Generating constrained random graphs using multiple edge switches

The generation of random graphs using edge swaps provides a reliable method to draw uniformly random samples of sets of graphs respecting some simple constraints, e.g. degree distributions. However, in general, it is not necessarily possible to access all graphs obeying some given con- straints through a classical switching procedure calling on pairs of edges. We therefore propose to get round this issue by generalizing this classical approach through the use of higher-order edge switches. This method, which we denote by "k-edge switching", makes it possible to progres- sively improve the covered portion of a set of constrained graphs, thereby providing an increasing, asymptotically certain confidence on the statistical representativeness of the obtained sample.Comment: 15 page

Extracting information from biological networks

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2010.Cataloged from PDF version of thesis.Includes bibliographical references (p. 175-194).Systems biology, the study of biological systems in a holistic manner, has been catalyzed by a dramatic improvement in experimental techniques, coupled with a constantly increasing availability of biological data. The representation and analysis of this heterogeneous data is facilitated by the powerful abstraction of biological networks. This thesis examines several types of these networks and looks in detail at the kind of information their analysis can yield. The first part discusses protein interaction networks. We introduce a new algorithm for the pairwise alignment of these networks. We show that these alignments can provide important clues to the function of proteins as well as insights into the evolutionary history of the species under examination. The second part discusses regulatory networks. We present an approach for validating putative drug targets based on the information contained in these networks. We show how this approach can also be used to discover drug targets. The third part discusses metabolic networks. We provide new insights into the structure of constraint-based models of cell metabolism and describe a methodology for performing a complete analysis of a metabolic network. We also present an implementation of this methodology and discuss its application to a variety of problems related to the metabolism of bacteria. The final part describes an application of our methodology to Mycobacterium tuberculosis, the pathogen responsible for almost 2 million deaths around the world every year. We introduce a method for reconciling metabolic network reconstructions and apply it to merge the two published networks for tuberculosis. We analyze the merged network and show how it can be refined based on available experimental data to improve its predictive power. We conclude with a list of potential drug targets.by Leonid Alexandrovich Chindelevitch.Ph.D