Network amplification of local fluctuations causes high spike rate variability, fractal firing patterns and oscillatory local field potentials

• Authors: Marius Usher;Martin Stemmler;Christof Koch;Zeev Olami
• Venue: Neural Computation
• Year: 1994

We investigate a model for neural activity in a two-dimensionalsheet of leaky integrate-and-fire neurons with feedbackconnectivity consisting of local excitation and surroundinhibition. Each neuron receives stochastic input from an externalsource, independent in space and time. As recently suggested bySoftky and Koch (1992, 1993), independent stochastic input alonecannot explain the high interspike interval variability exhibitedby cortical neurons in behaving monkeys. We show that highvariability can be obtained due to the amplification of correlatedfluctuations in a recurrent network. Furthermore, thecross-correlation functions have a dual structure, with a sharppeak on top of a much broader hill. This is due to the inhibitoryand excitatory feedback connections, which cause "hotspots" ofneural activity to form within the network. These localizedpatterns of excitation appear as clusters or stripes that coalesce,disintegrate, or fluctuate in size while simultaneously moving in arandom walk constrained by the interaction with other clusters. Thesynaptic current impinging upon a single neuron shows largefluctuations at many time scales, leading to a large coefficient ofvariation (CV) for the interspike intervalstatistics. The power spectrum associated with single units shows a1/f decay for small frequencies and is flat at higherfrequencies, while the power spectrum of the spiking activityaveraged over many cells---equivalent to the local fieldpotential---shows no 1/f decay but a prominent peak around40 Hz, in agreement with data recorded from cat and monkey cortex(Gray et al. 1990; Eckhorn et al. 1993). Firing ratesexhibit self-similarity between 20 and 800 msec, resulting in1/f-like noise, consistent with the fractal nature of neuralspike trains (Teich 1992).