Rigorous Information-theoretic tools for Comparative Interactomics.

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Molecular signals in the living cell can be in a first approximation mostly attributed to Protein-Protein Interactions (PPI) and their complex cross-talk. Since the recent completion of the Human Genome project, it has now become possible to identify and map a large part of the proteins encoded in our genes. However, more details about the molecular interactions involved in signal transduction pathways need to be uncovered before we can truly understand the complex biology of our cellular system. This represents one of the major challenges for the next years of research in biology and medicine. Molecules signal information through interaction with specific binding partners. The binding induces a conformational change in at least one of the partner molecules, which triggers the next biomolecular step in the signaling cascade. The mechanisms of interaction between proteins are therefore crucial to all biological functions, and the effectiveness of this cross-talk during signal transduction plays a fundamental role in many 'healthy' biological processes and in many diseases (e.g. cancers). Several large-scale experimental studies have been published in recent years, to detect PPIs for diverse species, and have been deposited in publicly available databases. Current experimental techniques, such as yeast two-hybrid (Y2H) and co-affinity purification combined with mass spectrometry (AP-MS), have, however, been shown to samplesubsets of the interaction data space with only very limited overlap. We have recently developed a theoretically sound and accurate mathematical framework for comparing interactome data (PPI networks, PPIN) and to evaluate, in an unbiased way, their distance in terms of macroscopic topological properties. Preliminary analysis revealed that networks of the same species and sampled by the same method are similar, and more similar than networks sampled by the same method but different species. Therefore, networks generated from similar experimental conditions have similar topological features, despite their small overlap of the individual PPIs. To our knowledge this has not yet been shown so clearly and in such an unbiased way. Moreover, we could see very clearly, upon comparing networks sampled with different methods,that the data bias induced by the sampling method presently overshadows species related structural properties. Again, although methodological biases have been acknowledged in the literature, our ability to quantify their impact by using objective distance measures opens a powerful new window on proteome data and their quality control. In this project we seek to add a further essential ingredient to the theory: to include in our macroscopic characterizations of networks the statistics of short loops (beyond quantifying structure only via degree statistics and degree correlations, on which the earlier work was based). The rationale is that functional modules involving a small number of nodes (typically 3-6) appear to play an important role in the overall transduction mechanism. To derive formulae that improve upon those we have used in the previous PPIN comparison, we now need to calculate analytically the Shannon entropy for random graphs with constrained loops. This step is theoretically very difficult, and will involve half of the project duration. If fully exact evaluation is too demanding, we will resort to well-defined and sensible approximations of the loop statistics instead. Numerical simulations will be performed on suitably constructed families of synthetic networks, generated identically or close to those of realistic PPIN. This step will be used as control experiment and/or validation of the developed theory. Finally, the theory will be applied to a large collection of PPIN from different species. The methodological approach developed here should aid experimentalists in the design and interpretation of future studies.