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  • Review Article
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Micro-connectomics: probing the organization of neuronal networks at the cellular scale

Nature Reviews Neuroscience volume 18, pages 131–146 (2017)Cite this article

Subjects

Key Points

  • Micro-connectomics provides a promising approach to studying the wiring rules of neuronal network organization at the cellular scale and eventually developing models of neuronal function.

  • Analysis of fully reconstructed nervous systems demonstrates that micro-connectomes are often governed by wiring economy principles, such as to conserve space, time and material.

  • Pioneering work from patch-clamp recordings and electron microscopic reconstruction in the mammalian brain indicates that generic motifs in neuronal network organization translate across scales and species.

  • Understanding the specific functional implications of neuronal topology will require a systematic integration of connectomes with behavioural data, functional imaging and insights into the development of cells and connectivity.

Abstract

Defining the organizational principles of neuronal networks at the cellular scale, or micro-connectomics, is a key challenge of modern neuroscience. In this Review, we focus on graph theoretical parameters of micro-connectome topology, often informed by economical principles that conceptually originated with Ramón y Cajal's conservation laws. First, we summarize results from studies in intact small organisms and in samples from larger nervous systems. We then evaluate the evidence for an economical trade-off between biological cost and functional value in the organization of neuronal networks. Various results suggest that many aspects of neuronal network organization are indeed the outcome of competition between these two fundamental selection pressures.

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Figure 1: Complex topological properties of the Caenorhabditis elegans connectome.
Figure 2: Linking structure and function in the Caenorhabditis elegans connectome.
Figure 3: Network motifs support information processing in Drosophila melanogaster.
Figure 4: Dendritic arborization and optimal wiring.
Figure 5: Complex topological features in mammalian local connectivity.

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References

  1. Ramón y Cajal, S. R. Histology of the Nervous System of Man and Vertebrates Vol. 1 (Oxford Univ. Press, 1995).

    Google Scholar 

  2. Bullmore, E. & Sporns, O. The economy of brain network organization. Nat. Rev. Neurosci. 13, 336–349 (2012).

    Article  CAS  PubMed  Google Scholar 

  3. Sterling, P. & Laughlin, S. Principles of Neural Design (MIT Press, 2015).

    Google Scholar 

  4. Sporns, O. Discovering the Human Connectome (MIT Press, 2012).

    Book  Google Scholar 

  5. White, J. G., Southgate, E., Thomson, J. N. & Brenner, S. The structure of the nervous system of the nematode Caenorhabditis elegans. Phil. Trans. R. Soc. Lond. B 314, 1–340 (1986).

    Article  CAS  Google Scholar 

  6. Varshney, L. R. et al. Structural properties of the Caenorhabditis elegans neuronal network. PLoS Comput. Biol. 7, e1001066 (2011). This article provides a comprehensive and detailed analysis of the topological properties of the C. elegans connectome. The authors also introduce ways to visualize information flow in the worm.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  7. Jarrell, T. A. et al. The connectome of a decision-making neural network. Science 337, 437–444 (2012).

    Article  CAS  PubMed  Google Scholar 

  8. Sporns, O. & Kotter, R. Motifs in brain networks. PLoS Biol. 2, 1910–1918 (2004).

    Article  CAS  Google Scholar 

  9. Borst, A. & Helmstaedter, M. Common circuit design in fly and mammalian motion vision. Nat. Neurosci. 18, 1067–1076 (2015).

    Article  CAS  PubMed  Google Scholar 

  10. Helmstaedter, M. Cellular-resolution connectomics: challenges of dense neural circuit reconstruction. Nat. Methods 10, 501–507 (2013).

    Article  CAS  PubMed  Google Scholar 

  11. Lichtman, J. W. & Denk, W. The big and the small: challenges of imaging the brain's circuits. Science 334, 618–623 (2011).

    Article  CAS  PubMed  Google Scholar 

  12. Bargmann, C. I. Beyond the connectome: how neuromodulators shape neural circuits. Bioessays 34, 458–465 (2012).

    Article  CAS  PubMed  Google Scholar 

  13. Bargmann, C. I. & Marder, E. From the connectome to brain function. Nat. Methods 10, 483–490 (2013). This is an excellent review of historical and more-recent connectome studies, in particular studies of C. elegans and the connectivity of the stomatogastric ganglion of the crab. The authors also provide a good overview of the limitations of current connectomic approaches.

    Article  CAS  PubMed  Google Scholar 

  14. Menzel, R. The honeybee as a model for understanding the basis of cognition. Nat. Rev. Neurosci. 13, 758–768 (2012).

    Article  CAS  PubMed  Google Scholar 

  15. Frazier, W. T., Kandel, E. R., Kupfermann, I., Waziri, R. & Coggeshall, R. E. Morphological and functional properties of identified neurons in the abdominal ganglion of Aplysia californica. J. Neurophysiol. 30, 1288–1351 (1967).

    Article  Google Scholar 

  16. Cassenaer, S. & Laurent, G. Conditional modulation of spike-timing-dependent plasticity for olfactory learning. Nature 482, 47–52 (2012).

    Article  CAS  PubMed  Google Scholar 

  17. Marder, E. & Bucher, D. Understanding circuit dynamics using the stomatogastric nervous system of lobsters and crabs. Annu. Rev. Physiol. 69, 291–316 (2007).

    Article  CAS  PubMed  Google Scholar 

  18. Randel, N. et al. Neuronal connectome of a sensory-motor circuit for visual navigation. eLife 3, e02730 (2014).

    Article  PubMed Central  Google Scholar 

  19. Zucker, R. S., Kennedy, D. & Selverston, A. I. Neuronal circuit mediating escape responses in crayfish. Science 173, 645–650 (1971).

    Article  CAS  PubMed  Google Scholar 

  20. Hodgkin, A. L. & Huxley, A. F. A quantitative description of membrane current and its application to conduction and excitation in nerve. J. Physiol. 117, 500–544 (1952).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  21. Ahrens, M. B. & Engert, F. Large-scale imaging in small brains. Curr. Opin. Neurobiol. 32, 78–86 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  22. Bargmann, C. I. Neurobiology of the Caenorhabditis elegans genome. Science 282, 2028–2033 (1998).

    Article  CAS  PubMed  Google Scholar 

  23. Adams, M. D. et al. The genome sequence of Drosophila melanogaster. Science 287, 2185–2195 (2000).

    Article  PubMed  Google Scholar 

  24. Bullmore, E. & Sporns, O. Complex brain networks: graph theoretical analysis of structural and functional systems. Nat. Rev. Neurosci. 10, 186–198 (2009).

    Article  CAS  PubMed  Google Scholar 

  25. Pereira, L. et al. A cellular and regulatory map of the cholinergic nervous system of C. elegans. eLife 4, e12432 (2015). This study provides an important update on the neurotransmitter systems in the worm C. elegans and combines this molecular information with connectomic data in a motif analysis.

    Article  PubMed  PubMed Central  Google Scholar 

  26. Chatterjee, N. & Sinha, S. Understanding the mind of a worm: hierarchical network structure underlying nervous system function in C. elegans. Prog. Brain Res. 168, 145–153 (2007).

    Article  Google Scholar 

  27. Sohn, Y., Choi, M.-K., Ahn, Y.-Y., Lee, J. & Jeong, J. Topological cluster analysis reveals the systemic organization of the Caenorhabditis elegans connectome. PLoS Comput. Biol. 7, e1001139 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Pan, R. K., Chatterjee, N. & Sinha, S. Mesoscopic organization reveals the constraints governing Caenorhabditis elegans nervous system. PLoS ONE 5, e9240 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  29. Pavlovic, D. M., Vértes, P. E., Bullmore, E. T., Schafer, W. R. & Nichols, T. E. Stochastic blockmodeling of the modules and core of the Caenorhabditis elegans connectome. PLoS ONE 9, e97584 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  30. Bassett, D. S. et al. Efficient physical embedding of topologically complex information processing networks in brains and computer circuits. PLoS Comput. Biol. 6, e1000748 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  31. Watts, D. J. & Strogatz, S. H. Collective dynamics of small-world networks. Nature 393, 440–442 (1998).

    Article  CAS  PubMed  Google Scholar 

  32. Barabasi, A. L. & Albert, R. Emergence of scaling in random networks. Science 286, 509–512 (1999).

    Article  CAS  PubMed  Google Scholar 

  33. Milo, R. Network motifs: simple building blocks of complex networks. Science 298, 824–827 (2002).

    Article  CAS  PubMed  Google Scholar 

  34. Towlson, E. K., Vértes, P. E., Ahnert, S. E., Schafer, W. R. & Bullmore, E. T. The rich club of the C. elegans neuronal connectome. J. Neurosci. 33, 6380–6387 (2013). This study demonstrates the presence of a rich club in the C. elegans connectome and shows that this network core is formed early during development.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  35. Colizza, V., Flammini, A., Serrano, M. A. & Vespignani, A. Detecting rich-club ordering in complex networks. Nat. Phys. 2, 110–115 (2006).

    Article  CAS  Google Scholar 

  36. Tsalik, E. L. & Hobert, O. Functional mapping of neurons that control locomotory behavior in Caenorhabditis elegans. J. Neurobiol. 56, 178–197 (2003).

    Article  PubMed  Google Scholar 

  37. Zhen, M. & Samuel, A. D. C. elegans locomotion: small circuits, complex functions. Curr. Opin. Neurobiol. 33, 117–126 (2015).

    Article  CAS  PubMed  Google Scholar 

  38. Latora, V. & Marchiori, M. Efficient behaviour of small-world networks. Phys. Rev. Lett. 87, 198701 (2001).

    Article  CAS  PubMed  Google Scholar 

  39. Kaiser, M. & Hilgetag, C. C. Nonoptimal component placement, but short processing paths, due to long-distance projections in neural systems. PLoS Comput. Biol. 2, e95 (2006).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Chen, B. L., Hall, D. H. & Chklovskii, D. B. Wiring optimization can relate neuronal structure and function. Proc. Natl Acad. Sci. USA 103, 4723–4728 (2006). This study demonstrates that wiring minimization principles can be used to predict the placement of many neurons in the C. elegans connectome.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  41. Pérez-Escudero, A. & de Polavieja, G. G. Optimally wired subnetwork determines neuroanatomy of Caenorhabditis elegans. Proc. Natl Acad. Sci. USA 104, 17180–17185 (2007).

    Article  PubMed  PubMed Central  Google Scholar 

  42. Laurent, P. et al. Decoding a neural circuit controlling global animal state in C. elegans. eLife 4, e04241 (2015).

    Article  CAS  PubMed Central  Google Scholar 

  43. Macosko, E. Z. et al. A hub-and-spoke circuit drives pheromone attraction and social behaviour in C. elegans. Nature 458, 1171–1175 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  44. Kawano, T. et al. An imbalancing act: gap junctions reduce the backward motor circuit activity to bias C. elegans for forward locomotion. Neuron 72, 572–586 (2011).

    Article  CAS  PubMed  Google Scholar 

  45. Roberts, W. M. et al. A stochastic neuronal model predicts random search behaviors at multiple spatial scales in C. elegans. eLife 5, e12572 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  46. Hobert, O. A map of terminal regulators of neuronal identity in Caenorhabditis elegans. Wiley Interdiscip. Rev. Dev. Biol. 5, 474–498 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  47. Briggman, K. L. & Kristan, W. B. Jr. Multifunctional pattern-generating circuits. Annu. Rev. Neurosci. 31, 271–294 (2008).

    Article  CAS  PubMed  Google Scholar 

  48. Trojanowski, N. F., Padovan-Merhar, O., Raizen, D. M. & Fang-Yen, C. Neural and genetic degeneracy underlies Caenorhabditis elegans feeding behavior. J. Neurophysiol. 112, 951–961 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  49. Sulston, J. E., Schierenberg, E., White, J. G. & Thomson, J. N. The embryonic cell lineage of the nematode Caenorhabditis elegans. Dev. Biol. 100, 64–119 (1983).

    Article  CAS  PubMed  Google Scholar 

  50. Kato, S. et al. Global brain dynamics embed the motor command sequence of Caenorhabditis elegans. Cell 163, 656–669 (2015).

    Article  CAS  PubMed  Google Scholar 

  51. Avena-Koenigsberger, A., Goñi, J., Solé, R. & Sporns, O. Network morphospace. J. R. Soc. Interface 12, 20140881 (2015).

    Article  PubMed  PubMed Central  Google Scholar 

  52. Bumbarger, D. J., Riebesell, M., Rödelsperger, C. & Sommer, R. J. System-wide rewiring underlies behavioral differences in predatory and bacterial-feeding nematodes. Cell 152, 109–119 (2013).

    Article  CAS  PubMed  Google Scholar 

  53. Rein, K., Zöckler, M., Mader, M. T., Grübel, C. & Heisenberg, M. The Drosophila standard brain. Curr. Biol. 12, 227–231 (2002).

    Article  CAS  PubMed  Google Scholar 

  54. Ito, K. et al. A systematic nomenclature for the insect brain. Neuron 81, 755–765 (2014).

    Article  CAS  PubMed  Google Scholar 

  55. Chiang, A.-S. et al. Three-dimensional reconstruction of brain-wide wiring networks in Drosophila at single-cell resolution. Curr. Biol. 21, 1–11 (2011).

    Article  CAS  PubMed  Google Scholar 

  56. Ito, M., Masuda, N., Shinomiya, K., Endo, K. & Ito, K. Systematic analysis of neural projections reveals clonal composition of the Drosophila brain. Curr. Biol. 23, 644–655 (2013).

    Article  CAS  PubMed  Google Scholar 

  57. Shih, C.-T. et al. Connectomics-based analysis of information flow in the Drosophila brain. Curr. Biol. 25, 1249–1258 (2015).

    Article  CAS  PubMed  Google Scholar 

  58. Meinertzhagen, I. A. & Lee, C.-H. in Advances in Genetics Vol. 80 (eds Friedmann, T., Dunlap, J. C. & Goodwin, S. F.) 99–151 (Academic Press, 2012).

    Google Scholar 

  59. Meinertzhagen, I. A. & O'Neil, S. D. Synaptic organization of columnar elements in the lamina of the wild type in Drosophila melanogaster. J. Comp. Neurol. 305, 232–263 (1991).

    Article  CAS  PubMed  Google Scholar 

  60. Rivera-Alba, M. et al. Wiring economy and volume exclusion determine neuronal placement in the Drosophila brain. Curr. Biol. 21, 2000–2005 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  61. Takemura, S. et al. A visual motion detection circuit suggested by Drosophila connectomics. Nature 500, 175–181 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  62. Takemura, S. et al. Synaptic circuits and their variations within different columns in the visual system of Drosophila. Proc. Natl Acad. Sci. USA 112, 13711–13716 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  63. Chklovskii, D. B. & Koulakov, A. A. Maps in the brain: what can we learn from them? Annu. Rev. Neurosci. 27, 369–392 (2004).

    Article  CAS  PubMed  Google Scholar 

  64. Serbe, E., Meier, M., Leonhardt, A. & Borst, A. Comprehensive characterization of the major presynaptic elements to the Drosophila OFF motion detector. Neuron 89, 829–841 (2016).

    Article  CAS  PubMed  Google Scholar 

  65. Jeanne, J. M. & Wilson, R. I. Convergence, divergence, and reconvergence in a feedforward network improves neural speed and accuracy. Neuron 88, 1014–1026 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  66. Ohyama, T. et al. A multilevel multimodal circuit enhances action selection in Drosophila. Nature 520, 633–639 (2015).

    Article  CAS  PubMed  Google Scholar 

  67. Euler, T., Haverkamp, S., Schubert, T. & Baden, T. Retinal bipolar cells: elementary building blocks of vision. Nat. Rev. Neurosci. 15, 507–519 (2014).

    Article  CAS  PubMed  Google Scholar 

  68. Vogelstein, J. T. et al. Discovery of brainwide neural-behavioral maps via multiscale unsupervised structure learning. Science 344, 386–392 (2014).

    Article  CAS  PubMed  Google Scholar 

  69. Bhatla, N., Droste, R., Sando, S. R., Huang, A. & Horvitz, H. R. Distinct neural circuits control rhythm inhibition and spitting by the myogenic pharynx of C. elegans. Curr. Biol. 25, 2075–2089 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  70. Osten, P. & Margrie, T. W. Mapping brain circuitry with a light microscope. Nat. Methods 10, 515–523 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  71. Oh, S. W. et al. A mesoscale connectome of the mouse brain. Nature 508, 207–214 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  72. Rubinov, M., Ypma, R. J., Watson, C. & Bullmore, E. T. Wiring cost and topological participation of the mouse brain connectome. Proc. Natl Acad. Sci. USA 112, 10032–10037 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  73. Peters, A. & Feldman, M. L. The projection of the lateral geniculate nucleus to area 17 of the rat cerebral cortex. I. General description. J. Neurocytol. 5, 63–84 (1976).

    Article  CAS  PubMed  Google Scholar 

  74. Braitenberg, V. & Schüz, A. Cortex: Statistics and Geometry of Neuronal Connectivity (Springer Berlin, 1998).

    Book  Google Scholar 

  75. Kasthuri, N. et al. Saturated reconstruction of a volume of neocortex. Cell 162, 648–661 (2015).

    Article  CAS  PubMed  Google Scholar 

  76. Mishchenko, Y. et al. Ultrastructural analysis of hippocampal neuropil from the connectomics perspective. Neuron 67, 1009–1020 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  77. Briggman, K. L., Helmstaedter, M. & Denk, W. Wiring specificity in the direction-selectivity circuit of the retina. Nature 471, 183–188 (2011).

    Article  CAS  PubMed  Google Scholar 

  78. Branco, T. & Häusser, M. The single dendritic branch as a fundamental functional unit in the nervous system. Curr. Opin. Neurobiol. 20, 494–502 (2010).

    Article  CAS  PubMed  Google Scholar 

  79. Klausberger, T. & Somogyi, P. Neuronal diversity and temporal dynamics: the unity of hippocampal circuit operations. Science 321, 53–57 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  80. Boergens, K. M., Berning, M. & Helmstaedter, M. in Dendrites (eds Stuart, G., Spruston, N. & Häusser, M.) 623–638 (Oxford Univ. Press, 2016).

    Book  Google Scholar 

  81. Sholl, D. A. Dendritic organization in the neurons of the visual and motor cortices of the cat. J. Anat. 87, 387 (1953).

    CAS  PubMed  PubMed Central  Google Scholar 

  82. Cuntz, H., Forstner, F., Borst, A. & Häusser, M. One rule to grow them all: a general theory of neuronal branching and its practical application. PLoS Comput. Biol. 6, e1000877 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  83. Budd, J. M. et al. Neocortical axon arbors trade-off material and conduction delay conservation. PLoS Comput. Biol. 6, e1000711 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  84. Wen, Q., Stepanyants, A., Elston, G. N., Grosberg, A. Y. & Chklovskii, D. B. Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors. Proc. Natl Acad. Sci. USA 106, 12536–12541 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  85. Wen, Q. & Chklovskii, D. B. A. Cost–benefit analysis of neuronal morphology. J. Neurophysiol. 99, 2320–2328 (2008).

    Article  PubMed  Google Scholar 

  86. Cuntz, H., Mathy, A. & Häusser, M. A scaling law derived from optimal dendritic wiring. Proc. Natl Acad. Sci. USA 109, 11014–11018 (2012). This study found that key aspects in the branching structure of dendrites follow scaling laws, which can be predicted by a simple model of wiring cost minimization.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  87. Lu, J., Tapia, J. C., White, O. L. & Lichtman, J. W. The interscutularis muscle connectome. PLoS Biol. 7, e1000032 (2009).

    Article  CAS  PubMed Central  Google Scholar 

  88. Smith, T. G., Marks, W. B., Lange, G. D., Sheriff, W. H. & Neale, E. A. A fractal analysis of cell images. J. Neurosci. Methods 27, 173–180 (1989).

    Article  PubMed  Google Scholar 

  89. Werner, G. Fractals in the nervous system: conceptual implications for theoretical neuroscience. Front. Physiol. 1, 15 (2010).

    PubMed  PubMed Central  Google Scholar 

  90. Fernández, E. & Jelinek, H. F. Use of fractal theory in neuroscience: methods, advantages, and potential problems. Methods 24, 309–321 (2001).

    Article  CAS  PubMed  Google Scholar 

  91. Mitchison, G. Neuronal branching patterns and the economy of cortical wiring. Proc. Biol. Sci. 245, 151–158 (1991).

    Article  CAS  PubMed  Google Scholar 

  92. Ascoli, G. A. Mobilizing the base of neuroscience data: the case of neuronal morphologies. Nat. Rev. Neurosci. 7, 318–324 (2006).

    Article  CAS  PubMed  Google Scholar 

  93. Lefebvre, J. L., Sanes, J. R. & Kay, J. N. Development of dendritic form and function. Annu. Rev. Cell Dev. Biol. 31, 741–777 (2015).

    Article  CAS  PubMed  Google Scholar 

  94. Stepanyants, A. & Chklovskii, D. B. Neurogeometry and potential synaptic connectivity. Trends Neurosci. 28, 387–394 (2005).

    Article  CAS  PubMed  Google Scholar 

  95. Buzsáki, G. & Mizuseki, K. The log-dynamic brain: how skewed distributions affect network operations. Nat. Rev. Neurosci. 15, 264–278 (2014). This comprehensive review discusses a wide range of studies that reported heavy-tailed distributions in key physiological parameters of the nervous systems.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  96. Holmgren, C., Harkany, T., Svennenfors, B. & Zilberter, Y. Pyramidal cell communication within local networks in layer 2/3 of rat neocortex. J. Physiol. 551, 139–153 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  97. Lefort, S., Tomm, C., Sarria, J.-C. F. & Petersen, C. C. The excitatory neuronal network of the C2 barrel column in mouse primary somatosensory cortex. Neuron 61, 301–316 (2009).

    Article  CAS  PubMed  Google Scholar 

  98. Perin, R., Berger, T. K. & Markram, H. A synaptic organizing principle for cortical neuronal groups. Proc. Natl Acad. Sci. USA 108, 5419–5424 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  99. Ko, H. et al. Functional specificity of local synaptic connections in neocortical networks. Nature 473, 87–91 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  100. Mizuseki, K. & Buzsáki, G. Preconfigured, skewed distribution of firing rates in the hippocampus and entorhinal cortex. Cell Rep. 4, 1010–1021 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  101. Pajevic, S. & Plenz, D. The organization of strong links in complex networks. Nat. Phys. 8, 429–436 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  102. Yassin, L. et al. An embedded subnetwork of highly active neurons in the neocortex. Neuron 68, 1043–1050 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  103. Cossell, L. et al. Functional organization of excitatory synaptic strength in primary visual cortex. Nature 518, 399–403 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  104. Li, Y., Ibrahim, L. A., Liu, B., Zhang, L. I. & Tao, H. W. Linear transformation of thalamocortical input by intracortical excitation. Nat. Neurosci. 16, 1324–1330 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  105. Schröter, M. S., Charlesworth, P., Kitzbichler, M. G., Paulsen, O. & Bullmore, E. T. Emergence of rich-club topology and coordinated dynamics in development of hippocampal functional networks in vitro. J. Neurosci. 35, 5459–5470 (2015).

    Article  CAS  Google Scholar 

  106. Nigam, S. et al. Rich-club organization in effective connectivity among cortical neurons. J. Neurosci. 36, 670–684 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  107. Bonifazi, P. et al. GABAergic hub neurons orchestrate synchrony in developing hippocampal networks. Science 326, 1419–1424 (2009).

    Article  CAS  PubMed  Google Scholar 

  108. Marissal, T. et al. Pioneer glutamatergic cells develop into a morpho-functionally distinct population in the juvenile CA3 hippocampus. Nat. Commun. 3, 1316 (2012).

    Article  CAS  PubMed  Google Scholar 

  109. Cossart, R. Operational hub cells: a morpho-physiologically diverse class of GABAergic neurons united by a common function. Curr. Opin. Neurobiol. 26, 51–56 (2014).

    Article  CAS  PubMed  Google Scholar 

  110. Melzer, S. et al. Long-range–projecting GABAergic neurons modulate inhibition in hippocampus and entorhinal cortex. Science 335, 1506–1510 (2012).

    Article  CAS  PubMed  Google Scholar 

  111. Jinno, S. et al. Neuronal diversity in GABAergic long-range projections from the hippocampus. J. Neurosci. 27, 8790–8804 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  112. Picardo, M. A. et al. Pioneer GABA cells comprise a subpopulation of hub neurons in the developing hippocampus. Neuron 71, 695–709 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  113. Quilichini, P. P. et al. Hub GABA neurons mediate gamma-frequency oscillations at ictal-like event onset in the immature hippocampus. Neuron 74, 57–64 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  114. Ellender, T. J., Nissen, W., Colgin, L. L., Mann, E. O. & Paulsen, O. Priming of hippocampal population bursts by individual perisomatic-targeting interneurons. J. Neurosci. 30, 5979–5991 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  115. Buzsáki, G., Geisler, C., Henze, D. A. & Wang, X.-J. Interneuron diversity series: circuit complexity and axon wiring economy of cortical interneurons. Trends Neurosci. 27, 186–193 (2004).

    Article  CAS  PubMed  Google Scholar 

  116. Shimono, M. & Beggs, J. M. Functional clusters, hubs, and communities in the cortical microconnectome. Cereb. Cortex 25, 3743–3757 (2015). This study demonstrates interesting parallels in topological properties of functional connectivity derived from spontaneous activity and previous work that used patch-clamp recordings.

    Article  PubMed  Google Scholar 

  117. Druckmann, S. et al. Structured synaptic connectivity between hippocampal regions. Neuron 81, 629–640 (2014).

    Article  CAS  PubMed  Google Scholar 

  118. Koulakov, A. A., Hromádka, T. & Zador, A. M. Correlated connectivity and the distribution of firing rates in the neocortex. J. Neurosci. 29, 3685–3694 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  119. Yu, S., Huang, D., Singer, W. & Nikolić, D. A small world of neuronal synchrony. Cereb. Cortex 18, 2891–2901 (2008).

    Article  PubMed  PubMed Central  Google Scholar 

  120. Gerhard, F., Pipa, G., Lima, B., Neuenschwander, S. & Gerstner, W. Extraction of network topology from multi-electrode recordings: is there a small-world effect? Front. Comput. Neurosci. 5, 4 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  121. Pajevic, S. & Plenz, D. Efficient network reconstruction from dynamical cascades identifies small-world topology of neuronal avalanches. PLoS Comput. Biol. 5, e1000271 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  122. Bettencourt, L. M., Stephens, G. J., Ham, M. I. & Gross, G. W. Functional structure of cortical neuronal networks grown in vitro. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 75, 21915 (2007).

    Article  CAS  Google Scholar 

  123. Downes, J. H. et al. Emergence of a small-world functional network in cultured neurons. PLoS Comput. Biol. 8, e1002522 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  124. Srinivas, K. V., Jain, R., Saurav, S. & Sikdar, S. K. Small-world network topology of hippocampal neuronal network is lost, in an in vivo glutamate injury model of epilepsy. Eur. J. Neurosci. 25, 3276–3286 (2007).

    Article  PubMed  Google Scholar 

  125. Takahashi, N., Sasaki, T., Matsumoto, W., Matsuki, N. & Ikegaya, Y. Circuit topology for synchronizing neurons in spontaneously active networks. Proc. Natl Acad. Sci. USA 107, 10244–10249 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  126. Stetter, O., Battaglia, D., Soriano, J. & Geisel, T. Model-free reconstruction of excitatory neuronal connectivity from calcium imaging signals. PLoS Comput. Biol. 8, e1002653 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  127. de Santos-Sierra, D. et al. Emergence of small-world anatomical networks in self-organizing clustered neuronal cultures. PLoS ONE 9, e85828 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  128. Song, S., Sjostrom, P. J., Reigl, M., Nelson, S. & Chklovskii, D. B. Highly nonrandom features of synaptic connectivity in local cortical circuits. PLoS Biol. 3, e68 (2005).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  129. Song, H. F., Kennedy, H. & Wang, X.-J. Spatial embedding of structural similarity in the cerebral cortex. Proc. Natl Acad. Sci. USA 111, 16580–16585 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  130. Kleindienst, T., Winnubst, J., Roth-Alpermann, C., Bonhoeffer, T. & Lohmann, C. Activity-dependent clustering of functional synaptic inputs on developing hippocampal dendrites. Neuron 72, 1012–1024 (2011).

    Article  CAS  PubMed  Google Scholar 

  131. Gritsun, T. A., le Feber, J. & Rutten, W. L. Growth dynamics explain the development of spatiotemporal burst activity of young cultured neuronal networks in detail. PLoS ONE 7, e43352 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  132. Kwok, H. F., Jurica, P., Raffone, A. & van Leeuwen, C. Robust emergence of small-world structure in networks of spiking neurons. Cogn. Neurodyn. 1, 39–51 (2007).

    Article  PubMed  Google Scholar 

  133. Kube, K., Herzog, A., Michaelis, B., de Lima, A. D. & Voigt, T. Spike-timing-dependent plasticity in small-world networks. Neurocomputing 71, 1694–1704 (2008).

    Article  Google Scholar 

  134. Kim, S.-Y. & Lim, W. Effect of small-world connectivity on fast sparsely synchronized cortical rhythms. Physica A. 421, 109–123 (2015).

    Article  Google Scholar 

  135. Gökçe, O., Bonhoeffer, T. & Scheuss, V. Clusters of synaptic inputs on dendrites of layer 5 pyramidal cells in mouse visual cortex. eLife 5, e09222 (2016).

    Article  PubMed  PubMed Central  Google Scholar 

  136. Wilson, D. E., Whitney, D. E., Scholl, B. & Fitzpatrick, D. Orientation selectivity and the functional clustering of synaptic inputs in primary visual cortex. Nat. Neurosci. 19, 1003–1009 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  137. Wertz, A. et al. Single-cell–initiated monosynaptic tracing reveals layer-specific cortical network modules. Science 349, 70–74 (2015).

    Article  CAS  PubMed  Google Scholar 

  138. Lee, W.-C. A. et al. Anatomy and function of an excitatory network in the visual cortex. Nature 532, 370–374 (2016). This recent study reconstructs excitatory synaptic connectivity in the mouse visual cortex and demonstrates that its connectivity is modular with functionally related neurons forming preferential connectivity with each other.

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  139. Morgan, J. L., Berger, D. R., Wetzel, A. W. & Lichtman, J. W. The fuzzy logic of network connectivity in mouse visual thalamus. Cell 165, 192–206 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  140. Markram, H., Lübke, J., Frotscher, M., Roth, A. & Sakmann, B. Physiology and anatomy of synaptic connections between thick tufted pyramidal neurones in the developing rat neocortex. J. Physiol. 500, 409–440 (1997).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  141. Wang, Y. et al. Heterogeneity in the pyramidal network of the medial prefrontal cortex. Nat. Neurosci. 9, 534–542 (2006).

    Article  CAS  PubMed  Google Scholar 

  142. Rieubland, S., Roth, A. & Häusser, M. Structured connectivity in cerebellar inhibitory networks. Neuron 81, 913–929 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  143. Rothschild, G., Nelken, I. & Mizrahi, A. Functional organization and population dynamics in the mouse primary auditory cortex. Nat. Neurosci. 13, 353–360 (2010).

    Article  CAS  PubMed  Google Scholar 

  144. Ohki, K., Chung, S., Ch'ng, Y. H., Kara, P. & Reid, R. C. Functional imaging with cellular resolution reveals precise micro-architecture in visual cortex. Nature 433, 597–603 (2005).

    Article  CAS  PubMed  Google Scholar 

  145. Otsuka, T. & Kawaguchi, Y. Firing-pattern-dependent specificity of cortical excitatory feed-forward subnetworks. J. Neurosci. 28, 11186–11195 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  146. Jouhanneau, J.-S., Kremkow, J., Dorrn, A. L. & Poulet, J. F. A. In vivo monosynaptic excitatory transmission between layer 2 cortical pyramidal neurons. Cell Rep. 13, 2098–2106 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  147. Pala, A. & Petersen, C. C. In vivo measurement of cell-type-specific synaptic connectivity and synaptic transmission in layer 2/3 mouse barrel cortex. Neuron 85, 68–75 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  148. Li, L., Li, Y., Zhou, M., Tao, H. W. & Zhang, L. I. Intracortical multiplication of thalamocortical signals in mouse auditory cortex. Nat. Neurosci. 16, 1179–1181 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  149. Douglas, R. J., Koch, C., Mahowald, M., Martin, K. A. & Suarez, H. H. Recurrent excitation in neocortical circuits. Science 269, 981–985 (1995).

    Article  CAS  PubMed  Google Scholar 

  150. Harris, K. D., Csicsvari, J., Hirase, H., Dragoi, G. & Buzsáki, G. Organization of cell assemblies in the hippocampus. Nature 424, 552–556 (2003).

    Article  CAS  PubMed  Google Scholar 

  151. Miller, J. K., Ayzenshtat, I., Carrillo-Reid, L. & Yuste, R. Visual stimuli recruit intrinsically generated cortical ensembles. Proc. Natl Acad. Sci. USA 111, E4053–E4061 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  152. Tremblay, R., Lee, S. & Rudy, B. GABAergic interneurons in the neocortex: from cellular properties to circuits. Neuron 91, 260–292 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  153. Womelsdorf, T., Valiante, T. A., Sahin, N. T., Miller, K. J. & Tiesinga, P. Dynamic circuit motifs underlying rhythmic gain control, gating and integration. Nat. Neurosci. 17, 1031–1039 (2014). This is a comprehensive survey of how specific connectivity motifs may relate to synchronous neuronal activity and canonical neuronal computations.

    Article  CAS  PubMed  Google Scholar 

  154. Harris, K. D. & Mrsic-Flogel, T. D. Cortical connectivity and sensory coding. Nature 503, 51–58 (2013).

    Article  CAS  PubMed  Google Scholar 

  155. Brunel, N. Is cortical connectivity optimized for storing information? Nat. Neurosci. 19, 749–755 (2016).

    Article  CAS  PubMed  Google Scholar 

  156. Batista-Brito, R. & Fishell, G. The developmental integration of cortical interneurons into a functional network. Curr. Top. Dev. Biol. 87, 81–118 (2009).

    Article  PubMed  PubMed Central  Google Scholar 

  157. Gao, P., Sultan, K. T., Zhang, X.-J. & Shi, S.-H. Lineage-dependent circuit assembly in the neocortex. Development 140, 2645–2655 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  158. Greig, L. C., Woodworth, M. B., Galazo, M. J., Padmanabhan, H. & Macklis, J. D. Molecular logic of neocortical projection neuron specification, development and diversity. Nat. Rev. Neurosci. 14, 755–769 (2013).

    Article  CAS  PubMed  Google Scholar 

  159. Kolodkin, A. L. & Tessier-Lavigne, M. Mechanisms and molecules of neuronal wiring: a primer. Cold Spring Harb. Perspect. Biol. 3, a001727 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  160. Rakic, P. Evolution of the neocortex: a perspective from developmental biology. Nat. Rev. Neurosci. 10, 724–735 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  161. Shen, K. & Scheiffele, P. Genetics and cell biology of building specific synaptic connectivity. Annu. Rev. Neurosci. 33, 473 (2010).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  162. Sur, M. & Rubenstein, J. L. Patterning and plasticity of the cerebral cortex. Science 310, 805–810 (2005).

    Article  CAS  PubMed  Google Scholar 

  163. Van Ooyen, A. Using theoretical models to analyse neural development. Nat. Rev. Neurosci. 12, 311–326 (2011).

    Article  CAS  PubMed  Google Scholar 

  164. Varier, S. & Kaiser, M. Neural development features: spatio-temporal development of the Caenorhabditis elegans neuronal network. PLoS Comput. Biol. 7, e1001044 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  165. Yu, Y.-C. et al. Preferential electrical coupling regulates neocortical lineage-dependent microcircuit assembly. Nature 486, 113–117 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  166. Yu, Y.-C., Bultje, R. S., Wang, X. & Shi, S.-H. Specific synapses develop preferentially among sister excitatory neurons in the neocortex. Nature 458, 501–504 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  167. Li, Y. et al. Clonally related visual cortical neurons show similar stimulus feature selectivity. Nature 486, 118–121 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  168. Deguchi, Y., Donato, F., Galimberti, I., Cabuy, E. & Caroni, P. Temporally matched subpopulations of selectively interconnected principal neurons in the hippocampus. Nat. Neurosci. 14, 495–504 (2011).

    Article  CAS  PubMed  Google Scholar 

  169. Xu, H.-T. et al. Distinct lineage-dependent structural and functional organization of the hippocampus. Cell 157, 1552–1564 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  170. Marín, O. & Rubenstein, J. L. R. A long, remarkable journey: tangential migration in the telencephalon. Nat. Rev. Neurosci. 2, 780–790 (2001).

    Article  CAS  PubMed  Google Scholar 

  171. Brown, K. N. et al. Clonal production and organization of inhibitory interneurons in the neocortex. Science 334, 480–486 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  172. Valcanis, H. & Tan, S.-S. Layer specification of transplanted interneurons in developing mouse neocortex. J. Neurosci. 23, 5113–5122 (2003).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  173. López-Bendito, G. et al. Preferential origin and layer destination of GAD65-GFP cortical interneurons. Cereb. Cortex 14, 1122–1133 (2004).

    Article  PubMed  Google Scholar 

  174. Ciceri, G. et al. Lineage-specific laminar organization of cortical GABAergic interneurons. Nat. Neurosci. 16, 1199–1210 (2013).

    Article  CAS  PubMed  Google Scholar 

  175. Bliss, T. V. P. & Lømo, T. Long-lasting potentiation of synaptic transmission in the dentate area of the anaesthetized rabbit following stimulation of the perforant path. J. Physiol. 232, 331–356 (1973).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  176. Mulkey, R. M. & Malenka, R. C. Mechanisms underlying induction of homosynaptic long-term depression in area CA1 of the hippocampus. Neuron 9, 967–975 (1992).

    Article  CAS  PubMed  Google Scholar 

  177. Dudek, S. M. & Bear, M. F. Homosynaptic long-term depression in area CA1 of hippocampus and effects of N-methyl-d-aspartate receptor blockade. Proc. Natl Acad. Sci. USA 89, 4363–4367 (1992).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  178. Larson, J. & Lynch, G. Induction of synaptic potentiation in hippocampus by patterned stimulation involves two events. Science 232, 985–988 (1986).

    Article  CAS  PubMed  Google Scholar 

  179. Rodriguez-Moreno, A. et al. Presynaptic self-depression at developing neocortical synapses. Neuron 77, 35–42 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  180. Markram, H., Lübke, J., Frotscher, M. & Sakmann, B. Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275, 213–215 (1997).

    Article  CAS  PubMed  Google Scholar 

  181. Bi, G. & Poo, M. Synaptic modifications in cultured hippocampal neurons: dependence on spike timing, synaptic strength, and postsynaptic cell type. J. Neurosci. 18, 10464–10472 (1998).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  182. McNaughton, B. L., Douglas, R. M. & Goddard, G. V. Synaptic enhancement in fascia dentata: cooperativity among coactive afferents. Brain Res. 157, 277–293 (1978).

    Article  CAS  PubMed  Google Scholar 

  183. Sjöström, P. J., Turrigiano, G. G. & Nelson, S. B. Rate, timing, and cooperativity jointly determine cortical synaptic plasticity. Neuron 32, 1149–1164 (2001).

    Article  PubMed  Google Scholar 

  184. Turrigiano, G. G., Leslie, K. R., Desai, N. S., Rutherford, L. C. & Nelson, S. B. Activity-dependent scaling of quantal amplitude in neocortical neurons. Nature 391, 892–896 (1998).

    Article  CAS  PubMed  Google Scholar 

  185. Abbott, L. F. & Nelson, S. B. Synaptic plasticity: taming the beast. Nat. Neurosci. 3, 1178–1183 (2000).

    Article  CAS  PubMed  Google Scholar 

  186. Kullmann, D. M. & Lamsa, K. P. Long-term synaptic plasticity in hippocampal interneurons. Nat. Rev. Neurosci. 8, 687–699 (2007).

    Article  CAS  PubMed  Google Scholar 

  187. Seol, G. H. et al. Neuromodulators control the polarity of spike-timing-dependent synaptic plasticity. Neuron 55, 919–929 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  188. Mishra, R. K., Kim, S., Guzman, S. J. & Jonas, P. Symmetric spike timing-dependent plasticity at CA3–CA3 synapses optimizes storage and recall in autoassociative networks. Nat. Commun. 7, 11552 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  189. Gilson, M. & Fukai, T. Stability versus neuronal specialization for STDP: long-tail weight distributions solve the dilemma. PLoS ONE 6, e25339 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  190. Ko, H. et al. The emergence of functional microcircuits in visual cortex. Nature 496, 96–100 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  191. Vértes, P. E., Alexander-Bloch, A. & Bullmore, E. T. Generative models of rich clubs in Hebbian neuronal networks and large-scale human brain networks. Phil. Trans. R. Soc. B 369, 20130531 (2014).

    Article  PubMed  PubMed Central  Google Scholar 

  192. Butz, M., Steenbuck, I. D. & van Ooyen, A. Homeostatic structural plasticity increases the efficiency of small-world networks. Front. Synaptic Neurosci. https://doi.org/10.3389/fnsyn.2014.00007 (2014).

  193. van den Heuvel, M. P., Bullmore, E. T. & Sporns, O. Comparative connectomics. Trends Cogn. Sci. 20, 345–361 (2016).

    Article  PubMed  Google Scholar 

  194. Marcus, G., Marblestone, A. & Dean, T. The atoms of neural computation. Science 346, 551–552 (2014).

    Article  CAS  PubMed  Google Scholar 

  195. Miller, K. D. Synaptic economics: competition and cooperation in synaptic plasticity. Neuron 17, 371–374 (1996).

    Article  CAS  PubMed  Google Scholar 

  196. Nicosia, V., Vértes, P. E., Schafer, W. R., Latora, V. & Bullmore, E. T. Phase transition in the economically modeled growth of a cellular nervous system. Proc. Natl Acad. Sci. USA 110, 7880–7885 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  197. Schwabe, T., Borycz, J. A., Meinertzhagen, I. A. & Clandinin, T. R. Differential adhesion determines the organization of synaptic fascicles in the Drosophila visual system. Curr. Biol. 24, 1304–1313 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  198. Kaschula, R. & Salecker, I. Neural circuit assembly: economically wired by a single cadherin. Curr. Biol. 24, R555–R557 (2014).

    Article  CAS  PubMed  Google Scholar 

  199. Olshausen, B. A. & Field, D. J. Sparse coding of sensory inputs. Curr. Opin. Neurobiol. 14, 481–487 (2004).

    Article  CAS  PubMed  Google Scholar 

  200. Fornito, A., Zalesky, A. & Bullmore, E. Fundamentals of Brain Network Analysis (Academic Press, 2016).

    Google Scholar 

  201. Sporns, O. & Betzel, R. F. Modular brain networks. Annu. Rev. Psychol. 67, 613–640 (2016).

    Article  PubMed  Google Scholar 

  202. Simon, H. A. in Facets of Systems Science (ed. Klir, G. J.) 457–476 (Springer US, 1991).

    Book  Google Scholar 

  203. Thomson, A. M., West, D. C., Wang, Y. & Bannister, A. P. Synaptic connections and small circuits involving excitatory and inhibitory neurons in layers 2–5 of adult rat and cat neocortex: triple intracellular recordings and biocytin labelling in vitro. Cereb. Cortex 12, 936–953 (2002).

    Article  PubMed  Google Scholar 

  204. Thomson, A. M. & Lamy, C. Functional maps of neocortical local circuitry. Front. Neurosci. 1, 19 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  205. Watts, J. & Thomson, A. M. Excitatory and inhibitory connections show selectivity in the neocortex. J. Physiol. 562, 89–97 (2005).

    Article  CAS  PubMed  Google Scholar 

  206. Stepanyants, A., Martinez, L. M., Ferecskó, A. S. & Kisvárday, Z. F. The fractions of short-and long-range connections in the visual cortex. Proc. Natl Acad. Sci. USA 106, 3555–3560 (2009).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  207. Harris, K. D. & Shepherd, G. M. The neocortical circuit: themes and variations. Nat. Neurosci. 18, 170–181 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  208. Yoshimura, Y. & Callaway, E. M. Fine-scale specificity of cortical networks depends on inhibitory cell type and connectivity. Nat. Neurosci. 8, 1552–1559 (2005).

    Article  CAS  PubMed  Google Scholar 

  209. Rudy, B., Fishell, G., Lee, S. & Hjerling-Leffler, J. Three groups of interneurons account for nearly 100% of neocortical GABAergic neurons. Dev. Neurobiol. 71, 45–61 (2011).

    Article  PubMed  PubMed Central  Google Scholar 

  210. Kepecs, A. & Fishell, G. Interneuron cell types are fit to function. Nature 505, 318–326 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  211. Pfeffer, C. K., Xue, M., He, M., Huang, Z. J. & Scanziani, M. Inhibition of inhibition in visual cortex: the logic of connections between molecularly distinct interneurons. Nat. Neurosci. 16, 1068–1076 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  212. Karnani, M. M. et al. Cooperative subnetworks of molecularly similar interneurons in mouse neocortex. Neuron 90, 86–100 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  213. Avermann, M., Tomm, C., Mateo, C., Gerstner, W. & Petersen, C. C. Microcircuits of excitatory and inhibitory neurons in layer 2/3 of mouse barrel cortex. J. Neurophysiol. 107, 3116–3134 (2012).

    Article  CAS  PubMed  Google Scholar 

  214. Ma, Y., Hu, H. & Agmon, A. Short-term plasticity of unitary inhibitory-to-inhibitory synapses depends on the presynaptic interneuron subtype. J. Neurosci. 32, 983–988 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  215. Lee, S., Kruglikov, I., Huang, Z. J., Fishell, G. & Rudy, B. A disinhibitory circuit mediates motor integration in the somatosensory cortex. Nat. Neurosci. 16, 1662–1670 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  216. Pi, H.-J. et al. Cortical interneurons that specialize in disinhibitory control. Nature 503, 521–524 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  217. Hangya, B., Pi, H.-J., Kvitsiani, D., Ranade, S. P. & Kepecs, A. From circuit motifs to computations: mapping the behavioral repertoire of cortical interneurons. Curr. Opin. Neurobiol. 26, 117–124 (2014).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  218. Hofer, S. B. et al. Differential connectivity and response dynamics of excitatory and inhibitory neurons in visual cortex. Nat. Neurosci. 14, 1045–1052 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  219. Kapfer, C., Glickfeld, L. L., Atallah, B. V. & Scanziani, M. Supralinear increase of recurrent inhibition during sparse activity in the somatosensory cortex. Nat. Neurosci. 10, 743–753 (2007).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  220. Fujisawa, S., Amarasingham, A., Harrison, M. T. & Buzsáki, G. Behavior-dependent short-term assembly dynamics in the medial prefrontal cortex. Nat. Neurosci. 11, 823–833 (2008).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

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Acknowledgements

This work was supported by the National Institute of Health Research Cambridge Biomedical Research Centre. The authors thank D. Bassett and L. Papadopoulus for sharing code to reproduce part b of figure 1, E. Towlson for help with reproducing part e of figure 1, and P. Vértes, C. Stadler and A. Roth for discussions and/or comments on an earlier version of the manuscript.

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Authors and Affiliations

  1. Department of Psychiatry and Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge Biomedical Campus, Cambridge, CB2 0SZ, UK

    Manuel Schröter & Edward T. Bullmore

  2. Department of Biosystems Science and Engineering, Bio Engineering Laboratory, ETH Zurich, Mattenstrasse 26, Basel, CH-4058, Switzerland

    Manuel Schröter

  3. Department of Physiology, Development and Neuroscience, University of Cambridge, Physiological Laboratory, Downing Street, Cambridge, CB2 3EG, UK

    Ole Paulsen

  4. ImmunoPsychiatry, Immuno-Inflammation Therapeutic Area Unit, GlaxoSmithKline R&D, Stevenage, SG1 2NY, UK

    Edward T. Bullmore

  5. Cambridgeshire and Peterborough NHS Foundation Trust, Cambridge Road, Cambridge, CB21 5HH, Fulbourn, UK

    Edward T. Bullmore

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  1. Manuel Schröter
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Correspondence to Manuel Schröter, Ole Paulsen or Edward T. Bullmore.

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E.T.B. is employed half-time by the University of Cambridge and half-time by GlaxoSmithKline (GSK), and holds stock in GSK. M.S. and O.P. declare no competing interests.

PowerPoint slides

Glossary

Cost

Used as an umbrella term for biological pressures and expenditures (that is, metabolism, material, and so on) that are incurred during development and maintenance of neuronal networks. Long-range connections, for example, are costly because their myelination requires a lot of cellular material.

Connectome

An abstract network representation of the connections between neurons in the whole nervous system or parts of a nervous system.

Motifs

Patterns of connectivity between a few (typically fewer than10) nodes. Some motifs are over-represented in connectomes. For example, the closed triangular motif between three nodes is typical of highly clustered neuronal networks.

Topology

Mathematics of the pattern of connections between elements, regardless of their organization in physical space.

Genetic fate mapping

An approach in which the statistics of mature cellular connectivity are related to neuronal birth dates or embryonic origin.

Small-world organization

A metric of global network complexity. Compared with random graphs, small-world networks have high clustering but approximately equivalent path length.

Rich club

A topologically integrative network feature that comprises greater-than-random connectivity between a relatively small number of high-degree hubs. A rich club is linked by feeder connections to a large number of more-peripheral and sparsely connected nodes.

Core

A subset of nodes in the network that are highly interconnected and contribute to the global integrity of the network.

Centrality

A general term for the topological importance of a node in a network. Centrality can be quantified in many ways including the degree and closeness of each neuron.

Economy

Here, this term describes the trade-off between the biological cost and the functional value of topologically complex networks.

Degeneracy

This term describes the property of a system in which different structural components can give rise to very similar functions.

Morphospace

The low-dimensional space of network phenotypes observed in natural populations and simulated by generative models of network development and evolution.

Scale-free networks

A class of complex networks defined by a heavy-tailed degree distribution that can be approximated by a power-law. High-degree hubs have a higher probability in scale-free networks than in comparable random graphs.

Topological efficiency

A metric of network integration that is calculated as the inverse of the average shortest path length of a network.

Clustering coefficient

The clustering coefficient of a node is calculated as the fraction of triangular connections between the nearest neighbours of a node divided by the maximal possible number of such connected triangles.

Graph theory

The mathematical analysis of graphs comprising nodes and edges. Graphs can have directed or undirected, weighted or non-weighted edges.

Retinotopical organization

A common feature that is found in visual cortical areas, which describes the spatially ordered mapping of visual inputs from the retina to cortical neurons.

Peters's rule

The assumption that synaptic connectivity can be inferred from the spatial overlap of axons and dendrites.

Fractal dimension

A measure of the extent to which a self-similar process, like a dendritic tree, completely occupies the Euclidean dimensions of space in which it is embedded; more intricately branching arborization will have higher fractal dimension indicating greater space occupancy.

Minimum-spanning-tree

An undirected graph that connects all nodes in the network with the minimum number of connections.

Transfer entropy

An information theoretic measure for the directed interaction between two time series; it measures the information that the past of a source variable provides about the current value of a target variable, beyond the information provided by the past of the target variable alone.

Preferential attachment

A generative model or growth rule for the formation of scale-free networks. During development, new nodes are more likely to connect to hub nodes that already have high degree and many connections to other nodes. It is often referred to as the 'rich-get-richer' rule.

Sparse coding

A parsimonious neuronal signalling strategy that requires only a small set of active neurons to encode an item.

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Schröter, M., Paulsen, O. & Bullmore, E. Micro-connectomics: probing the organization of neuronal networks at the cellular scale. Nat Rev Neurosci 18, 131–146 (2017). https://doi.org/10.1038/nrn.2016.182

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