On the prediction of neuronal microscale topology descriptors based on mesoscale recordings

The brain possesses structural and functional hierarchical architectures organized over multiple scales. Considering that functional recordings commonly focused on a single spatial level, and because multiple scales interact with one another, we explored the behaviour of in silico neuronal networks across different scales. We established ad hoc relations of several topological descriptors (average clustering coefficient, average path length, small-world propensity, modularity, network degree, synchronizability and fraction of long-term connections) between different scales upon application and empirical validation of a Euclidian renormalization approach. We tested a simple network (distance-dependent model) as well as an artificial cortical network (Vertex; undirected and directed networks) finding the same qualitative power law relations of the parameters across levels: their quantitative nature is model dependent. Those findings were then organized in a workflow that can be used to predict, with approximation, microscale topologies from mesoscale recordings. The present manuscript not only presents a theoretical framework for the renormalization of biological neuronal network and their study across scales in light of the spatial features of the recording method but also proposes an applicable workflow to compare real functional networks across scales.