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Slow dynamics and high variability in balanced cortical networks with clustered connections

Abstract

Anatomical studies demonstrate that excitatory connections in cortex are not uniformly distributed across a network but instead exhibit clustering into groups of highly connected neurons. The implications of clustering for cortical activity are unclear. We studied the effect of clustered excitatory connections on the dynamics of neuronal networks that exhibited high spike time variability owing to a balance between excitation and inhibition. Even modest clustering substantially changed the behavior of these networks, introducing slow dynamics during which clusters of neurons transiently increased or decreased their firing rate. Consequently, neurons exhibited both fast spiking variability and slow firing rate fluctuations. A simplified model shows how stimuli bias networks toward particular activity states, thereby reducing firing rate variability as observed experimentally in many cortical areas. Our model thus relates cortical architecture to the reported variability in spontaneous and evoked spiking activity.

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Figure 1: Comparison between uniform and clustered network connectivity and dynamics.
Figure 2: Marginal and pairwise spiking statistics for neurons in clustered and uniform networks.
Figure 3: Heterogeneous clustered network.
Figure 4: Effect of increased clustered connection probability.
Figure 5: Emergence of bistability in simplified model.
Figure 6: Effects of stimulation.
Figure 7: Effect of stimulation on spiking variability and dynamics.
Figure 8: Effect of stimulation on inhibitory neuron spiking variability.

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Acknowledgements

We thank R. da Silveira and H. Sompolinsky for discussions that helped shape an early version of this work. We also thank B. Yu and J. de la Rocha for comments. B.D. was supported by the US National Science Foundation (NSFDMS-1121784) and a Sloan research fellowship. A.L.-K. was supported by the US National Defense Science & Engineering Graduate Fellowship program.

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A.L.-K. and B.D. conceived the study and wrote the manuscript. A.L.-K. performed the simulations and analyzed the data.

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Correspondence to Ashok Litwin-Kumar or Brent Doiron.

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The authors declare no competing financial interests.

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Litwin-Kumar, A., Doiron, B. Slow dynamics and high variability in balanced cortical networks with clustered connections. Nat Neurosci 15, 1498–1505 (2012). https://doi.org/10.1038/nn.3220

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