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Published September 1994 | Published
Journal Article Open

Network Amplification of Local Fluctuations Causes High Spike Rate Variability, Fractal Firing Patterns and Oscillatory Local Field Potentials


We investigate a model for neural activity in a two-dimensional sheet of leaky integrate-and-fire neurons with feedback connectivity consisting of local excitation and surround inhibition. Each neuron receives stochastic input from an external source, independent in space and time. As recently suggested by Softky and Koch (1992, 1993), independent stochastic input alone cannot explain the high interspike interval variability exhibited by cortical neurons in behaving monkeys. We show that high variability can be obtained due to the amplification of correlated fluctuations in a recurrent network. Furthermore, the cross-correlation functions have a dual structure, with a sharp peak on top of a much broader hill. This is due to the inhibitory and excitatory feedback connections, which cause "hotspots" of neural activity to form within the network. These localized patterns of excitation appear as clusters or stripes that coalesce, disintegrate, or fluctuate in size while simultaneously moving in a random walk constrained by the interaction with other clusters. The synaptic current impinging upon a single neuron shows large fluctuations at many time scales, leading to a large coefficient of variation (C_V) for the interspike interval statistics. The power spectrum associated with single units shows a 1/f decay for small frequencies and is flat at higher frequencies, while the power spectrum of the spiking activity averaged over many cells—equivalent to the local field potential—shows no 1/f decay but a prominent peak around 40 Hz, in agreement with data recorded from cat and monkey cortex (Gray et al. 1990; Eckhorn et al. 1993). Firing rates exhibit self-similarity between 20 and 800 msec, resulting in 1/f-like noise, consistent with the fractal nature of neural spike trains (Teich 1992).

Additional Information

© 1994 Massachusetts Institute of Technology. Received August 24, 1993; accepted November 5, 1993. We thank William Softky for many invaluable comments and ideas regarding the origin and the function of the high variability in cortical cells. We are also indebted to Terry Sejnowski, Wyeth Bair, and Ernst Niebur for insightful discussions. Our research was supported by a Myron A. Bantrell Research Fellowship, the Howard Hughes Medical Institute, the National Science Foundation, the Office of Naval Research, and the Air Force Office of Scientific Research.

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September 14, 2023
September 14, 2023