The Preferred Directions of Conjunctive Grid X Head Direction Cells in the Medial Entorhinal Cortex Are Periodically Organized

The discovery of speed-modulated grid, head direction, and conjunctive grid x head direction cells in the medial entorhinal cortex has led to the hypothesis that path integration, the updating of one’s spatial representation based on movement, may be carried out within this region. This hypothesis has been formalized by many computational models, including a class known as attractor network models. While many of these models propose specific mechanisms by which path integration might occur, predictions of these specific mechanisms have not been tested. Here I derive and test a key prediction of one attractor network path integration mechanism. Specifically, I first demonstrate that this mechanism predicts a periodic distribution of conjunctive cell preferred directions in order to minimize drift. Next, I test whether conjunctive cell preferred directions are in fact periodically organized. Results indicate that conjunctive cells are preferentially tuned to increments of 36°, consistent with drift minimization in this path integration mechanism. By contrast, no periodicity was observed in the preferred directions of either pure grid or pure head direction cells. These results provide the first neural evidence of a nonuniform structure in the directional preferences of any head direction representation found in the brain.     

Spiking Neurons in a Hierarchical Self-Organizing Map Model Can Learn to Develop Spatial and Temporal Properties of Entorhinal Grid Cells and Hippocampal Place Cells

Medial entorhinal grid cells and hippocampal place cells provide neural correlates of spatial representation in the brain. A place cell typically fires whenever an animal is present in one or more spatial regions, or places, of an environment. A grid cell typically fires in multiple spatial regions that form a regular hexagonal grid structure extending throughout the environment. Different grid and place cells prefer spatially offset regions, with their firing fields increasing in size along the dorsoventral axes of the medial entorhinal cortex and hippocampus. The spacing between neighboring fields for a grid cell also increases along the dorsoventral axis. This article presents a neural model whose spiking neurons operate in a hierarchy of self-organizing maps, each obeying the same laws. This spiking GridPlaceMap model simulates how grid cells and place cells may develop. It responds to realistic rat navigational trajectories by learning grid cells with hexagonal grid firing fields of multiple spatial scales and place cells with one or more firing fields that match neurophysiological data about these cells and their development in juvenile rats. The place cells represent much larger spaces than the grid cells, which enable them to support navigational behaviors. Both self-organizing maps amplify and learn to categorize the most frequent and energetic co-occurrences of their inputs. The current results build upon a previous rate-based model of grid and place cell learning, and thus illustrate a general method for converting rate-based adaptive neural models, without the loss of any of their analog properties, into models whose cells obey spiking dynamics. New properties of the spiking GridPlaceMap model include the appearance of theta band modulation. The spiking model also opens a path for implementation in brain-emulating nanochips comprised of networks of noisy spiking neurons with multiple-level adaptive weights for controlling autonomous adaptive robots capable of spatial navigation.     

Place cells, neocortex and spatial navigation: a short review

Hippocampal place cells are characterized by location-specific firing, that is each cell fires in a restricted region of the environment explored by the rat. In this review, we briefly examine the sensory information used by place cells to anchor their firing fields in space and show that, among the various sensory cues that can influence place cell activity, visual and motion-related cues are the most relevant. We then explore the contribution of several cortical areas to the generation of the place cell signal with an emphasis on the role of the visual cortex and parietal cortex. Finally, we address the functional significance of place cell activity and demonstrate the existence of a clear relationship between place cell positional activity and spatial navigation performance. We conclude that place cells, together with head direction cells, provide information useful for spatially guided movements, and thus provide a unique model of how spatial information is encoded in the brain.     

The mechanism of rate remapping in the dentate gyrus

Rate remapping is a recently revealed neural code in which sensory information modulates the firing rate of hippocampal place cells. The mechanism underlying rate remapping is unknown. Its characteristic modulation, however, must arise from the interaction of the two major inputs to the hippocampus, the medial entorhinal cortex (MEC), in which grid cells represent the spatial position of the rat, and the lateral entorhinal cortex (LEC), in which cells represent the sensory properties of the environment. We have used computational methods to elucidate the mechanism by which this interaction produces rate remapping. We show that the convergence of LEC and MEC inputs, in conjunction with a competitive network process mediated by feedback inhibition, can account quantitatively for this phenomenon. The same principle accounts for why different place fields of the same cell vary independently as sensory information is altered. Our results show that rate remapping can be explained in terms of known mechanisms.     

Coordinated learning of grid cell and place cell spatial and temporal properties: multiple scales,attention and oscillations

A neural model proposes how entorhinal grid cells and hippocampal place cells may develop as spatial categories in a hierarchy of self-organizing maps (SOMs). The model responds to realistic rat navigational trajectories by learning both grid cells with hexagonal grid firing fields of multiple spatial scales, and place cells with one or more firing fields, that match neurophysiological data about their development in juvenile rats. Both grid and place cells can develop by detecting, learning and remembering the most frequent and energetic co-occurrences of their inputs. The model''s parsimonious properties include: similar ring attractor mechanisms process linear and angular path integration inputs that drive map learning; the same SOM mechanisms can learn grid cell and place cell receptive fields; and the learning of the dorsoventral organization of multiple spatial scale modules through medial entorhinal cortex to hippocampus (HC) may use mechanisms homologous to those for temporal learning through lateral entorhinal cortex to HC (‘neural relativity’). The model clarifies how top-down HC-to-entorhinal attentional mechanisms may stabilize map learning, simulates how hippocampal inactivation may disrupt grid cells, and explains data about theta, beta and gamma oscillations. The article also compares the three main types of grid cell models in the light of recent data.     

Continuous Attractor Network Model for Conjunctive Position-by-Velocity Tuning of Grid Cells

The spatial responses of many of the cells recorded in layer II of rodent medial entorhinal cortex (MEC) show a triangular grid pattern, which appears to provide an accurate population code for animal spatial position. In layer III, V and VI of the rat MEC, grid cells are also selective to head-direction and are modulated by the speed of the animal. Several putative mechanisms of grid-like maps were proposed, including attractor network dynamics, interactions with theta oscillations or single-unit mechanisms such as firing rate adaptation. In this paper, we present a new attractor network model that accounts for the conjunctive position-by-velocity selectivity of grid cells. Our network model is able to perform robust path integration even when the recurrent connections are subject to random perturbations.     

How environment geometry affects grid cell symmetry and what we can learn from it

The mammalian hippocampal formation provides neuronal representations of environmental location but the underlying mechanisms are unclear. The majority of cells in medial entorhinal cortex and parasubiculum show spatially periodic firing patterns. Grid cells exhibit hexagonal symmetry and form an important subset of this more general class. Occasional changes between hexagonal and non-hexagonal firing patterns imply a common underlying mechanism. Importantly, the symmetrical properties are strongly affected by the geometry of the environment. Here, we introduce a field–boundary interaction model where we demonstrate that the grid cell pattern can be formed from competing place-like and boundary inputs. We show that the modelling results can accurately capture our current experimental observations.     

Robust path integration in the entorhinal grid cell system with hippocampal feed-back

Animals are able to update their knowledge about their current position solely by integrating the speed and the direction of their movement, which is known as path integration. Recent discoveries suggest that grid cells in the medial entorhinal cortex might perform some of the essential underlying computations of path integration. However, a major concern over path integration is that as the measurement of speed and direction is inaccurate, the representation of the position will become increasingly unreliable. In this paper, we study how allothetic inputs can be used to continually correct the accumulating error in the path integrator system. We set up the model of a mobile agent equipped with the entorhinal representation of idiothetic (grid cell) and allothetic (visual cells) information and simulated its place learning in a virtual environment. Due to competitive learning, a robust hippocampal place code emerges rapidly in the model. At the same time, the hippocampo-entorhinal feed-back connections are modified via Hebbian learning in order to allow hippocampal place cells to influence the attractor dynamics in the entorhinal cortex. We show that the continuous feed-back from the integrated hippocampal place representation is able to stabilize the grid cell code. This research was supported by the EU Framework 6 ICEA project (IST-4-027819-IP).     

Functional connectivity of the entorhinal–hippocampal space circuit

The mammalian space circuit is known to contain several functionally specialized cell types, such as place cells in the hippocampus and grid cells, head-direction cells and border cells in the medial entorhinal cortex (MEC). The interaction between the entorhinal and hippocampal spatial representations is poorly understood, however. We have developed an optogenetic strategy to identify functionally defined cell types in the MEC that project directly to the hippocampus. By expressing channelrhodopsin-2 (ChR2) selectively in the hippocampus-projecting subset of entorhinal projection neurons, we were able to use light-evoked discharge as an instrument to determine whether specific entorhinal cell groups—such as grid cells, border cells and head-direction cells—have direct hippocampal projections. Photoinduced firing was observed at fixed minimal latencies in all functional cell categories, with grid cells as the most abundant hippocampus-projecting spatial cell type. We discuss how photoexcitation experiments can be used to distinguish the subset of hippocampus-projecting entorhinal neurons from neurons that are activated indirectly through the network. The functional breadth of entorhinal input implied by this analysis opens up the potential for rich dynamic interactions between place cells in the hippocampus and different functional cell types in the entorhinal cortex (EC).     

Functional split between parietal and entorhinal cortices in the rat

Posterior parietal cortex (PPC) and medial entorhinal cortex (MEC) are important elements of the neural circuit for space, but whether representations in these areas are controlled by the same factors is unknown. We recorded single units simultaneously in PPC and MEC of freely foraging rats and found that a subset of PPC cells are tuned to specific modes of movement irrespective of the animals' location or heading, whereas grid cells in MEC expressed static spatial maps. The behavioral correlates of PPC cells switched completely when the same animals ran in a spatially structured maze or when they ran similar stereotypic sequences in an open arena. Representations in PPC were similar in identical mazes in different rooms where grid cells completely realigned their firing fields. The data suggest that representations in PPC are determined by the organization of actions while cells in MEC are driven by spatial inputs.     

A Continuous Attractor Network Model Without Recurrent Excitation: Maintenance and Integration in the Head Direction Cell System

Motivated by experimental observations of the head direction system, we study a three population network model that operates as a continuous attractor network. This network is able to store in a short-term memory an angular variable (the head direction) as a spatial profile of activity across neurons in the absence of selective external inputs, and to accurately update this variable on the basis of angular velocity inputs. The network is composed of one excitatory population and two inhibitory populations, with inter-connections between populations but no connections within the neurons of a same population. In particular, there are no excitatory-to-excitatory connections. Angular velocity signals are represented as inputs in one inhibitory population (clockwise turns) or the other (counterclockwise turns). The system is studied using a combination of analytical and numerical methods. Analysis of a simplified model composed of threshold-linear neurons gives the conditions on the connectivity for (i) the emergence of the spatially selective profile, (ii) reliable integration of angular velocity inputs, and (iii) the range of angular velocities that can be accurately integrated by the model. Numerical simulations allow us to study the proposed scenario in a large network of spiking neurons and compare their dynamics with that of head direction cells recorded in the rat limbic system. In particular, we show that the directional representation encoded by the attractor network can be rapidly updated by external cues, consistent with the very short update latencies observed experimentally by Zugaro et al. (2003) in thalamic head direction cells.     

A feedforward model for the formation of a grid field where spatial information is provided solely from place cells

Grid cells (GCs) in the medial entorhinal cortex (mEC) have the property of having their firing activity spatially tuned to a regular triangular lattice. Several theoretical models for grid field formation have been proposed, but most assume that place cells (PCs) are a product of the grid cell system. There is, however, an alternative possibility that is supported by various strands of experimental data. Here we present a novel model for the emergence of gridlike firing patterns that stands on two key hypotheses: (1) spatial information in GCs is provided from PC activity and (2) grid fields result from a combined synaptic plasticity mechanism involving inhibitory and excitatory neurons mediating the connections between PCs and GCs. Depending on the spatial location, each PC can contribute with excitatory or inhibitory inputs to GC activity. The nature and magnitude of the PC input is a function of the distance to the place field center, which is inferred from rate decoding. A biologically plausible learning rule drives the evolution of the connection strengths from PCs to a GC. In this model, PCs compete for GC activation, and the plasticity rule favors efficient packing of the space representation. This leads to gridlike firing patterns. In a new environment, GCs continuously recruit new PCs to cover the entire space. The model described here makes important predictions and can represent the feedforward connections from hippocampus CA1 to deeper mEC layers.     

Hippocampal Remapping Is Constrained by Sparseness rather than Capacity

Grid cells in the medial entorhinal cortex encode space with firing fields that are arranged on the nodes of spatial hexagonal lattices. Potential candidates to read out the space information of this grid code and to combine it with other sensory cues are hippocampal place cells. In this paper, we investigate a population of grid cells providing feed-forward input to place cells. The capacity of the underlying synaptic transformation is determined by both spatial acuity and the number of different spatial environments that can be represented. The codes for different environments arise from phase shifts of the periodical entorhinal cortex patterns that induce a global remapping of hippocampal place fields, i.e., a new random assignment of place fields for each environment. If only a single environment is encoded, the grid code can be read out at high acuity with only few place cells. A surplus in place cells can be used to store a space code for more environments via remapping. The number of stored environments can be increased even more efficiently by stronger recurrent inhibition and by partitioning the place cell population such that learning affects only a small fraction of them in each environment. We find that the spatial decoding acuity is much more resilient to multiple remappings than the sparseness of the place code. Since the hippocampal place code is sparse, we thus conclude that the projection from grid cells to the place cells is not using its full capacity to transfer space information. Both populations may encode different aspects of space.     

Models of place and grid cell firing and theta rhythmicity

Neuronal firing in the hippocampal formation (HF) of freely moving rodents shows striking examples of spatialorganization in the form of place, directional, boundary vector and grid cells. The firing of place and grid cells shows an intriguing form of temporal organization known as 'theta phase precession'. We review the mechanisms underlying theta phase precession of place cell firing, ranging from membrane potential oscillations to recurrent connectivity, and the relevant intra-cellular and extra-cellular data. We then consider the use of these models to explain the spatial structure of grid cell firing, and review the relevant intra-cellular and extra-cellular data. Finally, we consider the likely interaction between place cells, grid cells and boundary vector cells in estimating self-location as a compromise between path-integration and environmental information.     

How to build a grid cell

Neurons in the medial entorhinal cortex fire action potentials at regular spatial intervals, creating a striking grid-like pattern of spike rates spanning the whole environment of a navigating animal. This remarkable spatial code may represent a neural map for path integration. Recent advances using patch-clamp recordings from entorhinal cortex neurons in vitro and in vivo have revealed how the microcircuitry in the medial entorhinal cortex may contribute to grid cell firing patterns, and how grid cells may transform synaptic inputs into spike output during firing field crossings. These new findings provide key insights into the ingredients necessary to build a grid cell.     

How Entorhinal Grid Cells May Learn Multiple Spatial Scales from a Dorsoventral Gradient of Cell Response Rates in a Self-organizing Map

Place cells in the hippocampus of higher mammals are critical for spatial navigation. Recent modeling clarifies how this may be achieved by how grid cells in the medial entorhinal cortex (MEC) input to place cells. Grid cells exhibit hexagonal grid firing patterns across space in multiple spatial scales along the MEC dorsoventral axis. Signals from grid cells of multiple scales combine adaptively to activate place cells that represent much larger spaces than grid cells. But how do grid cells learn to fire at multiple positions that form a hexagonal grid, and with spatial scales that increase along the dorsoventral axis? In vitro recordings of medial entorhinal layer II stellate cells have revealed subthreshold membrane potential oscillations (MPOs) whose temporal periods, and time constants of excitatory postsynaptic potentials (EPSPs), both increase along this axis. Slower (faster) subthreshold MPOs and slower (faster) EPSPs correlate with larger (smaller) grid spacings and field widths. A self-organizing map neural model explains how the anatomical gradient of grid spatial scales can be learned by cells that respond more slowly along the gradient to their inputs from stripe cells of multiple scales, which perform linear velocity path integration. The model cells also exhibit MPO frequencies that covary with their response rates. The gradient in intrinsic rhythmicity is thus not compelling evidence for oscillatory interference as a mechanism of grid cell firing. A response rate gradient combined with input stripe cells that have normalized receptive fields can reproduce all known spatial and temporal properties of grid cells along the MEC dorsoventral axis. This spatial gradient mechanism is homologous to a gradient mechanism for temporal learning in the lateral entorhinal cortex and its hippocampal projections. Spatial and temporal representations may hereby arise from homologous mechanisms, thereby embodying a mechanistic “neural relativity” that may clarify how episodic memories are learned.     

Inducible and cell-type restricted manipulation in the entorhinal cortex

The entorhinal cortex functions as the gateway to the hippocampal formation. However, its role in formation and consolidation of hippocampus-dependent memory remains relatively unexplored. In this issue of Neuron, Yasuda and Mayford report an elegant cell-type restricted inducible transgenic mouse overexpressing a mutant form of CaM kinase II selectively in superficial layers of medial entorhinal cortex and its upstream regions. These animals display a selective spatial memory deficit during the immediate posttraining period as well as during acquisition in the Morris water maze. Similar to the hippocampus, this time-limited involvement of entorhinal cortex in spatial memory processing suggests a crucial role for hippocampal-entorhinal circuitry in spatial memory formation.     

Path integration and the neural basis of the 'cognitive map'

The hippocampal formation can encode relative spatial location, without reference to external cues, by the integration of linear and angular self-motion (path integration). Theoretical studies, in conjunction with recent empirical discoveries, suggest that the medial entorhinal cortex (MEC) might perform some of the essential underlying computations by means of a unique, periodic synaptic matrix that could be self-organized in early development through a simple, symmetry-breaking operation. The scale at which space is represented increases systematically along the dorsoventral axis in both the hippocampus and the MEC, apparently because of systematic variation in the gain of a movement-speed signal. Convergence of spatially periodic input at multiple scales, from so-called grid cells in the entorhinal cortex, might result in non-periodic spatial firing patterns (place fields) in the hippocampus.     

Solving navigational uncertainty using grid cells on robots

To successfully navigate their habitats, many mammals use a combination of two mechanisms, path integration and calibration using landmarks, which together enable them to estimate their location and orientation, or pose. In large natural environments, both these mechanisms are characterized by uncertainty: the path integration process is subject to the accumulation of error, while landmark calibration is limited by perceptual ambiguity. It remains unclear how animals form coherent spatial representations in the presence of such uncertainty. Navigation research using robots has determined that uncertainty can be effectively addressed by maintaining multiple probabilistic estimates of a robot's pose. Here we show how conjunctive grid cells in dorsocaudal medial entorhinal cortex (dMEC) may maintain multiple estimates of pose using a brain-based robot navigation system known as RatSLAM. Based both on rodent spatially-responsive cells and functional engineering principles, the cells at the core of the RatSLAM computational model have similar characteristics to rodent grid cells, which we demonstrate by replicating the seminal Moser experiments. We apply the RatSLAM model to a new experimental paradigm designed to examine the responses of a robot or animal in the presence of perceptual ambiguity. Our computational approach enables us to observe short-term population coding of multiple location hypotheses, a phenomenon which would not be easily observable in rodent recordings. We present behavioral and neural evidence demonstrating that the conjunctive grid cells maintain and propagate multiple estimates of pose, enabling the correct pose estimate to be resolved over time even without uniquely identifying cues. While recent research has focused on the grid-like firing characteristics, accuracy and representational capacity of grid cells, our results identify a possible critical and unique role for conjunctive grid cells in filtering sensory uncertainty. We anticipate our study to be a starting point for animal experiments that test navigation in perceptually ambiguous environments.