MultiNet: Multi-omic multi-scale comparative and integrative network analyses

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Due to technological advances in experimental biology, we now have an astounding amount of various molecular and clinical data describing different aspects of the functioning of the cells. These complex big data carry biomedical information that is currently hidden from us within their large sizes and complexities. Hence, some of the foremost computational challenges that the data pose are:

1) how to analyze complex omics networks individually;

2) how to analyze them jointly; and

3) how to comparatively extract new biomedical information.

This is non trivial and requires the development of heuristic new algorithms due to the computational intractability of the underlying problems. This proposal addresses several such algorithmic challenges that the data pose and applies the new algorithms to the most up-to-date, versatile omics data. In a cell, molecules interact in pair wise fashion, but also jointly forming larger molecular machines. Hence, omics data are naturally represented both by simple graphs, as well as by models that capture multi-scale molecular organization, including hypergraphs and abstract simplicial complexes.

Prof. Przulj introduced graphlets as a sensitive algorithmic tool measuring the structure (topology) of networks and nodes. They have since become a highly-cited, important tool for algorithmic development yielding substantial domain specific insight in many areas, including biology. Prof. Przulj generalized graphlets to hypergraphlets and simplets to enable analyses of multi-scale models of molecular interactions modelled by hypergraphs and abstract simplicial complexes. However, none of these allow for weights on edges, while molecular networks are naturally weighted. Hence, we propose extensions of algorithms that use graphlets, hypergraphlets and simplets to compute with weights on edges and thus include this important biological information into mining algorithms. In addition, we propose to generalize Graphlet Laplacians to deal with automorphism orbits of graphlets, as well as graphlet based clustering coefficients uniting graphlet and clustering properties of networks.