Parabolic avalanche scaling in the synchronization of cortical cell assemblies

Abstract

Neurons in the cerebral cortex fire coincident action potentials during ongoing activity and in response to sensory inputs. These synchronized cell assemblies are fundamental to cortex function, yet basic dynamical aspects of their size and duration are largely unknown. Using 2-photon imaging of neurons in the superficial cortex of awake mice, we show that synchronized cell assemblies organize as scale-invariant avalanches that quadratically grow with duration. The quadratic avalanche scaling was only found for correlated neurons, required temporal coarse-graining to compensate for spatial subsampling of the imaged cortex, and suggested cortical dynamics to be critical as demonstrated in simulations of balanced E/I-networks. The corresponding time course of an inverted parabola with exponent of χ = 2 described cortical avalanches of coincident firing for up to 5 s duration over an area of 1 mm2. These parabolic avalanches maximized temporal complexity in the ongoing activity of prefrontal and somatosensory cortex and in visual responses of primary visual cortex. Our results identify a scale-invariant temporal order in the synchronization of highly diverse cortical cell assemblies in the form of parabolic avalanches.

Empirical mode decomposition of local field potential data from optogenetic experiments

“…Such behavior, described by power laws, is called scale independence (or invariance; Goldenfeld, 1992 ). Power laws in critically self-organized systems extend past the size distribution of neural activity avalanches found from in vitro (Beggs and Plenz, 2003 ; Mazzoni et al, 2007 ; Pasquale et al, 2008 ) and in vivo (Petermann et al, 2009 ; Hahn et al, 2010 ; Capek et al, 2023 ; Salners et al, 2023 ) experiments. Such power laws include different macroscopically measurable quantities, such as the duration distribution of functional connections in EEG recordings (Lee et al, 2010 ), the duration of neural avalanches (Ehsani and Jost, 2023 ), and the power spectrum.…”

“…Such behavior, described by power laws, is called scale independence (or invariance; Goldenfeld, 1992). Power laws in critically self-organized systems extend past the size distribution of neural activity avalanches found from in vitro (Beggs and Plenz, 2003;Mazzoni et al, 2007;Pasquale et al, 2008) and in vivo (Petermann et al, 2009;Hahn et al, 2010;Capek et al, 2023;Salners et al, 2023) (Lee et al, 2010), the duration of neural avalanches (Ehsani and Jost, 2023), and the power spectrum. While most studies found that a power-law exponent of neural avalanche duration is around −1.5 (Beggs and Plenz, 2003;Millman et al, 2010;Cowan et al, 2013;Hesse and Gross, 2014), steeper exponents were induced by dopamine modulation (Stewart and Plenz, 2006), and by D1 receptor antagonists (Gireesh and Plenz, 2008).…”

“…In other words, the power spectral density vs. frequency should be derived from the equations describing the individual neurons and their connectivities. The ubiquity and simplicity of power law relationships revealed across brain regions might be deceptive compared to the complexity of neurons and their synaptic connections (Beggs and Plenz, 2003 ; Friedman et al, 2012 ; Capek et al, 2023 ). This is why theoretical foundations and underlying mechanisms must be worked out first to make testable predictions.…”

“…The broad range of power law exponents observed in experiments and modes is due to widely different targeted areas and underlying mechanisms (Beggs and Plenz, 2003 ). Among the most prevalent mechanism envisioned for scale invariance in neural activity is homeostatic plasticity, with different implementation details that also can drive variations in observed exponents (Friedman et al, 2012 ; Capek et al, 2023 ).…”

Neural criticality from effective latent variables

“…A genuine challenge in comparing exponents estimated from different experiments with different recording modalities (spiking activity, calcium imaging, LFP, EEG, or MEG) arises from differences in spatial and temporal scale specific to a particular recording, as well as the myriad decisions made in avalanche analysis, such as defining thresholds or binning in time. Thus, one possible reason for differences in exponents across studies may derive from how the system is sub-sampled in space or coarse-grained in time, both of which systematically change exponents and ( Beggs and Plenz, 2003 ; Shew et al, 2015 ) and could account for differences in ( Capek et al, 2023 ). The model we presented here could be used as a test bed for examining how specific analysis choices affect exponents estimated from recordings.…”