A boundary vector cell model of place field repetition

Navigation and the efficiency of spatial coding: insights from closed-loop simulations

Spatial learning is critical for survival and its underlying neuronal mechanisms have been studied extensively. These studies have revealed a wealth of information about the neural representations of space, such as place cells and boundary cells. While many studies have focused on how these representations emerge in the brain, their functional role in driving spatial learning and navigation has received much less attention. We extended an existing computational modeling tool-chain to study the functional role of spatial representations using closed-loop simulations of spatial learning. At the heart of the model agent was a spiking neural network that formed a ring attractor. This network received inputs from place and boundary cells and the location of the activity bump in this network was the output. This output determined the movement directions of the agent. We found that the navigation performance depended on the parameters of the place cell input, such as their number, the place field sizes, and peak firing rate, as well as, unsurprisingly, the size of the goal zone. The dependence on the place cell parameters could be accounted for by just a single variable, the overlap index, but this dependence was nonmonotonic. By contrast, performance scaled monotonically with the Fisher information of the place cell population. Our results therefore demonstrate that efficiently encoding spatial information is critical for navigation performance.

Learning to predict future locations with internally generated theta sequences

Representing past, present and future locations is key for spatial navigation. Indeed, within each cycle of the theta oscillation, the population of hippocampal place cells appears to represent trajectories starting behind the current position of the animal and sweeping ahead of it. In particular, we reported recently that the position represented by CA1 place cells at a given theta phase corresponds to the location where animals were or will be located at a fixed time interval into the past or future assuming the animal ran at its typical, not the current, speed through that part of the environment. This coding scheme leads to longer theta trajectories, larger place fields and shallower phase precession in areas where animals typically run faster. Here we present a mechanistic computational model that accounts for these experimental observations. The model consists of a continuous attractor network with short-term synaptic facilitation and depression that internally generates theta sequences that advance at a fixed pace. Spatial locations are then mapped onto the active units via modified Hebbian plasticity. As a result, neighboring units become associated with spatial locations further apart where animals run faster, reproducing our earlier experimental results. The model also accounts for the higher density of place fields generally observed where animals slow down, such as around rewards. Furthermore, our modeling results reveal that an artifact of the decoding analysis might be partly responsible for the observation that theta trajectories start behind the animal's current position. Overall, our results shed light on how the hippocampal code might arise from the interplay between behavior, sensory input and predefined network dynamics.

Rapid learning of spatial representations for goal-directed navigation based on a novel model of hippocampal place fields

The discovery of place cells and other spatially modulated neurons in the hippocampal complex of rodents has been crucial to elucidating the neural basis of spatial cognition. More recently, the replay of neural sequences encoding previously experienced trajectories has been observed during consummatory behavior-potentially with implications for rapid learning, quick memory consolidation, and behavioral planning. Several promising models for robotic navigation and reinforcement learning have been proposed based on these and previous findings. Most of these models, however, use carefully engineered neural networks, and sometimes require long learning periods. In this paper, we present a self-organizing model incorporating place cells and replay, and demonstrate its utility for rapid one-shot learning in non-trivial environments with obstacles.

Spatial goal coding in the hippocampal formation

The mammalian hippocampal formation contains several distinct populations of neurons involved in representing self-position and orientation. These neurons, which include place, grid, head direction, and boundary-vector cells, are thought to collectively instantiate cognitive maps supporting flexible navigation. However, to flexibly navigate, it is necessary to also maintain internal representations of goal locations, such that goal-directed routes can be planned and executed. Although it has remained unclear how the mammalian brain represents goal locations, multiple neural candidates have recently been uncovered during different phases of navigation. For example, during planning, sequential activation of spatial cells may enable simulation of future routes toward the goal. During travel, modulation of spatial cells by the prospective route, or by distance and direction to the goal, may allow maintenance of route and goal-location information, supporting navigation on an ongoing basis. As the goal is approached, an increased activation of spatial cells may enable the goal location to become distinctly represented within cognitive maps, aiding goal localization. Lastly, after arrival at the goal, sequential activation of spatial cells may represent the just-taken route, enabling route learning and evaluation. Here, we review and synthesize these and other evidence for goal coding in mammalian brains, relate the experimental findings to predictions from computational models, and discuss outstanding questions and future challenges.

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.

A general model of hippocampal and dorsal striatal learning and decision making

Humans and other animals use multiple strategies for making decisions. Reinforcement-learning theory distinguishes between stimulus-response (model-free; MF) learning and deliberative (model-based; MB) planning. The spatial-navigation literature presents a parallel dichotomy between navigation strategies. In "response learning," associated with the dorsolateral striatum (DLS), decisions are anchored to an egocentric reference frame. In "place learning," associated with the hippocampus, decisions are anchored to an allocentric reference frame. Emerging evidence suggests that the contribution of hippocampus to place learning may also underlie its contribution to MB learning by representing relational structure in a cognitive map. Here, we introduce a computational model in which hippocampus subserves place and MB learning by learning a "successor representation" of relational structure between states; DLS implements model-free response learning by learning associations between actions and egocentric representations of landmarks; and action values from either system are weighted by the reliability of its predictions. We show that this model reproduces a range of seemingly disparate behavioral findings in spatial and nonspatial decision tasks and explains the effects of lesions to DLS and hippocampus on these tasks. Furthermore, modeling place cells as driven by boundaries explains the observation that, unlike navigation guided by landmarks, navigation guided by boundaries is robust to "blocking" by prior state-reward associations due to learned associations between place cells. Our model, originally shaped by detailed constraints in the spatial literature, successfully characterizes the hippocampal-striatal system as a general system for decision making via adaptive combination of stimulus-response learning and the use of a cognitive map.

Neuronal vector coding in spatial cognition

Several types of neurons involved in spatial navigation and memory encode the distance and direction (that is, the vector) between an agent and items in its environment. Such vectorial information provides a powerful basis for spatial cognition by representing the geometric relationships between the self and the external world. Here, we review the explicit encoding of vectorial information by neurons in and around the hippocampal formation, far from the sensory periphery. The parahippocampal, retrosplenial and parietal cortices, as well as the hippocampal formation and striatum, provide a plethora of examples of vector coding at the single neuron level. We provide a functional taxonomy of cells with vectorial receptive fields as reported in experiments and proposed in theoretical work. The responses of these neurons may provide the fundamental neural basis for the (bottom-up) representation of environmental layout and (top-down) memory-guided generation of visuospatial imagery and navigational planning.

Neurobiological successor features for spatial navigation

The hippocampus has long been observed to encode a representation of an animal's position in space. Recent evidence suggests that the nature of this representation is somewhat predictive and can be modeled by learning a successor representation (SR) between distinct positions in an environment. However, this discretization of space is subjective making it difficult to formulate predictions about how some environmental manipulations should impact the hippocampal representation. Here, we present a model of place and grid cell firing as a consequence of learning a SR from a basis set of known neurobiological features—boundary vector cells (BVCs). The model describes place cell firing as the successor features of the SR, with grid cells forming a low‐dimensional representation of these successor features. We show that the place and grid cells generated using the BVC‐SR model provide a good account of biological data for a variety of environmental manipulations, including dimensional stretches, barrier insertions, and the influence of environmental geometry on the hippocampal representation of space.

The Neurobiology of Mammalian Navigation

Mammals have evolved specialized brain systems to support efficient navigation within diverse habitats and over varied distances, but while navigational strategies and sensory mechanisms vary across species, core spatial components appear to be widely shared. This review presents common elements found in mammalian spatial mapping systems, focusing on the cells in the hippocampal formation representing orientational and locational spatial information, and 'core' mammalian hippocampal circuitry. Mammalian spatial mapping systems make use of both allothetic cues (space-defining cues in the external environment) and idiothetic cues (cues derived from self-motion). As examples of each cue type, we discuss: environmental boundaries, which control both orientational and locational neuronal activity and behaviour; and 'path integration', a process that allows the estimation of linear translation from velocity signals, thought to depend upon grid cells in the entorhinal cortex. Building cognitive maps entails sampling environments: we consider how the mapping system controls exploration to acquire spatial information, and how exploratory strategies may integrate idiothetic with allothetic information. We discuss how 'replay' may act to consolidate spatial maps, and simulate trajectories to aid navigational planning. Finally, we discuss grid cell models of vector navigation.

Neural Dynamics Indicate Parallel Integration of Environmental and Self-Motion Information by Place and Grid Cells

Place cells and grid cells in the hippocampal formation are thought to integrate sensory and self-motion information into a representation of estimated spatial location, but the precise mechanism is unknown. We simulated a parallel attractor system in which place cells form an attractor network driven by environmental inputs and grid cells form an attractor network performing path integration driven by self-motion, with inter-connections between them allowing both types of input to influence firing in both ensembles. We show that such a system is needed to explain the spatial patterns and temporal dynamics of place cell firing when rats run on a linear track in which the familiar correspondence between environmental and self-motion inputs is changed. In contrast, the alternative architecture of a single recurrent network of place cells (performing path integration and receiving environmental inputs) cannot reproduce the place cell firing dynamics. These results support the hypothesis that grid and place cells provide two different but complementary attractor representations (based on self-motion and environmental sensory inputs, respectively). Our results also indicate the specific neural mechanism and main predictors of hippocampal map realignment and make predictions for future studies.