Estimating neuronal firing density: A quantitative analysis of firing rate map algorithms.

The analysis of neurons that exhibit receptive fields dependent on an organism's spatial location, such as grid, place or boundary cells typically begins by mapping their activity in space using firing rate maps. However, mapping approaches are varied and depend on multiple tuning parameters that are usually chosen qualitatively by the experimenter and thus vary significantly across studies. Small changes in parameters such as these can impact results significantly, yet, to date a quantitative investigation of firing rate maps has not been attempted. Using simulated datasets, we examined how tuning parameters, recording duration and firing field size affect the accuracy of spatial maps generated using the most widely used approaches. For each approach we found a clear subset of parameters which yielded low-error firing rate maps and isolated the parameters yielding 1) the least error possible and 2) the Pareto-optimal parameter set which balanced error, computation time, place field detection accuracy and the extrapolation of missing values. Smoothed bivariate histograms and averaged shifted histograms were consistently associated with the fastest computation times while still providing accurate maps. Adaptive smoothing and binning approaches were found to compensate for low positional sampling the most effectively. Kernel smoothed density estimation also compensated for low sampling well and resulted in accurate maps, but it was also among the slowest methods tested. Overall, the bivariate histogram, coupled with spatial smoothing, is likely the most desirable method in the majority of cases.

Temporal context and latent state inference in the hippocampal splitter signal.

The hippocampus is thought to enable the encoding and retrieval of ongoing experience, the organization of that experience into structured representations like contexts, maps, and schemas, and the use of these structures to plan for the future. A central goal is to understand what the core computations supporting these functions are, and how these computations are realized in the collective action of single neurons. A potential access point into this issue is provided by 'splitter cells', hippocampal neurons that fire differentially on the overlapping segment of trajectories that differ in their past and/or future. However, the literature on splitter cells has been fragmented and confusing, owing to differences in terminology, behavioral tasks, and analysis methods across studies. In this review, we synthesize consistent findings from this literature, establish a common set of terms, and translate between single-cell and ensemble perspectives. Most importantly, we examine the combined findings through the lens of two major theoretical ideas about hippocampal function: representation of temporal context and latent state inference. We find that unique signature properties of each of these models are necessary to account for the data, but neither theory, by itself, explains all of its features. Specifically, the temporal gradedness of the splitter signal is strong support for temporal context, but is hard to explain using state models, while its flexibility and task-dependence is naturally accounted for using state inference, but poses a challenge otherwise. These theories suggest a number of avenues for future work, and we believe their application to splitter cells is a timely and informative domain for testing and refining theoretical ideas about hippocampal function.

Environment Symmetry Drives a Multidirectional Code in Rat Retrosplenial Cortex.

We investigated how environment symmetry shapes the neural processing of direction by recording directionally tuned retrosplenial neurons in male Lister hooded rats exploring multicompartment environments that had different levels of global rotational symmetry. Our hypothesis built on prior observations of twofold symmetry in the directional tuning curves of rats in a globally twofold-symmetric environment. To test whether environment symmetry was the relevant factor shaping the directional responses, here we deployed the same apparatus (two connected rectangular boxes) plus one with fourfold symmetry (a 2 × 2 array of connected square boxes) and one with onefold symmetry (a circular open-field arena). Consistent with our hypothesis we found many neurons with tuning curve symmetries that mirrored these environment symmetries, having twofold, fourfold, or onefold symmetric tuning, respectively. Some cells expressed this pattern only globally (across the whole environment), maintaining singular tuning curves in each subcompartment. However, others also expressed it locally within each subcompartment. Because multidirectionality has not been reported in naive rats in single environmental compartments, this suggests an experience-dependent effect of global environment symmetry on local firing symmetry. An intermingled population of directional neurons were classic head direction cells with globally referenced directional tuning. These cells were electrophysiologically distinct, with narrower tuning curves and a burstier firing pattern. Thus, retrosplenial directional neurons can simultaneously encode overall head direction and local head direction (relative to compartment layout). Furthermore, they can learn about global environment symmetry and express this locally. This may be important for the encoding of environment structure beyond immediate perceptual reach.SIGNIFICANCE STATEMENT We investigated how environment symmetry shapes the neural code for space by recording directionally tuned neurons from the retrosplenial cortex of rats exploring single- or multicompartment environments having onefold, twofold, or fourfold rotational symmetry. We found that many cells expressed a symmetry in their head direction tuning curves that matched the corresponding global environment symmetry, indicating plasticity of their directional tuning. They were also electrophysiologically distinct from canonical head directional cells. Notably, following exploration of the global space, many multidirectionally tuned neurons encoded global environment symmetry, even in local subcompartments. Our results suggest that multidirectional head direction codes contribute to the cognitive mapping of the complex structure of multicompartmented spaces.

Predictive maps in rats and humans for spatial navigation.

Much of our understanding of navigation comes from the study of individual species, often with specific tasks tailored to those species. Here, we provide a novel experimental and analytic framework integrating across humans, rats, and simulated reinforcement learning (RL) agents to interrogate the dynamics of behavior during spatial navigation. We developed a novel open-field navigation task ("Tartarus maze") requiring dynamic adaptation (shortcuts and detours) to frequently changing obstructions on the path to a hidden goal. Humans and rats were remarkably similar in their trajectories. Both species showed the greatest similarity to RL agents utilizing a "successor representation," which creates a predictive map. Humans also displayed trajectory features similar to model-based RL agents, which implemented an optimal tree-search planning procedure. Our results help refine models seeking to explain mammalian navigation in dynamic environments and highlight the utility of modeling the behavior of different species to uncover the shared mechanisms that support behavior.

The Neural Correlates of Spatial Disorientation in Head Direction Cells.

While the brain has evolved robust mechanisms to counter spatial disorientation, their neural underpinnings remain unknown. To explore these underpinnings, we monitored the activity of anterodorsal thalamic head direction (HD) cells in rats while they underwent unidirectional or bidirectional rotation at different speeds and under different conditions (light vs dark, freely-moving vs head-fixed). Under conditions that promoted disorientation, HD cells did not become quiescent but continued to fire, although their firing was no longer direction specific. Peak firing rates, burst frequency, and directionality all decreased linearly with rotation speed, consistent with previous experiments where rats were inverted or climbed walls/ceilings in zero gravity. However, access to visual landmarks spared the stability of preferred firing directions (PFDs), indicating that visual landmarks provide a stabilizing signal to the HD system while vestibular input likely maintains direction-specific firing. In addition, we found evidence that the HD system underestimated angular velocity at the beginning of head-fixed rotations, consistent with the finding that humans often underestimate rotations. When head-fixed rotations in the dark were terminated HD cells fired in bursts that matched the frequency of rotation. This postrotational bursting shared several striking similarities with postrotational "nystagmus" in the vestibulo-ocular system, consistent with the interpretation that the HD system receives input from a vestibular velocity storage mechanism that works to reduce spatial disorientation following rotation. Thus, the brain overcomes spatial disorientation through multisensory integration of different motor-sensory inputs.

Irregular distribution of grid cell firing fields in rats exploring a 3D volumetric space.

We investigated how entorhinal grid cells encode volumetric space. On a horizontal surface, grid cells usually produce multiple, spatially focal, approximately circular firing fields that are evenly sized and spaced to form a regular, close-packed, hexagonal array. This spatial regularity has been suggested to underlie navigational computations. In three dimensions, theoretically the equivalent firing pattern would be a regular, hexagonal close packing of evenly sized spherical fields. In the present study, we report that, in rats foraging in a cubic lattice, grid cells maintained normal temporal firing characteristics and produced spatially stable firing fields. However, although most grid fields were ellipsoid, they were sparser, larger, more variably sized and irregularly arranged, even when only fields abutting the lower surface (equivalent to the floor) were considered. Thus, grid self-organization is shaped by the environment's structure and/or movement affordances, and grids may not need to be regular to support spatial computations.

Hippocampal place cells encode global location but not connectivity in a complex space.

Flexible navigation relies on a cognitive map of space, thought to be implemented by hippocampal place cells: neurons that exhibit location-specific firing. In connected environments, optimal navigation requires keeping track of one's location and of the available connections between subspaces. We examined whether the dorsal CA1 place cells of rats encode environmental connectivity in four geometrically identical boxes arranged in a square. Rats moved between boxes by pushing saloon-type doors that could be locked in one or both directions. Although rats demonstrated knowledge of environmental connectivity, their place cells did not respond to connectivity changes, nor did they represent doorways differently from other locations. Place cells coded location in a global reference frame, with a different map for each box and minimal repetitive fields despite the repetitive geometry. These results suggest that CA1 place cells provide a spatial map that does not explicitly include connectivity.

Volumetric spatial behaviour in rats reveals the anisotropic organisation of navigation.

We investigated how access to the vertical dimension influences the natural exploratory and foraging behaviour of rats. Using high-accuracy three-dimensional tracking of position in two- and three-dimensional environments, we sought to determine (i) how rats navigated through the environments with respect to gravity, (ii) where rats chose to form their home bases in volumetric space, and (iii) how they navigated to and from these home bases. To evaluate how horizontal biases may affect these behaviours, we compared a 3D maze where animals preferred to move horizontally to a different 3D configuration where all axes were equally energetically costly to traverse. Additionally, we compared home base formation in two-dimensional arenas with and without walls to the three-dimensional climbing mazes. We report that many behaviours exhibited by rats in horizontal spaces naturally extend to fully volumetric ones, such as home base formation and foraging excursions. We also provide further evidence for the strong differentiation of the horizontal and vertical axes: rats showed a horizontal movement bias, they formed home bases mainly in the bottom layers of both mazes and they generally solved the vertical component of return trajectories before and faster than the horizontal component. We explain the bias towards horizontal movements in terms of energy conservation, while the locations of home bases are explained from an information gathering view as a method for correcting self-localisation.

The place-cell representation of volumetric space in rats.

Place cells are spatially modulated neurons found in the hippocampus that underlie spatial memory and navigation: how these neurons represent 3D space is crucial for a full understanding of spatial cognition. We wirelessly recorded place cells in rats as they explored a cubic lattice climbing frame which could be aligned or tilted with respect to gravity. Place cells represented the entire volume of the mazes: their activity tended to be aligned with the maze axes, and when it was more difficult for the animals to move vertically the cells represented space less accurately and less stably. These results demonstrate that even surface-dwelling animals represent 3D space and suggests there is a fundamental relationship between environment structure, gravity, movement and spatial memory.

Insensitivity of Place Cells to the Value of Spatial Goals in a Two-Choice Flexible Navigation Task.

Hippocampal place cells show position-specific activity thought to reflect a self-localization signal. Several reports also point to some form of goal encoding by place cells. We investigated this by asking whether they also encode the value of spatial goals, which is crucial information for optimizing goal-directed navigation. We used a continuous place navigation task in which male rats navigate to one of two (freely chosen) unmarked locations and wait, triggering the release of reward, which is then located and consumed elsewhere. This allows sampling of place fields and dissociates spatial goal from reward consumption. The two goals varied in the amount of reward provided, allowing assessment of whether the rats factored goal value into their navigational choice and of possible neural correlates of this value. Rats successfully learned the task, indicating goal localization, and they preferred higher-value goals, indicating processing of goal value. Replicating previous findings, there was goal-related activity in the out-of-field firing of CA1 place cells, with a ramping-up of firing rate during the waiting period, but no general overrepresentation of goals by place fields, an observation that we extended to CA3 place cells. Importantly, place cells were not modulated by goal value. This suggests that dorsal hippocampal place cells encode space independently of its associated value despite the effect of that value on spatial behavior. Our findings are consistent with a model of place cells in which they provide a spontaneously constructed value-free spatial representation rather than encoding other navigationally relevant but nonspatial information.SIGNIFICANCE STATEMENT We investigated whether hippocampal place cells, which compute a self-localization signal, also encode the relative value of places, which is essential information for optimal navigation. When choosing between two spatial goals of different value, rats preferred the higher-value goal. We saw out-of-field goal firing in place cells, replicating previous observations that the cells are influenced by the goal, but their activity was not modulated by the value of these goals. Our results suggest that place cells do not encode all of the navigationally relevant aspects of a place, but instead form a value-free "map" that links to such aspects in other parts of the brain.

Lesions of the Head Direction Cell System Increase Hippocampal Place Field Repetition.

A central tenet of systems neuroscience is that the mammalian hippocampus provides a cognitive map of the environment. This view is supported by the finding of place cells, neurons whose firing is tuned to specific locations in an animal's environment, within this brain region. Recent work, however, has shown that these cells repeat their firing fields across visually identical maze compartments [1, 2]. This repetition is not observed if these compartments face different directions, suggesting that place cells use a directional input to differentiate otherwise similar local environments [3, 4]. A clear candidate for this input is the head direction cell system. To test this, we disrupted the head direction cell system by lesioning the lateral mammillary nuclei and then recorded place cells as rats explored multiple, connected compartments, oriented in the same or in different directions. As shown previously, we found that place cells in control animals exhibited repeated fields in compartments arranged in parallel, but not in compartments facing different directions. In contrast, the place cells of animals with lesions of the head direction cell system exhibited repeating fields in both conditions. Thus, directional information provided by the head direction cell system appears essential for the angular disambiguation by place cells of visually identical compartments.

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.

The Yin and Yang of Memory Consolidation: Hippocampal and Neocortical.

While hippocampal and cortical mechanisms of memory consolidation have long been studied, their interaction is poorly understood. We sought to investigate potential interactions with respect to trace dominance, strengthening, and interference associated with postencoding novelty or sleep. A learning procedure was scheduled in a watermaze that placed the impact of novelty and sleep in opposition. Distinct behavioural manipulations-context preexposure or interference during memory retrieval-differentially affected trace dominance and trace survival, respectively. Analysis of immediate early gene expression revealed parallel up-regulation in the hippocampus and cortex, sustained in the hippocampus in association with novelty but in the cortex in association with sleep. These findings shed light on dynamically interacting mechanisms mediating the stabilization of hippocampal and neocortical memory traces. Hippocampal memory traces followed by novelty were more dominant by default but liable to interference, whereas sleep engaged a lasting stabilization of cortical traces and consequent trace dominance after preexposure.

The representation of space in the brain.

Animals can navigate vast distances and often display behaviours or activities that indicate a detailed, internal spatial representation of their surrounding environment or a 'cognitive map'. Over a century of behavioural research on spatial navigation in humans and animals has greatly increased our understanding of how this highly complex feat is achieved. In turn this has inspired half a century of electrophysiological spatial navigation and memory research which has further advanced our understanding of the brain. In particular, three functional cell types have been suggested to underlie cognitive mapping processes; place cells, head direction cells and grid cells. However, there are numerous other spatially modulated neurons in the brain. For a more complete understanding of the electrophysiological systems and behavioural processes underlying spatial navigation we must also examine these lesser understood neurons. In this review we will briefly summarise the literature surrounding place cells, head direction cells, grid cells and the evidence that these cells collectively form the neural basis of a cognitive map. We will then review literature covering many other spatially modulated neurons in the brain that perhaps further augment this cognitive map.

Place cells on a maze encode routes rather than destinations.

Hippocampal place cells fire at different rates when a rodent runs through a given location on its way to different destinations. However, it is unclear whether such firing represents the animal's intended destination or the execution of a specific trajectory. To distinguish between these possibilities, Lister Hooded rats (n = 8) were trained to navigate from a start box to three goal locations via four partially overlapping routes. Two of these led to the same goal location. Of the cells that fired on these two routes, 95.8% showed route-dependent firing (firing on only one route), whereas only two cells (4.2%) showed goal-dependent firing (firing similarly on both routes). In addition, route-dependent place cells over-represented the less discriminable routes, and place cells in general over-represented the start location. These results indicate that place cell firing on overlapping routes reflects the animal's route, not its goals, and that this firing may aid spatial discrimination.

How does the brain represent the outside world? One way of answering this question is to study the brains of rats, because the basic plan of a rodent's brain is similar to that of other mammals, such as humans. For example, the brains of rodents and humans both contain a structure called the hippocampus, which plays important roles in navigation and spatial memory. Cells within the hippocampus called place cells support these processes by firing electrical impulses whenever the animal occupies a specific location. When a rat runs along a corridor in a maze, its place cells often fire as it approaches a choice point. A given place cell will typically fire before the rat chooses a path leading towards one particular location, but not before choices that lead to other locations. The firing that occurs prior to the choice point is termed "prospective firing". However, it is not known whether the prospective firing of place cells represents the rat's final destination, or the specific route the animal takes to get there. To address this question, Grieves et al. designed a maze in which two different paths from a starting corridor led to the same goal location. If place cells represent the goal location, they should fire whichever route the rat chooses. However, if they represent the specific path the rat takes to the goal, they should fire on one or the other route, but not both. Grieves et al. found that almost all place cells with prospective activity in the starting corridor fired on a single route, as opposed to firing on both routes to the common goal. This suggests that the prospective firing in the hippocampus reflects the route the animal will take, rather than its intended destination. A future challenge will be to understand how the way the hippocampus codes routes interacts with brain circuits that code for intended goals, and how the activity of these circuits influences the animal's ability to navigate.

Place field repetition and spatial learning in a multicompartment environment.

Recent studies have shown that place cells in the hippocampus possess firing fields that repeat in physically similar, parallel environments. These results imply that it should be difficult for animals to distinguish parallel environments at a behavioral level. To test this, we trained rats on a novel odor-location task in an environment with four parallel compartments which had previously been shown to yield place field repetition. A second group of animals was trained on the same task, but with the compartments arranged in different directions, an arrangement we hypothesised would yield less place field repetition. Learning of the odor-location task in the parallel compartments was significantly impaired relative to learning in the radially arranged compartments. Fewer animals acquired the full discrimination in the parallel compartments compared to those trained in the radial compartments, and the former also required many more sessions to reach criterion compared to the latter. To confirm that the arrangement of compartments yielded differences in place cell repetition, in a separate group of animals we recorded from CA1 place cells in both environments. We found that CA1 place cells exhibited repeated fields across four parallel local compartments, but did not do so when the same compartments were arranged radially. To confirm that the differences in place field repetition across the parallel and radial compartments depended on their angular arrangement, and not incidental differences in access to an extra-maze visual landmark, we repeated the recordings in a second set of rats in the absence of the orientation landmark. We found, once again, that place fields showed repetition in parallel compartments, and did not do so in radially arranged compartments. Thus place field repetition, or lack thereof, in these compartments was not dependent on extra-maze cues. Together, these results imply that place field repetition constrains spatial learning.