Topological Analysis of the Connectome of Digital Reconstructions of Neural Microcircuits

A recent publication provides the network graph for a neocortical microcircuit comprising 8 million connections between 31,000 neurons [7]. Since traditional graph-theoretical methods may not be sufficient to understand the immense complexity of such a biological network, we explored whether methods from algebraic topology could provide a new perspective on its structural and functional organization. Structural topological analysis revealed that directed graphs representing connectivity among neurons in the microcircuit deviated significantly from different varieties of randomized graph. In particular, the directed graphs contained in the order of 107 simplices groups of neurons with all-to-all directed connectivity. Some of these simplices contained up to 8 neurons, making them the most extreme neuronal clustering motif ever reported. Functional topological analysis of simulated neuronal activity in the microcircuit revealed novel spatio-temporal metrics that provide an effective classification of functional responses to qualitatively different stimuli. This study represents the first algebraic topological analysis of structural connectomics and connectomics-based spatio-temporal activity in a biologically realistic neural microcircuit. The methods used in the study show promise for more general applications in network science. The Blue Brain Project (BBP) has recently generated the first draft digital reconstruction and simulation of a microcircuit of neurons in the neocortex of a two-week-old rat (Figure 1A) [7]. This reconstruction is made available through the Neocortical Microcircuit Portal (https://bbpnmc.epfl.ch) [11]. Based on sparse anatomical and physiological data for neurons and synapses and on a variety of biologically motivated organizing principles, the complete connectivity between neurons belonging to a neocortical microcircuit was digitally reconstructed – a microconnectome. The structural properties of the reconstruction have been extensively validated against independent data, and simulations of the reconstruction reproduced multiple in vitro and in vivo experiments without adjusting any parameter, further validating its biological accuracy. In this article we apply methods from topology to the analysis of 42 variants of the digital reconstruction, grouped in six sets of seven microciruits each. The first five sets of microcircuits take into account biological variability in layer heights, proportions of cell types, and cell densities from five individual rats, while the sixth set is based on the average reconstruction across the five individuals. To form each