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.     

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.     

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).     

Laminar and Dorsoventral Molecular Organization of the Medial Entorhinal Cortex Revealed by Large-scale Anatomical Analysis of Gene Expression

Neural circuits in the medial entorhinal cortex (MEC) encode an animal’s position and orientation in space. Within the MEC spatial representations, including grid and directional firing fields, have a laminar and dorsoventral organization that corresponds to a similar topography of neuronal connectivity and cellular properties. Yet, in part due to the challenges of integrating anatomical data at the resolution of cortical layers and borders, we know little about the molecular components underlying this organization. To address this we develop a new computational pipeline for high-throughput analysis and comparison of in situ hybridization (ISH) images at laminar resolution. We apply this pipeline to ISH data for over 16,000 genes in the Allen Brain Atlas and validate our analysis with RNA sequencing of MEC tissue from adult mice. We find that differential gene expression delineates the borders of the MEC with neighboring brain structures and reveals its laminar and dorsoventral organization. We propose a new molecular basis for distinguishing the deep layers of the MEC and show that their similarity to corresponding layers of neocortex is greater than that of superficial layers. Our analysis identifies ion channel-, cell adhesion- and synapse-related genes as candidates for functional differentiation of MEC layers and for encoding of spatial information at different scales along the dorsoventral axis of the MEC. We also reveal laminar organization of genes related to disease pathology and suggest that a high metabolic demand predisposes layer II to neurodegenerative pathology. In principle, our computational pipeline can be applied to high-throughput analysis of many forms of neuroanatomical data. Our results support the hypothesis that differences in gene expression contribute to functional specialization of superficial layers of the MEC and dorsoventral organization of the scale of spatial representations.     

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.     

Spatial representation along the proximodistal axis of CA1

CA1 cells receive direct input from space-responsive cells in medial entorhinal cortex (MEC), such as grid cells, as well as more nonspatial cells in lateral entorhinal cortex (LEC). Because MEC projects preferentially to the proximal part of the CA1, bordering CA2, whereas LEC innervates only the distal part, bordering subiculum, we asked if spatial tuning is graded along the transverse axis of CA1. Tetrodes were implanted along the entire proximodistal axis of dorsal CA1 in rats. Data were recorded in cylinders large enough to elicit firing at more than one location in many neurons. Distal CA1 cells showed more dispersed firing and had a larger number of firing fields than proximal cells. Phase-locking of spikes to MEC theta oscillations was weaker in distal CA1 than in proximal CA1. The findings suggest that spatial firing in CA1 is organized transversally, with the strongest spatial modulation occurring in the MEC-associated proximal part.     

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.     

A model of grid cells based on a twisted torus topology

The grid cells of the rat medial entorhinal cortex (MEC) show an increased firing frequency when the position of the animal correlates with multiple regions of the environment that are arranged in regular triangular grids. Here, we describe an artificial neural network based on a twisted torus topology, which allows for the generation of regular triangular grids. The association of the activity of pre-defined hippocampal place cells with entorhinal grid cells allows for a highly robust-to-noise calibration mechanism, suggesting a role for the hippocampal back-projections to the entorhinal cortex.     

Preparation of Parasagittal Slices for the Investigation of Dorsal-ventral Organization of the Rodent Medial Entorhinal Cortex

Computation in the brain relies on neurons responding appropriately to their synaptic inputs. Neurons differ in their complement and distribution of membrane ion channels that determine how they respond to synaptic inputs. However, the relationship between these cellular properties and neuronal function in behaving animals is not well understood. One approach to this problem is to investigate topographically organized neural circuits in which the position of individual neurons maps onto information they encode or computations they carry out¹. Experiments using this approach suggest principles for tuning of synaptic responses underlying information encoding in sensory and cognitive circuits^2,3.The topographical organization of spatial representations along the dorsal-ventral axis of the medial entorhinal cortex (MEC) provides an opportunity to establish relationships between cellular mechanisms and computations important for spatial cognition. Neurons in layer II of the rodent MEC encode location using grid-like firing fields^4-6. For neurons found at dorsal positions in the MEC the distance between the individual firing fields that form a grid is on the order of 30 cm, whereas for neurons at progressively more ventral positions this distance increases to greater than 1 m. Several studies have revealed cellular properties of neurons in layer II of the MEC that, like the spacing between grid firing fields, also differ according to their dorsal-ventral position, suggesting that these cellular properties are important for spatial computation^2,7-10.Here we describe procedures for preparation and electrophysiological recording from brain slices that maintain the dorsal-ventral extent of the MEC enabling investigation of the topographical organization of biophysical and anatomical properties of MEC neurons. The dorsal-ventral position of identified neurons relative to anatomical landmarks is difficult to establish accurately with protocols that use horizontal slices of MEC^7,8,11,12, as it is difficult to establish reference points for the exact dorsal-ventral location of the slice. The procedures we describe enable accurate and consistent measurement of location of recorded cells along the dorsal-ventral axis of the MEC as well as visualization of molecular gradients^2,10. The procedures have been developed for use with adult mice (> 28 days) and have been successfully employed with mice up to 1.5 years old. With adjustments they could be used with younger mice or other rodent species. A standardized system of preparation and measurement will aid systematic investigation of the cellular and microcircuit properties of this area.     

An isomorphic mapping hypothesis of the grid representation

We introduce a grid cell microcircuit hypothesis. We propose the ‘grid in the world’ (evident in grid cell discharges) is generated by a ‘grid in the cortex’. This cortical grid is formed by patches of calbindin-positive pyramidal neurons in layer 2 of medial entorhinal cortex (MEC). Our isomorphic mapping hypothesis assumes three types of isomorphism: (i) metric correspondence of neural space (the two-dimensional cortical sheet) and the external two-dimensional space within patches; (ii) isomorphism between cellular connectivity matrix and firing field; (iii) isomorphism between single cell and population activity. Each patch is a grid cell lattice arranged in a two-dimensional map of space with a neural : external scale of approximately 1 : 2000 in the dorsal part of rat MEC. The lattice behaves like an excitable medium with neighbouring grid cells exciting each other. Spatial scale is implemented as an intrinsic scaling factor for neural propagation speed. This factor varies along the dorsoventral cortical axis. A connectivity scheme of the grid system is described. Head direction input specifies the direction of activity propagation. We extend the theory to neurons between grid patches and predict a rare discharge pattern (inverted grid cells) and the relative location and proportion of grid cells and spatial band cells.     

Olfactory predictive codes and stimulus templates in piriform cortex

Neuroscientific models of sensory perception suggest that the brain utilizes predictive codes in advance of a stimulus encounter, enabling organisms to infer forthcoming sensory events. However, it is poorly understood how such mechanisms are implemented in the olfactory system. Combining high-resolution functional magnetic resonance imaging with multivariate (pattern-based) analyses, we examined the spatiotemporal evolution of odor perception in the human brain during an olfactory search task. Ensemble activity patterns in anterior piriform cortex (APC) and orbitofrontal cortex (OFC) reflected the attended odor target both before and after stimulus onset. In contrast, prestimulus ensemble representations of the odor target in posterior piriform cortex (PPC) gave way to poststimulus representations of the odor itself. Critically, the robustness of target-related patterns in PPC predicted subsequent behavioral performance. Our findings directly show that the brain generates predictive templates or "search images" in PPC, with physical correspondence to odor-specific pattern representations, to augment olfactory perception.     

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.     

Dissociation between Dorsal and Ventral Posterior Parietal Cortical Responses to Incidental Changes in Natural Scenes

Background

The posterior parietal cortex (PPC) is thought to interact with the medial temporal lobe (MTL) to support spatial cognition and topographical memory. While the response of medial temporal lobe regions to topographical stimuli has been intensively studied, much less research has focused on the role of PPC and its functional connectivity with the medial temporal lobe.

Methodology/Principle Findings

Here we report a dissociation between dorsal and ventral regions of PPC in response to different types of change in natural scenes using an fMRI adaptation paradigm. During scanning subjects performed an incidental target detection task whilst viewing trial unique sequentially presented pairs of natural scenes, each containing a single prominent object. We observed a dissociation between the superior parietal gyrus and the angular gyrus, with the former showing greater sensitivity to spatial change, and the latter showing greater sensitivity to scene novelty. In addition, we observed that the parahippocampal cortex has increased functional connectivity with the angular gyrus, but not superior parietal gyrus, when subjects view change to the scene content.

Conclusions/Significance

Our findings provide support for proposed dissociations between dorsal and ventral regions of PPC and suggest that the dorsal PPC may support the spatial coding of the visual environment even when this information is incidental to the task at hand. Further, through revealing the differential functional interactions of the SPG and AG with the MTL our results help advance our understanding of how the MTL and PPC cooperate to update representations of the world around us.     

A novel somatosensory spatial navigation system outside the hippocampal formation

Spatially selective firing of place cells, grid cells, boundary vector/border cells and head direction cells constitutes the basic building blocks of a canonical spatial navigation system centered on the hippocampal-entorhinal complex. While head direction cells can be found throughout the brain, spatial tuning outside the hippocampal formation is often non-specific or conjunctive to other representations such as a reward. Although the precise mechanism of spatially selective firing activity is not understood, various studies show sensory inputs, particularly vision, heavily modulate spatial representation in the hippocampal-entorhinal circuit. To better understand the contribution of other sensory inputs in shaping spatial representation in the brain, we performed recording from the primary somatosensory cortex in foraging rats. To our surprise, we were able to detect the full complement of spatially selective firing patterns similar to that reported in the hippocampal-entorhinal network, namely, place cells, head direction cells, boundary vector/border cells, grid cells and conjunctive cells, in the somatosensory cortex. These newly identified somatosensory spatial cells form a spatial map outside the hippocampal formation and support the hypothesis that location information modulates body representation in the somatosensory cortex. Our findings provide transformative insights into our understanding of how spatial information is processed and integrated in the brain, as well as functional operations of the somatosensory cortex in the context of rehabilitation with brain-machine interfaces.Subject terms: Biological techniques, Cell biology     

A neural field model of the somatosensory cortex: formation, maintenance and reorganization of ordered topographic maps

We investigate the formation and maintenance of ordered topographic maps in the primary somatosensory cortex as well as the reorganization of representations after sensory deprivation or cortical lesion. We consider both the critical period (postnatal) where representations are shaped and the post-critical period where representations are maintained and possibly reorganized. We hypothesize that feed-forward thalamocortical connections are an adequate site of plasticity while cortico-cortical connections are believed to drive a competitive mechanism that is critical for learning. We model a small skin patch located on the distal phalangeal surface of a digit as a set of 256 Merkel ending complexes (MEC) that feed a computational model of the primary somatosensory cortex (area 3b). This model is a two-dimensional neural field where spatially localized solutions (a.k.a. bumps) drive cortical plasticity through a Hebbian-like learning rule. Simulations explain the initial formation of ordered representations following repetitive and random stimulations of the skin patch. Skin lesions as well as cortical lesions are also studied and results confirm the possibility to reorganize representations using the same learning rule and depending on the type of the lesion. For severe lesions, the model suggests that cortico-cortical connections may play an important role in complete recovery.     

Lesions to right posterior parietal cortex impair visual depth perception from disparity but not motion cues

The posterior parietal cortex (PPC) is understood to be active when observers perceive three-dimensional (3D) structure. However, it is not clear how central this activity is in the construction of 3D spatial representations. Here, we examine whether PPC is essential for two aspects of visual depth perception by testing patients with lesions affecting this region. First, we measured subjects'' ability to discriminate depth structure in various 3D surfaces and objects using binocular disparity. Patients with lesions to right PPC (N = 3) exhibited marked perceptual deficits on these tasks, whereas those with left hemisphere lesions (N = 2) were able to reliably discriminate depth as accurately as control subjects. Second, we presented an ambiguous 3D stimulus defined by structure from motion to determine whether PPC lesions influence the rate of bistable perceptual alternations. Patients'' percept durations for the 3D stimulus were generally within a normal range, although the two patients with bilateral PPC lesions showed the fastest perceptual alternation rates in our sample. Intermittent stimulus presentation reduced the reversal rate similarly across subjects. Together, the results suggest that PPC plays a causal role in both inferring and maintaining the perception of 3D structure with stereopsis supported primarily by the right hemisphere, but do not lend support to the view that PPC is a critical contributor to bistable perceptual alternations.This article is part of the themed issue ‘Vision in our three-dimensional world’.     

A Sensorimotor Model for Computing Intended Reach Trajectories

The presumed role of the primate sensorimotor system is to transform reach targets from retinotopic to joint coordinates for producing motor output. However, the interpretation of neurophysiological data within this framework is ambiguous, and has led to the view that the underlying neural computation may lack a well-defined structure. Here, I consider a model of sensorimotor computation in which temporal as well as spatial transformations generate representations of desired limb trajectories, in visual coordinates. This computation is suggested by behavioral experiments, and its modular implementation makes predictions that are consistent with those observed in monkey posterior parietal cortex (PPC). In particular, the model provides a simple explanation for why PPC encodes reach targets in reference frames intermediate between the eye and hand, and further explains why these reference frames shift during movement. Representations in PPC are thus consistent with the orderly processing of information, provided we adopt the view that sensorimotor computation manipulates desired movement trajectories, and not desired movement endpoints.     

Task phase-specific involvement of the rat posterior parietal cortex in performance of the TUNL task

The posterior parietal cortex (PPC) participates in cognitive processes including working memory (WM), sensory evidence accumulation, and perceptually guided decision making. However, surprisingly little work has used temporally precise manipulations to dissect its role in different epochs of behavior taking place over short timespans, such as WM tasks. As a result, a consistent view of the temporally precise role of the PPC in these processes has not been described. In the present study, we investigated the temporally specific role of the PPC in the Trial-Unique, Nonmatching-to-Location (TUNL) task, a touchscreen-based, visuospatial WM task that relies on the PPC. To disrupt PPC activity in a temporally precise manner, we applied mild intracranial electrical stimulation (ICES). We found that intra-PPC ICES (100 μA) significantly impaired accuracy in TUNL without significantly altering response latency. Moreover, we found that the impairment was specific to ICES applied during the delay and test phases of TUNL. Consistent with previous reports showing delay- and choice-specific neuronal activity in the PPC, the results provide evidence that the rat PPC is required for maintaining memory representations of stimuli over a delay period as well as for making successful comparisons and choices between test stimuli. In contrast, the PPC appears not to be critical for initial encoding of sample stimuli. This pattern of results may indicate that early encoding of visual stimuli is independent of the PPC or that the PPC becomes engaged only when visual stimuli are spatially complex or involve memory or decision making.     

Human posterior parietal cortex flexibly determines reference frames for reaching based on sensory context

Current models of sensorimotor transformations emphasize the dominant role of gaze-centered representations for reach planning in the posterior parietal cortex (PPC). Here we exploit fMRI repetition suppression to test whether the sensory modality of a target determines the reference frame used to define the motor goal in the PPC and premotor cortex. We show that when targets are defined visually, the anterior precuneus selectively encodes the motor goal in gaze-centered coordinates, whereas the parieto-occipital junction, Brodman Area 5 (BA 5), and PMd use a mixed gaze- and body-centered representation. In contrast, when targets are defined by unseen proprioceptive cues, activity in these areas switches to represent the motor goal predominantly in body-centered coordinates. These results support computational models arguing for flexibility in reference frames for action according to sensory context. Critically, they provide neuroanatomical evidence that flexibility is achieved by exploiting a multiplicity of reference frames that can be expressed within individual areas.     

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.