Abstract
Lévy walks describe patterns of intermittent motion with variable step sizes. In complex biological systems, Lévy walks (non-Brownian, superdiffusive random walks) are associated with behaviors such as search patterns of animals foraging for food. Here we show that Lévy walks also describe patterns of oscillatory activity in primate cerebral cortex. We used a combination of empirical observation and modeling to investigate high-frequency (gamma band) local field potential activity in visual motion-processing cortical area MT of marmoset monkeys. We found that gamma activity is organized as localized burst patterns that propagate across the cortical surface with Lévy walk dynamics. Lévy walks are fundamentally different from either global synchronization, or regular propagating waves, because they include large steps that enable activity patterns to move rapidly over cortical modules. The presence of Lévy walk dynamics therefore represents a previously undiscovered mode of brain activity, and implies a novel way for the cortex to compute. We apply a biophysically realistic circuit model to explain that the Lévy walk dynamics arise from critical-state transitions between asynchronous and localized propagating wave states, and that these dynamics yield optimal spatial sampling of the cortical sheet. We hypothesise that Lévy walk dynamics could help the cortex to efficiently process variable inputs, and to find links in patterns of activity among sparsely spiking populations of neurons.
Highlights
Lévy walks describe patterns of intermittent motion with variable step sizes
Recent evidence showed that Lévy walk dynamics can be intrinsically generated by neural circuits in Drosophila larvae[8], but the question whether Lévy walks are a characteristic of vertebrate brain activity remains open
We propose that Lévy walk dynamics of gamma bursts enable efficient functional linking of sparsely distributed spikes across the cortical surface, and rapid state switching to process rapid changes in the locations and timing of inputs to cortical circuits
Summary
Lévy walks describe patterns of intermittent motion with variable step sizes. In complex biological systems, Lévy walks (non-Brownian, superdiffusive random walks) are associated with behaviors such as search patterns of animals foraging for food. Lévy walks dwell near one location for a while and intermittently switch to new locations, leading to a “heavy-tail” probability distribution of movement step lengths (Fig. 1b) This heavy-tail property naturally generates a bursting characteristic in time and space (Fig. 1a). To explain our experimental findings, we employ a spatiallyextended cortical circuit model of spiking neurons[15] to show that the Lévy walk dynamic of gamma bursts is produced by transitions between asynchronous and regular wave cortical states. We show that this mechanism allows functional interactions in the cortex across many spatial scales, without large increases in spiking rate
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