Gunnar W. Klau

Identifying functional modules in protein–protein interaction networks

Motivation: With the exponential growth of expression and protein–protein interaction (PPI) data, the frontier of research in systems biology shifts more and more to the integrated analysis of these large datasets. Of particular interest is the identification of functional modules in PPI networks, sharing common cellular function beyond the scope of classical pathways, by means of detecting differentially expressed regions in PPI networks. This requires on the one hand an adequate scoring of the nodes in the network to be identified and on the other hand the availability of an effective algorithm to find the maximally scoring network regions. Various heuristic approaches have been proposed in the literature. Results: Here we present the first exact solution for this problem, which is based on integer-linear programming and its connection to the well-known prize-collecting Steiner tree problem from Operations Research. Despite the NP-hardness of the underlying combinatorial problem, our method typically computes provably optimal subnetworks in large PPI networks in a few minutes. An essential ingredient of our approach is a scoring function defined on network nodes. We propose a new additive score with two desirable properties: (i) it is scalable by a statistically interpretable parameter and (ii) it allows a smooth integration of data from various sources. We apply our method to a well-established lymphoma microarray dataset in combination with associated survival data and the large interaction network of HPRD to identify functional modules by computing optimal-scoring subnetworks. In particular, we find a functional interaction module associated with proliferation over-expressed in the aggressive ABC subtype as well as modules derived from non-malignant by-stander cells. Availability: Our software is available freely for non-commercial purposes at http://www.planet-lisa.net. Contact: tobias.mueller@biozentrum.uni-wuerzburg.de

An Algorithmic Framework for the Exact Solution of the Prize-Collecting Steiner Tree Problem

The Prize-Collecting Steiner Tree Problem (PCST) on a graph with edge costs and vertex profits asks for a subtree minimizing the sum of the total cost of all edges in the subtree plus the total profit of all vertices not contained in the subtree. PCST appears frequently in the design of utility networks where profit generating customers and the network connecting them have to be chosen in the most profitable way.Our main contribution is the formulation and implementation of a branch-and-cut algorithm based on a directed graph model where we combine several state-of-the-art methods previously used for the Steiner tree problem. Our method outperforms the previously published results on the standard benchmark set of problems.We can solve all benchmark instances from the literature to optimality, including some of them for which the optimum was not known. Compared to a recent algorithm by Lucena and Resende, our new method is faster by more than two orders of magnitude. We also introduce a new class of more challenging instances and present computational results for them. Finally, for a set of large-scale real-world instances arising in the design of fiber optic networks, we also obtain optimal solution values.

An integer linear programming approach for finding deregulated subgraphs in regulatory networks.

Deregulation of cell signaling pathways plays a crucial role in the development of tumors. The identification of such pathways requires effective analysis tools that facilitate the interpretation of expression differences. Here, we present a novel and highly efficient method for identifying deregulated subnetworks in a regulatory network. Given a score for each node that measures the degree of deregulation of the corresponding gene or protein, the algorithm computes the heaviest connected subnetwork of a specified size reachable from a designated root node. This root node can be interpreted as a molecular key player responsible for the observed deregulation. To demonstrate the potential of our approach, we analyzed three gene expression data sets. In one scenario, we compared expression profiles of non-malignant primary mammary epithelial cells derived from BRCA1 mutation carriers and of epithelial cells without BRCA1 mutation. Our results suggest that oxidative stress plays an important role in epithelial cells of BRCA1 mutation carriers and that the activation of stress proteins may result in avoidance of apoptosis leading to an increased overall survival of cells with genetic alterations. In summary, our approach opens new avenues for the elucidation of pathogenic mechanisms and for the detection of molecular key players.

A new graph-based method for pairwise global network alignment

BackgroundIn addition to component-based comparative approaches, network alignments provide the means to study conserved network topology such as common pathways and more complex network motifs. Yet, unlike in classical sequence alignment, the comparison of networks becomes computationally more challenging, as most meaningful assumptions instantly lead to NP-hard problems. Most previous algorithmic work on network alignments is heuristic in nature.ResultsWe introduce the graph-based maximum structural matching formulation for pairwise global network alignment. We relate the formulation to previous work and prove NP-hardness of the problem.Based on the new formulation we build upon recent results in computational structural biology and present a novel Lagrangian relaxation approach that, in combination with a branch-and-bound method, computes provably optimal network alignments. The Lagrangian algorithm alone is a powerful heuristic method, which produces solutions that are often near-optimal and – unlike those computed by pure heuristics – come with a quality guarantee.ConclusionComputational experiments on the alignment of protein-protein interaction networks and on the classification of metabolic subnetworks demonstrate that the new method is reasonably fast and has advantages over pure heuristics. Our software tool is freely available as part of the LI SA library.

BioNet: an R-Package for the functional analysis of biological networks

MOTIVATION Increasing quantity and quality of data in transcriptomics and interactomics create the need for integrative approaches to network analysis. Here, we present a comprehensive R-package for the analysis of biological networks including an exact and a heuristic approach to identify functional modules. RESULTS The BioNet package provides an extensive framework for integrated network analysis in R. This includes the statistics for the integration of transcriptomic and functional data with biological networks, the scoring of nodes as well as methods for network search and visualization. AVAILABILITY The BioNet package and a tutorial are available from http://bionet.bioapps.biozentrum.uni-wuerzburg.de.

Ancient Dispersal of the Human Fungal Pathogen Cryptococcus gattii from the Amazon Rainforest

Over the past two decades, several fungal outbreaks have occurred, including the high-profile ‘Vancouver Island’ and ‘Pacific Northwest’ outbreaks, caused by Cryptococcus gattii, which has affected hundreds of otherwise healthy humans and animals. Over the same time period, C. gattii was the cause of several additional case clusters at localities outside of the tropical and subtropical climate zones where the species normally occurs. In every case, the causative agent belongs to a previously rare genotype of C. gattii called AFLP6/VGII, but the origin of the outbreak clades remains enigmatic. Here we used phylogenetic and recombination analyses, based on AFLP and multiple MLST datasets, and coalescence gene genealogy to demonstrate that these outbreaks have arisen from a highly-recombining C. gattii population in the native rainforest of Northern Brazil. Thus the modern virulent C. gattii AFLP6/VGII outbreak lineages derived from mating events in South America and then dispersed to temperate regions where they cause serious infections in humans and animals.

Accurate multiple sequence-structure alignment of RNA sequences using combinatorial optimization

BackgroundThe discovery of functional non-coding RNA sequences has led to an increasing interest in algorithms related to RNA analysis. Traditional sequence alignment algorithms, however, fail at computing reliable alignments of low-homology RNA sequences. The spatial conformation of RNA sequences largely determines their function, and therefore RNA alignment algorithms have to take structural information into account.ResultsWe present a graph-based representation for sequence-structure alignments, which we model as an integer linear program (ILP). We sketch how we compute an optimal or near-optimal solution to the ILP using methods from combinatorial optimization, and present results on a recently published benchmark set for RNA alignments.ConclusionThe implementation of our algorithm yields better alignments in terms of two published scores than the other programs that we tested: This is especially the case with an increasing number of input sequences. Our program LARA is freely available for academic purposes from http://www.planet-lisa.net.

Charge Group Partitioning in Biomolecular Simulation

Molecular simulation techniques are increasingly being used to study biomolecular systems at an atomic level. Such simulations rely on empirical force fields to represent the intermolecular interactions. There are many different force fields available--each based on a different set of assumptions and thus requiring different parametrization procedures. Recently, efforts have been made to fully automate the assignment of force-field parameters, including atomic partial charges, for novel molecules. In this work, we focus on a problem arising in the automated parametrization of molecules for use in combination with the GROMOS family of force fields: namely, the assignment of atoms to charge groups such that for every charge group the sum of the partial charges is ideally equal to its formal charge. In addition, charge groups are required to have size at most k. We show NP-hardness and give an exact algorithm that solves practical problem instances to provable optimality in a fraction of a second.

Investigating human-computer optimization

Scheduling, routing, and layout tasks are examples of hard optimization problems with broad application in industry. Past research in this area has focused on algorithmic issues. However, this approach neglects many important human-computer interaction issues that must be addressed to provide people with practical solutions to optimization problems. Automatic methods do not leverage human expertise and can only find solutions that are optimal with regard to an invariably over-simplified problem description. Furthermore, users must understand the generated solutions in order to implement, justify, or modify them. Interactive optimization helps address these issues but has not previously been studied in detail. This paper describes experiments on an interactive optimization system that explore the most appropriate way to combine the respective strengths of people and computers. Our results show that users can successfully identify promising areas of the search space as well as manage the amount of computational effort expended on different subproblems

Optimal robust non-unique probe selection using Integer Linear Programming

MOTIVATION Besides their prevalent use for analyzing gene expression, microarrays are an efficient tool for biological, medical and industrial applications due to their ability to assess the presence or absence of biological agents, the targets, in a sample. Given a collection of genetic sequences of targets one faces the challenge of finding short oligonucleotides, the probes, which allow detection of targets in a sample. Each hybridization experiment determines whether the probe binds to its corresponding sequence in the target. Depending on the problem, the experiments are conducted using either unique or non-unique probes and usually assume that only one target is present in the sample. The problem at hand is to compute a design, i.e. a minimal set of probes that allows to infer the targets in the sample from the result of the hybridization experiment. If we allow to test for more than one target in the sample, the design of the probe set becomes difficult in the case of non-unique probes. RESULTS Building upon previous work on group testing for microarrays, we describe the first approach to select a minimal probe set for the case of non-unique probes in the presence of a small number of multiple targets in the sample. The approach is based on an ILP formulation and a branch-and-cut algorithm. Our preliminary implementation greatly reduces the number of probes needed while preserving the decoding capabilities. AVAILABILITY http://www.inf.fu-berlin.de/inst/ag-bio