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The predictive map hypothesis is a promising candidate principle for hippocampal function. A favoured formalisation of this hypothesis, called the successor representation, proposes that each place cell encodes the expected state occupancy of its target location in the near future. This predictive framework is supported by behavioural as well as electrophysiological evidence and has desirable consequences for both the generalisability and efficiency of reinforcement learning algorithms. However, it is unclear how the successor representation might be learnt in the brain. Error-driven temporal difference learning, commonly used to learn successor representations in artificial agents, is not known to be implemented in hippocampal networks. Instead, we demonstrate that spike-timing dependent plasticity (STDP), a form of Hebbian learning, acting on temporally compressed trajectories known as 'theta sweeps', is sufficient to rapidly learn a close approximation to the successor representation. The model is biologically plausible - it uses spiking neurons modulated by theta-band oscillations, diffuse and overlapping place cell-like state representations, and experimentally matched parameters. We show how this model maps onto known aspects of hippocampal circuitry and explains substantial variance in the temporal difference successor matrix, consequently giving rise to place cells that demonstrate experimentally observed successor representation-related phenomena including backwards expansion on a 1D track and elongation near walls in 2D. Finally, our model provides insight into the observed topographical ordering of place field sizes along the dorsal-ventral axis by showing this is necessary to prevent the detrimental mixing of larger place fields, which encode longer timescale successor representations, with more fine-grained predictions of spatial location., Competing Interests: TG, Wd, CB No competing interests declared, KS is affiliated with DeepMind. The author has no financial interests to declare, (© 2023, George, de Cothi et al.)

Grid cells have been proposed to encode both the self-location of an animal and the relative position of locations within an environment. We reassess the validity of these roles in light of recent evidence demonstrating grid patterns to be less temporally and spatially stable than previously thought., (Copyright © 2016 The Authors. Published by Elsevier Ltd.. All rights reserved.)

A recent study has found that the periodic spatial activity of grid cells is completely degraded when animals are moved passively around an enclosure, strengthening the view that grid-firing is generated on the basis of self-motion information., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

Mammals are able to navigate to hidden goal locations by direct routes that may traverse previously unvisited terrain. Empirical evidence suggests that this "vector navigation" relies on an internal representation of space provided by the hippocampal formation. The periodic spatial firing patterns of grid cells in the hippocampal formation offer a compact combinatorial code for location within large-scale space. Here, we consider the computational problem of how to determine the vector between start and goal locations encoded by the firing of grid cells when this vector may be much longer than the largest grid scale. First, we present an algorithmic solution to the problem, inspired by the Fourier shift theorem. Second, we describe several potential neural network implementations of this solution that combine efficiency of search and biological plausibility. Finally, we discuss the empirical predictions of these implementations and their relationship to the anatomy and electrophysiology of the hippocampal formation., (Copyright © 2015 The Authors. Published by Elsevier Inc. All rights reserved.)

Grid cells represent an animal's location by firing in multiple fields arranged in a striking hexagonal array. Such an impressive and constant regularity prompted suggestions that grid cells represent a universal and environmental-invariant metric for navigation. Originally the properties of grid patterns were believed to be independent of the shape of the environment and this notion has dominated almost all theoretical grid cell models. However, several studies indicate that environmental boundaries influence grid firing, though the strength, nature and longevity of this effect is unclear. Here we show that grid orientation, scale, symmetry and homogeneity are strongly and permanently affected by environmental geometry. We found that grid patterns orient to the walls of polarized enclosures such as squares, but not circles. Furthermore, the hexagonal grid symmetry is permanently broken in highly polarized environments such as trapezoids, the pattern being more elliptical and less homogeneous. Our results provide compelling evidence for the idea that environmental boundaries compete with the internal organization of the grid cell system to drive grid firing. Notably, grid cell activity is more local than previously thought and as a consequence cannot provide a universal spatial metric in all environments.

The unitary firing fields of hippocampal place cells are commonly assumed to be generated by input from entorhinal grid cell modules with differing spatial scales. Here, we review recent research that brings this assumption into doubt. Instead, we propose that place cell spatial firing patterns are determined by environmental sensory inputs, including those representing the distance and direction to environmental boundaries, while grid cells provide a complementary self-motion related input that contributes to maintaining place cell firing. In this view, grid and place cell firing patterns are not successive stages of a processing hierarchy, but complementary and interacting representations that work in combination to support the reliable coding of large-scale space., (Copyright © 2014 Elsevier Ltd. All rights reserved.)

We examined the accuracy with which the location of an agent moving within an environment could be decoded from the simulated firing of systems of grid cells. Grid cells were modelled with Poisson spiking dynamics and organized into multiple 'modules' of cells, with firing patterns of similar spatial scale within modules and a wide range of spatial scales across modules. The number of grid cells per module, the spatial scaling factor between modules and the size of the environment were varied. Errors in decoded location can take two forms: small errors of precision and larger errors resulting from ambiguity in decoding periodic firing patterns. With enough cells per module (e.g. eight modules of 100 cells each) grid systems are highly robust to ambiguity errors, even over ranges much larger than the largest grid scale (e.g. over a 500 m range when the maximum grid scale is 264 cm). Results did not depend strongly on the precise organization of scales across modules (geometric, co-prime or random). However, independent spatial noise across modules, which would occur if modules receive independent spatial inputs and might increase with spatial uncertainty, dramatically degrades the performance of the grid system. This effect of spatial uncertainty can be mitigated by uniform expansion of grid scales. Thus, in the realistic regimes simulated here, the optimal overall scale for a grid system represents a trade-off between minimizing spatial uncertainty (requiring large scales) and maximizing precision (requiring small scales). Within this view, the temporary expansion of grid scales observed in novel environments may be an optimal response to increased spatial uncertainty induced by the unfamiliarity of the available spatial cues.

We examined simultaneously recorded spikes from multiple rat grid cells, to explain mechanisms underlying their activity. Among grid cells with similar spatial periods, the population activity was confined to lie close to a two-dimensional (2D) manifold: grid cells differed only along two dimensions of their responses and otherwise were nearly identical. Relationships between cell pairs were conserved despite extensive deformations of single-neuron responses. Results from novel environments suggest such structure is not inherited from hippocampal or external sensory inputs. Across conditions, cell-cell relationships are better conserved than responses of single cells. Finally, the system is continually subject to perturbations that, were the 2D manifold not attractive, would drive the system to inhabit a different region of state space than observed. These findings have strong implications for theories of grid-cell activity and substantiate the general hypothesis that the brain computes using low-dimensional continuous attractors.

How do we know where we are? Orientation in space is key to our daily existence as we follow familiar routes, navigate to a previous location, or just try to get home as quickly as possible. As well as being interesting in its own right, spatial cognition is also a useful model system in which to understand the neural bases of cognition and memory formation more generally. Spatial behavior offers potentially straightforward correlates of neuronal activity that can be studied similarly in adults and infants of both human and non-human animals. The neural mechanisms of spatial behavior can be realistically investigated in a well-controlled way with the aid of virtual reality technologies in humans and rodents. Virtual reality can thus help to bridge the gap between electrophysiological studies in rodents and brain imaging studies using functional magnetic resonance imaging in humans. Within this framework, this article aims to translate findings from the single cell level in rodents to understand the neural and systems level mechanisms of spatial cognition in the human brain.

Grid cells in the entorhinal cortex of freely moving rats provide a strikingly periodic representation of self-location which is indicative of very specific computational mechanisms. However, the existence of grid cells in humans and their distribution throughout the brain are unknown. Here we show that the preferred firing directions of directionally modulated grid cells in rat entorhinal cortex are aligned with the grids, and that the spatial organization of grid-cell firing is more strongly apparent at faster than slower running speeds. Because the grids are also aligned with each other, we predicted a macroscopic signal visible to functional magnetic resonance imaging (fMRI) in humans. We then looked for this signal as participants explored a virtual reality environment, mimicking the rats' foraging task: fMRI activation and adaptation showing a speed-modulated six-fold rotational symmetry in running direction. The signal was found in a network of entorhinal/subicular, posterior and medial parietal, lateral temporal and medial prefrontal areas. The effect was strongest in right entorhinal cortex, and the coherence of the directional signal across entorhinal cortex correlated with spatial memory performance. Our study illustrates the potential power of combining single-unit electrophysiology with fMRI in systems neuroscience. Our results provide evidence for grid-cell-like representations in humans, and implicate a specific type of neural representation in a network of regions which supports spatial cognition and also autobiographical memory.

The firing pattern of entorhinal 'grid cells' is thought to provide an intrinsic metric for space. We report a strong experience-dependent environmental influence: the spatial scales of the grids (which are aligned and have fixed relative sizes within each animal) vary parametrically with changes to a familiar environment's size and shape. Thus grid scale reflects an interaction between intrinsic, path-integrative calculation of location and learned associations to the external environment.

Following Hartley et al. (Hartley et al. (2000) Hippocampus 10:369-379), we present a simple feed-forward model of place cell (PC) firing predicated on neocortical information regarding the environmental geometry surrounding the animal. Incorporating the idea of boundaries with distinct sensory qualities, we show that synaptic plasticity mediated by a BCM-like rule (Bienenstock et al. (1982) J Neurosci 2:32-48) produces PCs that encode position relative to specific extended landmarks. In an unchanging environment the model is shown to undergo an initial phase of learning, resulting in the formation of stable place fields. In familiar environments, perturbation of environmental cues produces graded changes in the firing rate and position of place fields. Model simulations are compared favorably with three sets of experimental data: (1) Results published by Barry et al. (Barry et al. (2006) Rev Neurosci 17:71-97) showing the slow disappearance of duplicate place fields produced when a barrier is placed into a familiar environment. (2) Rivard et al.'s (Rivard et al. (2004) J Gen Physiol 124:9-25) study showing a graded response in PC firing such that fields near to a centrally placed object encode space relative to the object, whereas more distant fields respond to the surrounding environment. (3) Fenton et al.'s (Fenton et al. (2000a) J Gen Physiol 116:191-209) observation that inconsistent rotation of cue cards produces parametric changes in place field positions. The merits of the model are discussed in terms of its extensibility and biological plausibility., ((c) 2007 Wiley-Liss, Inc.)

We expand upon our proposal that the oscillatory interference mechanism proposed for the phase precession effect in place cells underlies the grid-like firing pattern of dorsomedial entorhinal grid cells (O'Keefe and Burgess (2005) Hippocampus 15:853-866). The original one-dimensional interference model is generalized to an appropriate two-dimensional mechanism. Specifically, dendritic subunits of layer II medial entorhinal stellate cells provide multiple linear interference patterns along different directions, with their product determining the firing of the cell. Connection of appropriate speed- and direction-dependent inputs onto dendritic subunits could result from an unsupervised learning rule which maximizes postsynaptic firing (e.g. competitive learning). These inputs cause the intrinsic oscillation of subunit membrane potential to increase above theta frequency by an amount proportional to the animal's speed of running in the "preferred" direction. The phase difference between this oscillation and a somatic input at theta-frequency essentially integrates velocity so that the interference of the two oscillations reflects distance traveled in the preferred direction. The overall grid pattern is maintained in environmental location by phase reset of the grid cell by place cells receiving sensory input from the environment, and environmental boundaries in particular. We also outline possible variations on the basic model, including the generation of grid-like firing via the interaction of multiple cells rather than via multiple dendritic subunits. Predictions of the interference model are given for the frequency composition of EEG power spectra and temporal autocorrelograms of grid cell firing as functions of the speed and direction of running and the novelty of the environment., ((c) 2007 Wiley-Liss, Inc.)

We review evidence for the boundary vector cell model of the environmental determinants of the firing of hippocampal place cells. Preliminary experimental results are presented concerning the effects of addition or removal of environmental boundaries on place cell firing and evidence that boundary vector cells may exist in the subiculum. We review and update computational simulations predicting the location of human search within a virtual environment of variable geometry, assuming that boundary vector cells provide one of the input representations of location used in mammalian spatial memory. Finally, we extend the model to include experience-dependent modification of connection strengths through a BCM-like learning rule - the size and sign of strength change is influenced by historic activity of the postsynaptic cell. Simulations are compared to experimental data on the firing of place cells under geometrical manipulations to their environment. The relationship between neurophysiological results in rats and spatial behaviour in humans is discussed.

Place cells in the mammalian hippocampus signal self-location with sparse spatially stable firing fields. Based on observation of place cell activity it is possible to accurately decode an animal’s location. The precision of this decoding sets a lower bound for the amount of information that the hippocampal population conveys about the location of the animal. In this work we use a novel recurrent neural network (RNN) decoder to infer the location of freely moving rats from single unit hippocampal recordings. RNNs are biologically plausible models of neural circuits that learn to incorporate relevant temporal context without the need to make complicated assumptions about the use of prior information to predict the current state. When decoding animal position from spike counts in 1D and 2D-environments, we show that the RNN consistently outperforms a standard Bayesian approach with either flat priors or with memory. In addition, we also conducted a set of sensitivity analysis on the RNN decoder to determine which neurons and sections of firing fields were the most influential. We found that the application of RNNs to neural data allowed flexible integration of temporal context, yielding improved accuracy relative to the more commonly used Bayesian approaches and opens new avenues for exploration of the neural code. [ABSTRACT FROM AUTHOR]

Precisely timed interactions between hippocampal and cortical neurons during replay epochs are thought to support learning. Indeed, research has shown that replay is associated with heightened hippocampal-cortical synchrony. Yet many caveats remain in our understanding. Namely, it remains unclear how this offline synchrony comes about, whether it is specific to particular behavioral states, and how—if at all—it relates to learning. In this study, we sought to address these questions by analyzing coordination between CA1 cells and neurons of the deep layers of the medial entorhinal cortex (dMEC) while rats learned a novel spatial task. During movement, we found a subset of dMEC cells that were particularly locked to hippocampal LFP theta-band oscillations and that were preferentially coordinated with hippocampal replay during offline periods. Further, dMEC synchrony with CA1 replay peaked ∼10 ms after replay initiation in CA1, suggesting that the distributed replay reflects extra-hippocampal information propagation and is specific to "offline" periods. Finally, theta-modulated dMEC cells showed a striking experience-dependent increase in synchronization with hippocampal replay trajectories, mirroring the animals' acquisition of the novel task and coupling to the hippocampal local field. Together, these findings provide strong support for the hypothesis that synergistic hippocampal-cortical replay supports learning and highlights phase locking to hippocampal theta oscillations as a potential mechanism by which such cross-structural synchrony comes about. • Spatially tuned dMEC cells display mixed coupling to hippocampal theta oscillations • Theta-coupled dMEC cells are preferentially coordinated with hippocampal replay • dMEC-hippocampal replay coordination is specific to rest periods • The coordination increases in tandem with the animals' ability to carry out a task Santos-Pata et al. report that spatially modulated dMEC cells that are locked to hippocampal theta-band oscillations preferentially coordinate with hippocampal replay recorded during rest periods. The replay coordination only emerges after an animal's first encounter with the task environment and then shows a learned-related increase. [ABSTRACT FROM AUTHOR]