1The habenula is an evolutionarily conserved structure of the vertebrate brain that is essential for behavioural flexibility 2 and mood control. It is spontaneously active and is able to access diverse states when the animal is exposed to sensory 3 stimuli or reward. Here we analyze two-photon calcium imaging time-series of the habenula of larval zebrafish and find 4 that percolation occurs, indicating the presence of long-range spatial correlations within each side of the habenula, with 5 percolation occurring independently in each side. On the other hand, the analysis of neuronal avalanches suggests that the 6 system is subcritical, implying that the flexibility in its dynamics may result from other dynamical processes. 7 130[36].
131Upon analyzing the pairwise correlation function for the four datasets we observe two distinct behaviors for the power 132 law regime. We saw that the four datasets can be divided into two groups with distinct power law exponents. We note that 133 this may potentially reflect differences in mode of activity of the habenula, or simply be a variation due to the fish itself, 134 which we are unable to determine at this point in time. Nevertheless, the scale invariant behavior of the function suggests 135 long-range spatial correlations among the neurons in the habenula. More importantly, the scale invariant regime extends 136 only up to the scale of any one side of the habenula, which suggests that percolation occurs independently in each side.
137The presence of long-range spatial correlation suggests that the temporal aspect may display critical behavior as well.
138Despite so, our analysis suggests that the habenula are subcritical, i.e. the spatiotemporal neuronal dynamics are less active 139 than the critical state.
140In the absence of criticality, then, how could the habenula achieve its flexibility in terms of accessing different modes 141 of activity? Two possibilities come to mind; the first of which is that the habenula operates not at, but near criticality, as 142 has been suggested in literature [39]. Being near criticality may also explain why we observe the other telltale signs of 143 criticality (including percolation), while failing only the more stringent properties (such as the scaling relation).
144Another possibility lies in our fundamental assumption, which is that only adjacent cells are taken to be connected.
145While it is known that gap junction (which mediates communication among adjacent neurons) are present in habenula 146 7 neurons [40], it could be the case that long-range connections play an important role in the development and transmission 147 of avalanches, i.e. the habenula is actually critical, but we perceive it to be otherwise due to the omission of long-range 148 connections. In such a situation, one large (and long-lasting) avalanche would be perceived as multiple smaller (and 149 potentially shorter) avalanches, causing the probability mass in both distributions to bias towards the left side. Hence, it 150 could explain the sub-power law regim...