TORQUE: topology-free querying of protein interaction networks.

TORQUE is a tool for cross-species querying of protein-protein interaction networks. It aims to answer the following question: given a set of proteins constituting a known complex or a pathway in one species, can a similar complex or pathway be found in the protein network of another species? To this end, Torque seeks a matching set of proteins that are sequence similar to the query proteins and span a connected region of the target network, while allowing for both insertions and deletions. Unlike existing approaches, TORQUE does not require knowledge of the interconnections among the query proteins. It can handle large queries of up to 25 proteins. The Torque web server is freely available for use at http://www.cs.tau.ac.il/~bnet/torque.html.

Faspad: fast signaling pathway detection.

UNLABELLED: Faspad is a user-friendly tool that detects candidates for linear signaling pathways in protein interaction networks based on an approach by Scott et al. (Journal of Computational Biology, 2006). Using recent algorithmic insights, it can solve the underlying NP-hard problem quite fast: for protein networks of typical size (several thousand nodes), pathway candidates of length up to 13 proteins can be found within seconds and with a 99.9% probability of optimality. Faspad graphically displays all candidates that are found; for evaluation and comparison purposes, an overlay of several candidates and the surrounding network context can also be shown. AVAILABILITY: Faspad is available as free software under the GPL license at http://theinf1.informatik.uni-jena.de/faspad/ and runs under Linux and Windows.

Developing fixed-parameter algorithms to solve combinatorially explosive biological problems.

Fixed-parameter algorithms can efficiently find optimal solutions to some computationally hard (NP-hard) problems. This chapter surveys five main practical techniques to develop such algorithms. Each technique is circumstantiated by case studies of applications to biological problems. It also presents other known bioinformatics-related applications and gives pointers to experimental results.

Matching algorithms for assigning orthologs after genome duplication events.

In this paper, we introduce and analyze two graph-based models for assigning orthologs in the presence of whole-genome duplications, using similarity information between pairs of genes. The common feature of our two models is that genes of the first genome may be assigned two orthologs from the second genome, which has undergone a whole-genome duplication. Additionally, our models incorporate the new notion of duplication bonus, a parameter that reflects how assigning two orthologs to a given gene should be rewarded or penalized. Our work is mainly focused on developing exact and reasonably time-consuming algorithms for these two models: we show that the first one is polynomial-time solvable, while the second is NP-hard. For the latter, we thus design two fixed-parameter algorithms, i.e. exact algorithms whose running times are exponential only with respect to a small and well-chosen input parameter. Finally, for both models, we evaluate our algorithms on pairs of plant genomes. Our experiments show that the NP-hard model yields a better cluster quality at the cost of lower coverage, due to the fact that our instances cannot be completely solved by our algorithms. However, our results are altogether encouraging and show that our methods yield biologically significant predictions of orthologs when the duplication bonus value is properly chosen.

Parameterized Algorithmics for Finding Exact Solutions of NP-Hard Biological Problems.

Fixed-parameter algorithms are designed to efficiently find optimal solutions to some computationally hard (NP-hard) problems by identifying and exploiting "small" problem-specific parameters. We survey practical techniques to develop such algorithms. Each technique is introduced and supported by case studies of applications to biological problems, with additional pointers to experimental results.

A graph modification approach for finding core-periphery structures in protein interaction networks.

The core-periphery model for protein interaction (PPI) networks assumes that protein complexes in these networks consist of a dense core and a possibly sparse periphery that is adjacent to vertices in the core of the complex. In this work, we aim at uncovering a global core-periphery structure for a given PPI network. We propose two exact graph-theoretic formulations for this task, which aim to fit the input network to a hypothetical ground truth network by a minimum number of edge modifications. In one model each cluster has its own periphery, and in the other the periphery is shared. We first analyze both models from a theoretical point of view, showing their NP-hardness. Then, we devise efficient exact and heuristic algorithms for both models and finally perform an evaluation on subnetworks of the S. cerevisiae PPI network.

Partitioning Biological Networks into Highly Connected Clusters with Maximum Edge Coverage.

A popular clustering algorithm for biological networks which was proposed by Hartuv and Shamir identifies nonoverlapping highly connected components. We extend the approach taken by this algorithm by introducing the combinatorial optimization problem Highly Connected Deletion, which asks for removing as few edges as possible from a graph such that the resulting graph consists of highly connected components. We show that Highly Connected Deletion is NP-hard and provide a fixed-parameter algorithm and a kernelization. We propose exact and heuristic solution strategies, based on polynomial-time data reduction rules and integer linear programming with column generation. The data reduction typically identifies 75 percent of the edges that are deleted for an optimal solution; the column generation method can then optimally solve protein interaction networks with up to 6,000 vertices and 13,500 edges within five hours. Additionally, we present a new heuristic that finds more clusters than the method by Hartuv and Shamir.

Exploiting bounded signal flow for graph orientation based on cause-effect pairs.

BACKGROUND: We consider the following problem: Given an undirected network and a set of sender-receiver pairs, direct all edges such that the maximum number of "signal flows" defined by the pairs can be routed respecting edge directions. This problem has applications in understanding protein interaction based cell regulation mechanisms. Since this problem is NP-hard, research so far concentrated on polynomial-time approximation algorithms and tractable special cases. RESULTS: We take the viewpoint of parameterized algorithmics and examine several parameters related to the maximum signal flow over vertices or edges. We provide several fixed-parameter tractability results, and in one case a sharp complexity dichotomy between a linear-time solvable case and a slightly more general NP-hard case. We examine the value of these parameters for several real-world network instances. CONCLUSIONS: Several biologically relevant special cases of the NP-hard problem can be solved to optimality. In this way, parameterized analysis yields both deeper insight into the computational complexity and practical solving strategies.

Topology-free querying of protein interaction networks.

In the network querying problem, one is given a protein complex or pathway of species A and a protein-protein interaction network of species B; the goal is to identify subnetworks of B that are similar to the query in terms of sequence, topology, or both. Existing approaches mostly depend on knowledge of the interaction topology of the query in the network of species A; however, in practice, this topology is often not known. To address this problem, we develop a topology-free querying algorithm, which we call Torque. Given a query, represented as a set of proteins, Torque seeks a matching set of proteins that are sequence-similar to the query proteins and span a connected region of the network, while allowing both insertions and deletions. The algorithm uses alternatively dynamic programming and integer linear programming for the search task. We test Torque with queries from yeast, fly, and human, where we compare it to the QNet topology-based approach, and with queries from less studied species, where only topology-free algorithms apply. Torque detects many more matches than QNet, while giving results that are highly functionally coherent.