Metabolic network alignment in large scale by network compression

Metabolic network alignment is a system scale comparative analysis that discovers important similarities and differences across different metabolisms and organisms. Although the problem of aligning metabolic networks has been considered in the past, the computational complexity of the existing solutions has so far limited their use to moderately sized networks. In this paper, we address the problem of aligning two metabolic networks, particularly when both of them are too large to be dealt with using existing methods. We develop a generic framework that can significantly improve the scale of the networks that can be aligned in practical time. Our framework has three major phases, namely the compression phase, the alignment phase and the refinement phase. For the first phase, we develop an algorithm which transforms the given networks to a compressed domain where they are summarized using fewer nodes, termed supernodes, and interactions. In the second phase, we carry out the alignment in the compressed domain using an existing network alignment method as our base algorithm. This alignment results in supernode mappings in the compressed domain, each of which are smaller instances of network alignment problem. In the third phase, we solve each of the instances using the base alignment algorithm to refine the alignment results. We provide a user defined parameter to control the number of compression levels which generally determines the tradeoff between the quality of the alignment versus how fast the algorithm runs. Our experiments on the networks from KEGG pathway database demonstrate that the compression method we propose reduces the sizes of metabolic networks by almost half at each compression level which provides an expected speedup of more than an order of magnitude. We also observe that the alignments obtained by only one level of compression capture the original alignment results with high accuracy. Together, these suggest that our framework results in alignments that are comparable to existing algorithms and can do this with practical resource utilization for large scale networks that existing algorithms could not handle. As an example of our method's performance in practice, the alignment of organism-wide metabolic networks of human (1615 reactions) and mouse (1600 reactions) was performed under three minutes by only using a single level of compression.     

The players may change but the game remains: network analyses of ruminal microbiomes suggest taxonomic differences mask functional similarity

By mapping translated metagenomic reads to a microbial metabolic network, we show that ruminal ecosystems that are rather dissimilar in their taxonomy can be considerably more similar at the metabolic network level. Using a new network bi-partition approach for linking the microbial network to a bovine metabolic network, we observe that these ruminal metabolic networks exhibit properties consistent with distinct metabolic communities producing similar outputs from common inputs. For instance, the closer in network space that a microbial reaction is to a reaction found in the host, the lower will be the variability of its enzyme copy number across hosts. Similarly, these microbial enzymes that are nearby to host nodes are also higher in copy number than are more distant enzymes. Collectively, these results demonstrate a widely expected pattern that, to our knowledge, has not been explicitly demonstrated in microbial communities: namely that there can exist different community metabolic networks that have the same metabolic inputs and outputs but differ in their internal structure.     

Seed selection strategy in global network alignment without destroying the entire structures of functional modules

Background

Network alignment is one of the most common biological network comparison methods. Aligning protein-protein interaction (PPI) networks of different species is of great important to detect evolutionary conserved pathways or protein complexes across species through the identification of conserved interactions, and to improve our insight into biological systems. Global network alignment (GNA) problem is NP-complete, for which only heuristic methods have been proposed so far. Generally, the current GNA methods fall into global heuristic seed-and-extend approaches. These methods can not get the best overall consistent alignment between networks for the opinionated local seed. Furthermore These methods are lost in maximizing the number of aligned edges between two networks without considering the original structures of functional modules.

Methods

We present a novel seed selection strategy for global network alignment by constructing the pairs of hub nodes of networks to be aligned into multiple seeds. Beginning from every hub seed and using the membership similarity of nodes to quantify to what extent the nodes can participate in functional modules associated with current seed topologically we align the networks by modules. By this way we can maintain the functional modules are not damaged during the heuristic alignment process. And our method is efficient in resolving the fatal problem of most conventional algorithms that the initialization selected seeds have a direct influence on the alignment result. The similarity measures between network nodes (e.g., proteins) include sequence similarity, centrality similarity, and dynamic membership similarity and our algorithm can be called Multiple Hubs-based Alignment (MHA).

Results

When applying our seed selection strategy to several pairs of real PPI networks, it is observed that our method is working to strike a balance, extending the conserved interactions while maintaining the functional modules unchanged. In the case study, we assess the effectiveness of MHA on the alignment of the yeast and fly PPI networks. Our method outperforms state-of-the-art algorithms at detecting conserved functional modules and retrieves in particular 86% more conserved interactions than IsoRank.

Conclusions

We believe that our seed selection strategy will lead us to obtain more topologically and biologically similar alignment result. And it can be used as the reference and complement of other heuristic methods to seek more meaningful alignment results.

     

Inference of signaling and gene regulatory networks by steady-state perturbation experiments: structure and accuracy

One of the fundamental problems of cell biology is the understanding of complex regulatory networks. Such networks are ubiquitous in cells and knowledge of their properties is essential for the understanding of cellular behavior. In earlier work (Kholodenko et al. (PNAS 99: 12841), it was shown how the structure of biological networks can be quantified from experimental measurements of steady-state concentrations of key intermediates as a result of perturbations using a simple algorithm called "unravelling". Here, we study the effect of experimental uncertainty on the accuracy of the inferred structure (i.e. whether interactions are excitatory or inhibitory) of the networks determined using the unravelling algorithm. We show that the accuracy of the network structure depends not only on the noise level but on the strength of the interactions within the network. In particular, both very small and very large values of the connection strengths lead to large uncertainty in the inferred network. We describe a powerful geometric tool for the intuitive understanding of the effect of experimental error on the qualitative accuracy of the inferred network. In addition, we show that the use of additional data beyond that needed to minimally constrain the network not only improves the accuracy of the inferred network, but also may allow the detection of situations in which the initial assumptions of unravelling with respect to the network and the perturbations have been violated. Our ideas are illustrated using the mitogen-activated protein kinase (MAPK) signaling network as an example.     

Selective integration of multiple biological data for supervised network inference

MOTIVATION: Inferring networks of proteins from biological data is a central issue of computational biology. Most network inference methods, including Bayesian networks, take unsupervised approaches in which the network is totally unknown in the beginning, and all the edges have to be predicted. A more realistic supervised framework, proposed recently, assumes that a substantial part of the network is known. We propose a new kernel-based method for supervised graph inference based on multiple types of biological datasets such as gene expression, phylogenetic profiles and amino acid sequences. Notably, our method assigns a weight to each type of dataset and thereby selects informative ones. Data selection is useful for reducing data collection costs. For example, when a similar network inference problem must be solved for other organisms, the dataset excluded by our algorithm need not be collected. RESULTS: First, we formulate supervised network inference as a kernel matrix completion problem, where the inference of edges boils down to estimation of missing entries of a kernel matrix. Then, an expectation-maximization algorithm is proposed to simultaneously infer the missing entries of the kernel matrix and the weights of multiple datasets. By introducing the weights, we can integrate multiple datasets selectively and thereby exclude irrelevant and noisy datasets. Our approach is favorably tested in two biological networks: a metabolic network and a protein interaction network. AVAILABILITY: Software is available on request.     

Discovering large conserved functional components in global network alignment by graph matching

Background

Aligning protein-protein interaction (PPI) networks is very important to discover the functionally conserved sub-structures between different species. In recent years, the global PPI network alignment problem has been extensively studied aiming at finding the one-to-one alignment with the maximum matching score. However, finding large conserved components remains challenging due to its NP-hardness.

Results

We propose a new graph matching method GMAlign for global PPI network alignment. It first selects some pairs of important proteins as seeds, followed by a gradual expansion to obtain an initial matching, and then it refines the current result to obtain an optimal alignment result iteratively based on the vertex cover. We compare GMAlign with the state-of-the-art methods on the PPI network pairs obtained from the largest BioGRID dataset and validate its performance. The results show that our algorithm can produce larger size of alignment, and can find bigger and denser common connected subgraphs as well for the first time. Meanwhile, GMAlign can achieve high quality biological results, as measured by functional consistency and semantic similarity of the Gene Ontology terms. Moreover, we also show that GMAlign can achieve better results which are structurally and biologically meaningful in the detection of large conserved biological pathways between species.

Conclusions

GMAlign is a novel global network alignment tool to discover large conserved functional components between PPI networks. It also has many potential biological applications such as conserved pathway and protein complex discovery across species. The GMAlign software and datasets are avaialbile at https://github.com/yzlwhu/GMAlign.

     

An algorithm for linear metabolic pathway alignment

Metabolic pathway alignment represents one of the most powerful tools for comparative analysis of metabolism. It involves recognition of metabolites common to a set of functionally-related metabolic pathways, interpretation of biological evolution processes and determination of alternative metabolic pathways. Moreover, it is of assistance in function prediction and metabolism modeling. Although research on genomic sequence alignment is extensive, the problem of aligning metabolic pathways has received less attention. We are motivated to develop an algorithm of metabolic pathway alignment to reveal the similarities between metabolic pathways. A new definition of the metabolic pathway is introduced. The algorithm has been implemented into the PathAligner system; its web-based interface is available at http://bibiserv.techfak.uni-bielefeld.de/pathaligner/.     

B-cell ligand processing pathways detected by large-scale comparative analysis

The initiation of B-cell ligand recognition is a critical step for the generation of an immune response against foreign bodies.We sought to identify the biochemical pathways involved in the B-cell ligand recognition cascade and sets of ligands that trigger similar immunological responses.We utilized several comparative approaches to analyze the gene coexpression networks generated from a set of microarray experiments spanning 33 different ligands.First,we compared the degree distributions of the generated networks.Second,we utilized a pairwise network alignment algorithm,BiNA,to align the networks based on the hubs in the networks.Third,we aligned the networks based on a set of K_EGG pathways.We summarized our results by constructing a consensus hierarchy of pathways that are involved in B cell ligand recognition.The resulting pathways were further validated through literature for their common physiological responses.Collectively,the results based on our comparative analyses of degree distributions,alignment of hubs,and alignment based on KEGG pathways provide a basis for molecular characterization of the immune response states of B-cells and demonstrate the power of comparative approaches(e.g.,gene coexpression network alignment algorithms) in elucidating biochemical pathways involved in complex signaling events in cells.     

Topac: alignment of gene regulatory networks using topology-aware coloring

We consider the problem of finding a subnetwork in a given biological network (i.e. target network) that is most similar to a given small query network. We aim to find the optimal solution (i.e. the subnetwork with the largest alignment score) with a provable confidence bound. There is no known polynomial time solution to this problem in the literature. Alon et al. has developed a state-of-the-art coloring method that reduces the cost of this problem. This method randomly colors the target network prior to alignment for many iterations until a user-supplied confidence is reached. Here we develop a novel coloring method, named k-hop coloring (k is a positive integer), that achieves a provable confidence value in a small number of iterations without sacrificing the optimality. Our method considers the color assignments already made in the neighborhood of each target network node while assigning a color to a node. This way, it preemptively avoids many color assignments that are guaranteed to fail to produce the optimal alignment. We also develop a filtering method that eliminates the nodes that cannot be aligned without reducing the alignment score after each coloring instance. We demonstrate both theoretically and experimentally that our coloring method outperforms that of Alon et al., which is also used by a number network alignment methods, including QPath and QNet, by a factor of three without reducing the confidence in the optimality of the result. Our experiments also suggest that the resulting alignment method is capable of identifying functionally enriched regions in the target network successfully.     

SMETANA: Accurate and Scalable Algorithm for Probabilistic Alignment of Large-Scale Biological Networks

In this paper we introduce an efficient algorithm for alignment of multiple large-scale biological networks. In this scheme, we first compute a probabilistic similarity measure between nodes that belong to different networks using a semi-Markov random walk model. The estimated probabilities are further enhanced by incorporating the local and the cross-species network similarity information through the use of two different types of probabilistic consistency transformations. The transformed alignment probabilities are used to predict the alignment of multiple networks based on a greedy approach. We demonstrate that the proposed algorithm, called SMETANA, outperforms many state-of-the-art network alignment techniques, in terms of computational efficiency, alignment accuracy, and scalability. Our experiments show that SMETANA can easily align tens of genome-scale networks with thousands of nodes on a personal computer without any difficulty. The source code of SMETANA is available upon request. The source code of SMETANA can be downloaded from http://www.ece.tamu.edu/~bjyoon/SMETANA/.     

Efficient detection of network motifs

Motifs in a given network are small connected subnetworks that occur in significantly higher frequencies than would be expected in random networks. They have recently gathered much attention as a concept to uncover structural design principles of complex networks. Kashtan et al. [Bioinformatics, 2004] proposed a sampling algorithm for performing the computationally challenging task of detecting network motifs. However, among other drawbacks, this algorithm suffers from a sampling bias and scales poorly with increasing subgraph size. Based on a detailed analysis of the previous algorithm, we present a new algorithm for network motif detection which overcomes these drawbacks. Furthermore, we present an efficient new approach for estimating the frequency of subgraphs in random networks that, in contrast to previous approaches, does not require the explicit generation of random networks. Experiments on a testbed of biological networks show our new algorithms to be orders of magnitude faster than previous approaches, allowing for the detection of larger motifs in bigger networks than previously possible and thus facilitating deeper insight into the field     

Detecting conserved interaction patterns in biological networks.

Molecular interaction data plays an important role in understanding biological processes at a modular level by providing a framework for understanding cellular organization, functional hierarchy, and evolutionary conservation. As the quality and quantity of network and interaction data increases rapidly, the problem of effectively analyzing this data becomes significant. Graph theoretic formalisms, commonly used for these analysis tasks, often lead to computationally hard problems due to their relation to subgraph isomorphism. This paper presents an innovative new algorithm, MULE, for detecting frequently occurring patterns and modules in biological networks. Using an innovative graph simplification technique based on ortholog contraction, which is ideally suited to biological networks, our algorithm renders these problems computationally tractable and scalable to large numbers of networks. We show, experimentally, that our algorithm can extract frequently occurring patterns in metabolic pathways and protein interaction networks from the KEGG, DIP, and BIND databases within seconds. When compared to existing approaches, our graph simplification technique can be viewed either as a pruning heuristic, or a closely related, but computationally simpler task. When used as a pruning heuristic, we show that our technique reduces effective graph sizes significantly, accelerating existing techniques by several orders of magnitude! Indeed, for most of the test cases, existing techniques could not even be applied without our pruning step. When used as a stand-alone analysis technique, MULE is shown to convey significant biological insights at near-interactive rates. The software, sample input graphs, and detailed results for comprehensive analysis of nine eukaryotic PPI networks are available at www.cs.purdue.edu/homes/koyuturk/mule.