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Neural oscillations are ubiquitously observed in many brain areas. One proposed functional role of these oscillations is that they serve as an internal clock, or ‘frame of reference’. Information can be encoded by the timing of neural activity relative to thephaseof such oscillations. In line with this hypothesis, there have been multiple empirical observations of suchphase codesin the brain. Here we ask: What kind of neural dynamics support phase coding of information with neural oscillations? We tackled this question by analyzing recurrent neural networks (RNNs) that were trained on a working memory task. The networks were given access to an external reference oscillation and tasked to produce an oscillation, such that the phase difference between the reference and output oscillation maintains the identity of transient stimuli. We found that networks converged to stable oscillatory dynamics. Reverse engineering these networks revealed that each phase-coded memory corresponds to a separate limit cycle attractor. We characterized how the stability of the attractor dynamics depends on both reference oscillation amplitude and frequency, properties that can be experimentally observed. To understand the connectivity structures that underlie these dynamics, we showed that trained networks can be described as two phase-coupled oscillators. Using this insight, we condensed our trained networks to a reduced model consisting of two functional modules: One that generates an oscillation and one that implements a coupling function between the internal oscillation and external reference. In summary, by reverse engineering the dynamics and connectivity of trained RNNs, we propose a mechanism by which neural networks can harness reference oscillations for working memory. Specifically, we propose that a phase-coding network generates autonomous oscillations which it couples to an external reference oscillation in a multi-stable fashion.Author summaryMany of our actions are rhythmic—walking, breathing, digesting and more. It is not surprising that neural activity can have a strong oscillatory component. Indeed, such brain waves are common, and can even be measured using EEG from the scalp. Perhaps less obvious is the presence of such oscillations during non-rhythmic behavior—such as memory maintenance and other cognitive functions. Reports of these cognitive oscillations have accumulated over the years, and various theories were raised regarding their origin and utilization. In particular, oscillations have been proposed to serve as a clock signal that can be used for temporal-, or phase-coding of information in working memory. Here, we studied the dynamical systems underlying this kind of coding, by using trained artificial neural networks as hypothesis generators. We trained recurrent neural networks to perform a working memory task, while giving them access to a reference oscillation. We were then able to reverse engineer the learned dynamics of the networks. Our analysis revealed that phase coded memories correspond to stable attractors in the dynamical landscape of the model. These attractors arose from the coupling of the external reference oscillation with oscillations generated internally by the network.

Neonatal apneas and hypopneas present a serious risk for healthy infant development. Treating these adverse events requires frequent manual stimulation by skilled personnel, which can lead to alert fatigue. Automatically predicting these adverse events before they occur would enable the use of methods for automatic intervention. In this work, we propose a neural additive model to predict individual events of neonatal apnea and hypopnea and apply it to a physiological dataset from infants with Robin sequence at risk of upper airway obstruction. The dataset will be made publicly available together with this study. Our model achieved an average area under the receiver operating characteristic curve of 0.80 by additively combining information from different modalities of the respiratory polygraphy recording. This permits the prediction of individual apneas and hypopneas up to 15 seconds before they occur. Its additive nature makes the model inherently interpretable, which allowed insights into how important a given signal modality is for prediction and which patterns in the signal are discriminative. For our problem of predicting apneas and hyponeas in infants with Robin sequence, prior irregularities in breathing-related modalities as well as decreases in SpO2levels were especially discriminative.

We can now measure the connectivity of every neuron in a neural circuit, but we are still blind to other biological details, including the dynamical characteristics of each neuron. The degree to which connectivity measurements alone can inform understanding of neural computation is an open question. Here we show that with only measurements of the connectivity of a biological neural network, we can predict the neural activity underlying neural computation. We constructed a model neural network with the experimentally determined connectivity for 64 cell types in the motion pathways of the fruit fly optic lobe but with unknown parameters for the single neuron and single synapse properties. We then optimized the values of these unknown parameters using techniques from deep learning, to allow the model network to detect visual motion. Our mechanistic model makes detailed experimentally testable predictions for each neuron in the connectome. We found that model predictions agreed with experimental measurements of neural activity across 24 studies. Our work demonstrates a strategy for generating detailed hypotheses about the mechanisms of neural circuit function from connectivity measurements. We show that this strategy is more likely to be successful when neurons are sparsely connected—a universally observed feature of biological neural networks across species and brain regions.

A prominent theory proposes that the temporal order of a sequence of items held in memory is reflected in ordered firing of neurons at different phases of theta oscillations 1. We probe this theory by directly measuring single neuron activity (1420 neurons) and local field potentials (LFP, 921 channels) in the medial temporal lobe of 16 epilepsy patients performing a working memory task for temporal order. We observe theta oscillations and preferential firing of single neurons at theta phase during memory maintenance. We find that - depending on memory performance - phase of firing is related to item position within a sequence. However, in contrast to the theory, phase order did not match item order. To investigate underlying mechanisms, we subsequently trained recurrent neural networks (RNNs) to perform an analogous task. Similar to recorded neural activity, we show that RNNs generate theta oscillations during memory maintenance. Importantly, model neurons exhibit theta phase-dependent firing related to item position, where phase of firing again did not match item order. Instead, we observed a mechanistic link between phase order, stimulus timing and oscillation frequency - a relationship we subsequently confirmed in our neural recordings. Taken together, in both biological and artificial neural networks we provide validating evidence for the role of phase-of-firing in memory processing while at the same time challenging a long-held theory about the functional role of spiking and oscillations in sequence memory.

Neural circuits can produce similar activity patterns from vastly different combinations of channel and synaptic conductances. These conductances are tuned for specific activity patterns but might also reflect additional constraints, such as metabolic cost or robustness to perturbations. How do such constraints influence the range of permissible conductances? Here, we investigate how metabolic cost affects the parameters of neural circuits with similar activity in a model of the pyloric network of the crab Cancer borealis. We use a novel machine learning method to identify a range of network models that can generate activity patterns matching experimental data, and find that neural circuits can consume largely different amounts of energy despite similar circuit activity. Furthermore, a reduced but still significant range of circuit parameters gives rise to energy-efficient circuits. We then examine the space of parameters of energy-efficient circuits and identify potential tuning strategies for low metabolic cost. Finally, we investigate the interaction between metabolic cost and temperature robustness. We show that metabolic cost can vary across temperatures, but that robustness to temperature changes does not necessarily incur an increased metabolic cost. Our analyses show that, despite metabolic efficiency and temperature robustness constraining circuit parameters, neural systems can generate functional, efficient, and robust network activity with widely disparate sets of conductances.

The hippocampal dentate gyrus is an important relay conveying sensory information from the entorhinal cortex to the hippocampus proper. During exploration, the dentate gyrus has been proposed to act as a pattern separator. However, the dentate gyrus also shows structured activity during immobility and sleep. The properties of these activity patterns at cellular resolution, and their role in hippocampal-dependent memory processes have remained unclear. Using dual-color in-vivo two-photon Ca2+ imaging, we show that in immobile mice dentate granule cells generate sparse, synchronized activity patterns associated with entorhinal cortex activation. These population events are structured and modified by changes in the environment; and they incorporate place- and speed cells. Importantly, they recapitulate population patterns evoked during self-motion. Using optogenetic inhibition during immobility, we show that granule cell activity during immobility is required to form dentate gyrus-dependent spatial memories. These data suggest that memory formation is supported by dentate gyrus replay of population codes of the current environment.