprehensive set of KEGG organisms, represented through their abstract metabolic network. We performed pairwise comparisons using graph kernel methods and analyse the results through exploratory data analysis and machine learning techniques. The results show that abstract metabolic networks discriminate macro evolutionary events, indicating that they are expressive enough to capture key steps in metabolism evolution.

Challenges and Limitations of Biological Network Analysis

High-Throughput technologies are producing an increasing volume of data that needs large amounts of data storage, effective data models and efficient, possibly parallel analysis algorithms. Pathway and interactomics data are represented as graphs and add a new dimension of analysis, allowing, among other features, graph-based comparison of organisms’ properties. For instance, in biological pathway representation, the nodes can represent proteins, RNA and fat molecules, while the edges represent the interaction between molecules. Otherwise, biological networks such as Protein–Protein Interaction (PPI) Networks, represent the biochemical interactions among proteins by using nodes that model the proteins from a given organism, and edges that model the protein–protein interactions, whereas pathway networks enable the representation of biochemical-reaction cascades that happen within the cells or tissues. In this paper, we discuss the main models for standard representation of pathways and PPI networks, the data models for the representation and exchange of pathway and protein interaction data, the main databases in which they are stored and the alignment algorithms for the comparison of pathways and PPI networks of different organisms. Finally, we discuss the challenges and the limitations of pathways and PPI network representation and analysis. We have identified that network alignment presents a lot of open problems worthy of further investigation, especially concerning pathway alignment.

Low-Cost Algorithms for Metabolic Pathway Pairwise Comparison

Metabolic pathways provide key information for achieving a better understanding of life and all its processes; this is useful information for the improvement of medicine, agronomy, pharmacy, and other similar areas. The main analysis tool used to study these pathways is based on pathway comparison, using graph data structures. Metabolic pathway comparison has been defined as a computationally complex task. In a previous work, two new algorithms were introduced to treat the problem of metabolic pathway pairwise comparison. Here we provide an extended analysis with more data and a deeper analysis of metabolic pathway comparison as listed in the discussion and results section.

MetNet: A two-level approach to reconstructing and comparing metabolic networks

Metabolic pathway comparison and interaction between different species can detect important information for drug engineering and medical science. In the literature, proposals for reconstructing and comparing metabolic networks present two main problems: network reconstruction requires usually human intervention to integrate information from different sources and, in metabolic comparison, the size of the networks leads to a challenging computational problem. We propose to automatically reconstruct a metabolic network on the basis of KEGG database information. Our proposal relies on a two-level representation of the huge metabolic network: the first level is graph-based and depicts pathways as nodes and relations between pathways as edges; the second level represents each metabolic pathway in terms of its reactions content. The two-level representation complies with the KEGG database, which decomposes the metabolism of all the different organisms into “reference” pathways in a standardised way. On the basis of this two-level representation, we introduce some similarity measures for both levels. They allow for both a local comparison, pathway by pathway, and a global comparison of the entire metabolism. We developed a tool, MetNet, that implements the proposed methodology. MetNet makes it possible to automatically reconstruct the metabolic network of two organisms selected in KEGG and to compare their two networks both quantitatively and visually. We validate our methodology by presenting some experiments performed with MetNet.

Detecting list-colored graph motifs in biological networks using branch-and-bound strategy

In this work, we study the list-colored graph motif problem, which was introduced to detect functional motifs in biological networks. Given a multi-set M of colors as the query motif and a list-colored graph G where each vertex in G is associated with a set of colors, the aim of this problem is to find a sub-graph of G whose vertex set is colored exactly as motif M. To solve this problem, we present a heuristic method to efficiently and accurately detect list-colored graph motifs in biological networks using branch-and-bound strategy. We transform the detection of list-colored graph motif to the search of connected induced sub-graphs in list-colored graph, where the vertices in the sub-graph are assigned to distinctive colors of query motif. This transformation enables our method to accurately discover the occurrences of query motif without enumerating and verifying all sub-graphs. Furthermore, a new initial vertex selection strategy based on the colors of vertices is proposed to accurately determine the search scope of motifs. Experiments conducted on metabolic networks and protein-interaction networks demonstrate that our method can achieve better performance in accuracy and efficiency in comparison to other existing methods.

Graph-theoretical comparison of normal and tumor networks in identifying BRCA genes

BACKGROUND

Identification of driver genes related to certain types of cancer is an important research topic. Several systems biology approaches have been suggested, in particular for the identification of breast cancer (BRCA) related genes. Such approaches usually rely on differential gene expression and/or mutational landscape data. In some cases interaction network data is also integrated to identify cancer-related modules computationally.

RESULTS

We provide a framework for the comparative graph-theoretical analysis of networks integrating the relevant gene expression, mutations, and potein-protein interaction network data. The comparisons involve a graph-theoretical analysis of normal and tumor network pairs across all instances of a given set of breast cancer samples. The network measures under consideration are based on appropriate formulations of various centrality measures: betweenness, clustering coefficients, degree centrality, random walk distances, graph-theoretical distances, and Jaccard index centrality.

CONCLUSIONS

Among all the studied centrality-based graph-theoretical properties, we show that a betweenness-based measure differentiates BRCA genes across all normal versus tumor network pairs, than the rest of the popular centrality-based measures. The AUROC and AUPR values of the gene lists ordered with respect to the measures under study as compared to NCBI BioSystems pathway and the COSMIC database of cancer genes are the largest with the betweenness-based differentiation, followed by the measure based on degree centrality. In order to test the robustness of the suggested measures in prioritizing cancer genes, we further tested the two most promising measures, those based on betweenness and degree centralities, on randomly rewired networks. We show that both measures are quite resilient to noise in the input interaction network. We also compared the same measures against a state-of-the-art alternative disease gene prioritization method, MUFFFINN. We show that both our graph-theoretical measures outperform MUFFINN prioritizations in terms of ROC and precions/recall analysis. Finally, we filter the ordered list of the best measure, the betweenness-based differentiation, via a maximum-weight independent set formulation and investigate the top 50 genes in regards to literature verification. We show that almost all genes in the list are verified by the breast cancer literature and three genes are presented as novel genes that may potentialy be BRCA-related but missing in literature.

Metabolomics analysis: Finding out metabolic building blocks

In this paper we propose a new methodology for the analysis of metabolic networks. We use the notion of strongly connected components of a graph, called in this context metabolic building blocks. Every strongly connected component is contracted to a single node in such a way that the resulting graph is a directed acyclic graph, called a metabolic DAG, with a considerably reduced number of nodes. The property of being a directed acyclic graph brings out a background graph topology that reveals the connectivity of the metabolic network, as well as bridges, isolated nodes and cut nodes. Altogether, it becomes a key information for the discovery of functional metabolic relations. Our methodology has been applied to the glycolysis and the purine metabolic pathways for all organisms in the KEGG database, although it is general enough to work on any database. As expected, using the metabolic DAGs formalism, a considerable reduction on the size of the metabolic networks has been obtained, specially in the case of the purine pathway due to its relative larger size. As a proof of concept, from the information captured by a metabolic DAG and its corresponding metabolic building blocks, we obtain the core of the glycolysis pathway and the core of the purine metabolism pathway and detect some essential metabolic building blocks that reveal the key reactions in both pathways. Finally, the application of our methodology to the glycolysis pathway and the purine metabolism pathway reproduce the tree of life for the whole set of the organisms represented in the KEGG database which supports the utility of this research.

Aligning Metabolic Pathways Exploiting Binary Relation of Reactions

Metabolic pathway alignment has been widely used to find one-to-one and/or one-to-many reaction mappings to identify the alternative pathways that have similar functions through different sets of reactions, which has important applications in reconstructing phylogeny and understanding metabolic functions. The existing alignment methods exhaustively search reaction sets, which may become infeasible for large pathways. To address this problem, we present an effective alignment method for accurately extracting reaction mappings between two metabolic pathways. We show that connected relation between reactions can be formalized as binary relation of reactions in metabolic pathways, and the multiplications of zero-one matrices for binary relations of reactions can be accomplished in finite steps. By utilizing the multiplications of zero-one matrices for binary relation of reactions, we efficiently obtain reaction sets in a small number of steps without exhaustive search, and accurately uncover biologically relevant reaction mappings. Furthermore, we introduce a measure of topological similarity of nodes (reactions) by comparing the structural similarity of the k-neighborhood subgraphs of the nodes in aligning metabolic pathways. We employ this similarity metric to improve the accuracy of the alignments. The experimental results on the KEGG database show that when compared with other state-of-the-art methods, in most cases, our method obtains better performance in the node correctness and edge correctness, and the number of the edges of the largest common connected subgraph for one-to-one reaction mappings, and the number of correct one-to-many reaction mappings. Our method is scalable in finding more reaction mappings with better biological relevance in large metabolic pathways.

Functional Alignment of Metabolic Networks

Network alignment has become a standard tool in comparative biology, allowing the inference of protein function, interaction, and orthology. However, current alignment techniques are based on topological properties of networks and do not take into account their functional implications. Here we propose, for the first time, an algorithm to align two metabolic networks by taking advantage of their coupled metabolic models. These models allow us to assess the functional implications of genes or reactions, captured by the metabolic fluxes that are altered following their deletion from the network. Such implications may spread far beyond the region of the network where the gene or reaction lies. We apply our algorithm to align metabolic networks from various organisms, ranging from bacteria to humans, showing that our alignment can reveal functional orthology relations that are missed by conventional topological alignments.