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Dense gap-junction connections support dynamic Turing structures in the cortex

The recent report by Fukuda et al [1] provides convincing evidence for dense gap-junction connectivity between inhibitory neurons in the cat visual cortex, each neuron making 60 +/- 12 gap-junction dendritic connections with neurons in both the same and adjoining orientation columns. These resistive connections provide a source of diffusive current to the receiving neuron, supplementing the chemical-synaptic currents generated by incoming action-potential spike activity. Fukuda et al describe how the gap junctions form a dense and homogeneous electrical coupling of interneurons, and propose that this diffusion-coupled network provides the substrate for synchronization of neuronal populations.

To date, large-scale population-based mathematical models of the cortex have ignored diffusive communication between neurons. Here we augment a well-established mean-field cortical model [2] by incorporating gap-junction-mediated diffusion currents, and we investigate the implications of strong diffusive coupling. The significant result is the model prediction that the 2D cortex can spontaneously generate centimetre-scale Turing structures (spatial patterns), in which regions of high-firing activity are intermixed with regions of low-firing activity (see Fig. 1). Since coupling strength decreases with increases in firing rate, these patterns are expected to exchange contrast on a slow time-scale, with low-firing patches increasing their activity at the expense of high-firing patches. These theoretical predictions are consistent with the slowly fluctuating large-scale brain-activity images detected from the BOLD (blood oxygen-level-dependent) signal [3].

Figure 1
figure1

Diffusion-induced Turing patterns in a square cortex of side 25 cm. Panel a shows the case of zero diffusion: the cortex organizes into a diffuse, cloud-like pattern, but fails to generate a Turing structure. Panels b-d show increasing inhibitory diffusion. These cases evolve into stable serpentine Turing patterns containing alternating regions of low-(blue) and high-firing (red) cells.

References

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    Kosaka T, Singer W, Galuske RAW: Gap junctions among dendrites of cortical GABAergic neurons establish a dense and widespread intercolumnar network. J Neurosci. 2006, 26: 3434-3443. 10.1523/JNEUROSCI.4076-05.2006.

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    Steyn-Ross DA, Steyn-Ross ML, Sleigh JW, Wilson MT, Gillies IP, Wright JJ: The sleep cycle modelled as a cortical phase transition. J Biol Phys. 2005, 31: 547-569. 10.1007/s10867-005-1285-2.

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    Fox MD, Snyder AZ, Vincent JL, Corbetta M, van Essen DC, Raichle ME: The human brain is intrinsically organized into dynamic, anticorrelated functional networks. Proc Nat Acad Sci USA. 102: 9673-9678. 10.1073/pnas.0504136102.

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Correspondence to D Alistair Steyn-Ross.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Keywords

  • Diffusive Coupling
  • Inhibitory Neuron
  • Electrical Coupling
  • Cortical Model
  • Orientation Column