doi:10.1093/bioinformatics/btl234

We consider a graph orientation problem arising in the study of biological networks. Given an undirected graph and a list of ordered source-target pairs, the goal is to orient the graph so that a maximum number of pairs will admit a directed path from the source to the target. We show that the problem is NP-hard and hard to approximate to within a constant ratio. We then study restrictions of the problem to various graph classes, and provide an O(log n) approximation algorithm for the general case. We show that this algorithm achieves very tight approximation ratios in practice and is able to infer edge directions with high accuracy on both simulated and real network data.

Here we present additional theoretical and experimental results, algorithm pseudocode, and details regarding both the datasets used and our implementations. Source code for our algorithms is available at

Abstract. We introduce an extended computational framework for studying biological systems. Our approach combines formalization of existing qualitative models that are in wide but informal use today, with probabilistic modeling and integration of high throughput experimental data. Using our methods, it is possible to interpret genomewide measurements in the context of prior knowledge on the system, to assign statistical meaning to the accuracy of such knowledge and to learn refined models with improved fit to the experiments. Our model is represented as a probabilistic factor graph and the framework accommodates partial measurements of diverse biological elements. We develop methods for inference and learning in the model. We compare the performance of standard inference algorithms and tailor-made ones and show that hidden variables can be reliably inferred even in the presence of feedback loops and complex logic. We develop a formulation for the learning problem in our model which is based on deterministic hypothesis testing, and show how to derive p-values for learned model features. We test our methodology and algorithms on both simulated and real yeast data. In particular, we use our method to study the response of S. cerevisiae to hyperosmotic shock, and explore uncharacterized logical relations between important regulators in the system. 1

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Abstract. In a network orientation problem one is given a mixed graph, consisting of directed and undirected edges, and a set of source-target vertex pairs. The goal is to orient the undirected edges so that a maximum number of pairs admit a directed path from the source to the target. This problem is NP-complete and no approximation algorithms are known for it. It arises in the context of analyzing physical networks of protein-protein and protein-dna interactions. While the latter are naturally directed from a transcription factor to a gene, the direction of signal flow in protein-protein interactions is often unknown or cannot be measured en masse. One then tries to infer this information by using causality data on pairs of genes such that the perturbation of one gene changes the expression level of the other gene. Here we provide a first polynomial-size ilp formulation for this problem, which can be efficiently solved on current networks. We apply our algorithm to orient protein-protein interactions in yeast and measure our performance using edges with known orientations. We find that our algorithm achieves high accuracy and coverage in the orientation, outperforming simplified algorithmic variants that do not use information on edge directions. The obtained orientations can lead to better understanding of the structure and function of the network. Key words: network orientation, protein-protein interaction, proteindna interaction, integer linear program, mixed graph 1

Abstract. Graph orientation is a fundamental problem in graph theory that has recently arisen in the study of signaling-regulatory pathways in protein networks. Given a graph and a list of ordered source-target vertex pairs, it calls for assigning directions to the edges of the graph so as to maximize the number of pairs that admit a directed source-to-target path. When the input graph is undirected, a sub-logarithmic approximation is known for the problem. However, the approximability of the biologically-relevant variant, in which the input graph has both directed and undirected edges, was left open. Here we give the first approximation algorithm to this problem. Our algorithm provides a sub-linear guarantee in the general case, and logarithmic guarantees for structured instances. Key words: protein-protein interaction network, mixed graph, graph orientation, approximation algorithm 1

Abstract. Mapping intra-cellular signaling networks is a critical step in developing an understanding of and treatments for many devastating diseases. The predominant ways of discovering pathways in these networks are knockout and pharmacological inhibition experiments. However, experimental evidence for new pathways can be difficult to explain within existing maps of signaling networks. In this paper, we present a novel computational method that integrates pharmacological intervention experiments with protein interaction data in order to predict new signaling pathways that explain unexpected experimental results. Biologists can use these hypotheses to design experiments to further elucidate underlying signaling mechanisms or to directly augment an existing signaling network model. When applied to experimental results from human breast cancer cells targeting the epidermal growth factor receptor (EGFR) network, our method proposes several new, biologically-viable pathways that explain the evidence for a new signaling pathway. These results demonstrate that the method has potential for aiding biologists in generating hypothetical pathways to explain experimental findings. Our method is implemented as part of the PathwayOracle toolkit and is available from the authors upon request. 1

First and foremost, I would like to thank my supervisor prof. Nir Friedman for bringing me into the world of research and showing me the ways of science. I would also like to thank my dear friends in the lab: Gal Elidan, Dana Peer, Ariel Jaimovich, Tommy Kaplan, Yoseph Barash, Iftach Nachman, Ori Shachar, Matan Ninio, Omri Peleg, Hillel Fleischer, and Ilan Wapinski, for helping me in each and every step; without them, this work would have never been written. I am deeply thankful to Ronnen Segman, Naftali Kaminski and the rest of the PTSD team, for proving how fruitful an interdisciplinary collaboration can be. I am also grateful to Zohar Itzhaki for his part in the investigation of classification significance, and for working together. I am indebted to my family and friends for their patience and support along the way. And last but not least, I would like to thank Eli, for his wise advice, enormous support and infinite love. i

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