Stochastic Oscillation in Self-Organized Critical States of Small Systems: Sensitive Resting State in Neural Systems

Abstract

Self-organized critical states (SOCs) and stochastic oscillations (SOs) are simultaneously observed in neural systems, which appears to be theoretically contradictory since SOCs are characterized by scale-free avalanche sizes but oscillations indicate typical scales. Here, we show that SOs can emerge in SOCs of small size systems due to temporal correlation between large avalanches at the finite-size cutoff, resulting from the accumulation-release process in SOCs. In contrast, the critical branching process without accumulation-release dynamics cannot exhibit oscillations. The reconciliation of SOCs and SOs is demonstrated both in the sandpile model and robustly in biologically plausible neuronal networks. The oscillations can be suppressed if external inputs eliminate the prominent slow accumulation process, providing a potential explanation of the widely studied Berger effect or event-related desynchronization in neural response. The features of neural oscillations and suppression are confirmed during task processing in monkey eye-movement experiments. Our results suggest that finite-size, columnar neural circuits may play an important role in generating neural oscillations around the critical states, potentially enabling functional advantages of both SOCs and oscillations for sensitive response to transient stimuli. DOI: 10.1103/PhysRevLett.116.018101 Self-organized criticality [1] is a key concept for describing the emergence of complexity in many natural systems [2]. The fingerprint of self-organized critical states (SOCs), the power-law distribution of avalanche sizes, means that the activity has no characteristic scale in the thermodynamic limit. As excellent functional complex systems in nature, neural systems in the brain have been supposed to operate at SOCs. Indeed, SOCs of neuronal firing activity have been observed in experiments with electrode arrays [2-4] and have been studied intensively in computational models [2,5,6]. It has been shown that critical states have functional advantages for both the sensory system [7] and memory [8], and they play an important role in the development of neural systems [9].On the other hand, stochastic oscillation (SO) in brain activity has been observed for more than 80 years [10]. Oscillations characterized by repetition of activities with typical scales are believed to be essential to brain functions, especially to provide timing, predictability, coherence, and integration in neural information processing [11]. Several different oscillation bands exist and appear in different states of the brain [10]. The synchronization between inhibitory neurons has been found to be crucial for gamma oscillations (30-70 Hz) [12]. Neural field models [13] indicated that resonance between thalamus and cortex can generate alpha oscillations (8-13 Hz). Despite many modeling studies, a commonly accepted mechanism of alpha rhythm is still lacking [14]. This slow oscillation is particularly obvious during the resting states without systematic external stimuli (i.e., eyes closed). I...

Co-emergence of multi-scale cortical activities of irregular firing, oscillations and avalanches achieves cost-efficient information capacity

“…Besides, the moderately synchronized states also correspond to the oscillation onset (also indicated in Fig 2D , bottom inset), where the oscillation power goes through a clear transition from low to high as shown in Fig 3H . Therefore, neuronal avalanches and gamma oscillations emerge jointly, which is consistent with in vivo observations [ 8 , 40 ]. Specifically, neuronal avalanches are achieved by aggregating different groups of neurons into clusters at different time instants and sparsely synchronized oscillations emerge when the clusters are organized with typical time-scales.…”

Heterogeneity of synaptic input connectivity regulates spike-based neuronal avalanches

“…Our results confirmed that spike-based neuronal avalanches are likely to appear at a moderately synchronized firing state and can coexist with both irregular firing and stochastic oscillations. These observations might provide important biological implications, because the similar co-emergence of multi-scale cortical activities has been observed in both experimental and computational recordings (Gireesh & Plenz, 2008;S.-J. Wang, et al, 2016;Yang, et al, 2017;Yu, et al, 2011).…”

The scale-invariant, temporal profile of neuronal avalanches in relation to cortical γ–oscillations

“…Previous work in in vitro and in rodents reported nested θ/β/γ–oscillations 63,64 embedded in avalanches. Simulations also demonstrate that oscillations can emerge during avalanches 65–68 . However, it had yet to be determined whether cortical avalanches in the awake mammal exhibit a distinct temporal profile that is scale-invariant, nor had it been known how that profile might relate to the scale of an oscillation.…”