Front. Comput. Neurosci., 12 June 2017
Cliques of Neurons Bound into Cavities Provide a Missing Link between Structure and Function
Michael W. Reimann1†, Max Nolte1†, Martina Scolamiero2, Katharine Turner2, Rodrigo Perin3, Giuseppe Chindemi1, Paweł Dłotko4‡, Ran Levi5‡, Kathryn Hess2*‡ and Henry Markram1,3*‡
1Blue Brain Project, École Polytechnique Fédérale de Lausanne, Geneva, Switzerland
2Laboratory for Topology and Neuroscience, Brain Mind Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
3Laboratory of Neural Microcircuitry, Brain Mind Institute, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
4DataShape, INRIA Saclay, Palaiseau, France
5Institute of Mathematics, University of Aberdeen, Aberdeen, United Kingdom
Source/Fonte: Psychology Today
The lack of a formal link between neural network structure and its emergent function has hampered our understanding of how the brain processes information. We have now come closer to describing such a link by taking the direction of synaptic transmission into account, constructing graphs of a network that reflect the direction of information flow, and analyzing these directed graphs using algebraic topology. Applying this approach to a local network of neurons in the neocortex revealed a remarkably intricate and previously unseen topology of synaptic connectivity. The synaptic network contains an abundance of cliques of neurons bound into cavities that guide the emergence of correlated activity. In response to stimuli, correlated activity binds synaptically connected neurons into functional cliques and cavities that evolve in a stereotypical sequence toward peak complexity. We propose that the brain processes stimuli by forming increasingly complex functional cliques and cavities.
Author Contributions
HM and RL developed and initially conceived the study over 10 years of discussions. HM, RL, and KH conceived and directed the final study. KH and RL directed the applicability of concepts in algebraic topology to neuroscience. HM directed the relevance of algebraic topology in neuroscience. The Blue Brain Project team reconstructed the microcircuit and developed the capability to simulate the activity. MN performed the simulations. MN, MR, and PD generated the directed flag complexes from the connection matrices for analysis. KH and RL developed the theory for directed cliques and directed simplicial complexes. MR and RL developed the definition of directionality within motifs and directed cliques. MR developed the definition for transmission response matrices. PD developed the code to isolate simplices and directed simplices and performed initial computations. MS performed topological and statistical analyses on the flag complexes and on the C. elegans connectome . KT helped with initial statistical analysis of network responses to stimuli. MR and MN analyzed the simulation data, mapped it onto the topological data and generated the figures. RP performed the patch-clamp experiments. GC and MR performed the corresponding in silico experiments. HM, KH, RL, MR, and MN wrote the paper.
Conflict of Interest Statement
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
Acknowledgments
This work was supported by funding from the ETH Domain for the Blue Brain Project and the Laboratory of Neural Microcircuitry. The Blue Brain Project's IBM BlueGene /Q system, BlueBrain IV, is funded by the ETH Board and hosted at the Swiss National Supercomputing Center (CSCS). MS was supported by the NCCR Synapsy grant of the Swiss National Science Foundation. Partial support for PD was provided by the GUDHI project, supported by an Advanced Investigator Grant of the European Research Council and hosted by INRIA. We thank Eilif Muller for providing input on the analysis, Magdalena Kedziorek for help with proving maximality in directed cliques, Gard Spreemann for help with the analysis of the C. elegans connectome , and Taylor H. Newton for helpful discussions about statistical methods.
Supplementary Material
The Supplementary Material for this article can be found online at: http://journal.frontiersin.org/article/10.3389/fncom.2017.00048/full#supplementary-material
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