Scale-Free Dynamics of the Mouse Wakefulness and Sleep Electroencephalogram Quantified Using Wavelet-Leaders

Scale-free analysis of brain activity reveals a complexity of synchronous neuronal firing which is different from that assessed using classic rhythmic quantifications such as spectral analysis of the electroencephalogram (EEG). In humans, scale-free activity of the EEG depends on the behavioral state and reflects cognitive processes. We aimed to verify if fractal patterns of the mouse EEG also show variations with behavioral states and topography, and to identify molecular determinants of brain scale-free activity using the 'multifractal formalism' (Wavelet-Leaders). We found that scale-free activity was more anti-persistent (i.e., more different between time scales) during wakefulness, less anti-persistent (i.e., less different between time scales) during non-rapid eye movement sleep, and generally intermediate during rapid eye movement sleep. The scale-invariance of the frontal/motor cerebral cortex was generally more anti-persistent than that of the posterior cortex, and scale-invariance during wakefulness was strongly modulated by time of day and the absence of the synaptic protein Neuroligin-1. Our results expose that the complexity of the scale-free pattern of organized neuronal firing depends on behavioral state in mice, and that patterns expressed during wakefulness are modulated by one synaptic component.