Uncovering fundamental features of biological networks

VL Christian, Alexis Benichoux, Jean Baptiste Masson

Abstract: Many biological networks are truly complex systems, displaying highly irregular yet significantly non-random structure. Extracting the statistical regularities of a biological network is a challenging inverse problem since one often has access to only a single experimental realization. In this case the analysis necessarily relies on a statistical model, typically a random graph null model against which statistical significance is defined. Results of the analysis may crucially depend on the choice of null model, leading to possible uncontrolled biases when this choice is ambiguous. This is notably the case for network motifs, defined as subgraphs that are significantly overrepresented as compared to what would be expected if they had not been selected for by evolution, a hypothesis that does not readily translate to a network null model. Here we develop an orthogonal approach to mining significant network features: instead of relying on a single null model, we apply a hierarchy of increasingly constrained microcanonical random graph models. This allows us to systematically unravel a hierarchy of fundamental features that together describe the structure of a network and filter out features that can be explained as statistical consequences of these fundamental features. We demonstrate our methodology by characterizing the structure of physical synaptic-resolution connectomes in small insects obtained from serial electron microscopy imaging. We applied it to learn fundamental microscopic node-level features and microcircuits as well mesoscopic block structures of the connectomes. We compare the structures discovered in different brain regions and between species and identify distinct features which may be linked to the biological function of each region.