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The reconstruction of phylogenetic trees from mixed populations has become important in the study of cancer evolution, as sequencing is often performed on bulk tumor tissue containing mixed populations of cells. Recent work has shown how to reconstruct a perfect phylogeny tree from samples that contain mixtures of two-state characters, where each character/locus is either mutated or not. However, most cancers contain more complex mutations, such as copy-number aberrations, that exhibit more than two states. We formulate the Multi-State Perfect Phylogeny Mixture Deconvolution Problem of reconstructing a multi-state perfect phylogeny tree given mixtures of the leaves of the tree. We characterize the solutions of this problem as a restricted class of spanning trees in a graph constructed from the input data, and prove that the problem is NP-complete. We derive an algorithm to enumerate such trees in the important special case of cladisitic characters, where the ordering of the states of each character is given. We apply our algorithm to simulated data and to two cancer datasets. On simulated data, we find that for a small number of samples, the Multi-State Perfect Phylogeny Mixture Deconvolution Problem often has many solutions, but that this ambiguity declines quickly as the number of samples increases. On real data, we recover copy-neutral loss of heterozygosity, single-copy amplification and single-copy deletion events, as well as their interactions with single-nucleotide variants., Comment: RECOMB 2016

Given an undirected node-weighted graph, the Maximum-Weight Connected Subgraph problem (MWCS) is to identify a subset of nodes of maximalsum of weights that induce a connected subgraph. MWCS is closely related to the well-studied Prize Collecting Steiner Tree problem and has many applications in different areas, including computational biology, network design and computer vision. The problem is NP-hard and even hard to approximate within a constant factor. In this work we describe an algorithmic scheme for solving MWCS to provable optimality, which is based on preprocessing rules, new results on decomposing an instance into its biconnected and triconnected components and a branch-and-cut approach combined with a primal heuristic. We demonstrate the performance of our method on the benchmark instances of the 11th DIMACS implementation challenge consisting of MWCS as well as transformed PCST instances., Comment: 11th DIMACS implementation challenge

Background: Biological networks have a growing importance for the interpretation of high-throughput omics data. Integrative network analysis makes use of statistical and combinatorial methods to extract smaller subnetwork modules, and performs enrichment analysis to annotate the modules with ontology terms or other available knowledge. This process results in an annotated module, which retains the original network structure and includes enrichment information as a set system. A major bottleneck is a lack of tools that allow exploring both network structure of extracted modules and its annotations. Results: Thispaperpresentsavisualanalysisapproachthattargetssmallmoduleswithmanyset-based annotations, and which displays the annotations as contours on top of a node-link diagram. We introduce an extension of self-organizing maps to lay out nodes, links, and contours in a unified way. An implementation of this approach is freely available as the Cytoscape app eXamine. Conclusions: eXamine accurately conveys small and annotated modules consisting of several dozens of proteins and annotations. We demonstrate that eXamine facilitates the interpretation of integrative network analysis results in a guided case study. This study has resulted in a novel biological insight regarding the virally-encoded G-protein coupled receptor US28., Comment: BioVis 2014 conference

Background. Biological networks have growing importance for the interpretation of high-throughput "omics" data. Statistical and combinatorial methods allow to obtain mechanistic insights through the extraction of smaller subnetwork modules. Further enrichment analyses provide set-based annotations of these modules. Results. We present eXamine, a set-oriented visual analysis approach for annotated modules that displays set membership as contours on top of a node-link layout. Our approach extends upon Self Organizing Maps to simultaneously lay out nodes, links, and set contours. Conclusions. We implemented eXamine as a freely available Cytoscape app. Using eXamine we study a module that is activated by the virally-encoded G-protein coupled receptor US28 and formulate a novel hypothesis about its functioning.

Data on molecular interactions is increasing at a tremendous pace, while the development of solid methods for analyzing this network data is lagging behind. This holds in particular for the field of comparative network analysis, where one wants to identify commonalities between biological networks. Since biological functionality primarily operates at the network level, there is a clear need for topology-aware comparison methods. In this paper we present a method for global network alignment that is fast and robust, and can flexibly deal with various scoring schemes taking both node-to-node correspondences as well as network topologies into account. It is based on an integer linear programming formulation, generalizing the well-studied quadratic assignment problem. We obtain strong upper and lower bounds for the problem by improving a Lagrangian relaxation approach and introduce the software tool natalie 2.0, a publicly available implementation of our method. In an extensive computational study on protein interaction networks for six different species, we find that our new method outperforms alternative state-of-the-art methods with respect to quality and running time.