The Structure of Hippocampal CA1 Interactions Optimizes Spatial Coding across Experience

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

Flexible coding of time or distance in hippocampal cells

Analysis of neuronal activity in the hippocampus of behaving animals has revealed cells acting as 'Time Cells', which exhibit selective spiking patterns at specific time intervals since a triggering event, and 'Distance Cells', which encode the traversal of specific distances. Other neurons exhibit a combination of these features, alongside place selectivity. This study aims to investigate how the task performed by animals during recording sessions influences the formation of these representations. We analyzed data from a treadmill running study conducted by Kraus et al., 2013, in which rats were trained to run at different velocities. The rats were recorded in two trial contexts: a 'fixed time' condition, where the animal ran on the treadmill for a predetermined duration before proceeding, and a 'fixed distance' condition, where the animal ran a specific distance on the treadmill. Our findings indicate that the type of experimental condition significantly influenced the encoding of hippocampal cells. Specifically, distance-encoding cells dominated in fixed-distance experiments, whereas time-encoding cells dominated in fixed-time experiments. These results underscore the flexible coding capabilities of the hippocampus, which are shaped by over-representation of salient variables associated with reward conditions.

Optrode recording of an entorhinal-cortical circuit in freely moving mice

The deep layers of medial entorhinal cortex (MEC) are considered a crucial station for spatial cognition and memory. The deep sublayer Va of MEC (MECVa) serves as the output stage of the entorhinal-hippocampal system and sends extensive projections to brain cortical areas. However, the functional heterogeneity of these efferent neurons in MECVa is poorly understood, due to the difficulty of performing single-neuron activity recording from the narrow band of cell population while the animals are behaving. In the current study, we combined multi-electrode electrophysiological recording and optical stimulation to record cortical-projecting MECVa neurons at single-neuron resolution in freely moving mice. First, injection of a viral Cre-LoxP system was used to express channelrhodopsin-2 specifically in MECVa neurons that project to the medial part of the secondary visual cortex (V2M-projecting MECVa neurons). Then, a lightweight, self-made optrode was implanted into MECVa to identify the V2M-projecting MECVa neurons and to enable single-neuron activity recordings in mice performing the open field test and 8-arm radial maze. Our results demonstrate that optrode approach is an accessible and reliable method for single-neuron recording of V2M-projecting MECVa neurons in freely moving mice, paving the way for future circuit studies designed to characterize the activity of MECVa neurons during specific tasks.

The chicken and egg problem of grid cells and place cells

Place cells and grid cells are major building blocks of the hippocampal cognitive map. The prominent forward model postulates that grid-cell modules are generated by a continuous attractor network; that a velocity signal evoked during locomotion moves entorhinal activity bumps; and that place-cell activity constitutes summation of entorhinal grid-cell modules. Experimental data support the first postulate, but not the latter two. Several families of solutions that depart from these postulates have been put forward. We suggest a modified model (spatial modulation continuous attractor network; SCAN), whereby place cells are generated from spatially selective nongrid cells. Locomotion causes these cells to move the hippocampal activity bump, leading to movement of the entorhinal manifolds. Such inversion accords with the shift of hippocampal thought from navigation to more abstract functions.

Noise correlations in neural ensemble activity limit the accuracy of hippocampal spatial representations

Neurons in the CA1 area of the mouse hippocampus encode the position of the animal in an environment. However, given the variability in individual neurons responses, the accuracy of this code is still poorly understood. It was proposed that downstream areas could achieve high spatial accuracy by integrating the activity of thousands of neurons, but theoretical studies point to shared fluctuations in the firing rate as a potential limitation. Using high-throughput calcium imaging in freely moving mice, we demonstrated the limiting factors in the accuracy of the CA1 spatial code. We found that noise correlations in the hippocampus bound the estimation error of spatial coding to ~10 cm (the size of a mouse). Maximal accuracy was obtained using approximately [300-1400] neurons, depending on the animal. These findings reveal intrinsic limits in the brain's representations of space and suggest that single neurons downstream of the hippocampus can extract maximal spatial information from several hundred inputs.

Microcircuits for spatial coding in the medial entorhinal cortex

The hippocampal formation is critically involved in learning and memory and contains a large proportion of neurons encoding aspects of the organism's spatial surroundings. In the medial entorhinal cortex (MEC), this includes grid cells with their distinctive hexagonal firing fields as well as a host of other functionally defined cell types including head direction cells, speed cells, border cells, and object-vector cells. Such spatial coding emerges from the processing of external inputs by local microcircuits. However, it remains unclear exactly how local microcircuits and their dynamics within the MEC contribute to spatial discharge patterns. In this review we focus on recent investigations of intrinsic MEC connectivity, which have started to describe and quantify both excitatory and inhibitory wiring in the superficial layers of the MEC. Although the picture is far from complete, it appears that these layers contain robust recurrent connectivity that could sustain the attractor dynamics posited to underlie grid pattern formation. These findings pave the way to a deeper understanding of the mechanisms underlying spatial navigation and memory.

A Model of Spatial Cell Development in Rat Hippocampus Based on Artificial Neural Network

Physiological studies have shown that the hippocampal structure of rats develops at different stages, in which the place cells continue to develop during the whole juvenile period of rats and mature after the juvenile period. As the main information source of place cells, grid cells should mature earlier than place cells. In order to make better use of the biological information exhibited by the rat brain hippocampus in the environment, we propose a position cognition model based on the spatial cell development mechanism of rat hippocampus. The model uses a recurrent neural network with parametric bias (RNNPB) to simulate changes in the discharge characteristics during the development of a single stripe cell. The oscillatory interference mechanism is able to fuse the developing stripe waves, thus indirectly simulating the developmental process of the grid cells. The output of the grid cells is then used as the information input of the place cells, whose development process is simulated by BP neural network. After the place cells matured, the position matrix generated by the place cell group was used to realize the position cognition of rats in a given spatial region. The experimental results show that this model can simulate the development process of grid cells and place cells, and it can realize high precision positioning in the given space area. Moreover, the experimental effect of cognitive map construction using this model is basically consistent with the effect of RatSLAM, which verifies the validity and accuracy of the model.

Deep entorhinal cortex: from circuit organization to spatial cognition and memory

The deep layers of the entorhinal cortex are important for spatial cognition, as well as memory storage, consolidation and retrieval. A long-standing hypothesis is that deep-layer neurons relay spatial and memory-related signals between the hippocampus and telencephalon. We review the implications of recent circuit-level analyses that suggest more complex roles. The organization of deep entorhinal layers is consistent with multi-stage processing by specialized cell populations; in this framework, hippocampal, neocortical, and subcortical inputs are integrated to generate representations for use by targets in the telencephalon and for feedback to the superficial entorhinal cortex and hippocampus. Addressing individual sublayers of the deep entorhinal cortex in future experiments and models will be important for establishing systems-level mechanisms for spatial cognition and episodic memory.

Recurrent amplification of grid-cell activity

High-level cognitive abilities such as navigation and spatial memory are thought to rely on the activity of grid cells in the medial entorhinal cortex (MEC), which encode the animal's position in space with periodic triangular patterns. Yet the neural mechanisms that underlie grid-cell activity are still unknown. Recent in vitro and in vivo experiments indicate that grid cells are embedded in highly structured recurrent networks. But how could recurrent connectivity become structured during development? And what is the functional role of these connections? With mathematical modeling and simulations, we show that recurrent circuits in the MEC could emerge under the supervision of weakly grid-tuned feedforward inputs. We demonstrate that a learned excitatory connectivity could amplify grid patterns when the feedforward sensory inputs are available and sustain attractor states when the sensory cues are lost. Finally, we propose a Fourier-based measure to quantify the spatial periodicity of grid patterns: the grid-tuning index.

A Generalized Linear Model of a Navigation Network

Navigation by mammals is believed to rely on a network of neurons in the hippocampal formation, which includes the hippocampus, the medial entorhinal cortex (MEC), and additional nearby regions. Neurons in these regions represent spatial information by tuning to the position, orientation, and speed of the animal in the form of head direction cells, speed cells, grid cells, border cells, and unclassified spatially modulated cells. While the properties of single cells are well studied, little is known about the functional structure of the network in the MEC. Here, we use a generalized linear model to study the network of spatially modulated cells in the MEC. We found connectivity patterns between all spatially encoding cells and not only grid cells. In addition, the neurons’ past activity contributed to the overall activity patterns. Finally, position-modulated cells and head direction cells differed in the dependence of the activity on the history. Our results indicate that MEC neurons form a local interacting network to support spatial information representations and suggest an explanation for their complex temporal properties.

Toward a Unified Framework for Cognitive Maps

In this study, we integrated neural encoding and decoding into a unified framework for spatial information processing in the brain. Specifically, the neural representations of self-location in the hippocampus (HPC) and entorhinal cortex (EC) play crucial roles in spatial navigation. Intriguingly, these neural representations in these neighboring brain areas show stark differences. Whereas the place cells in the HPC fire as a unimodal function of spatial location, the grid cells in the EC show periodic tuning curves with different periods for different subpopulations (called modules). By combining an encoding model for this modular neural representation and a realistic decoding model based on belief propagation, we investigated the manner in which self-location is encoded by neurons in the EC and then decoded by downstream neurons in the HPC. Through the results of numerical simulations, we first show the positive synergy effects of the modular structure in the EC. The modular structure introduces more coupling between heterogeneous modules with different periodicities, which provides increased error-correcting capabilities. This is also demonstrated through a comparison of the beliefs produced for decoding two- and four-module codes. Whereas the former resulted in a complete decoding failure, the latter correctly recovered the self-location even from the same inputs. Further analysis of belief propagation during decoding revealed complex dynamics in information updates due to interactions among multiple modules having diverse scales. Therefore, the proposed unified framework allows one to investigate the overall flow of spatial information, closing the loop of encoding and decoding self-location in the brain.

Grid cells are modulated by local head direction

Grid and head direction codes represent cognitive spaces for navigation and memory. Pure grid cells generate grid codes that have been assumed to be independent of head direction, whereas conjunctive cells generate grid representations that are tuned to a single head direction. Here, we demonstrate that pure grid cells also encode head direction, but through distinct mechanisms. We show that individual firing fields of pure grid cells are tuned to multiple head directions, with the preferred sets of directions differing between fields. This local directional modulation is not predicted by previous continuous attractor or oscillatory interference models of grid firing but is accounted for by models in which pure grid cells integrate inputs from co-aligned conjunctive cells with firing rates that differ between their fields. We suggest that local directional signals from grid cells may contribute to downstream computations by decorrelating different points of view from the same location.

Untethered firing fields and intermittent silences: Why grid-cell discharge is so variable

Grid cells in medial entorhinal cortex are notoriously variable in their responses, despite the striking hexagonal arrangement of their spatial firing fields. Indeed, when the animal moves through a firing field, grid cells often fire much more vigorously than predicted or do not fire at all. The source of this trial-to-trial variability is not completely understood. By analyzing grid-cell spike trains from mice running in open arenas and on linear tracks, we characterize the phenomenon of "missed" firing fields using the statistical theory of zero inflation. We find that one major cause of grid-cell variability lies in the spatial representation itself: firing fields are not as strongly anchored to spatial location as the averaged grid suggests. In addition, grid fields from different cells drift together from trial to trial, regardless of whether the environment is real or virtual, or whether the animal moves in light or darkness. Spatial realignment across trials sharpens the grid representation, yielding firing fields that are more pronounced and significantly narrower. These findings indicate that ensembles of grid cells encode relative position more reliably than absolute position.

Spatial Navigation

The hippocampus is critical for spatial navigation. In this review, we focus on the role of the hippocampus in three basic strategies used for spatial navigation: path integration, stimulus-response association, and map-based navigation. First, the hippocampus is not required for path integration unless the path of path integration is too long and complex. The hippocampus provides mnemonic support when involved in the process of path integration. Second, the hippocampus's involvement in stimulus-response association is dependent on how the strategy is conducted. The hippocampus is not required for the habit form of stimulus-response association. Third, while the hippocampus is fully engaged in map-based navigation, the shared characteristics of place cells, grid cells, head direction cells, and other spatial encoding cells, which are detected in the hippocampus and associated areas, offer a possibility that there is a stand-alone allocentric space perception (or mental representation) of the environment outside and independent of the hippocampus, and the spatially specific firing patterns of these spatial encoding cells are the unfolding of the intermediate stages of the processing of this allocentric spatial information when conveyed into the hippocampus for information storage or retrieval. Furthermore, the presence of all the spatially specific firing patterns in the hippocampus and the related neural circuits during the path integration and map-based navigation support such a notion that in essence, path integration is the same allocentric space perception provided with only idiothetic inputs. Taken together, the hippocampus plays a general mnemonic role in spatial navigation.

During hippocampal inactivation, grid cells maintain synchrony, even when the grid pattern is lost

The grid cell network in the medial entorhinal cortex (MEC) has been subject to thorough testing and analysis, and many theories for their formation have been suggested. To test some of these theories, we re-analyzed data from Bonnevie et al., 2013, in which the hippocampus was inactivated and grid cells were recorded in the rat MEC. We investigated whether the firing associations of grid cells depend on hippocampal inputs. Specifically, we examined temporal and spatial correlations in the firing times of simultaneously recorded grid cells before and during hippocampal inactivation. Our analysis revealed evidence of network coherence in grid cells even in the absence of hippocampal input to the MEC, both in regular grid cells and in those that became head-direction cells after hippocampal inactivation. This favors models, which suggest that phase relations between grid cells in the MEC are dependent on intrinsic connectivity within the MEC.

A geometric attractor mechanism for self-organization of entorhinal grid modules

Grid cells in the medial entorhinal cortex (MEC) respond when an animal occupies a periodic lattice of 'grid fields' in the environment. The grids are organized in modules with spatial periods, or scales, clustered around discrete values separated on average by ratios in the range 1.4-1.7. We propose a mechanism that produces this modular structure through dynamical self-organization in the MEC. In attractor network models of grid formation, the grid scale of a single module is set by the distance of recurrent inhibition between neurons. We show that the MEC forms a hierarchy of discrete modules if a smooth increase in inhibition distance along its dorso-ventral axis is accompanied by excitatory interactions along this axis. Moreover, constant scale ratios between successive modules arise through geometric relationships between triangular grids and have values that fall within the observed range. We discuss how interactions required by our model might be tested experimentally.

Structural modularity and grid activity in the medial entorhinal cortex

Following the groundbreaking discovery of grid cells, the medial entorhinal cortex (MEC) has become the focus of intense anatomical, physiological, and computational investigations. Whether and how grid activity maps onto cell types and cortical architecture is still an open question. Fundamental similarities in microcircuits, function, and connectivity suggest a homology between rodent MEC and human posteromedial entorhinal cortex. Both are specialized for spatial processing and display similar cellular organization, consisting of layer 2 pyramidal/calbindin cell patches superimposed on scattered stellate neurons. Recent data indicate the existence of a further nonoverlapping modular system (zinc patches) within the superficial MEC layers. Zinc and calbindin patches have been shown to receive largely segregated inputs from the presubiculum and parasubiculum. Grid cells are also clustered in the MEC, and we discuss possible structure-function schemes on how grid activity could map onto cortical patch systems. We hypothesize that in the superficial layers of the MEC, anatomical location can be predictive of function; thus relating functional properties and neuronal morphologies to the cortical modules will be necessary for resolving how grid activity maps onto cortical architecture. Imaging or cell identification approaches in freely moving animals will be required for testing this hypothesis.

Spatial representation in the hippocampal formation: a history

Since the first place cell was recorded and the cognitive-map theory was subsequently formulated, investigation of spatial representation in the hippocampal formation has evolved in stages. Early studies sought to verify the spatial nature of place cell activity and determine its sensory origin. A new epoch started with the discovery of head direction cells and the realization of the importance of angular and linear movement-integration in generating spatial maps. A third epoch began when investigators turned their attention to the entorhinal cortex, which led to the discovery of grid cells and border cells. This review will show how ideas about integration of self-motion cues have shaped our understanding of spatial representation in hippocampal-entorhinal systems from the 1970s until today. It is now possible to investigate how specialized cell types of these systems work together, and spatial mapping may become one of the first cognitive functions to be understood in mechanistic detail.

A single-cell spiking model for the origin of grid-cell patterns

Spatial cognition in mammals is thought to rely on the activity of grid cells in the entorhinal cortex, yet the fundamental principles underlying the origin of grid-cell firing are still debated. Grid-like patterns could emerge via Hebbian learning and neuronal adaptation, but current computational models remained too abstract to allow direct confrontation with experimental data. Here, we propose a single-cell spiking model that generates grid firing fields via spike-rate adaptation and spike-timing dependent plasticity. Through rigorous mathematical analysis applicable in the linear limit, we quantitatively predict the requirements for grid-pattern formation, and we establish a direct link to classical pattern-forming systems of the Turing type. Our study lays the groundwork for biophysically-realistic models of grid-cell activity.

Parvalbumin and Somatostatin Interneurons Control Different Space-Coding Networks in the Medial Entorhinal Cortex

The medial entorhinal cortex (MEC) contains several discrete classes of GABAergic interneurons, but their specific contributions to spatial pattern formation in this area remain elusive. We employed a pharmacogenetic approach to silence either parvalbumin (PV)- or somatostatin (SOM)-expressing interneurons while MEC cells were recorded in freely moving mice. PV-cell silencing antagonized the hexagonally patterned spatial selectivity of grid cells, especially in layer II of MEC. The impairment was accompanied by reduced speed modulation in colocalized speed cells. Silencing SOM cells, in contrast, had no impact on grid cells or speed cells but instead decreased the spatial selectivity of cells with discrete aperiodic firing fields. Border cells and head direction cells were not affected by either intervention. The findings point to distinct roles for PV and SOM interneurons in the local dynamics underlying periodic and aperiodic firing in spatially modulated cells of the MEC.

Video Abstract

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Parvalbumin (PV) interneurons maintain spatially periodic firing in grid cells

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PV interneurons are necessary for speed tuning in entorhinal speed cells

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Somatostatin (SOM) interneurons maintain selectivity of aperiodic spatial cells

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PV and SOM cells regulate discrete subsets of spatially tuned entorhinal cell types

Theta sequences of grid cell populations can provide a movement-direction signal

It has been proposed that path integration in mammals is performed by the convergence of internally generated speed and directional inputs onto grid cells. Although this hypothesis has been supported by the discovery that head direction, speed, and grid cells are intermixed within entorhinal cortex and by the recent finding that head-direction inputs are necessary for grid firing, many details on how grid cells are generated have remained elusive. For example, analysis of recording data suggests that substituting head direction for movement direction accrues errors that preclude the formation of grid patterns. To address this discrepancy, we propose that the organization of grid networks makes it plausible that movement-direction signals are an output from grid cells and that temporally precise grid cell sequences provide a robust directional signal to other spatial and directional cell types.

Layer-Specific Organization of Local Excitatory and Inhibitory Synaptic Connectivity in the Rat Presubiculum

The presubiculum is part of the parahippocampal spatial navigation system and contains head direction and grid cells upstream of the medial entorhinal cortex. This position within the parahippocampal cortex renders the presubiculum uniquely suited for analyzing the circuit requirements underlying the emergence of spatially tuned neuronal activity. To identify the local circuit properties, we analyzed the topology of synaptic connections between pyramidal cells and interneurons in all layers of the presubiculum by testing 4250 potential synaptic connections using multiple whole-cell recordings of up to 8 cells simultaneously. Network topology showed layer-specific organization of microcircuits consistent with the prevailing distinction of superficial and deep layers. While connections among pyramidal cells were almost absent in superficial layers, deep layers exhibited an excitatory connectivity of 3.9%. In contrast, synaptic connectivity for inhibition was higher in superficial layers though markedly lower than in other cortical areas. Finally, synaptic amplitudes of both excitatory and inhibitory connections showed log-normal distributions suggesting a nonrandom functional connectivity. In summary, our study provides new insights into the microcircuit organization of the presubiculum by revealing area- and layer-specific connectivity rules and sets new constraints for future models of the parahippocampal navigation system.

Probabilistic Learning by Rodent Grid Cells

Mounting evidence shows mammalian brains are probabilistic computers, but the specific cells involved remain elusive. Parallel research suggests that grid cells of the mammalian hippocampal formation are fundamental to spatial cognition but their diverse response properties still defy explanation. No plausible model exists which explains stable grids in darkness for twenty minutes or longer, despite being one of the first results ever published on grid cells. Similarly, no current explanation can tie together grid fragmentation and grid rescaling, which show very different forms of flexibility in grid responses when the environment is varied. Other properties such as attractor dynamics and grid anisotropy seem to be at odds with one another unless additional properties are assumed such as a varying velocity gain. Modelling efforts have largely ignored the breadth of response patterns, while also failing to account for the disastrous effects of sensory noise during spatial learning and recall, especially in darkness. Here, published electrophysiological evidence from a range of experiments are reinterpreted using a novel probabilistic learning model, which shows that grid cell responses are accurately predicted by a probabilistic learning process. Diverse response properties of probabilistic grid cells are statistically indistinguishable from rat grid cells across key manipulations. A simple coherent set of probabilistic computations explains stable grid fields in darkness, partial grid rescaling in resized arenas, low-dimensional attractor grid cell dynamics, and grid fragmentation in hairpin mazes. The same computations also reconcile oscillatory dynamics at the single cell level with attractor dynamics at the cell ensemble level. Additionally, a clear functional role for boundary cells is proposed for spatial learning. These findings provide a parsimonious and unified explanation of grid cell function, and implicate grid cells as an accessible neuronal population readout of a set of probabilistic spatial computations.

Cells in the mammalian hippocampal formation are thought to be central for spatial learning and stable spatial representations. Of the known spatial cells, grid cells form strikingly regular and stable patterns of activity, even in darkness. Hence, grid cells may provide the universal metric upon which spatial cognition is based. However, a more fundamental problem is how grids themselves may form and stabilise, since sensory information is noisy and can vary tremendously with environmental conditions. Furthermore, the same grid cell can display substantially different yet stable patterns of activity in different environments. Currently, no model explains how vastly different sensory cues can give rise to the diverse but stable grid patterns. Here, a new probabilistic model is proposed which combines information encoded by grid cells and boundary cells. This noise-tolerant model performs robust spatial learning, under a variety of conditions, and produces varied yet stable grid cell response patterns like rodent grid cells. Across numerous experimental manipulations, rodent and probabilistic grid cell responses are similar or even statistically indistinguishable. These results complement a growing body of evidence suggesting that mammalian brains are inherently probabilistic, and suggest for the first time that grid cells may be involved.

Ten Years of Grid Cells

The medial entorhinal cortex (MEC) creates a neural representation of space through a set of functionally dedicated cell types: grid cells, border cells, head direction cells, and speed cells. Grid cells, the most abundant functional cell type in the MEC, have hexagonally arranged firing fields that tile the surface of the environment. These cells were discovered only in 2005, but after 10 years of investigation, we are beginning to understand how they are organized in the MEC network, how their periodic firing fields might be generated, how they are shaped by properties of the environment, and how they interact with the rest of the MEC network. The aim of this review is to summarize what we know about grid cells and point out where our knowledge is still incomplete.

Extracting grid cell characteristics from place cell inputs using non-negative principal component analysis

Many recent models study the downstream projection from grid cells to place cells, while recent data have pointed out the importance of the feedback projection. We thus asked how grid cells are affected by the nature of the input from the place cells. We propose a single-layer neural network with feedforward weights connecting place-like input cells to grid cell outputs. Place-to-grid weights are learned via a generalized Hebbian rule. The architecture of this network highly resembles neural networks used to perform Principal Component Analysis (PCA). Both numerical results and analytic considerations indicate that if the components of the feedforward neural network are non-negative, the output converges to a hexagonal lattice. Without the non-negativity constraint, the output converges to a square lattice. Consistent with experiments, grid spacing ratio between the first two consecutive modules is -1.4. Our results express a possible linkage between place cell to grid cell interactions and PCA.

Representation of memories in the cortical-hippocampal system: Results from the application of population similarity analyses

Here we consider the value of neural population analysis as an approach to understanding how information is represented in the hippocampus and cortical areas and how these areas might interact as a brain system to support memory. We argue that models based on sparse coding of different individual features by single neurons in these areas (e.g., place cells, grid cells) are inadequate to capture the complexity of experience represented within this system. By contrast, population analyses of neurons with denser coding and mixed selectivity reveal new and important insights into the organization of memories. Furthermore, comparisons of the organization of information in interconnected areas suggest a model of hippocampal-cortical interactions that mediates the fundamental features of memory.

Connecting multiple spatial scales to decode the population activity of grid cells

Mammalian grid cells fire when an animal crosses the points of an imaginary hexagonal grid tessellating the environment. We show how animals can navigate by reading out a simple population vector of grid cell activity across multiple spatial scales, even though neural activity is intrinsically stochastic. This theory of dead reckoning explains why grid cells are organized into discrete modules within which all cells have the same lattice scale and orientation. The lattice scale changes from module to module and should form a geometric progression with a scale ratio of around 3/2 to minimize the risk of making large-scale errors in spatial localization. Such errors should also occur if intermediate-scale modules are silenced, whereas knocking out the module at the smallest scale will only affect spatial precision. For goal-directed navigation, the allocentric grid cell representation can be readily transformed into the egocentric goal coordinates needed for planning movements. The goal location is set by nonlinear gain fields that act on goal vector cells. This theory predicts neural and behavioral correlates of grid cell readout that transcend the known link between grid cells of the medial entorhinal cortex and place cells of the hippocampus.

Molecularly Defined Circuitry Reveals Input-Output Segregation in Deep Layers of the Medial Entorhinal Cortex

Deep layers of the medial entorhinal cortex are considered to relay signals from the hippocampus to other brain structures, but pathways for routing of signals to and from the deep layers are not well established. Delineating these pathways is important for a circuit level understanding of spatial cognition and memory. We find that neurons in layers 5a and 5b have distinct molecular identities, defined by the transcription factors Etv1 and Ctip2, and divergent targets, with extensive intratelencephalic projections originating in layer 5a, but not 5b. This segregation of outputs is mirrored by the organization of glutamatergic input from stellate cells in layer 2 and from the hippocampus, with both preferentially targeting layer 5b over 5a. Our results suggest a molecular and anatomical organization of input-output computations in deep layers of the MEC, reveal precise translaminar microcircuitry, and identify molecularly defined pathways for spatial signals to influence computation in deep layers.

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The transcription factors Etv1 and Ctip2 distinguish entorhinal layers 5a and 5b

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Layer 5a has extensive intratelencephalic projections, but layer 5b does not

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Terminals of layer 2 stellate, but not pyramidal cells, are enriched in deep layers

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Hippocampal and stellate cell inputs preferentially target layer 5b neurons