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 consist ing of local excitation and surround inhibition. Each neuron receives stochastic input from an external source, independent in space and tim e. As recently suggested by Softky and Koch (1992, 1993), independent stochastic input alone cannot explain the high interspike interval var iability exhibited by cortical neurons in behaving monkeys. We show th at high variability can be obtained due to the amplification of correl ated fluctuations in a recurrent network. Furthermore, the crosscorrel ation functions have a dual structure, with a sharp peak on top of a m uch broader hill. This is due to the inhibitory and excitatory feedbac k connections, which cause ''hotspots'' of neural activity to form wit hin the network. These localized patterns of excitation appear as clus ters or stripes that coalesce, disintegrate, or fluctuate in size whil e simultaneously moving in a random walk constrained by the interactio n with other clusters. The synaptic current impinging upon a single ne uron 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 t o the local field potential-shows no 1/f decay but a prominent peak ar ound 40 Hz, in agreement with data recorded from cat and monkey cortex (Gray et al. 1990; Eckhorn et al. 1993). Firing rates exhibit self-si milarity between 20 and 800 msec, resulting in 1/f-like noise, consist ent with the fractal nature of neural spike trains (Teich 1992).