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While sleeping, many vertebrate groups alternate between at least two sleep stages: rapid eye movement and slow wave sleep 1 – 4 , in part characterized by wake-like and synchronous brain activity, respectively. Here we delineate neural and behavioural correlates of two stages of sleep in octopuses, marine invertebrates that evolutionarily diverged from vertebrates roughly 550 million years ago (ref. 5 ) and have independently evolved large brains and behavioural sophistication. ‘Quiet’ sleep in octopuses is rhythmically interrupted by approximately 60-s bouts of pronounced body movements and rapid changes in skin patterning and texture 6 . We show that these bouts are homeostatically regulated, rapidly reversible and come with increased arousal threshold, representing a distinct ‘active’ sleep stage. Computational analysis of active sleep skin patterning reveals diverse dynamics through a set of patterns conserved across octopuses and strongly resembling those seen while awake. High-density electrophysiological recordings from the central brain reveal that the local field potential (LFP) activity during active sleep resembles that of waking. LFP activity differs across brain regions, with the strongest activity during active sleep seen in the superior frontal and vertical lobes, anatomically connected regions associated with learning and memory function 7 – 10 . During quiet sleep, these regions are relatively silent but generate LFP oscillations resembling mammalian sleep spindles 11 , 12 in frequency and duration. The range of similarities with vertebrates indicates that aspects of two-stage sleep in octopuses may represent convergent features of complex cognition. Octopuses possess a distinct active sleep stage, with behavioural and neural correlates resembling vertebrate REM sleep, which may represent convergent features of complex cognition.

Recent technological breakthroughs in large-scale neural recordings enable us to monitor simultaneously the activity of thousands of neurons. To shed light on the collective nature of the activity in these large populations of cells, we seek theoretical approaches that will help us simplify the rich dynamics they exhibit. We focus on optical imaging experiments of dorsal hippocampus in mice as they run along a virtual linear track. First, we build minimal models to capture the activity in populations of ∼80 neurons. About half the neurons in these networks are place cells - neurons that become active only when the animal enters a particular location in its environment. However, many of the neurons are not place cells in any given environment. We use maximum entropy models which approximate the distribution of activity patterns in these mixed populations, by matching the correlations between pairs of cells but otherwise assuming as little structure as possible. Despite their simplicity, the models capture the higher-order structure of activity patterns in the population, quantitatively. Moreover, they show that place and non{place neurons encode information collectively. Our results suggest that understanding the neural activity may require not only knowledge of the external variables modulating it but also of the internal network state. Next, we study hippocampal populations on larger scale - over 1000 neurons. In many large scale non-biological systems that consist of many interacting units, it is possible to describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization group concept. We develop explicit coarse-graining procedures that we apply to the activity in these large hippocampal populations. We see evidence of power-law dependencies in both static and dynamic quantities as we vary the coarse-graining scale over two decades. Furthermore, probability distributions of coarse-grained variables seem to approach a fixed non-Gaussian form. Taken together, the success of these strategies in capturing essential properties of population-level neural activity encourages us to think that simpler theories of neural network dynamics are possible.

The growing recognition that brain pathologies do not affect neurons only but rather are, to a large extent, pathologies of glial cells as well as of the vasculature opens to new perspectives in our understanding of genetic disorders of the CNS. To validate the role of the neuron-glial-vascular unit in the etiology of genome instability disorders, we report about cell death and morphological aspects of neuroglia networks and the associated vasculature in a mouse model of Ataxia Telangiectasia (A-T), a human genetic disorder that induces severe motor impairment. We found that A-T-mutated protein deficiency was consistent with aberrant astrocytic morphology and alterations of the vasculature, often accompanied by reactive gliosis. Interestingly similar findings could also be reported in the case of other genetic disorders. These observations bolster the notion that astrocyte-specific pathologies, hampered vascularization and astrocyte-endothelium interactions in the CNS could play a crucial role in the etiology of genome instability brain disorders and could underlie neurodegeneration.

Biological networks exhibit complex, coordinated patterns of activity. Can these patterns be captured precisely in simple models? Here we use measurements of simultaneous activity in 1000+ neurons in the mouse brain to test the validity of models grounded in statistical physics. When cells are dense samples from a small region, we find extremely detailed quantitative agreement between theory and experiment; sparse samples from larger regions lead to model failures. These results show we can aspire to more than qualitative agreement between simplifying theoretical ideas and the detailed behavior of a complex biological system.

We develop a phenomenological coarse--graining procedure for activity in a large network of neurons, and apply this to recordings from a population of 1000+ cells in the hippocampus. Distributions of coarse--grained variables seem to approach a fixed non--Gaussian form, and we see evidence of scaling in both static and dynamic quantities. These results suggest that the collective behavior of the network is described by a non--trivial fixed point.

Discussions of the hippocampus often focus on place cells, but many neurons are not place cells in any given environment. Here we describe the collective activity in such mixed populations, treating place and non-place cells on the same footing. We start with optical imaging experiments on CA1 in mice as they run along a virtual linear track, and use maximum entropy methods to approximate the distribution of patterns of activity in the population, matching the correlations between pairs of cells but otherwise assuming as little structure as possible. We find that these simple models accurately predict the activity of each neuron from the state of all the other neurons in the network, regardless of how well that neuron codes for position. These and other results suggest that place cells are not a distinct sub-network, but part of a larger system that encodes, collectively, more than just place information.

We study how recurrent neural networks (RNNs) solve a hierarchical inference task involving two latent variables and disparate timescales separated by 1-2 orders of magnitude. The task is of interest to the International Brain Laboratory, a global collaboration of experimental and theoretical neuroscientists studying how the mammalian brain generates behavior. We make four discoveries. First, RNNs learn behavior that is quantitatively similar to ideal Bayesian baselines. Second, RNNs perform inference by learning a two-dimensional subspace defining beliefs about the latent variables. Third, the geometry of RNN dynamics reflects an induced coupling between the two separate inference processes necessary to solve the task. Fourth, we perform model compression through a novel form of knowledge distillation on hidden representations - Representations and Dynamics Distillation (RADD)- to reduce the RNN dynamics to a low-dimensional, highly interpretable model. This technique promises a useful tool for interpretability of high dimensional nonlinear dynamical systems. Altogether, this work yields predictions to guide exploration and analysis of mouse neural data and circuity. Competing Interest Statement The authors have declared no competing interest. Footnotes * Author affiliation updated.

In many systems we can describe emergent macroscopic behaviors, quantitatively, using models that are much simpler than the underlying microscopic interactions; we understand the success of this simplification through the renormalization group. Could similar simplifications succeed in complex biological systems? We develop explicit coarse-graining procedures that we apply to experimental data on the electrical activity in large populations of neurons in the mouse hippocampus. Probability distributions of coarse-grained variables seem to approach a fixed non-Gaussian form, and we see evidence of power-law dependencies in both static and dynamic quantities as we vary the coarse-graining scale over two decades. Taken together, these results suggest that the collective behavior of the network is described by a non-trivial fixed point.