Collective Behavior of Place and Non-place Neurons in the Hippocampal Network

Spatial reasoning via recurrent neural dynamics in mouse retrosplenial cortex

From visual perception to language, sensory stimuli change their meaning depending on previous experience. Recurrent neural dynamics can interpret stimuli based on externally cued context, but it is unknown whether they can compute and employ internal hypotheses to resolve ambiguities. Here we show that mouse retrosplenial cortex (RSC) can form several hypotheses over time and perform spatial reasoning through recurrent dynamics. In our task, mice navigated using ambiguous landmarks that are identified through their mutual spatial relationship, requiring sequential refinement of hypotheses. Neurons in RSC and in artificial neural networks encoded mixtures of hypotheses, location and sensory information, and were constrained by robust low-dimensional dynamics. RSC encoded hypotheses as locations in activity space with divergent trajectories for identical sensory inputs, enabling their correct interpretation. Our results indicate that interactions between internal hypotheses and external sensory data in recurrent circuits can provide a substrate for complex sequential cognitive reasoning.

The estrous cycle modulates hippocampal spine dynamics, dendritic processing, and spatial coding

Histological evidence suggests that the estrous cycle exerts a powerful influence on CA1 neurons in the mammalian hippocampus. Decades have passed since this landmark observation, yet how the estrous cycle shapes dendritic spine dynamics and hippocampal spatial coding in vivo remains a mystery. Here, we used a custom hippocampal microperiscope and two-photon calcium imaging to track CA1 pyramidal neurons in female mice across multiple cycles. Estrous cycle stage had a potent effect on spine dynamics, with spine density peaking during proestrus when estradiol levels are highest. These morphological changes coincided with greater somatodendritic coupling and increased infiltration of back-propagating action potentials into the apical dendrite. Finally, tracking CA1 response properties during navigation revealed greater place field stability during proestrus, evident at both the single-cell and population levels. These findings demonstrate that the estrous cycle drives large-scale structural and functional plasticity in hippocampal neurons essential for learning and memory.

Social odors drive hippocampal CA2 place cell responses to social stimuli

Hippocampal region CA2 is essential for social memory processing. Interaction with social stimuli induces changes in CA2 place cell firing during active exploration and sharp wave-ripples during rest following a social interaction. However, it is unknown whether these changes in firing patterns are caused by integration of multimodal social stimuli or by a specific sensory modality associated with a social interaction. Rodents rely heavily on chemosensory cues in the form of olfactory signals for social recognition processes. To determine the extent to which social olfactory signals contribute to CA2 place cell responses to social stimuli, we recorded CA2 place cells in rats freely exploring environments containing stimuli that included or lacked olfactory content. We found that CA2 place cell firing patterns significantly changed only when social odors were prominent. Also, place cells that increased their firing in the presence of social odors alone preferentially increased their firing during subsequent sharp wave-ripples. Our results suggest that social olfactory cues are essential for changing CA2 place cell firing patterns during and after social interactions. These results support prior work suggesting CA2 performs social functions and shed light on processes underlying CA2 responses to social stimuli.

Latent learning drives sleep-dependent plasticity in distinct CA1 subpopulations

Latent learning is a process that enables the brain to transform experiences into "cognitive maps," a form of implicit memory, without requiring reinforced training. To investigate its neural mechanisms, we record from hippocampal neurons in mice during latent learning of spatial maps and observe that the high-dimensional neural state space gradually transforms into a low-dimensional manifold that closely resembles the physical environment. This transformation process is associated with the neural reactivation of navigational experiences during sleep. Additionally, we identify a subset of hippocampal neurons that, rather than forming place fields in a novel environment, maintain weak spatial tuning but gradually develop correlated activity with other neurons. The elevated correlation introduces redundancy into the ensemble code, transforming the neural state space into a low-dimensional manifold that effectively links discrete place fields of place cells into a map-like structure. These results suggest a potential mechanism for latent learning of spatial maps in the hippocampus.

Homeostatic synaptic normalization optimizes learning in network models of neural population codes

Studying and understanding the code of large neural populations hinge on accurate statistical models of population activity. A novel class of models, based on learning to weigh sparse nonlinear Random Projections (RP) of the population, has demonstrated high accuracy, efficiency, and scalability. Importantly, these RP models have a clear and biologically plausible implementation as shallow neural networks. We present a new class of RP models that are learned by optimizing the randomly selected sparse projections themselves. This 'reshaping' of projections is akin to changing synaptic connections in just one layer of the corresponding neural circuit model. We show that Reshaped RP models are more accurate and efficient than the standard RP models in recapitulating the code of tens of cortical neurons from behaving monkeys. Incorporating more biological features and utilizing synaptic normalization in the learning process, results in accurate models that are more efficient. Remarkably, these models exhibit homeostasis in firing rates and total synaptic weights of projection neurons. We further show that these sparse homeostatic reshaped RP models outperform fully connected neural network models. Thus, our new scalable, efficient, and highly accurate population code models are not only biologically plausible but are actually optimized due to their biological features. These findings suggest a dual functional role of synaptic normalization in neural circuits: maintaining spiking and synaptic homeostasis while concurrently optimizing network performance and efficiency in encoding information and learning.

Dynamical theory of complex systems with two-way micro-macro causation

In many complex systems encountered in the natural and social sciences, mechanisms governing system dynamics at a microscale depend upon the values of state variables characterizing the system at coarse-grained, macroscale (Goldenfeld and Woese, 2011, Noble et al., 2019, and Chater and Loewenstein, 2023). State variables, in turn, are averages over relevant probability distributions of the microscale variables. Neither inferential Top-Down nor mechanistic Bottom-Up modeling alone can predict responses of such scale-entwined systems to perturbations. We describe and explore the properties of a dynamic theory that combines Top-Down information-theoretic inference with Bottom-Up, state-variable-dependent mechanisms. The theory predicts the functional form of nonstationary probability distributions over microvariables and relates the trajectories of time-evolving macrovariables to the form of those distributions. Analytic expressions for the time evolution of Lagrange multipliers from Maxent solutions allow for rapid calculation of the time trajectories of state variables even in high dimensional systems. Examples of possible applications to scale-entwined systems in nonequilibrium chemical thermodynamics, epidemiology, economics, and ecology exemplify the potential multidisciplinary scope of the theory. A worked-out low-dimension example illustrates the structure of the theory and demonstrates how scale entwinement can result in slowed recovery from perturbations, reddened time series spectra in response to white-noise input, and hysteresis upon parameter displacement and subsequent restoration.

Mesoscale neuronal granular trial variability in vivo illustrated by nonlinear recurrent network in silico

Large-scale neural recording with single-neuron resolution has revealed the functional complexity of the neural systems. However, even under well-designed task conditions, the cortex-wide network exhibits highly dynamic trial variability, posing challenges to the conventional trial-averaged analysis. To study mesoscale trial variability, we conducted a comparative study between fluorescence imaging of layer-2/3 neurons in vivo and network simulation in silico. We imaged up to 40,000 cortical neurons' triggered responses by deep brain stimulus (DBS). And we build an in silico network to reproduce the biological phenomena we observed in vivo. We proved the existence of ineluctable trial variability and found it influenced by input amplitude and range. Moreover, we demonstrated that a spatially heterogeneous coding community accounts for more reliable inter-trial coding despite single-unit trial variability. A deeper understanding of trial variability from the perspective of a dynamical system may lead to uncovering intellectual abilities such as parallel coding and creativity.

The estrous cycle modulates hippocampal spine dynamics, dendritic processing, and spatial coding

Histological evidence suggests that the estrous cycle exerts a powerful effect on CA1 neurons in mammalian hippocampus. Decades have passed since this landmark observation, yet how the estrous cycle shapes dendritic spine dynamics and hippocampal spatial coding in vivo remains a mystery. Here, we used a custom hippocampal microperiscope and two-photon calcium imaging to track CA1 pyramidal neurons in female mice over multiple cycles. Estrous cycle stage had a potent effect on spine dynamics, with heightened density during periods of greater estradiol (proestrus). These morphological changes were accompanied by greater somatodendritic coupling and increased infiltration of back-propagating action potentials into the apical dendrite. Finally, tracking CA1 response properties during navigation revealed enhanced place field stability during proestrus, evident at the single-cell and population level. These results establish the estrous cycle as a driver of large-scale structural and functional plasticity in hippocampal circuits essential for learning and memory.

Dentate gyrus ensembles gate context-dependent neural states and memory retrieval

Memories of events are linked to the contexts in which they were encoded. This contextual linking ensures enhanced access to those memories that are most relevant to the context at hand, including specific associations that were previously learned in that context. This principle, referred to as encoding specificity, predicts that context-specific neural states should bias retrieval of particular associations over others, potentially allowing for the disambiguation of retrieval cues that may have multiple associations or meanings. Using a context-odor paired associate learning paradigm in mice, here, we show that chemogenetic manipulation of dentate gyrus ensembles corresponding to specific contexts reinstates context-specific neural states in downstream CA1 and biases retrieval toward context-specific associations.

Dynamic gating of perceptual flexibility by non-classically responsive cortical neurons

The ability to flexibly respond to sensory cues in dynamic environments is essential to adaptive auditory-guided behaviors. Cortical spiking responses during behavior are highly diverse, ranging from reliable trial-averaged responses to seemingly random firing patterns. While the reliable responses of 'classically responsive' cells have been extensively studied for decades, the contribution of irregular spiking 'non-classically responsive' cells to behavior has remained underexplored despite their prevalence. Here, we show that flexible auditory behavior results from interactions between local auditory cortical circuits comprised of heterogeneous responses and inputs from secondary motor cortex. Strikingly, non-classically responsive neurons in auditory cortex were preferentially recruited during learning, specifically during rapid learning phases when the greatest gains in behavioral performance occur. Population-level decoding revealed that during rapid learning mixed ensembles comprised of both classically and non-classically responsive cells encode significantly more task information than homogenous ensembles of either type and emerge as a functional unit critical for learning. Optogenetically silencing inputs from secondary motor cortex selectively modulated non-classically responsive cells in the auditory cortex and impaired reversal learning by preventing the remapping of a previously learned stimulus-reward association. Top-down inputs orchestrated highly correlated non-classically responsive ensembles in sensory cortex providing a unique task-relevant manifold for learning. Thus, non-classically responsive cells in sensory cortex are preferentially recruited by top-down inputs to enable neural and behavioral flexibility.

Contributions of cortical neuron firing patterns, synaptic connectivity, and plasticity to task performance

Neuronal responses during behavior are diverse, ranging from highly reliable 'classical' responses to irregular 'non-classically responsive' firing. While a continuum of response properties is observed across neural systems, little is known about the synaptic origins and contributions of diverse responses to network function, perception, and behavior. To capture the heterogeneous responses measured from auditory cortex of rodents performing a frequency recognition task, we use a novel task-performing spiking recurrent neural network incorporating spike-timing-dependent plasticity. Reliable and irregular units contribute differentially to task performance via output and recurrent connections, respectively. Excitatory plasticity shifts the response distribution while inhibition constrains its diversity. Together both improve task performance with full network engagement. The same local patterns of synaptic inputs predict spiking response properties of network units and auditory cortical neurons from in vivo whole-cell recordings during behavior. Thus, diverse neural responses contribute to network function and emerge from synaptic plasticity rules.

Multiplexed representation of others in the hippocampal CA1 subfield of female mice

Hippocampal place cells represent the position of a rodent within an environment. In addition, recent experiments show that the CA1 subfield of a passive observer also represents the position of a conspecific performing a spatial task. However, whether this representation is allocentric, egocentric or mixed is less clear. In this study we investigated the representation of others during free behavior and in a task where female mice learned to follow a conspecific for a reward. We found that most cells represent the position of others relative to self-position (social-vector cells) rather than to the environment, with a prevalence of purely egocentric coding modulated by context and mouse identity. Learning of a pursuit task improved the tuning of social-vector cells, but their number remained invariant. Collectively, our results suggest that the hippocampus flexibly codes the position of others in multiple coordinate systems, albeit favoring the self as a reference point.

The quality and complexity of pairwise maximum entropy models for large cortical populations

We investigate the ability of the pairwise maximum entropy (PME) model to describe the spiking activity of large populations of neurons recorded from the visual, auditory, motor, and somatosensory cortices. To quantify this performance, we use (1) Kullback-Leibler (KL) divergences, (2) the extent to which the pairwise model predicts third-order correlations, and (3) its ability to predict the probability that multiple neurons are simultaneously active. We compare these with the performance of a model with independent neurons and study the relationship between the different performance measures, while varying the population size, mean firing rate of the chosen population, and the bin size used for binarizing the data. We confirm the previously reported excellent performance of the PME model for small population sizes N < 20. But we also find that larger mean firing rates and bin sizes generally decreases performance. The performance for larger populations were generally not as good. For large populations, pairwise models may be good in terms of predicting third-order correlations and the probability of multiple neurons being active, but still significantly worse than small populations in terms of their improvement over the independent model in KL-divergence. We show that these results are independent of the cortical area and of whether approximate methods or Boltzmann learning are used for inferring the pairwise couplings. We compared the scaling of the inferred couplings with N and find it to be well explained by the Sherrington-Kirkpatrick (SK) model, whose strong coupling regime shows a complex phase with many metastable states. We find that, up to the maximum population size studied here, the fitted PME model remains outside its complex phase. However, the standard deviation of the couplings compared to their mean increases, and the model gets closer to the boundary of the complex phase as the population size grows.

Differential disruptions in population coding along the dorsal-ventral axis of CA1 in the APP/PS1 mouse model of Aβ pathology

Alzheimer's Disease (AD) is characterized by a range of behavioral alterations, including memory loss and psychiatric symptoms. While there is evidence that molecular pathologies, such as amyloid beta (Aβ), contribute to AD, it remains unclear how this histopathology gives rise to such disparate behavioral deficits. One hypothesis is that Aβ exerts differential effects on neuronal circuits across brain regions, depending on the neurophysiology and connectivity of different areas. To test this, we recorded from large neuronal populations in dorsal CA1 (dCA1) and ventral CA1 (vCA1), two hippocampal areas known to be structurally and functionally diverse, in the APP/PS1 mouse model of amyloidosis. Despite similar levels of Aβ pathology, dCA1 and vCA1 showed distinct disruptions in neuronal population activity as animals navigated a virtual reality environment. In dCA1, pairwise correlations and entropy, a measure of the diversity of activity patterns, were decreased in APP/PS1 mice relative to age-matched C57BL/6 controls. However, in vCA1, APP/PS1 mice had increased pair-wise correlations and entropy as compared to age matched controls. Finally, using maximum entropy models, we connected the microscopic features of population activity (correlations) to the macroscopic features of the population code (entropy). We found that the models' performance increased in predicting dCA1 activity, but decreased in predicting vCA1 activity, in APP/PS1 mice relative to the controls. Taken together, we found that Aβ exerts distinct effects across different hippocampal regions, suggesting that the various behavioral deficits of AD may reflect underlying heterogeneities in neuronal circuits and the different disruptions that Aβ pathology causes in those circuits.

Adaptive modeling and inference of higher-order coordination in neuronal assemblies: A dynamic greedy estimation approach

Central in the study of population codes, coordinated ensemble spiking activity is widely observable in neural recordings with hypothesized roles in robust stimulus representation, interareal communication, and learning and memory formation. Model-free measures of synchrony characterize coherent pairwise activity but not higher-order interactions, a limitation transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require repeated trials to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point-process model of ensemble spiking and a corresponding statistical inference framework to identify significant higher-order coordination. In the course of developing a precise statistical test, we show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings from human and rat cortical assemblies, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states.

Thermodynamic analog of integrate-and-fire neuronal networks by maximum entropy modelling

Recent results have evidenced that spontaneous brain activity signals are organized in bursts with scale free features and long-range spatio-temporal correlations. These observations have stimulated a theoretical interpretation of results inspired in critical phenomena. In particular, relying on maximum entropy arguments, certain aspects of time-averaged experimental neuronal data have been recently described using Ising-like models, allowing the study of neuronal networks under an analogous thermodynamical framework. This method has been so far applied to a variety of experimental datasets, but never to a biologically inspired neuronal network with short and long-term plasticity. Here, we apply for the first time the Maximum Entropy method to an Integrate-and-fire (IF) model that can be tuned at criticality, offering a controlled setting for a systematic study of criticality and finite-size effects in spontaneous neuronal activity, as opposed to experiments. We consider generalized Ising Hamiltonians whose local magnetic fields and interaction parameters are assigned according to the average activity of single neurons and correlation functions between neurons of the IF networks in the critical state. We show that these Hamiltonians exhibit a spin glass phase for low temperatures, having mostly negative intrinsic fields and a bimodal distribution of interaction constants that tends to become unimodal for larger networks. Results evidence that the magnetization and the response functions exhibit the expected singular behavior near the critical point. Furthermore, we also found that networks with higher percentage of inhibitory neurons lead to Ising-like systems with reduced thermal fluctuations. Finally, considering only neuronal pairs associated with the largest correlation functions allows the study of larger system sizes.

The Structure of Hippocampal CA1 Interactions Optimizes Spatial Coding across Experience

Although much is known about how single neurons in the hippocampus represent an animal's position, how circuit interactions contribute to spatial coding is less well understood. Using a novel statistical estimator and theoretical modeling, both developed in the framework of maximum entropy models, we reveal highly structured CA1 cell-cell interactions in male rats during open field exploration. The statistics of these interactions depend on whether the animal is in a familiar or novel environment. In both conditions the circuit interactions optimize the encoding of spatial information, but for regimes that differ in the informativeness of their spatial inputs. This structure facilitates linear decodability, making the information easy to read out by downstream circuits. Overall, our findings suggest that the efficient coding hypothesis is not only applicable to individual neuron properties in the sensory periphery, but also to neural interactions in the central brain.SIGNIFICANCE STATEMENT Local circuit interactions play a key role in neural computation and are dynamically shaped by experience. However, measuring and assessing their effects during behavior remains a challenge. Here, we combine techniques from statistical physics and machine learning to develop new tools for determining the effects of local network interactions on neural population activity. This approach reveals highly structured local interactions between hippocampal neurons, which make the neural code more precise and easier to read out by downstream circuits, across different levels of experience. More generally, the novel combination of theory and data analysis in the framework of maximum entropy models enables traditional neural coding questions to be asked in naturalistic settings.

Network size affects the complexity of activity in human iPSC-derived neuronal populations

Multi-electrode recording of neural activity in cultures offer opportunities for understanding how the structure of a network gives rise to function. Although it is hypothesized that network size is critical for determining the dynamics of activity, this relationship in human neural cultures remains largely unexplored. By applying new methods for analyzing neural activity to human iPSC derived cultures at either low-densities or high-densities, we uncovered the significant impacts that neuron number has on the individual neurophysiological properties of cells (such as firing rates), the collective behavior of the networks these cultures formed (as measured by entropy), and the relationship between the two. As a result, simply changing the densities of neurons generated dynamics and network behavior that differed not just in degree, but in kind. Beyond revealing the relationship between network structure and function, our findings provide a novel analytical framework to study diseases where network level activity is affected.

A manifold neural population code for space in hippocampal coactivity dynamics independent of place fields

Hippocampus place cell discharge is temporally unreliable across seconds and days, and place fields are multimodal, suggesting an "ensemble cofiring" spatial coding hypothesis with manifold dynamics that does not require reliable spatial tuning, in contrast to hypotheses based on place field (spatial tuning) stability. We imaged mouse CA1 (cornu ammonis 1) ensembles in two environments across three weeks to evaluate these coding hypotheses. While place fields "remap," being more distinct between than within environments, coactivity relationships generally change less. Decoding location and environment from 1-s ensemble location-specific activity is effective and improves with experience. Decoding environment from cell-pair coactivity relationships is also effective and improves with experience, even after removing place tuning. Discriminating environments from 1-s ensemble coactivity relies crucially on the cells with the most anti-coactive cell-pair relationships because activity is internally organized on a low-dimensional manifold of non-linear coactivity relationships that intermittently reregisters to environments according to the anti-cofiring subpopulation activity.

Adaptive modeling and inference of higher-order coordination in neuronal assemblies: a dynamic greedy estimation approach

Central in the study of population codes, coordinated ensemble spiking activity is widely observable in neural recordings with hypothesized roles in robust stimulus representation, interareal communication, and learning and memory formation. Model-free measures of synchrony characterize coherent pairwise activity but not higher-order interactions, a limitation transcended by statistical models of ensemble spiking activity. However, existing model-based analyses often impose assumptions about the relevance of higher-order interactions and require repeated trials to characterize dynamics in the correlational structure of ensemble activity. To address these shortcomings, we propose an adaptive greedy filtering algorithm based on a discretized mark point-process model of ensemble spiking and a corresponding statistical inference framework to identify significant higher-order coordination. In the course of developing a precise statistical test, we show that confidence intervals can be constructed for greedily estimated parameters. We demonstrate the utility of our proposed methods on simulated neuronal assemblies. Applied to multi-electrode recordings from human and rat cortical assemblies, our proposed methods provide new insights into the dynamics underlying localized population activity during transitions between brain states.

Exactly solvable statistical physics models for large neuronal populations

Maximum entropy methods provide a principled path connecting measurements of neural activity directly to statistical physics models, and this approach has been successful for populations of N ~ 100 neurons. As N increases in new experiments, we enter an undersampled regime where we have to choose which observables should be constrained in the maximum entropy construction. The best choice is the one that provides the greatest reduction in entropy, defining a "minimax entropy" principle. This principle becomes tractable if we restrict attention to correlations among pairs of neurons that link together into a tree; we can find the best tree efficiently, and the underlying statistical physics models are exactly solved. We use this approach to analyze experiments on N ~ 1500 neurons in the mouse hippocampus, and show that the resulting model captures the distribution of synchronous activity in the network.

The respective activation and silencing of striatal direct and indirect pathway neurons support behavior encoding

The basal ganglia are known to control actions and modulate movements. Neuronal activity in the two efferent pathways of the dorsal striatum is critical for appropriate behavioral control. Previous evidence has led to divergent conclusions on the respective engagement of both pathways during actions. Using calcium imaging to evaluate how neurons in the direct and indirect pathways encode behaviors during self-paced spontaneous explorations in an open field, we observed that the two striatal pathways exhibit distinct tuning properties. Supervised learning algorithms revealed that direct pathway neurons encode behaviors through their activation, whereas indirect pathway neurons exhibit behavior-specific silencing. These properties remain stable for weeks. Our findings highlight a complementary encoding of behaviors with congruent activations in the direct pathway encoding multiple accessible behaviors in a given context, and in the indirect pathway encoding the suppression of competing behaviors. This model reconciles previous conflicting conclusions on motor encoding in the striatum.

Object-centered population coding in CA1 of the hippocampus

Objects and landmarks are crucial for guiding navigation and must be integrated into the cognitive map of space. Studies of object coding in the hippocampus have primarily focused on activity of single cells. Here, we record simultaneously from large numbers of hippocampal CA1 neurons to determine how the presence of a salient object in the environment alters single-neuron and neural-population activity of the area. The majority of the cells showed some change in their spatial firing patterns when the object was introduced. At the neural-population level, these changes were systematically organized according to the animal's distance from the object. This organization was widely distributed across the cell sample, suggesting that some features of cognitive maps-including object representation-are best understood as emergent properties of neural populations.

A local circuit-basis for spatial navigation and memory processes in hippocampal area CA1

The hippocampus is a multi-stage neural circuit that is critical for memory formation. Its distinct anatomy has long inspired theories that rely on local interactions between neurons within each subregion in order to perform serial operations important for memory encoding and storage. These local computations have received less attention in CA1 area, the primary output node of the hippocampus, where excitatory neurons are thought to be only very sparsely interconnected. However, recent findings have demonstrated the power of local circuitry in CA1, with evidence for strong functional interactions among excitatory neurons, regulation by diverse inhibitory microcircuits, and novel plasticity rules that can profoundly reshape the hippocampal ensemble code. Here we review how these properties expand the dynamical repertoire of CA1 beyond the confines of feedforward processing, and what implications they have for hippocampo-cortical functions in memory formation.

Organization of hippocampal CA3 into correlated cell assemblies supports a stable spatial code

Hippocampal subfield CA3 is thought to stably store memories in assemblies of recurrently connected cells functioning as a collective. However, the collective hippocampal coding properties that are unique to CA3 and how such properties facilitate the stability or precision of the neural code remain unclear. Here, we performed large-scale Ca2+ imaging in hippocampal CA1 and CA3 of freely behaving mice that repeatedly explored the same, initially novel environments over weeks. CA3 place cells have more precise and more stable tuning and show a higher statistical dependence with their peers compared with CA1 place cells, uncovering a cell assembly organization in CA3. Surprisingly, although tuning precision and long-term stability are correlated, cells with stronger peer dependence exhibit higher stability but not higher precision. Overall, our results expose the three-way relationship between tuning precision, long-term stability, and peer dependence, suggesting that a cell assembly organization underlies long-term storage of information in the hippocampus.

Neural manifold analysis of brain circuit dynamics in health and disease

Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than those applicable to single-cell experiments. One approach that has gained recent popularity is neural manifold learning. This approach takes advantage of the fact that often, even though neural datasets may be very high dimensional, the dynamics of neural activity tends to traverse a much lower-dimensional space. The topological structures formed by these low-dimensional neural subspaces are referred to as "neural manifolds", and may potentially provide insight linking neural circuit dynamics with cognitive function and behavioral performance. In this paper we review a number of linear and non-linear approaches to neural manifold learning, including principal component analysis (PCA), multi-dimensional scaling (MDS), Isomap, locally linear embedding (LLE), Laplacian eigenmaps (LEM), t-SNE, and uniform manifold approximation and projection (UMAP). We outline these methods under a common mathematical nomenclature, and compare their advantages and disadvantages with respect to their use for neural data analysis. We apply them to a number of datasets from published literature, comparing the manifolds that result from their application to hippocampal place cells, motor cortical neurons during a reaching task, and prefrontal cortical neurons during a multi-behavior task. We find that in many circumstances linear algorithms produce similar results to non-linear methods, although in particular cases where the behavioral complexity is greater, non-linear methods tend to find lower-dimensional manifolds, at the possible expense of interpretability. We demonstrate that these methods are applicable to the study of neurological disorders through simulation of a mouse model of Alzheimer's Disease, and speculate that neural manifold analysis may help us to understand the circuit-level consequences of molecular and cellular neuropathology.

The geometry of cortical representations of touch in rodents

Neurons often encode highly heterogeneous non-linear functions of multiple task variables, a signature of a high-dimensional geometry. We studied the representational geometry in the somatosensory cortex of mice trained to report the curvature of objects touched by their whiskers. High-speed videos of the whiskers revealed that the task can be solved by linearly integrating multiple whisker contacts over time. However, the neural activity in somatosensory cortex reflects non-linear integration of spatio-temporal features of the sensory inputs. Although the responses at first appeared disorganized, we identified an interesting structure in the representational geometry: different whisker contacts are disentangled variables represented in approximately, but not fully, orthogonal subspaces of the neural activity space. This geometry allows linear readouts to perform a broad class of tasks of different complexities without compromising the ability to generalize to novel situations.

Neural assemblies uncovered by generative modeling explain whole-brain activity statistics and reflect structural connectivity

Patterns of endogenous activity in the brain reflect a stochastic exploration of the neuronal state space that is constrained by the underlying assembly organization of neurons. Yet, it remains to be shown that this interplay between neurons and their assembly dynamics indeed suffices to generate whole-brain data statistics. Here, we recorded the activity from ∼40,000 neurons simultaneously in zebrafish larvae, and show that a data-driven generative model of neuron-assembly interactions can accurately reproduce the mean activity and pairwise correlation statistics of their spontaneous activity. This model, the compositional Restricted Boltzmann Machine (cRBM), unveils ∼200 neural assemblies, which compose neurophysiological circuits and whose various combinations form successive brain states. We then performed in silico perturbation experiments to determine the interregional functional connectivity, which is conserved across individual animals and correlates well with structural connectivity. Our results showcase how cRBMs can capture the coarse-grained organization of the zebrafish brain. Notably, this generative model can readily be deployed to parse neural data obtained by other large-scale recording techniques.

From synapses to circuits and back: Bridging levels of understanding in animal models of Alzheimer's disease

Alzheimer's disease (AD) is a neurodegenerative disorder characterized by behavioural changes that include memory loss and cognitive decline and is associated with the appearance of amyloid-β plaques and neurofibrillary tangles throughout the brain. Although aspects of the disease percolate across multiple levels of neuronal organization, from the cellular to the behavioural, it is increasingly clear that circuits are a critical junction between the cellular pathology and the behavioural phenotypes that bookend these levels of analyses. In this review, we discuss critical aspects of neural circuit research, beginning with synapses and progressing to network activity and how they influence our understanding of disease processed in AD.

How does an organism extract relevant information from transcription factor concentrations?

How does an organism regulate its genes? The involved regulation typically occurs in terms of a signal processing chain: an externally applied stimulus or a maternally supplied transcription factor leads to the expression of some downstream genes, which, in turn, are transcription factors for further genes. Especially during development, these transcription factors are frequently expressed in amounts where noise is still important; yet, the signals that they provide must not be lost in the noise. Thus, the organism needs to extract exactly relevant information in the signal. New experimental approaches involving single-molecule measurements at high temporal precision as well as increased precision in manipulations directly on the genome are allowing us to tackle this question anew. These new experimental advances mean that also from the theoretical side, theoretical advances should be possible. In this review, I will describe, specifically on the example of fly embryo gene regulation, how theoretical approaches, especially from inference and information theory, can help in understanding gene regulation. To do so, I will first review some more traditional theoretical models for gene regulation, followed by a brief discussion of information-theoretical approaches and when they can be applied. I will then introduce early fly development as an exemplary system where such information-theoretical approaches have traditionally been applied and can be applied; I will specifically focus on how one such method, namely the information bottleneck approach, has recently been used to infer structural features of enhancer architecture.

Single-neuron detection of place cells remapping in short-term memory using motion microelectrode arrays

Place cells establish rapid mapping relationships between the external environment and themselves in a new context. However, the mapping relationships of environmental cues to place cells in short-term memory is still completely unknown. In this work, we designed a silicon-based motion microelectrode array (mMEA) and an implantation device to record electrophysiological signals of place cells in CA1, CA3, and DG regions in the hippocampus of ten mice in motion, and investigated the corresponding place fields under distal or local cues in just a few minutes. The mMEA can expand the detection area and greatly lower the motion noise. Finding and recording place cells of moving mice in short-term memory is made possible by the mMEA. The place-related cells were found for the first time. Unlike place cells, which only fire in a particular position of the environment, place-related cells fire in numerous areas of the environment. Furthermore, place cells in the CA1 and CA3 have the most stable place memory for time-preferred single cues, and they fire in concert with place-related cells during short-term memory dynamics, whereas place cells in the DG regions have overlapping and unstable place memory in a multi-cue context. These results demonstrate the consistency of place cells in CA1 and CA3 and reflect their different roles in spatial memory processing during familiarization with new environments. The mMEA provides a platform for studying the place cells of short-term memory.

Decomposing the Local Arrow of Time in Interacting Systems

We show that the evidence for a local arrow of time, which is equivalent to the entropy production in thermodynamic systems, can be decomposed. In a system with many degrees of freedom, there is a term that arises from the irreversible dynamics of the individual variables, and then a series of non-negative terms contributed by correlations among pairs, triplets, and higher-order combinations of variables. We illustrate this decomposition on simple models of noisy logical computations, and then apply it to the analysis of patterns of neural activity in the retina as it responds to complex dynamic visual scenes. We find that neural activity breaks detailed balance even when the visual inputs do not, and that this irreversibility arises primarily from interactions between pairs of neurons.

Emergence of local irreversibility in complex interacting systems

Living systems are fundamentally irreversible, breaking detailed balance and establishing an arrow of time. But how does the evident arrow of time for a whole system arise from the interactions among its multiple elements? We show that the local evidence for the arrow of time, which is the entropy production for thermodynamic systems, can be decomposed. First, it can be split into two components: an independent term reflecting the dynamics of individual elements and an interaction term driven by the dependencies among elements. Adapting tools from nonequilibrium physics, we further decompose the interaction term into contributions from pairs of elements, triplets, and higher-order terms. We illustrate our methods on models of cellular sensing and logical computations, as well as on patterns of neural activity in the retina as it responds to visual inputs. We find that neural activity can define the arrow of time even when the visual inputs do not, and that the dominant contribution to this breaking of detailed balance comes from interactions among pairs of neurons.

Information theory: A foundation for complexity science

Modeling and inference are central to most areas of science and especially to evolving and complex systems. Critically, the information we have is often uncertain and insufficient, resulting in an underdetermined inference problem; multiple inferences, models, and theories are consistent with available information. Information theory (in particular, the maximum information entropy formalism) provides a way to deal with such complexity. It has been applied to numerous problems, within and across many disciplines, over the last few decades. In this perspective, we review the historical development of this procedure, provide an overview of the many applications of maximum entropy and its extensions to complex systems, and discuss in more detail some recent advances in constructing comprehensive theory based on this inference procedure. We also discuss efforts at the frontier of information-theoretic inference: application to complex dynamic systems with time-varying constraints, such as highly disturbed ecosystems or rapidly changing economies.

Statistical properties of large data sets with linear latent features

Analytical understanding of how low-dimensional latent features reveal themselves in large-dimensional data is still lacking. We study this by defining a probabilistic linear latent features model with additive noise and by analytically and numerically computing the statistical distributions of pairwise correlations and eigenvalues of the data correlation matrix. This allows us to resolve the latent feature structure across a wide range of data regimes set by the number of recorded variables, observations, latent features, and the signal-to-noise ratio. We find a characteristic imprint of latent features in the distribution of correlations and eigenvalues and provide an analytic estimate for the boundary between signal and noise, even in the absence of a spectral gap.

In Vivo Multi-Day Calcium Imaging of CA1 Hippocampus in Freely Moving Rats Reveals a High Preponderance of Place Cells with Consistent Place Fields

Calcium imaging using GCaMP indicators and miniature microscopes has been used to image cellular populations during long timescales and in different task phases, as well as to determine neuronal circuit topology and organization. Because the hippocampus (HPC) is essential for tasks of memory, spatial navigation, and learning, calcium imaging of large populations of HPC neurons can provide new insight on cell changes over time during these tasks. All reported HPC in vivo calcium imaging experiments have been done in mouse. However, rats have many behavioral and physiological experimental advantages over mice. In this paper, we present the first (to our knowledge) in vivo calcium imaging from CA1 HPC in freely moving male rats. Using the UCLA Miniscope, we demonstrate that, in rat, hundreds of cells can be visualized and held across weeks. We show that calcium events in these cells are highly correlated with periods of movement, with few calcium events occurring during periods without movement. We additionally show that an extremely large percent of cells recorded during a navigational task are place cells (77.3 ± 5.0%, surpassing the percent seen during mouse calcium imaging), and that these cells enable accurate decoding of animal position and can be held over days with consistent place fields in a consistent spatial map. A detailed protocol is included, and implications of these advancements on in vivo imaging and place field literature are discussed.SIGNIFICANCE STATEMENT In vivo calcium imaging in freely moving animals allows the visualization of cellular activity across days. In this paper, we present the first in vivo Ca2+ recording from CA1 hippocampus (HPC) in freely moving rats. We demonstrate that hundreds of cells can be visualized and held across weeks, and that calcium activity corresponds to periods of movement. We show that a high percentage (77.3 ± 5.0%) of imaged cells are place cells, and that these place cells enable accurate decoding and can be held stably over days with little change in field location. Because the HPC is essential for many tasks involving memory, navigation, and learning, imaging of large populations of HPC neurons can shed new insight on cellular activity changes and organization.

On the dimensionality of behavior

How do we characterize animal behavior? Psychophysics started with human behavior in the laboratory, and focused on simple contexts, such as the decision among just a few alternative actions in response to sensory inputs. In contrast, ethology focused on animal behavior in the natural environment, emphasizing that evolution selects potentially complex behaviors that are useful in specific contexts. New experimental methods now make it possible to monitor animal and human behaviors in vastly greater detail. This “physics of behavior” holds the promise of combining the psychophysicist’s quantitative approach with the ethologist’s appreciation of natural context. One question surrounding this growing body of data concerns the dimensionality of behavior. Here I try to give this concept a precise definition.

There is a growing effort in the “physics of behavior” that aims at complete quantitative characterization of animal movements under more complex, naturalistic conditions. One reaction to the resulting explosion of high-dimensional data is the search for low-dimensional structure. Here I try to define more clearly what we mean by the dimensionality of behavior, where observable behavior may consist of either continuous trajectories or sequences of discrete states. This discussion also serves to isolate situations in which the dimensionality of behavior is effectively infinite.

Top-down control of hippocampal signal-to-noise by prefrontal long-range inhibition

Prefrontal cortex (PFC) is postulated to exert "top-down control" on information processing throughout the brain to promote specific behaviors. However, pathways mediating top-down control remain poorly understood. In particular, knowledge about direct prefrontal connections that might facilitate top-down control of hippocampal information processing remains sparse. Here we describe monosynaptic long-range GABAergic projections from PFC to hippocampus. These preferentially inhibit vasoactive intestinal polypeptide-expressing interneurons, which are known to disinhibit hippocampal microcircuits. Indeed, stimulating prefrontal-hippocampal GABAergic projections increases hippocampal feedforward inhibition and reduces hippocampal activity in vivo. The net effect of these actions is to specifically enhance the signal-to-noise ratio for hippocampal encoding of object locations and augment object-induced increases in spatial information. Correspondingly, activating or inhibiting these projections promotes or suppresses object exploration, respectively. Together, these results elucidate a top-down prefrontal pathway in which long-range GABAergic projections target disinhibitory microcircuits, thereby enhancing signals and network dynamics underlying exploratory behavior.

Goal discrimination in hippocampal nonplace cells when place information is ambiguous

SignificanceGoal-directed spatial navigation has been found to rely on hippocampal neurons that are spatially modulated. We show that "nonplace" cells without significant spatial modulation play a role in discriminating goals when environmental cues for goals are ambiguous. This nonplace cell activity is performance-dependent and is modulated by gamma oscillations. Finally, nonplace cell goal discrimination coding fails in a mouse model of Alzheimer's disease (AD). Together, these results show that nonplace cell firing can signal unique task-relevant information when spatial information is ambiguous; these signals depend on performance and are absent in a mouse model of AD.

Signal Detection in Nearly Continuous Spectra and ℤ2-Symmetry Breaking

The large scale behavior of systems having a large number of interacting degrees of freedom is suitably described using the renormalization group from non-Gaussian distributions. Renormalization group techniques used in physics are then expected to provide a complementary point of view on standard methods used in data science, especially for open issues. Signal detection and recognition for covariance matrices having nearly continuous spectra is currently an open issue in data science and machine learning. Using the field theoretical embedding introduced in Entropy, 23(9), 1132 to reproduce experimental correlations, we show in this paper that the presence of a signal may be characterized by a phase transition with Z2-symmetry breaking. For our investigations, we use the nonperturbative renormalization group formalism, using a local potential approximation to construct an approximate solution of the flow. Moreover, we focus on the nearly continuous signal build as a perturbation of the Marchenko-Pastur law with many discrete spikes.

Calcium Imaging Reveals Fast Tuning Dynamics of Hippocampal Place Cells and CA1 Population Activity during Free Exploration Task in Mice

Hippocampal place cells are a well-known object in neuroscience, but their place field formation in the first moments of navigating in a novel environment remains an ill-defined process. To address these dynamics, we performed in vivo imaging of neuronal activity in the CA1 field of the mouse hippocampus using genetically encoded green calcium indicators, including the novel NCaMP7 and FGCaMP7, designed specifically for in vivo calcium imaging. Mice were injected with a viral vector encoding calcium sensor, head-mounted with an NVista HD miniscope, and allowed to explore a completely novel environment (circular track surrounded by visual cues) without any reinforcement stimuli, in order to avoid potential interference from reward-related behavior. First, we calculated the average time required for each CA1 cell to acquire its place field. We found that 25% of CA1 place fields were formed at the first arrival in the corresponding place, while the average tuning latency for all place fields in a novel environment equaled 247 s. After 24 h, when the environment was familiar to the animals, place fields formed faster, independent of retention of cognitive maps during this session. No cumulation of selectivity score was observed between these two sessions. Using dimensionality reduction, we demonstrated that the population activity of rapidly tuned CA1 place cells allowed the reconstruction of the geometry of the navigated circular maze; the distribution of reconstruction error between the mice was consistent with the distribution of the average place field selectivity score in them. Our data thus show that neuronal activity recorded with genetically encoded calcium sensors revealed fast behavior-dependent plasticity in the mouse hippocampus, resulting in the rapid formation of place fields and population activity that allowed the reconstruction of the geometry of the navigated maze.

Large-scale neural recordings call for new insights to link brain and behavior

Neuroscientists today can measure activity from more neurons than ever before, and are facing the challenge of connecting these brain-wide neural recordings to computation and behavior. In the present review, we first describe emerging tools and technologies being used to probe large-scale brain activity and new approaches to characterize behavior in the context of such measurements. We next highlight insights obtained from large-scale neural recordings in diverse model systems, and argue that some of these pose a challenge to traditional theoretical frameworks. Finally, we elaborate on existing modeling frameworks to interpret these data, and argue that the interpretation of brain-wide neural recordings calls for new theoretical approaches that may depend on the desired level of understanding. These advances in both neural recordings and theory development will pave the way for critical advances in our understanding of the brain.

Modelling the neural code in large populations of correlated neurons

Neurons respond selectively to stimuli, and thereby define a code that associates stimuli with population response patterns. Certain correlations within population responses (noise correlations) significantly impact the information content of the code, especially in large populations. Understanding the neural code thus necessitates response models that quantify the coding properties of modelled populations, while fitting large-scale neural recordings and capturing noise correlations. In this paper, we propose a class of response model based on mixture models and exponential families. We show how to fit our models with expectation-maximization, and that they capture diverse variability and covariability in recordings of macaque primary visual cortex. We also show how they facilitate accurate Bayesian decoding, provide a closed-form expression for the Fisher information, and are compatible with theories of probabilistic population coding. Our framework could allow researchers to quantitatively validate the predictions of neural coding theories against both large-scale neural recordings and cognitive performance.

Information Theoretic Approaches to Deciphering the Neural Code with Functional Fluorescence Imaging

Information theoretic metrics have proven useful in quantifying the relationship between behaviorally relevant parameters and neuronal activity with relatively few assumptions. However, these metrics are typically applied to action potential (AP) recordings and were not designed for the slow timescales and variable amplitudes typical of functional fluorescence recordings (e.g., calcium imaging). The lack of research guidelines on how to apply and interpret these metrics with fluorescence traces means the neuroscience community has yet to realize the power of information theoretic metrics. Here, we used computational methods to create mock AP traces with known amounts of information. From these, we generated fluorescence traces and examined the ability of different information metrics to recover the known information values. We provide guidelines for how to use information metrics when applying them to functional fluorescence and demonstrate their appropriate application to GCaMP6f population recordings from mouse hippocampal neurons imaged during virtual navigation.

Divergence in Population Coding for Space between Dorsal and Ventral CA1

Molecular, anatomic, and behavioral studies show that the hippocampus is structurally and functionally heterogeneous, with dorsal hippocampus implicated in mnemonic processes and spatial navigation and ventral hippocampus involved in affective processes. By performing electrophysiological recordings of large neuronal populations in dorsal and ventral CA1 in head-fixed mice navigating a virtual environment, we found that this diversity resulted in different strategies for population coding of space. Populations of neurons in dorsal CA1 showed more complex patterns of activity, which resulted in a higher dimensionality of neural representations that translated to more information being encoded, as compared ensembles in vCA1. Furthermore, a pairwise maximum entropy model was better at predicting the structure of these global patterns of activity in ventral CA1 as compared with dorsal CA1. Taken together, the different coding strategies we uncovered likely emerge from anatomic and physiological differences along the longitudinal axis of hippocampus and that may, in turn, underpin the divergent ethological roles of dorsal and ventral CA1.

Behavior determines the hippocampal spatial mapping of a multisensory environment

Animals behave in multisensory environments guided by various modalities of spatial information. Mammalian navigation engages a cognitive map of space in the hippocampus. Yet it is unknown whether and how this map incorporates multiple modalities of spatial information. Here, we establish two behavioral tasks in which mice navigate the same multisensory virtual environment by either pursuing a visual landmark or tracking an odor gradient. These tasks engage different proportions of visuo-spatial and olfacto-spatial mapping CA1 neurons and different population-level representations of each sensory-spatial coordinate. Switching between tasks results in global remapping. In a third task, mice pursue a target of varying sensory modality, and this engages modality-invariant neurons mapping the abstract behaviorally relevant coordinate irrespective of its physical modality. These findings demonstrate that the hippocampus does not necessarily map space as one coherent physical variable but as a combination of sensory and abstract reference frames determined by the subject's behavioral goal.

Principles and open questions in functional brain network reconstruction

Graph theory is now becoming a standard tool in system-level neuroscience. However, endowing observed brain anatomy and dynamics with a complex network representation involves often covert theoretical assumptions and methodological choices which affect the way networks are reconstructed from experimental data, and ultimately the resulting network properties and their interpretation. Here, we review some fundamental conceptual underpinnings and technical issues associated with brain network reconstruction, and discuss how their mutual influence concurs in clarifying the organization of brain function.

Anterior Thalamic Inputs Are Required for Subiculum Spatial Coding, with Associated Consequences for Hippocampal Spatial Memory

Just as hippocampal lesions are principally responsible for "temporal lobe" amnesia, lesions affecting the anterior thalamic nuclei seem principally responsible for a similar loss of memory, "diencephalic" amnesia. Compared with the former, the causes of diencephalic amnesia have remained elusive. A potential clue comes from how the two sites are interconnected, as within the hippocampal formation, only the subiculum has direct, reciprocal connections with the anterior thalamic nuclei. We found that both permanent and reversible anterior thalamic nuclei lesions in male rats cause a cessation of subicular spatial signaling, reduce spatial memory performance to chance, but leave hippocampal CA1 place cells largely unaffected. We suggest that a core element of diencephalic amnesia stems from the information loss in hippocampal output regions following anterior thalamic pathology.SIGNIFICANCE STATEMENT At present, we know little about interactions between temporal lobe and diencephalic memory systems. Here, we focused on the subiculum, as the sole hippocampal formation region directly interconnected with the anterior thalamic nuclei. We combined reversible and permanent lesions of the anterior thalamic nuclei, electrophysiological recordings of the subiculum, and behavioral analyses. Our results were striking and clear: following permanent thalamic lesions, the diverse spatial signals normally found in the subiculum (including place cells, grid cells, and head-direction cells) all disappeared. Anterior thalamic lesions had no discernible impact on hippocampal CA1 place fields. Thus, spatial firing activity within the subiculum requires anterior thalamic function, as does successful spatial memory performance. Our findings provide a key missing part of the much bigger puzzle concerning why anterior thalamic damage is so catastrophic for spatial memory in rodents and episodic memory in humans.

Nonlocal spatiotemporal representation in the hippocampus of freely flying bats

Navigation occurs through a continuum of space and time. The hippocampus is known to encode the immediate position of moving animals. However, active navigation, especially at high speeds, may require representing navigational information beyond the present moment. Using wireless electrophysiological recordings in freely flying bats, we demonstrate that neural activity in area CA1 predominantly encodes nonlocal spatial information up to meters away from the bat's present position. This spatiotemporal representation extends both forward and backward in time, with an emphasis on future locations, and is found during both random exploration and goal-directed navigation. The representation of position thus extends along a continuum, with each moment containing information about past, present, and future, and may provide a key mechanism for navigating along self-selected and remembered paths.

Choice of method of place cell classification determines the population of cells identified

Place cells, spatially responsive hippocampal cells, provide the neural substrate supporting navigation and spatial memory. Historically most studies of these neurons have used electrophysiological recordings from implanted electrodes but optical methods, measuring intracellular calcium, are becoming increasingly common. Several methods have been proposed as a means to identify place cells based on their calcium activity but there is no common standard and it is unclear how reliable different approaches are. Here we tested four methods that have previously been applied to two-photon hippocampal imaging or electrophysiological data, using both model datasets and real imaging data. These methods use different parameters to identify place cells, including the peak activity in the place field, compared to other locations (the Peak method); the stability of cells' activity over repeated traversals of an environment (Stability method); a combination of these parameters with the size of the place field (Combination method); and the spatial information held by the cells (Information method). The methods performed differently from each other on both model and real data. In real datasets, vastly different numbers of place cells were identified using the four methods, with little overlap between the populations identified as place cells. Therefore, choice of place cell detection method dramatically affects the number and properties of identified cells. Ultimately, we recommend the Peak method be used in future studies to identify place cell populations, as this method is robust to moderate variations in place field within a session, and makes no inherent assumptions about the spatial information in place fields, unless there is an explicit theoretical reason for detecting cells with more narrowly defined properties.