Topological analysis of the connectome of digital reconstructions of neural microcircuits

Pawel Dlotko, Kathryn Hess, Ran Levi, Max Nolte, Eilif Muller, Michael Reimann, Martina Scolamiero, Katharine Turner, Henry Markram

Research output: Working paper


A recent publication provides the network graph for a neocortical microcircuit comprising 8 million connections between 31,000 neurons (H. Markram, et al., Reconstruction and simulation of neocortical microcircuitry, Cell, 163 (2015) no. 2, 456-492). 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 {\DH} 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.
Original languageEnglish
Number of pages28
Publication statusSubmitted - 7 Jan 2016

Bibliographical note

This work was supported by funding from the ETH Domain for the Blue Brain
Project (BBP). The BlueBrain IV IBM BlueGene/Q system is financed by ETH Board Funding to the Blue Brain Project and hosted at the Swiss National Supercomputing Center (CSCS). We thank Ahmet Bilgili for providing the visualization of the microcircuit in Figure 1. Partial support for P.D. was provided by the GUDHI project, supported by an Advanced Investigator Grant of the European Research Council and hosted by INRIA. M.S. was supported by the NCCR Synapsy of the Swiss National Science Foundation.


  • Topology
  • directed flag complex
  • Betti number
  • Euler characteristic
  • neocortical microcircuit


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