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Models of cortical networks with long-range patchy projections

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Abstract

The cortex exhibits an intricate vertical and horizontal architecture, the latter often featuring spatially clustered projection patterns, so-called patches. Many network studies of cortical dynamics ignore such spatial structures and assume purely random wiring. Here, we focus on non-random network structures provided by long-range horizontal (patchy) connections that remain inside the gray matter. We investigate how the spatial arrangement of patchy projections influences global network topology and predict its impact on the activity dynamics of the network. Since neuroanatomical data on horizontal projections is rather sparse, we suggest and compare four candidate scenarios of how patchy connections may be established. To identify a set of characteristic network properties that enables us to pin down the differences between the resulting network models, we employ the framework of stochastic graph theory. We find that patchy projections provide an exceptionally efficient way of wiring, as the resulting networks tend to exhibit small-world properties with significantly reduced wiring costs. Furthermore, the eigenvalue spectra, as well as the structure of common in- and output of the networks suggest that different spatial connectivity patterns support distinct types of activity propagation.

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References

  • Abeles, M. (1991). Corticonics: Neural circuits of the cerebral cortex. Cambridge: Cambridge University Press.

    Google Scholar 

  • Albert, R., & Barabási, A.-L. (2002). Statistical mechanics of complex networks. Reviews of Modern Physics, 74, 47–97.

    Article  Google Scholar 

  • Amir, Y., Harel, M., & Malach, R. (1993). Cortical hierarchy reflected in the organization of intrinsic connections in macaque monkey visual cortex. Journal of Comparative Neurology, 334, 19–46.

    Article  CAS  PubMed  Google Scholar 

  • Attwell, D., & Laughlin, S. B. (2001). An energy budget for signaling in the grey matter of the brain. Journal of Cerebral Blood Flow & Metabolism, 21, 1133–1145.

    Article  CAS  Google Scholar 

  • Bassett, D. S., & Bullmore, E. (2006). Small-world brain networks. Neuroscientist, 12(6), 512–523.

    Article  PubMed  Google Scholar 

  • Batschelet, E. (1981). Circular statistics in biology. London: Academic.

    Google Scholar 

  • Binzegger, T., Douglas, R. J., & Martin, K. A. C. (2004). A quantitative map of the circuit of cat primary visual cortex. Journal of Neuroscience, 39(24), 8441–8453.

    Article  Google Scholar 

  • Binzegger, T., Douglas, R. J., & Martin, K. A. C. (2007). Stereotypical bouton clustering of individual neurons in cat primary visual cortex. Journal of Neuroscience, 27(45), 12242–12254.

    Article  CAS  PubMed  Google Scholar 

  • Bonhoeffer, T., & Grinvald, A. (1991). Iso-orientation domains in cat visual cortex are arranged in pinwheel-like patterns. Nature, 353(6343), 429–431.

    Article  CAS  PubMed  Google Scholar 

  • Bonhoeffer, T., & Grinvald, A. (1993). The layout of iso-orientation domains in area 18 of cat visual cortex: Optical imaging reveals a pinwheel-like organization. Journal of Neuroscience, 12(10), 4157–4180.

    Google Scholar 

  • Bosking, W. H., Zhang, Y., Schofield, B., & Fitzpatrick, D. (1997). Orientation selectivity and the arrangement of horizontal connections in tree shrew striate cortex. Journal of Neuroscience, 17(6), 2112–2127.

    CAS  PubMed  Google Scholar 

  • Brunel, N. (2000). Dynamics of sparsely connected networks of excitatory and inhibitory spiking neurons. Journal of Computational Neuroscience, 8(3), 183–208.

    Article  CAS  PubMed  Google Scholar 

  • Burkhalter, A., & Charles, V. (1990). Organization of local axon collaterals of efferent projection neurons in the rat visual cortex. Journal of Comparative Neurology, 302, 920–934.

    Article  CAS  PubMed  Google Scholar 

  • Buzas, P., Kovacs, K., Ferecsko, A. S., Budd, J. M. L., Eysel, U. T., & Kisvarday, Z. F. (2006). Model-based analysis of excitatory lateral connections in the visual cortex. Journal of Comparative Neurology, 499, 861–881.

    Article  PubMed  Google Scholar 

  • Buzsaki, G., Geisler, C., Henze, D., & Wang, X.-J. (2004). Interneuron diversity series: Circuit complexity and axon wiring economy of cortical interneurons. TINS, 27(4), 186–193.

    CAS  PubMed  Google Scholar 

  • Callaway, E. M., & Katz, L. C. (1990). Emergence and refinement of clustered horizontal connections in cat striate cortex. Journal of Neuroscience, 10(4), 1134–1153.

    CAS  PubMed  Google Scholar 

  • Chisum, H. J., & Fitzpatrick, D. (2004). The contribution of vertical and horizontal connections to the receptive field center and surround in v1. Neural Networks, 17, 681693.

    Article  Google Scholar 

  • Chklovskii, D. (2000). Optimal sizes of dendritic and axonal arbors in a topographic projection. Journal of Neurophysiology, 83, 2113–2119.

    CAS  PubMed  Google Scholar 

  • Chklovskii, D. B. (2004). Synaptic connectivity and neuronal morphology: Two sides of the same coin. Neuron, 43, 609–617.

    CAS  PubMed  Google Scholar 

  • DeLosRios, P., & Petermann, T. (2007). Existence, cost and robustness of spatial small-world networks. IJBC, 17(7), 2331–2342.

    Google Scholar 

  • Denker, M., Timme, M., Diesmann, M., Wolf, F., & Geisel, T. (2004). Breaking synchrony by heterogeneity in complex networks. Physical Review Letters, 92, 074103.

    Article  PubMed  Google Scholar 

  • Diesmann, M., Gewaltig, M.-O., & Aertsen, A. (1999). Stable propagation of synchronous spiking in cortical neural networks. Nature, 402(6761), 529–533.

    Article  CAS  PubMed  Google Scholar 

  • Farkas, I. J., Derenyi, I., Barabasi, A.-L., & Vicsek, T. (2001). Spectra of real-world graphs: Beyond the semicircle law. Physical Review E, 64, 026704.

    Article  CAS  Google Scholar 

  • Fisher, N. I. (1993). Statistical analysis of circular data. Cambridge: Cambridge University Press.

    Google Scholar 

  • Gilbert, C. D., & Wiesel, T. N. (1983). Clustered intrinsic connections in cat visual cortex. Journal of Neuroscience, 5, 1116–1133.

    Google Scholar 

  • Gilbert, C. D., & Wiesel, T. N. (1989). Columnar specificity of intrinsic horizontal and corticocortical connections in cat visual cortex. Journal of Neuroscience, 9(7), 2432–2442.

    CAS  PubMed  Google Scholar 

  • Hellwig, B. (2000). A quantitative analysis of the local connectivity between pyramidal neurons in layers 2/3 of the rat visual cortex. Biological Cybernetics, 82, 111–121.

    Article  CAS  PubMed  Google Scholar 

  • Johansson, C., & Lansner, A. (2007). Imposing biological constraints onto an abstract neocortical attractor network model. Neural Computation, 19, 1871–1896.

    Article  PubMed  Google Scholar 

  • Johnson, D. M. G., Illig, K. R., Behan, M., & Haberly, L. B. (2000). New features of connectivity in piriform cortex visualized by intracellular injection of pyramidal cells suggest that primary olfactory cortex functions like association cortex in other sensory systems. Journal of Neuroscience, 20(18), 6974–6982.

    CAS  PubMed  Google Scholar 

  • Kaiser, M., & Hilgetag, C. C. (2004). Modelling the development of cortical systems networks. Neurocomputing, 58–60, 297–302.

    Article  Google Scholar 

  • Kalisman, N., Silberberg, G., & Markram, H. (2003). Deriving physical connectivity from neuronal morphology. Biological Cybernetics, 88(3), 210–218.

    Article  PubMed  Google Scholar 

  • Kisvarday, Z. F., & Eysel, U. T. (1992). Cellular organization of reciprocal patchy networks in layer III of cat visual cortex (area 17). Neuroscience, 46, 275–286.

    Article  CAS  PubMed  Google Scholar 

  • Koroutchev, K., & Korutcheva, E. (2006). Improved storage capacity of hebbian learning attractor neural network with bump formations. In LNCS (Vol. 4131, pp. 234–243).

  • Kriener, B., Helias, M., Aertsen, A., & Rotter, S. (2009). Correlations in spiking neuronal networks with distance dependent connections. Journal of Computational Neuroscience, 27, 177–200.

    Article  PubMed  Google Scholar 

  • Kriener, B., Tetzlaff, T., Aertsen, A., Diesmann, M., & Rotter, S. (2008). Correlations and population dynamics in cortical networks. Neural Computation, 20, 2185–2226.

    Article  PubMed  Google Scholar 

  • Kumar, A., Rotter, S., & Aertsen, A. (2008a). Conditions for propagating synchronous spiking and asynchronous firing rates in a cortical network model. Journal of Neuroscience, 28(20), 5268–5280.

    Article  CAS  PubMed  Google Scholar 

  • Kumar, A., Schrader, S., Aertsen, A., & Rotter, S. (2008b). The high-conductance state of cortical networks. Neural Computation, 20(1), 1–43.

    Article  PubMed  Google Scholar 

  • Levitt, J., & Lund, J. (2002). Intrinsic connections in mammalian cerebral cortex. In A. Schüz, & R. Miller (Eds.), Cortical areas: Unity and diversity (chap. 7, pp. 133–154). London: Taylor and Francis.

    Google Scholar 

  • Lewis, D., Melchitzky, D., & Burgos, G.-G. (2002). Specificity in the functional architecture of primate prefontal cortex. Journal of Neurocytology, 31, 265–276.

    Article  PubMed  Google Scholar 

  • Lohmann, H., & Rörig, B. (1994). Long-range horizontal connections between supragranular pyramidal cells in the extrastiate visual cortex of the rat. Journal of Comparative Neurology, 344, 543–558.

    Article  CAS  PubMed  Google Scholar 

  • Lund, J., Yoshioka, T., & Levitt, J. (1993). Comparison of intrinsic connectivity in different areas of macaque monkey cerebral cortex. Cerebral Cortex, 3(2), 148–162.

    Article  CAS  PubMed  Google Scholar 

  • Mehring, C., Hehl, U., Kubo, M., Diesmann, M., & Aertsen, A. (2003). Activity dynamics and propagation of synchronous spiking in locally connected random networks. Biological Cybernetics, 88(5), 395–408.

    Article  PubMed  Google Scholar 

  • Melchitzky, D. S., Gonzale-Burgos, G., Barrionuevo, G., & Lewis, D. A. (2001). Synaptic targets of the intrinsic axon collaterals of supragranular pyramidal neurons in monkey prefontal cortex. Journal of Comparative Neurology, 430, 209–221.

    Article  CAS  PubMed  Google Scholar 

  • Newman, M. E. J. (2003). The structure and function of complex networks. SIAM Review, 45(2), 167–256.

    Article  Google Scholar 

  • Ojima, H., & Takayanagi, M. (2004). Cortical convergence from different frequency domains in the cat primary auditory cortex. Neuroscience, 126, 203–212.

    Article  CAS  PubMed  Google Scholar 

  • Ojima, H., Honda, C. N., & Jones, E. G. (1991). Patterns of axon collateralization of identified supragranular pyramidal neurons in the cat auditory cortex. Cerebral Cortex, 1, 80–94.

    Article  CAS  PubMed  Google Scholar 

  • Pucak, M. L., Levitt, J. B., Lund, J. S., & Lewis, D. A. (1996). Patterns of intrinsic and associational circuitry in monkey prefrontal cortex. Journal of Comparative Neurology, 376, 614–630.

    Article  CAS  PubMed  Google Scholar 

  • Roudi, Y., & Treves, A. (2004). An associative network with spatially organized connectivity. Journal of Statistical Mechanics: Theory and Experiment (P07010).

  • Roudi, Y., & Treves, A. (2008). Representing where along with what information in a model of a cortical patch. PLoS Computers in Biology, 4(3), e1000012.

    Article  Google Scholar 

  • Roxin, A., Brunel, N., & Hansel, D. (2005). The role of delays in shaping spatio-temporal dynamics of neuronal activity in large networks. Physical Review Letters, 94(23), 238103.

    Article  PubMed  Google Scholar 

  • Rumberger, A., Tyler, C. J., & Lund, J. S. (2001). Intra- and inter-areal connectivity between the primary visual cortex V1 and the area immediately surrounding V1 in the rat. Neuroscience, 102, 35–52.

    Article  CAS  PubMed  Google Scholar 

  • Schüz, A., & Braitenberg, V. (2002). The human cortical white matter: Quantitative aspects of cortico-cortical long-range connectivity. In A. Schüz, & R. Miller (Eds.), Cortical areas: Unity and diversity (chap. 16, pp. 377–385). London: Taylor and Francis.

    Google Scholar 

  • Schüz, A., Chaimow, D., & Liewald, D. (2005). Quantitative aspects of corticocortical connections: A tracer study in the mouse. Cerebral Cortex, 16, 1474–1486.

    Article  PubMed  Google Scholar 

  • Sporns, O., & Zwi, D. Z. (2004). The small world of the cerebral cortex. Neuroinformatics, 2, 145–162.

    Article  PubMed  Google Scholar 

  • Stepanyants, A., Hirsch, J., Martinez, L. M., Kisvarday, Z. F., Ferecsko, A. S., & Chklovskii, D. B. (2008). Local potential connectivity in cat primary visual cortex. Cerebral Cortex, 18(1), 13–28.

    Article  PubMed  Google Scholar 

  • Strogatz, S. H. (2001). Exploring complex networks. Nature, 410, 268–276.

    Article  CAS  PubMed  Google Scholar 

  • Tetzlaff, T., Einevoll, G. T., & Diesmann, M. (2009). Synchronization and rate dynamics in embedded synfire chains: Effect of network heterogeneity and feedback. BMC Neuroscience, 10(Suppl 1):P258.

    Article  Google Scholar 

  • Tetzlaff, T., Morrison, A., Timme, M., & Diesmann, M. (2005). Heterogeneity breaks global synchrony in large networks. In Proceedings of the 30th Göttingen neurobiology conference.

  • Thomson, A. M., & Bannister, P. (2003). Interlaminar connections in the neocortex. Cerebral Cortex, 13, 5–14.

    Article  PubMed  Google Scholar 

  • van Hooser, S. D., Heimel, J. A., Chung, S., & Nelson, S. N. (2006). Lack of patchy horizontal connectivity in primary visual cortex of a mammal without orientation maps. Journal of Neuroscience, 26(29), 7680–7692.

    Article  PubMed  Google Scholar 

  • Voges, N. (2007). Statistical analysis of cortical networks based on neuroanatomical data. Ph.D. thesis, University of Freiburg.

  • Voges, N., & Perrinet, L. (2009). Phase space analysis of networks based on biologically realistic parameters. Journal of Physiology (Paris) (in press).

  • Voges, N., Aertsen, A., & Rotter, S. (2007). Statistical analysis of spatially embedded networks: From grid to random node positions. Neurocomputing, 70(10–12), 1833–1837.

    Article  Google Scholar 

  • Wallace, M. N., Kitzes, L. M., & Jones, E. G. (1991). Intrinsic inter- and intralaminar connections and their relationship to the tonotopic map in cat primary auditory cortex. Experimental Brain Research, 86(3), 527–544.

    CAS  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

We thank Almut Schüz and Valentino Braitenberg for stimulating discussions. Special thanks to Johannes Hausmann and Sarah Jarvis for help and encouragement during writing. This work was funded by a dissertation grant to N.V. from the Institute for Frontier Areas of Psychology and Mental Health, Freiburg. Further support was received from the BMBF (grant 01GQ0420) and the EU (grant 15879, FACETS).

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  1. Nicole Voges

    Present address: INSERM, UMR 751 Universite Aix-Marseille, 27 Bd Jean Moulin, 13385, Marseille Cedex 05, France

Authors and Affiliations

  1. Bernstein Center for Computational Neuroscience Freiburg, Albert-Ludwig University, Freiburg, Germany

    Nicole Voges, Ad Aertsen & Stefan Rotter

  2. Neurobiology & Biophysics, Faculty of Biology, Albert-Ludwig University, Freiburg, Germany

    Nicole Voges, Christian Guijarro & Ad Aertsen

  3. Computational Neuroscience, Faculty of Biology, Albert-Ludwig University, Freiburg, Germany

    Stefan Rotter

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  1. Nicole Voges
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Correspondence to Nicole Voges.

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Voges, N., Guijarro, C., Aertsen, A. et al. Models of cortical networks with long-range patchy projections. J Comput Neurosci 28, 137–154 (2010). https://doi.org/10.1007/s10827-009-0193-z

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