Place cells, grid cells, attractors, and remapping

Unweaving the Cognitive Map: A Personal History

I have been incredibly fortunate to have worked in the field of hippocampal spatial coding during three of its most exciting decades, the 1990s, 2000s, and 2010s. During this time I had a ringside view of some of the foundational discoveries that were made which have transformed our understanding of the hippocampal system and its role in cognition (especially spatial cognition) and memory. These discoveries inspired me in my own lab over the years to pursue three broad lines of enquiry-3D spatial encoding, context and the sense of direction-which are outlined here. If some of my personal recollections are a little inaccurate (such is the nature of episodic memory!) I apologize in advance.

Coherently remapping toroidal cells but not Grid cells are responsible for path integration in virtual agents

It is widely believed that grid cells provide cues for path integration, with place cells encoding an animal's location and environmental identity. When entering a new environment, these cells remap concurrently, sparking debates about their causal relationship. Using a continuous attractor recurrent neural network, we study spatial cell dynamics in multiple environments. We investigate grid cell remapping as a function of global remapping in place-like units through random resampling of place cell centers. Dimensionality reduction techniques reveal that a subset of cells manifest a persistent torus across environments. Unexpectedly, these toroidal cells resemble band-like cells rather than high grid score units. Subsequent pruning studies reveal that toroidal cells are crucial for path integration while grid cells are not. As we extend the model to operate across many environments, we delineate its generalization boundaries, revealing challenges with modeling many environments in current models.

Computational cross-species views of the hippocampal formation

The discovery of place cells and head direction cells in the hippocampal formation of freely foraging rodents has led to an emphasis of its role in encoding allocentric spatial relationships. In contrast, studies in head-fixed primates have additionally found representations of spatial views. We review recent experiments in freely moving monkeys that expand upon these findings and show that postural variables such as eye/head movements strongly influence neural activity in the hippocampal formation, suggesting that the function of the hippocampus depends on where the animal looks. We interpret these results in the light of recent studies in humans performing challenging navigation tasks which suggest that depending on the context, eye/head movements serve one of two roles-gathering information about the structure of the environment (active sensing) or externalizing the contents of internal beliefs/deliberation (embodied cognition). These findings prompt future experimental investigations into the information carried by signals flowing between the hippocampal formation and the brain regions controlling postural variables, and constitute a basis for updating computational theories of the hippocampal system to accommodate the influence of eye/head movements.

A proposed attention-based model for spatial memory formation and retrieval

Animals use sensory information and memory to build internal representations of space. It has been shown that such representations extend beyond the geometry of an environment and also encode rich sensory experiences usually referred to as context. In mammals, contextual inputs from sensory cortices appear to be converging on the hippocampus as a key area for spatial representations and memory. How metric and external sensory inputs (e.g., visual context) are combined into a coherent and stable place representation is not fully understood. Here, I review the evidence of attentional effects along the ventral visual pathway and in the medial temporal lobe and propose an attention-based model for the integration of visual context in spatial representations. I further suggest that attention-based retrieval of spatial memories supports a feedback mechanism that allows consolidation of old memories and new sensory experiences related to the same place, thereby contributing to the stability of spatial representations. The resulting model has the potential to generate new hypotheses to explain complex responses of spatial cells such as place cells in the hippocampus.

Homogeneous inhibition is optimal for the phase precession of place cells in the CA1 field

Place cells are hippocampal neurons encoding the position of an animal in space. Studies of place cells are essential to understanding the processing of information by neural networks of the brain. An important characteristic of place cell spike trains is phase precession. When an animal is running through the place field, the discharges of the place cells shift from the ascending phase of the theta rhythm through the minimum to the descending phase. The role of excitatory inputs to pyramidal neurons along the Schaffer collaterals and the perforant pathway in phase precession is described, but the role of local interneurons is poorly understood. Our goal is estimating of the contribution of field CA1 interneurons to the phase precession of place cells using mathematical methods. The CA1 field is chosen because it provides the largest set of experimental data required to build and verify the model. Our simulations discover optimal parameters of the excitatory and inhibitory inputs to the pyramidal neuron so that it generates a spike train with the effect of phase precession. The uniform inhibition of pyramidal neurons best explains the effect of phase precession. Among interneurons, axo-axonal neurons make the greatest contribution to the inhibition of pyramidal cells.

A hybrid biological neural network model for solving problems in cognitive planning

A variety of behaviors, like spatial navigation or bodily motion, can be formulated as graph traversal problems through cognitive maps. We present a neural network model which can solve such tasks and is compatible with a broad range of empirical findings about the mammalian neocortex and hippocampus. The neurons and synaptic connections in the model represent structures that can result from self-organization into a cognitive map via Hebbian learning, i.e. into a graph in which each neuron represents a point of some abstract task-relevant manifold and the recurrent connections encode a distance metric on the manifold. Graph traversal problems are solved by wave-like activation patterns which travel through the recurrent network and guide a localized peak of activity onto a path from some starting position to a target state.

From mechanisms to functions: The role of theta and gamma coherence in the intrahippocampal circuits

Brain rhythms are essential for information processing in neuronal networks. Oscillations recorded in different brain regions can be synchronized and have a constant phase difference, that is, they can be coherent. Coherence between local field potential (LFP) signals from different brain regions may be correlated with the performance of cognitive tasks, indicating that these regions of the brain are jointly involved in the information processing. Why does coherence occur and how is it related to the information transfer between different regions of the hippocampal formation? In this article, we discuss possible mechanisms of theta and gamma coherence and its role in the hippocampus-dependent attention and memory processes, since theta and gamma rhythms are most pronounced in these processes. We review in vivo studies of interactions between different regions of the hippocampal formation in theta and gamma frequency bands. The key propositions of the review are as follows: (1) coherence emerges from synchronous postsynaptic currents in principal neurons as a result of synchronization of neuronal spike activity; (2) the synchronization of neuronal spike patterns in two regions of the hippocampal formation can be realized through induction or resonance; (3) coherence at a specific time point reflects the transfer of information between the regions of the hippocampal formation; (4) the physiological roles of theta and gamma coherence are different due to their different functions and mechanisms of generation. All hippocampal neurons are involved in theta activity, and theta coherence arranges the firing order of principal neurons throughout the hippocampal formation. In contrast, gamma coherence reflects the coupling of active neuronal ensembles. Overall, the coherence of LFPs between different areas of the brain is an important physiological process based on the synchronized neuronal firing, and it is essential for cooperative information processing.

A model of head direction and landmark coding in complex environments

Environmental information is required to stabilize estimates of head direction (HD) based on angular path integration. However, it is unclear how this happens in real-world (visually complex) environments. We present a computational model of how visual feedback can stabilize HD information in environments that contain multiple cues of varying stability and directional specificity. We show how combinations of feature-specific visual inputs can generate a stable unimodal landmark bearing signal, even in the presence of multiple cues and ambiguous directional specificity. This signal is associated with the retrosplenial HD signal (inherited from thalamic HD cells) and conveys feedback to the subcortical HD circuitry. The model predicts neurons with a unimodal encoding of the egocentric orientation of the array of landmarks, rather than any one particular landmark. The relationship between these abstract landmark bearing neurons and head direction cells is reminiscent of the relationship between place cells and grid cells. Their unimodal encoding is formed from visual inputs via a modified version of Oja's Subspace Algorithm. The rule allows the landmark bearing signal to disconnect from directionally unstable or ephemeral cues, incorporate newly added stable cues, support orientation across many different environments (high memory capacity), and is consistent with recent empirical findings on bidirectional HD firing reported in the retrosplenial cortex. Our account of visual feedback for HD stabilization provides a novel perspective on neural mechanisms of spatial navigation within richer sensory environments, and makes experimentally testable predictions.

How environmental movement constraints shape the neural code for space

Study of the neural code for space in rodents has many insights to offer for how mammals, including humans, construct a mental representation of space. This code is centered on the hippocampal place cells, which are active in particular places in the environment. Place cells are informed by numerous other spatial cell types including grid cells, which provide a signal for distance and direction and are thought to help anchor the place cell signal. These neurons combine self-motion and environmental information to create and update their map-like representation. Study of their activity patterns in complex environments of varying structure has revealed that this "cognitive map" of space is not a fixed and rigid entity that permeates space, but rather is variably affected by the movement constraints of the environment. These findings are pointing toward a more flexible spatial code in which the map is adapted to the movement possibilities of the space. An as-yet-unanswered question is whether these different forms of representation have functional consequences, as suggested by an enactivist view of spatial cognition.

Dorsal CA1 hippocampal place cells form a multi-scale representation of megaspace

Spatially firing "place cells" within the hippocampal CA1 region form internal maps of the environment necessary for navigation and memory. In rodents, these neurons have been almost exclusively studied in small environments (<4 m²). It remains unclear how place cells encode a very large open 2D environment that is commensurate with the natural environments experienced by rodents and other mammals. Such an ethologically realistic environment would require a complex spatial representation, capable of simultaneously representing space at multiple overlapping fine-to-coarse informational scales. Here, we show that in a "megaspace" (18.6 m²), the majority of dorsal CA1 place cells exhibited multiple place subfields of different sizes, akin to those observed along the septo-temporal axis. Furthermore, the total area covered by the subfields of each cell was not correlated with the number of subfields, and increased with the scale of the environment. The multiple different-sized subfields exhibited by place cells in the megaspace suggest that the ensemble population of subfields form a multi-scale representation of space within the dorsal hippocampus. Our findings point to a new dorsal hippocampus ensemble coding scheme that simultaneously supports navigational processes at both fine- and coarse-grained resolutions. VIDEO ABSTRACT.

Distinct place cell dynamics in CA1 and CA3 encode experience in new environments

When exploring new environments animals form spatial memories that are updated with experience and retrieved upon re-exposure to the same environment. The hippocampus is thought to support these memory processes, but how this is achieved by different subnetworks such as CA1 and CA3 remains unclear. To understand how hippocampal spatial representations emerge and evolve during familiarization, we performed 2-photon calcium imaging in mice running in new virtual environments and compared the trial-to-trial dynamics of place cells in CA1 and CA3 over days. We find that place fields in CA1 emerge rapidly but tend to shift backwards from trial-to-trial and remap upon re-exposure to the environment a day later. In contrast, place fields in CA3 emerge gradually but show more stable trial-to-trial and day-to-day dynamics. These results reflect different roles in CA1 and CA3 in spatial memory processing during familiarization to new environments and constrain the potential mechanisms that support them.

A theory of joint attractor dynamics in the hippocampus and the entorhinal cortex accounts for artificial remapping and grid cell field-to-field variability

The representation of position in the mammalian brain is distributed across multiple neural populations. Grid cell modules in the medial entorhinal cortex (MEC) express activity patterns that span a low-dimensional manifold which remains stable across different environments. In contrast, the activity patterns of hippocampal place cells span distinct low-dimensional manifolds in different environments. It is unknown how these multiple representations of position are coordinated. Here, we develop a theory of joint attractor dynamics in the hippocampus and the MEC. We show that the system exhibits a coordinated, joint representation of position across multiple environments, consistent with global remapping in place cells and grid cells. In addition, our model accounts for recent experimental observations that lack a mechanistic explanation: variability in the firing rate of single grid cells across firing fields, and artificial remapping of place cells under depolarization, but not under hyperpolarization, of layer II stellate cells of the MEC.

On the Statistical Mechanics of Life: Schrödinger Revisited

We study the statistical underpinnings of life, in particular its increase in order and complexity over evolutionary time. We question some common assumptions about the thermodynamics of life. We recall that contrary to widespread belief, even in a closed system entropy growth can accompany an increase in macroscopic order. We view metabolism in living things as microscopic variables directly driven by the second law of thermodynamics, while viewing the macroscopic variables of structure, complexity and homeostasis as mechanisms that are entropically favored because they open channels for entropy to grow via metabolism. This perspective reverses the conventional relation between structure and metabolism, by emphasizing the role of structure for metabolism rather than the converse. Structure extends in time, preserving information along generations, particularly in the genetic code, but also in human culture. We argue that increasing complexity is an inevitable tendency for systems with these dynamics and explain this with the notion of metastable states, which are enclosed regions of the phase-space that we call “bubbles,” and channels between these, which are discovered by random motion of the system. We consider that more complex systems inhabit larger bubbles (have more available states), and also that larger bubbles are more easily entered and less easily exited than small bubbles. The result is that the system entropically wanders into ever-larger bubbles in the foamy phase space, becoming more complex over time. This formulation makes intuitive why the increase in order/complexity over time is often stepwise and sometimes collapses catastrophically, as in biological extinction.

The storage and recall of memories in the hippocampo-cortical system

A quantitative computational theory of the operation of the hippocampus as an episodic memory system is described. The CA3 system operates as a single attractor or autoassociation network (1) to enable rapid one-trial associations between any spatial location (place in rodents or spatial view in primates) and an object or reward and (2) to provide for completion of the whole memory during recall from any part. The theory is extended to associations between time and object or reward to implement temporal order memory, which is also important in episodic memory. The dentate gyrus performs pattern separation by competitive learning to create sparse representations producing, for example, neurons with place-like fields from entorhinal cortex grid cells. The dentate granule cells generate, by the very small number of mossy fibre connections to CA3, a randomizing pattern separation effect that is important during learning but not recall and that separates out the patterns represented by CA3 firing as being very different from each other. This is optimal for an unstructured episodic memory system in which each memory must be kept distinct from other memories. The direct perforant path input to CA3 is quantitatively appropriate for providing the cue for recall in CA3 but not for learning. The CA1 recodes information from CA3 to set up associatively learned backprojections to the neocortex to allow the subsequent retrieval of information to the neocortex, giving a quantitative account of the large number of hippocampo-neocortical and neocortical-neocortical backprojections. Tests of the theory including hippocampal subregion analyses and hippocampal NMDA receptor knockouts are described and support the theory.

Neurons in Primate Entorhinal Cortex Represent Gaze Position in Multiple Spatial Reference Frames

Primates rely predominantly on vision to gather information from the environment and neurons representing visual space and gaze position are found in many brain areas. Within the medial temporal lobe, a brain region critical for memory, neurons in the entorhinal cortex of macaque monkeys exhibit spatial selectivity for gaze position. Specifically, the firing rate of single neurons reflects fixation location within a visual image (Killian et al., 2012). In the rodents, entorhinal cells such as grid cells, border cells, and head direction cells show spatial representations aligned to visual environmental features instead of the body (Hafting et al., 2005; Sargolini et al., 2006; Solstad et al., 2008; Diehl et al., 2017). However, it is not known whether similar allocentric representations exist in primate entorhinal cortex. Here, we recorded neural activity in the entorhinal cortex in two male rhesus monkeys during a naturalistic, free-viewing task. Our data reveal that a majority of entorhinal neurons represent gaze position and that simultaneously recorded neurons represent gaze position relative to distinct spatial reference frames, with some neurons aligned to the visual image and others aligned to the monkey's head position. Our results also show that entorhinal neural activity can be used to predict gaze position with a high degree of accuracy. These findings demonstrate that visuospatial representation is a fundamental property of entorhinal neurons in primates and suggest that entorhinal cortex may support relational memory and motor planning by coding attentional locus in distinct, behaviorally relevant frames of reference.SIGNIFICANCE STATEMENT The entorhinal cortex, a brain area important for memory, shows striking spatial activity in rodents through grid cells, border cells, head direction cells, and nongrid spatial cells. The majority of entorhinal neurons signal the location of a rodent relative to visual environmental cues, representing the location of the animal relative to space in the world instead of the body. Recently, we found that entorhinal neurons can signal location of gaze while a monkey explores images visually. Here, we report that spatial entorhinal neurons are widespread in the monkey and these neurons are capable of showing a world-based spatial reference frame locked to the bounds of explored images. These results help connect the extensive findings in rodents to the primate.

Field repetition and local mapping in the hippocampus and the medial entorhinal cortex

Hippocampal place cells support spatial cognition and are thought to form the neural substrate of a global "cognitive map." A widely held view is that parts of the hippocampus also underlie the ability to separate patterns or to provide different neural codes for distinct environments. However, a number of studies have shown that in environments composed of multiple, repeating compartments, place cells and other spatially modulated neurons show the same activity in each local area. This repetition of firing fields may reflect pattern completion and may make it difficult for animals to distinguish similar local environments. In this review we 1) highlight some of the navigation difficulties encountered by humans in repetitive environments, 2) summarize literature demonstrating that place and grid cells represent local and not global space, and 3) attempt to explain the origin of these phenomena. We argue that the repetition of firing fields can be a useful tool for understanding the relationship between grid cells in the entorhinal cortex and place cells in the hippocampus, the spatial inputs shared by these cells, and the propagation of spatially related signals through these structures.

Brain rhythm attractor breakdown in Alzheimer's disease: Functional and pathologic implications

This perspective binds emerging evidence on the bidirectional relationship between Alzheimer's disease (AD) and sleep disorders through a model of brain rhythm attractor breakdown. This approach explains behavioral-cognitive changes in AD across the sleep-wake cycle and supports a causal association between early brainstem tau pathology and subsequent cortical amyloid β accumulation. Specifically, early tau dysregulation within brainstem-hypothalamic nuclei leads to breakdown of sleep-wake attractor networks, with patients displaying an attenuated range of behavioral and electrophysiological activity patterns, a "twilight zone" of constant activity between deep rest and full alertness. This constant cortical activity promotes activity-dependent amyloid β accumulation in brain areas that modulate their activity across sleep-wake states, especially the medial prefrontal cortex. In addition, the accompanying breakdown of hippocampal-medial prefrontal cortex interplay across sleep stages could explain deficient memory consolidation through dysregulation of synaptic plasticity. Clinical implications include the potential therapeutic benefit of attractor consolidation (e.g., slow-wave sleep enhancers) in delaying AD progression.

Megamap: flexible representation of a large space embedded with nonspatial information by a hippocampal attractor network

The problem of how the hippocampus encodes both spatial and nonspatial information at the cellular network level remains largely unresolved. Spatial memory is widely modeled through the theoretical framework of attractor networks, but standard computational models can only represent spaces that are much smaller than the natural habitat of an animal. We propose that hippocampal networks are built on a basic unit called a "megamap," or a cognitive attractor map in which place cells are flexibly recombined to represent a large space. Its inherent flexibility gives the megamap a huge representational capacity and enables the hippocampus to simultaneously represent multiple learned memories and naturally carry nonspatial information at no additional cost. On the other hand, the megamap is dynamically stable, because the underlying network of place cells robustly encodes any location in a large environment given a weak or incomplete input signal from the upstream entorhinal cortex. Our results suggest a general computational strategy by which a hippocampal network enjoys the stability of attractor dynamics without sacrificing the flexibility needed to represent a complex, changing world.

A hierarchical model of goal directed navigation selects trajectories in a visual environment

We have developed a Hierarchical Look-Ahead Trajectory Model (HiLAM) that incorporates the firing pattern of medial entorhinal grid cells in a planning circuit that includes interactions with hippocampus and prefrontal cortex. We show the model's flexibility in representing large real world environments using odometry information obtained from challenging video sequences. We acquire the visual data from a camera mounted on a small tele-operated vehicle. The camera has a panoramic field of view with its focal point approximately 5 cm above the ground level, similar to what would be expected from a rat's point of view. Using established algorithms for calculating perceptual speed from the apparent rate of visual change over time, we generate raw dead reckoning information which loses spatial fidelity over time due to error accumulation. We rectify the loss of fidelity by exploiting the loop-closure detection ability of a biologically inspired, robot navigation model termed RatSLAM. The rectified motion information serves as a velocity input to the HiLAM to encode the environment in the form of grid cell and place cell maps. Finally, we show goal directed path planning results of HiLAM in two different environments, an indoor square maze used in rodent experiments and an outdoor arena more than two orders of magnitude larger than the indoor maze. Together these results bridge for the first time the gap between higher fidelity bio-inspired navigation models (HiLAM) and more abstracted but highly functional bio-inspired robotic mapping systems (RatSLAM), and move from simulated environments into real-world studies in rodent-sized arenas and beyond.

Impairments in experience-dependent scaling and stability of hippocampal place fields limit spatial learning in a mouse model of Alzheimer's disease

Impaired spatial memory characterizes many mouse models for Alzheimer's disease, but we understand little about how this trait arises. Here, we use a transgenic model of amyloidosis to examine the relationship between behavioral performance in tests of spatial navigation and the function of hippocampal place cells. We find that amyloid precursor protein (APP) mice require considerably more training than controls to reach the same level of performance in a water maze task, and recall the trained location less well 24 h later. At a single cell level, place fields from control mice become more stable and spatially restricted with repeated exposure to a new environment, while those in APP mice improve less over time, ultimately producing a spatial code of lower resolution, accuracy, and reliability than controls. The limited refinement of place fields in APP mice likely contributes to their delayed water maze acquisition, and provides evidence for circuit dysfunction underlying cognitive impairment.

Theory and Simulation in Neuroscience

Modeling work in neuroscience can be classified using two different criteria. The first one is the complexity of the model, ranging from simplified conceptual models that are amenable to mathematical analysis to detailed models that require simulations in order to understand their properties. The second criterion is that of direction of workflow, which can be from microscopic to macroscopic scales (bottom-up) or from behavioral target functions to properties of components (top-down). We review the interaction of theory and simulation using examples of top-down and bottom-up studies and point to some current developments in the fields of computational and theoretical neuroscience.

Brain state-dependent neuronal computation

Neuronal firing pattern, which includes both the frequency and the timing of action potentials, is a key component of information processing in the brain. Although the relationship between neuronal output (the firing pattern) and function (during a task/behavior) is not fully understood, there is now considerable evidence that a given neuron can show very different firing patterns according to brain state. Thus, such neurons assembled into neuronal networks generate different rhythms (e.g., theta, gamma and sharp wave ripples), which sign specific brain states (e.g., learning, sleep). This implies that a given neuronal network, defined by its hard-wired physical connectivity, can support different brain state-dependent activities through the modulation of its functional connectivity. Here, we review data demonstrating that not only the firing pattern, but also the functional connections between neurons, can change dynamically. We then explore the possible mechanisms of such versatility, focusing on the intrinsic properties of neurons and the properties of the synapses they establish, and how they can be modified by neuromodulators, i.e., the different ways that neurons can use to switch from one mode of communication to the other.

Traveling in the dark: the legibility of a regular and predictable structure of the environment extends beyond its borders

The physical structure of the surrounding environment shapes the paths of progression, which in turn reflect the structure of the environment and the way that it shapes behavior. A regular and coherent physical structure results in paths that extend over the entire environment. In contrast, irregular structure results in traveling over a confined sector of the area. In this study, rats were tested in a dark arena in which half the area contained eight objects in a regular grid layout, and the other half contained eight objects in an irregular layout. In subsequent trials, a salient landmark was placed first within the irregular half, and then within the grid. We hypothesized that rats would favor travel in the area with regular order, but found that activity in the area with irregular object layout did not differ from activity in the area with grid layout, even when the irregular half included a salient landmark. Thus, the grid impact in one arena half extended to the other half and overshadowed the presumed impact of the salient landmark. This could be explained by mechanisms that control spatial behavior, such as grid cells and odometry. However, when objects were spaced irregularly over the entire arena, the salient landmark became dominant and the paths converged upon it, especially from objects with direct access to the salient landmark. Altogether, three environmental properties: (i) regular and predictable structure; (ii) salience of landmarks; and (iii) accessibility, hierarchically shape the paths of progression in a dark environment.