Grid cell hexagonal patterns formed by fast self-organized learning within entorhinal cortex

Visual boundary cues suffice to anchor place and grid cells in virtual reality

The hippocampal formation contains neurons responsive to an animal's current location and orientation, which together provide the organism with a neural map of space.1,2,3 Spatially tuned neurons rely on external landmark cues and internally generated movement information to estimate position.4,5 An important class of landmark cue are the boundaries delimiting an environment, which can define place cell field position6,7 and stabilize grid cell firing.8 However, the precise nature of the sensory information used to detect boundaries remains unknown. We used 2-dimensional virtual reality (VR)9 to show that visual cues from elevated walls surrounding the environment are both sufficient and necessary to stabilize place and grid cell responses in VR, when only visual and self-motion cues are available. By contrast, flat boundaries formed by the edges of a textured floor did not stabilize place and grid cells, indicating only specific forms of visual boundary stabilize hippocampal spatial firing. Unstable grid cells retain internally coherent, hexagonally arranged firing fields, but these fields "drift" with respect to the virtual environment over periods >5 s. Optic flow from a virtual floor does not slow drift dynamics, emphasizing the importance of boundary-related visual information. Surprisingly, place fields are more stable close to boundaries even with floor and wall cues removed, suggesting invisible boundaries are inferred using the motion of a discrete, separate cue (a beacon signaling reward location). Subsets of place cells show allocentric directional tuning toward the beacon, with strength of tuning correlating with place field stability when boundaries are removed.

Ring Attractors as the Basis of a Biomimetic Navigation System

The ability to navigate effectively in a rich and complex world is crucial for the survival of all animals. Specialist neural structures have evolved that are implicated in facilitating this ability, one such structure being the ring attractor network. In this study, we model a trio of Spiking Neural Network (SNN) ring attractors as part of a bio-inspired navigation system to maintain an internal estimate of planar translation of an artificial agent. This estimate is dynamically calibrated using a memory recall system of landmark-free allotheic multisensory experiences. We demonstrate that the SNN-based ring attractor system can accurately model motion through 2D space by integrating ideothetic velocity information and use recalled allothetic experiences as a positive corrective mechanism. This SNN based navigation system has potential for use in mobile robotics applications where power supply is limited and external sensory information is intermittent or unreliable.

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.

Effects of neuromodulation-inspired mechanisms on the performance of deep neural networks in a spatial learning task

In recent years, the biological underpinnings of adaptive learning have been modeled, leading to faster model convergence and various behavioral benefits in tasks including spatial navigation and cue-reward association. Furthermore, studies have investigated how the neuromodulatory system, a major driver of synaptic plasticity and state-dependent changes in the brain neuronal activities, plays a role in training deep neural networks (DNNs). In this study, we extended previous studies on neuromodulation-inspired DNNs and explored the effects of neuromodulatory components on learning and single unit activities in a spatial learning task. Under the multiscale neuromodulatory framework, plastic components, dropout probability modulation, and learning rate decay were added to the single unit, layer, and whole network levels of DNN models, respectively. We observed behavioral benefits including faster learning and smaller error of ambulation. We then concluded that neuromodulatory components can affect learning trajectories, outcomes, and single unit activities, in a component- and hyperparameter-dependent manner.

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.

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 Neural Model of Intrinsic and Extrinsic Hippocampal Theta Rhythms: Anatomy, Neurophysiology, and Function

This article describes a neural model of the anatomy, neurophysiology, and functions of intrinsic and extrinsic theta rhythms in the brains of multiple species. Topics include how theta rhythms were discovered; how theta rhythms organize brain information processing into temporal series of spatial patterns; how distinct theta rhythms occur within area CA1 of the hippocampus and between the septum and area CA3 of the hippocampus; what functions theta rhythms carry out in different brain regions, notably CA1-supported functions like learning, recognition, and memory that involve visual, cognitive, and emotional processes; how spatial navigation, adaptively timed learning, and category learning interact with hippocampal theta rhythms; how parallel cortical streams through the lateral entorhinal cortex (LEC) and the medial entorhinal cortex (MEC) represent the end-points of the What cortical stream for perception and cognition and the Where cortical stream for spatial representation and action; how the neuromodulator acetylcholine interacts with the septo-hippocampal theta rhythm and modulates category learning; what functions are carried out by other brain rhythms, such as gamma and beta oscillations; and how gamma and beta oscillations interact with theta rhythms. Multiple experimental facts about theta rhythms are unified and functionally explained by this theoretical synthesis.

Modeling the grid cell activity on non-horizontal surfaces based on oscillatory interference modulated by gravity

Internal representation of the space is a fundamental and crucial function of the animal's brain. Grid cells in the medial entorhinal cortex are thought to provide an environment-invariant metric system for the navigation of the animal. Most experimental and theoretical studies have focused on the horizontal planar codes of grid cell, while how this metric coordinate system is configured in the actual three-dimensional space remains unclear. Evidence has implied the spatial cognition may not be fully volumetric. We proposed an oscillatory interference model with a novel gravity and body plane modulation to simulate grid cell activity in complex space for rodents. The animal can perceive the rotation of its body plane along the local surface by sensing the gravity, causing the modulation to the dendritic oscillations. The results not only reproduce the firing patterns of the grid cell recorded from known experiments, but also predict the grid codes in novel environments. It further demonstrates that the gravity signal is indispensable for the animal's navigation, and supports the hypothesis that the periodic firing of the grid cell is intrinsically not a volumetric code in three-dimensional space. This will provide new insights to understand the spatial representation of the actual world in the brain.

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 computational model for grid maps in neural populations

Grid cells in the entorhinal cortex, together with head direction, place, speed and border cells, are major contributors to the organization of spatial representations in the brain. In this work we introduce a novel theoretical and algorithmic framework able to explain the optimality of hexagonal grid-like response patterns. We show that this pattern is a result of minimal variance encoding of neurons together with maximal robustness to neurons' noise and minimal number of encoding neurons. The novelty lies in the formulation of the encoding problem considering neurons as an overcomplete basis (a frame) where the position information is encoded. Through the modern Frame Theory language, specifically that of tight and equiangular frames, we provide new insights about the optimality of hexagonal grid receptive fields. The proposed model is based on the well-accepted and tested hypothesis of Hebbian learning, providing a simplified cortical-based framework that does not require the presence of velocity-driven oscillations (oscillatory model) or translational symmetries in the synaptic connections (attractor model). We moreover demonstrate that the proposed encoding mechanism naturally explains axis alignment of neighbor grid cells and maps shifts, rotations and scaling of the stimuli onto the shape of grid cells' receptive fields, giving a straightforward explanation of the experimental evidence of grid cells remapping under transformations of environmental cues.

Developmental Designs and Adult Functions of Cortical Maps in Multiple Modalities: Perception, Attention, Navigation, Numbers, Streaming, Speech, and Cognition

This article unifies neural modeling results that illustrate several basic design principles and mechanisms that are used by advanced brains to develop cortical maps with multiple psychological functions. One principle concerns how brains use a strip map that simultaneously enables one feature to be represented throughout its extent, as well as an ordered array of another feature at different positions of the strip. Strip maps include circuits to represent ocular dominance and orientation columns, place-value numbers, auditory streams, speaker-normalized speech, and cognitive working memories that can code repeated items. A second principle concerns how feature detectors for multiple functions develop in topographic maps, including maps for optic flow navigation, reinforcement learning, motion perception, and category learning at multiple organizational levels. A third principle concerns how brains exploit a spatial gradient of cells that respond at an ordered sequence of different rates. Such a rate gradient is found along the dorsoventral axis of the entorhinal cortex, whose lateral branch controls the development of time cells, and whose medial branch controls the development of grid cells. Populations of time cells can be used to learn how to adaptively time behaviors for which a time interval of hundreds of milliseconds, or several seconds, must be bridged, as occurs during trace conditioning. Populations of grid cells can be used to learn hippocampal place cells that represent the large spaces in which animals navigate. A fourth principle concerns how and why all neocortical circuits are organized into layers, and how functionally distinct columns develop in these circuits to enable map development. A final principle concerns the role of Adaptive Resonance Theory top-down matching and attentional circuits in the dynamic stabilization of early development and adult learning. Cortical maps are modeled in visual, auditory, temporal, parietal, prefrontal, entorhinal, and hippocampal cortices.

Entorhinal velocity signals reflect environmental geometry

The entorhinal cortex contains neurons that represent self-location, including grid cells that fire in periodic locations and velocity signals that encode running speed and head direction. Although the size and shape of the environment influence grid patterns, whether entorhinal velocity signals are equally influenced or provide a universal metric for self-motion across environments remains unknown. Here we report that speed cells rescale after changes to the size and shape of the environment. Moreover, head direction cells reorganize in an experience-dependent manner to align with the axis of environmental change. A knockout mouse model allows dissociation of the coordination between cell types, with grid and speed cells, but not head direction cells, responding in concert to environmental change. These results point to malleability in the coding features of multiple entorhinal cell types and have implications for which cell types contribute to the velocity signal used by computational models of grid cells.

Identifying Core Regions for Path Integration on Medial Entorhinal Cortex of Hippocampal Formation

Path integration is one of the functions that support the self-localization ability of animals. Path integration outputs position information after an animal’s movement when initial-position and movement information is input. The core region responsible for this function has been identified as the medial entorhinal cortex (MEC), which is part of the hippocampal formation that constitutes the limbic system. However, a more specific core region has not yet been identified. This research aims to clarify the detailed structure at the cell-firing level in the core region responsible for path integration from fragmentarily accumulated experimental and theoretical findings by reviewing 77 papers. This research draws a novel diagram that describes the MEC, the hippocampus, and their surrounding regions by focusing on the MEC’s input/output (I/O) information. The diagram was created by summarizing the results of exhaustively scrutinizing the papers that are relative to the I/O relationship, the connection relationship, and cell position and firing pattern. From additional investigations, we show function information related to path integration, such as I/O information and the relationship between multiple functions. Furthermore, we constructed an algorithmic hypothesis on I/O information and path-integration calculation method from the diagram and the information of functions related to path integration. The algorithmic hypothesis is composed of regions related to path integration, the I/O relations between them, the calculation performed there, and the information representations (cell-firing pattern) in them. Results of examining the hypothesis confirmed that the core region responsible for path integration was either stellate cells in layer II or pyramidal cells in layer III of the MEC.

The Embodied Brain of SOVEREIGN2: From Space-Variant Conscious Percepts During Visual Search and Navigation to Learning Invariant Object Categories and Cognitive-Emotional Plans for Acquiring Valued Goals

This article develops a model of how reactive and planned behaviors interact in real time. Controllers for both animals and animats need reactive mechanisms for exploration, and learned plans to efficiently reach goal objects once an environment becomes familiar. The SOVEREIGN model embodied these capabilities, and was tested in a 3D virtual reality environment. Neural models have characterized important adaptive and intelligent processes that were not included in SOVEREIGN. A major research program is summarized herein by which to consistently incorporate them into an enhanced model called SOVEREIGN2. Key new perceptual, cognitive, cognitive-emotional, and navigational processes require feedback networks which regulate resonant brain states that support conscious experiences of seeing, feeling, and knowing. Also included are computationally complementary processes of the mammalian neocortical What and Where processing streams, and homologous mechanisms for spatial navigation and arm movement control. These include: Unpredictably moving targets are tracked using coordinated smooth pursuit and saccadic movements. Estimates of target and present position are computed in the Where stream, and can activate approach movements. Motion cues can elicit orienting movements to bring new targets into view. Cumulative movement estimates are derived from visual and vestibular cues. Arbitrary navigational routes are incrementally learned as a labeled graph of angles turned and distances traveled between turns. Noisy and incomplete visual sensor data are transformed into representations of visual form and motion. Invariant recognition categories are learned in the What stream. Sequences of invariant object categories are stored in a cognitive working memory, whereas sequences of movement positions and directions are stored in a spatial working memory. Stored sequences trigger learning of cognitive and spatial/motor sequence categories or plans, also called list chunks, which control planned decisions and movements toward valued goal objects. Predictively successful list chunk combinations are selectively enhanced or suppressed via reinforcement learning and incentive motivational learning. Expected vs. unexpected event disconfirmations regulate these enhancement and suppressive processes. Adaptively timed learning enables attention and action to match task constraints. Social cognitive joint attention enables imitation learning of skills by learners who observe teachers from different spatial vantage points.

Position Estimation Based on Grid Cells and Self-Growing Self-Organizing Map

As the basis of animals' natal homing behavior, path integration can continuously provide current position information relative to the initial position. Some neurons in freely moving animals' brains can encode current positions and surrounding environments by special firing patterns. Research studies show that neurons such as grid cells (GCs) in the hippocampus of animals' brains are related to the path integration. They might encode the coordinate of the animal's current position in the same way as the residue number system (RNS) which is based on the Chinese remainder theorem (CRT). Hence, in order to provide vehicles a bionic position estimation method, we propose a model to decode the GCs' encoding information based on the improved traditional self-organizing map (SOM), and this model makes full use of GCs' firing characteristics. The details of the model are discussed in this paper. Besides, the model is realized by computer simulation, and its performance is analyzed under different conditions. Simulation results indicate that the proposed position estimation model is effective and stable.

Merging information in the entorhinal cortex: what can we learn from robotics experiments and modeling?

Place recognition is a complex process involving idiothetic and allothetic information. In mammals, evidence suggests that visual information stemming from the temporal and parietal cortical areas (‘what’ and ‘where’ information) is merged at the level of the entorhinal cortex (EC) to build a compact code of a place. Local views extracted from specific feature points can provide information important for view cells (in primates) and place cells (in rodents) even when the environment changes dramatically. Robotics experiments using conjunctive cells merging ‘what’ and ‘where’ information related to different local views show their important role for obtaining place cells with strong generalization capabilities. This convergence of information may also explain the formation of grid cells in the medial EC if we suppose that: (1) path integration information is computed outside the EC, (2) this information is compressed at the level of the EC owing to projection (which follows a modulo principle) of cortical activities associated with discretized vector fields representing angles and/or path integration, and (3) conjunctive cells merge the projections of different modalities to build grid cell activities. Applying modulo projection to visual information allows an interesting compression of information and could explain more recent results on grid cells related to visual exploration. In conclusion, the EC could be dedicated to the build-up of a robust yet compact code of cortical activity whereas the hippocampus proper recognizes these complex codes and learns to predict the transition from one state to another.

Saccade Velocity Driven Oscillatory Network Model of Grid Cells

Grid cells and place cells are believed to be cellular substrates for the spatial navigation functions of hippocampus as experimental animals physically navigated in 2D and 3D spaces. However, a recent saccade study on head fixated monkey has also reported grid-like representations on saccadic trajectory while the animal scanned the images on a computer screen. We present two computational models that explain the formation of grid patterns on saccadic trajectory formed on the novel Images. The first model named Saccade Velocity Driven Oscillatory Network -Direct PCA (SVDON—DPCA) explains how grid patterns can be generated on saccadic space using Principal Component Analysis (PCA) like learning rule. The model adopts a hierarchical architecture. We extend this to a network model viz. Saccade Velocity Driven Oscillatory Network—Network PCA (SVDON-NPCA) where the direct PCA stage is replaced by a neural network that can implement PCA using a neurally plausible algorithm. This gives the leverage to study the formation of grid cells at a network level. Saccade trajectory for both models is generated based on an attention model which attends to the salient location by computing the saliency maps of the images. Both models capture the spatial characteristics of grid cells such as grid scale variation on the dorso-ventral axis of Medial Entorhinal cortex. Adding one more layer of LAHN over the SVDON-NPCA model predicts the Place cells in saccadic space, which are yet to be discovered experimentally. To the best of our knowledge, this is the first attempt to model grid cells and place cells from saccade trajectory.

A hierarchical anti-Hebbian network model for the formation of spatial cells in three-dimensional space

Three-dimensional (3D) spatial cells in the mammalian hippocampal formation are believed to support the existence of 3D cognitive maps. Modeling studies are crucial to comprehend the neural principles governing the formation of these maps, yet to date very few have addressed this topic in 3D space. Here we present a hierarchical network model for the formation of 3D spatial cells using anti-Hebbian network. Built on empirical data, the model accounts for the natural emergence of 3D place, border, and grid cells, as well as a new type of previously undescribed spatial cell type which we call plane cells. It further explains the plausible reason behind the place and grid-cell anisotropic coding that has been observed in rodents and the potential discrepancy with the predicted periodic coding during 3D volumetric navigation. Lastly, it provides evidence for the importance of unsupervised learning rules in guiding the formation of higher-dimensional cognitive maps.

Neurons in the hippocampal formation encode diverse spatial properties. Here, the authors present a hierarchical network model for 3D spatial navigation that accounts for the observed neuronal representations and predict as yet unreported cell types with planar selectivity.

Inferring circuit mechanisms from sparse neural recording and global perturbation in grid cells

A goal of systems neuroscience is to discover the circuit mechanisms underlying brain function. Despite experimental advances that enable circuit-wide neural recording, the problem remains open in part because solving the 'inverse problem' of inferring circuity and mechanism by merely observing activity is hard. In the grid cell system, we show through modeling that a technique based on global circuit perturbation and examination of a novel theoretical object called the distribution of relative phase shifts (DRPS) could reveal the mechanisms of a cortical circuit at unprecedented detail using extremely sparse neural recordings. We establish feasibility, showing that the method can discriminate between recurrent versus feedforward mechanisms and amongst various recurrent mechanisms using recordings from a handful of cells. The proposed strategy demonstrates that sparse recording coupled with simple perturbation can reveal more about circuit mechanism than can full knowledge of network activity or the synaptic connectivity matrix.

A unified hierarchical oscillatory network model of head direction cells, spatially periodic cells, and place cells

Spatial cells in the hippocampal complex play a pivotal role in the navigation of an animal. Exact neural principles behind these spatial cell responses have not been completely unraveled yet. Here we present two models for spatial cells, namely the Velocity Driven Oscillatory Network (VDON) and Locomotor Driven Oscillatory Network. Both models have basically three stages in common such as direction encoding stage, path integration (PI) stage, and a stage of unsupervised learning of PI values. In the first model, the following three stages are implemented: head direction layer, frequency modulation by a layer of oscillatory neurons, and an unsupervised stage that extracts the principal components from the oscillator outputs. In the second model, a refined version of the first model, the stages are extraction of velocity representation from the locomotor input, frequency modulation by a layer of oscillators, and two cascaded unsupervised stages consisting of the lateral anti-hebbian network. The principal component stage of VDON exhibits grid cell-like spatially periodic responses including hexagonal firing fields. Locomotor Driven Oscillatory Network shows the emergence of spatially periodic grid cells and periodically active border-like cells in its lower layer; place cell responses are found in its higher layer. This model shows the inheritance of phase precession from grid cell to place cell in both one- and two-dimensional spaces. It also shows a novel result on the influence of locomotion rhythms on the grid cell activity. The study thus presents a comprehensive, unifying hierarchical model for hippocampal spatial cells.

An Analysis of Waves Underlying Grid Cell Firing in the Medial Enthorinal Cortex

Layer II stellate cells in the medial enthorinal cortex (MEC) express hyperpolarisation-activated cyclic-nucleotide-gated (HCN) channels that allow for rebound spiking via an [Formula: see text] current in response to hyperpolarising synaptic input. A computational modelling study by Hasselmo (Philos. Trans. R. Soc. Lond. B, Biol. Sci. 369:20120523, 2013) showed that an inhibitory network of such cells can support periodic travelling waves with a period that is controlled by the dynamics of the [Formula: see text] current. Hasselmo has suggested that these waves can underlie the generation of grid cells, and that the known difference in [Formula: see text] resonance frequency along the dorsal to ventral axis can explain the observed size and spacing between grid cell firing fields. Here we develop a biophysical spiking model within a framework that allows for analytical tractability. We combine the simplicity of integrate-and-fire neurons with a piecewise linear caricature of the gating dynamics for HCN channels to develop a spiking neural field model of MEC. Using techniques primarily drawn from the field of nonsmooth dynamical systems we show how to construct periodic travelling waves, and in particular the dispersion curve that determines how wave speed varies as a function of period. This exhibits a wide range of long wavelength solutions, reinforcing the idea that rebound spiking is a candidate mechanism for generating grid cell firing patterns. Importantly we develop a wave stability analysis to show how the maximum allowed period is controlled by the dynamical properties of the [Formula: see text] current. Our theoretical work is validated by numerical simulations of the spiking model in both one and two dimensions.

A neural model of normal and abnormal learning and memory consolidation: adaptively timed conditioning, hippocampus, amnesia, neurotrophins, and consciousness

How do the hippocampus and amygdala interact with thalamocortical systems to regulate cognitive and cognitive-emotional learning? Why do lesions of thalamus, amygdala, hippocampus, and cortex have differential effects depending on the phase of learning when they occur? In particular, why is the hippocampus typically needed for trace conditioning, but not delay conditioning, and what do the exceptions reveal? Why do amygdala lesions made before or immediately after training decelerate conditioning while those made later do not? Why do thalamic or sensory cortical lesions degrade trace conditioning more than delay conditioning? Why do hippocampal lesions during trace conditioning experiments degrade recent but not temporally remote learning? Why do orbitofrontal cortical lesions degrade temporally remote but not recent or post-lesion learning? How is temporally graded amnesia caused by ablation of prefrontal cortex after memory consolidation? How are attention and consciousness linked during conditioning? How do neurotrophins, notably brain-derived neurotrophic factor (BDNF), influence memory formation and consolidation? Is there a common output path for learned performance? A neural model proposes a unified answer to these questions that overcome problems of alternative memory models.

On Decoding Grid Cell Population Codes Using Approximate Belief Propagation

Neural systems are inherently noisy. One well-studied example of a noise reduction mechanism in the brain is the population code, where representing a variable with multiple neurons allows the encoded variable to be recovered with fewer errors. Studies have assumed ideal observer models for decoding population codes, and the manner in which information in the neural population can be retrieved remains elusive. This letter addresses a mechanism by which realistic neural circuits can recover encoded variables. Specifically, the decoding problem of recovering a spatial location from populations of grid cells is studied using belief propagation. We extend the belief propagation decoding algorithm in two aspects. First, beliefs are approximated rather than being calculated exactly. Second, decoding noises are introduced into the decoding circuits. Numerical simulations demonstrate that beliefs can be effectively approximated by combining polynomial nonlinearities with divisive normalization. This approximate belief propagation algorithm is tolerant to decoding noises. Thus, this letter presents a realistic model for decoding neural population codes and investigates fault-tolerant information retrieval mechanisms in the brain.

Modelling effects on grid cells of sensory input during self-motion

The neural coding of spatial location for memory function may involve grid cells in the medial entorhinal cortex, but the mechanism of generating the spatial responses of grid cells remains unclear. This review describes some current theories and experimental data concerning the role of sensory input in generating the regular spatial firing patterns of grid cells, and changes in grid cell firing fields with movement of environmental barriers. As described here, the influence of visual features on spatial firing could involve either computations of self-motion based on optic flow, or computations of absolute position based on the angle and distance of static visual cues. Due to anatomical selectivity of retinotopic processing, the sensory features on the walls of an environment may have a stronger effect on ventral grid cells that have wider spaced firing fields, whereas the sensory features on the ground plane may influence the firing of dorsal grid cells with narrower spacing between firing fields. These sensory influences could contribute to the potential functional role of grid cells in guiding goal-directed navigation.

Framing the grid: effect of boundaries on grid cells and navigation

Cells in the mammalian hippocampal formation subserve neuronal representations of environmental location and support navigation in familiar environments. Grid cells constitute one of the main cell types in the hippocampal formation and are widely believed to represent a universal metric of space independent of external stimuli. Recent evidence showing that grid symmetry is distorted in non-symmetrical environments suggests that a re-examination of this hypothesis is warranted. In this review we will discuss behavioural and physiological evidence for how environmental shape and in particular enclosure boundaries influence grid cell firing properties. We propose that grid cells encode the geometric layout of enclosures.

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.

Neuromorphic VLSI realization of the hippocampal formation

The medial entorhinal cortex grid cells, aided by the subicular head direction cells, are thought to provide a matrix which is utilized by the hippocampal place cells for calculation of position of an animal during spatial navigation. The place cells are thought to function as an internal GPS for the brain and provide a spatiotemporal stamp on episodic memories. Several computational neuroscience models have been proposed to explain the place specific firing patterns of the cells of the hippocampal formation - including the GRIDSmap model for grid cells and Bayesian integration for place cells. In this work, we present design and measurement results from a first ever system of silicon circuits which successfully realize the function of the hippocampal formation of brain based on these models.

Grids from bands, or bands from grids? An examination of the effects of single unit contamination on grid cell firing fields

Neural recording technology is improving rapidly, allowing for the detection of spikes from hundreds of cells simultaneously. The limiting step in multielectrode electrophysiology continues to be single cell isolation. However, this step is crucial to the interpretation of data from putative single neurons. We present here, in simulation, an illustration of possibly erroneous conclusions that may be reached when poorly isolated single cell data are analyzed. Grid cells are neurons recorded in rodents, and bats, that spike in equally spaced locations in a hexagonal pattern. One theory states that grid firing patterns arise from a combination of band firing patterns. However, we show here that summing the grid firing patterns of two poorly resolved neurons can result in spurious band-like patterns. Thus, evidence of neurons spiking in band patterns must undergo extreme scrutiny before it is accepted. Toward this aim, we discuss single cell isolation methods and metrics.

Using Grid Cells for Navigation

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

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Grid cells (GCs) are believed to provide a path integration input to place cells

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However, GCs also provide a powerful context-independent metric for large-scale space

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Hence, we show how GCs can be used for vector navigation between arbitrary locations

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We simulate various neural implementations and make testable experimental predictions

Neural mechanisms of self-location

The ability to self-localise and to navigate to remembered goals in complex and changeable environments is crucial to the survival of many mobile species. Electrophysiological investigations of the mammalian hippocampus and associated brain structures have identified several classes of neurons which represent information about an organism's position and orientation. These include place cells, grid cells, head direction cells, and boundary vector cells, as well as cells representing aspects of self-motion. Understanding how these neural representations are formed and updated from environmental sensory information and from information relating to self-motion is an important topic attracting considerable current interest. Here we review the computational mechanisms thought to underlie the formation of these different spatial representations, the interactions between them, and their use in guiding behaviour. These include some of the clearest examples of computational mechanisms of general interest to neuroscience, such as attractor dynamics, temporal coding and multi-modal integration. We also discuss the close relationships between computational modelling and experimental research which are driving progress in this area.

Grid cells in 3-D: Reconciling data and models

It is well documented that place cells and grid cells in echolocating bats show properties similar to those described in rodents, and yet, continuous theta-frequency oscillations, proposed to play a central role in grid/place cell formation, are not present in bat recordings. These comparative neurophysiological data have raised many questions about the role of theta-frequency oscillations in spatial memory and navigation. Additionally, spatial navigation in three-dimensions poses new challenges for the representation of space in neural models. Inspired by the literature on space representation in the echolocating bat, we have developed a nonoscillatory model of 3-D grid cell creation that shares many of the features of existing oscillatory-interference models. We discuss the model in the context of current knowledge of 3-D space representation and highlight directions for future research.

Current questions on space and time encoding

The Nobel Prize in Physiology or Medicine 2014 celebrated the groundbreaking findings on place cells and grid cells by John O'Keefe and May-Britt Moser and Edvard Moser. These findings provided an essential foothold for understanding the cognitive encoding of space and time in episodic memory function. This foothold provides a closer view of a broad new world of important research questions raised by the phenomena of place cells and grid cells. These questions concern the mechanisms of generation of place and grid cell firing, including sensory influences, circuit dynamics and intrinsic properties. Similar questions concern the generation of time cells. In addition, questions concern the functional role of place cells, grid cells and time cells in mediating goal-directed behavior and episodic memory function.

From grid cells and visual place cells to multimodal place cell: a new robotic architecture

In the present study, a new architecture for the generation of grid cells (GC) was implemented on a real robot. In order to test this model a simple place cell (PC) model merging visual PC activity and GC was developed. GC were first built from a simple "several to one" projection (similar to a modulo operation) performed on a neural field coding for path integration (PI). Robotics experiments raised several practical and theoretical issues. To limit the important angular drift of PI, head direction information was introduced in addition to the robot proprioceptive signal coming from the wheel rotation. Next, a simple associative learning between visual place cells and the neural field coding for the PI has been used to recalibrate the PI and to limit its drift. Finally, the parameters controlling the shape of the PC built from the GC have been studied. Increasing the number of GC obviously improves the shape of the resulting place field. Yet, other parameters such as the discretization factor of PI or the lateral interactions between GC can have an important impact on the place field quality and avoid the need of a very large number of GC. In conclusion, our results show our GC model based on the compression of PI is congruent with neurobiological studies made on rodent. GC firing patterns can be the result of a modulo transformation of PI information. We argue that such a transformation may be a general property of the connectivity from the cortex to the entorhinal cortex. Our model predicts that the effect of similar transformations on other kinds of sensory information (visual, tactile, auditory, etc…) in the entorhinal cortex should be observed. Consequently, a given EC cell should react to non-contiguous input configurations in non-spatial conditions according to the projection from its different inputs.

Oscillator-interference models of path integration do not require theta oscillations

Navigation and path integration in rodents seems to involve place cells, grid cells, and theta oscillations (4-12 Hz) in the local field potential. Two main theories have been proposed to explain the neurological underpinnings of how these phenomena relate to navigation and to each other. Attractor network (AN) models revolve around the idea that local excitation and long-range inhibition connectivity can spontaneously generate grid-cell-like activity patterns. Oscillator interference (OI) models propose that spatial patterns of activity are caused by the interference patterns between neural oscillators. In rats, these oscillators have a frequency close to the theta frequency. Recent studies have shown that bats do not exhibit a theta cycle when they crawl, and yet they still have grid cells. This has been interpreted as a criticism of OI models. However, OI models do not require theta oscillations. We explain why the absence of theta oscillations does not contradict OI models and discuss how the two families of models might be distinguished experimentally.

From brain synapses to systems for learning and memory: Object recognition, spatial navigation, timed conditioning, and movement control

This article provides an overview of neural models of synaptic learning and memory whose expression in adaptive behavior depends critically on the circuits and systems in which the synapses are embedded. It reviews Adaptive Resonance Theory, or ART, models that use excitatory matching and match-based learning to achieve fast category learning and whose learned memories are dynamically stabilized by top-down expectations, attentional focusing, and memory search. ART clarifies mechanistic relationships between consciousness, learning, expectation, attention, resonance, and synchrony. ART models are embedded in ARTSCAN architectures that unify processes of invariant object category learning, recognition, spatial and object attention, predictive remapping, and eye movement search, and that clarify how conscious object vision and recognition may fail during perceptual crowding and parietal neglect. The generality of learned categories depends upon a vigilance process that is regulated by acetylcholine via the nucleus basalis. Vigilance can get stuck at too high or too low values, thereby causing learning problems in autism and medial temporal amnesia. Similar synaptic learning laws support qualitatively different behaviors: Invariant object category learning in the inferotemporal cortex; learning of grid cells and place cells in the entorhinal and hippocampal cortices during spatial navigation; and learning of time cells in the entorhinal-hippocampal system during adaptively timed conditioning, including trace conditioning. Spatial and temporal processes through the medial and lateral entorhinal-hippocampal system seem to be carried out with homologous circuit designs. Variations of a shared laminar neocortical circuit design have modeled 3D vision, speech perception, and cognitive working memory and learning. A complementary kind of inhibitory matching and mismatch learning controls movement. This article is part of a Special Issue entitled SI: Brain and Memory.

The functional micro-organization of grid cells revealed by cellular-resolution imaging

Establishing how grid cells are anatomically arranged, on a microscopic scale, in relation to their firing patterns in the environment would facilitate a greater microcircuit-level understanding of the brain's representation of space. However, all previous grid cell recordings used electrode techniques that provide limited descriptions of fine-scale organization. We therefore developed a technique for cellular-resolution functional imaging of medial entorhinal cortex (MEC) neurons in mice navigating a virtual linear track, enabling a new experimental approach to study MEC. Using these methods, we show that grid cells are physically clustered in MEC compared to nongrid cells. Additionally, we demonstrate that grid cells are functionally micro-organized: the similarity between the environment firing locations of grid cell pairs varies as a function of the distance between them according to a "Mexican hat"-shaped profile. This suggests that, on average, nearby grid cells have more similar spatial firing phases than those further apart.

Grid cell firing patterns may arise from feedback interaction between intrinsic rebound spiking and transverse traveling waves with multiple heading angles

This article presents a model using cellular resonance and rebound properties to model grid cells in medial entorhinal cortex. The model simulates the intrinsic resonance properties of single layer II stellate cells with different frequencies due to the hyperpolarization activated cation current (h current). The stellate cells generate rebound spikes after a delay interval that differs for neurons with different resonance frequency. Stellate cells drive inhibitory interneurons to cause rebound from inhibition in an alternate set of stellate cells that drive interneurons to activate the first set of cells. This allows maintenance of activity with cycle skipping of the spiking of cells that matches recent physiological data on theta cycle skipping. The rebound spiking interacts with subthreshold oscillatory input to stellate cells or interneurons regulated by medial septal input and defined relative to the spatial location coded by neurons. The timing of rebound determines whether the network maintains the activity for the same location or shifts to phases of activity representing a different location. Simulations show that spatial firing patterns similar to grid cells can be generated with a range of different resonance frequencies, indicating how grid cells could be generated with low frequencies present in bats and in mice with knockout of the HCN1 subunit of the h current.

Real-time learning of predictive recognition categories that chunk sequences of items stored in working memory

How are sequences of events that are temporarily stored in a cognitive working memory unitized, or chunked, through learning? Such sequential learning is needed by the brain in order to enable language, spatial understanding, and motor skills to develop. In particular, how does the brain learn categories, or list chunks, that become selectively tuned to different temporal sequences of items in lists of variable length as they are stored in working memory, and how does this learning process occur in real time? The present article introduces a neural model that simulates learning of such list chunks. In this model, sequences of items are temporarily stored in an Item-and-Order, or competitive queuing, working memory before learning categorizes them using a categorization network, called a Masking Field, which is a self-similar, multiple-scale, recurrent on-center off-surround network that can weigh the evidence for variable-length sequences of items as they are stored in the working memory through time. A Masking Field hereby activates the learned list chunks that represent the most predictive item groupings at any time, while suppressing less predictive chunks. In a network with a given number of input items, all possible ordered sets of these item sequences, up to a fixed length, can be learned with unsupervised or supervised learning. The self-similar multiple-scale properties of Masking Fields interacting with an Item-and-Order working memory provide a natural explanation of George Miller's Magical Number Seven and Nelson Cowan's Magical Number Four. The article explains why linguistic, spatial, and action event sequences may all be stored by Item-and-Order working memories that obey similar design principles, and thus how the current results may apply across modalities. Item-and-Order properties may readily be extended to Item-Order-Rank working memories in which the same item can be stored in multiple list positions, or ranks, as in the list ABADBD. Comparisons with other models, including TRACE, MERGE, and TISK, are made.

A model of grid cell development through spatial exploration and spike time-dependent plasticity

Grid cell responses develop gradually after eye opening, but little is known about the rules that govern this process. We present a biologically plausible model for the formation of a grid cell network. An asymmetric spike time-dependent plasticity rule acts upon an initially unstructured network of spiking neurons that receive inputs encoding animal velocity and location. Neurons develop an organized recurrent architecture based on the similarity of their inputs, interacting through inhibitory interneurons. The mature network can convert velocity inputs into estimates of animal location, showing that spatially periodic responses and the capacity of path integration can arise through synaptic plasticity, acting on inputs that display neither. The model provides numerous predictions about the necessity of spatial exploration for grid cell development, network topography, the maturation of velocity tuning and neural correlations, the abrupt transition to stable patterned responses, and possible mechanisms to set grid period across grid modules.

Controlling phase noise in oscillatory interference models of grid cell firing

Oscillatory interference models account for the spatial firing properties of grid cells in terms of neuronal oscillators with frequencies modulated by the animal's movement velocity. The phase of such a "velocity-controlled oscillator" (VCO) relative to a baseline (theta-band) oscillation tracks displacement along a preferred direction. Input from multiple VCOs with appropriate preferred directions causes a grid cell's grid-like firing pattern. However, accumulating phase noise causes the firing pattern to drift and become corrupted. Here we show how multiple redundant VCOs can automatically compensate for phase noise. By entraining the baseline frequency to the mean VCO frequency, VCO phases remain consistent, ensuring a coherent grid pattern and reducing its spatial drift. We show how the spatial stability of grid firing depends on the variability in VCO phases, e.g., a phase SD of 3 ms per 125 ms cycle results in stable grids for 1 min. Finally, coupling N VCOs with similar preferred directions as a ring attractor, so that their relative phases remain constant, produces grid cells with consistently offset grids, and reduces VCO phase variability of the order square root of N. The results suggest a viable functional organization of the grid cell network, and highlight the benefit of integrating displacement along multiple redundant directions for the purpose of path integration.

Grid cells and cortical representation

One of the grand challenges in neuroscience is to comprehend neural computation in the association cortices, the parts of the cortex that have shown the largest expansion and differentiation during mammalian evolution and that are thought to contribute profoundly to the emergence of advanced cognition in humans. In this Review, we use grid cells in the medial entorhinal cortex as a gateway to understand network computation at a stage of cortical processing in which firing patterns are shaped not primarily by incoming sensory signals but to a large extent by the intrinsic properties of the local circuit.

How does the modular organization of entorhinal grid cells develop?

The entorhinal-hippocampal system plays a crucial role in spatial cognition and navigation. Since the discovery of grid cells in layer II of medial entorhinal cortex (MEC), several types of models have been proposed to explain their development and operation; namely, continuous attractor network models, oscillatory interference models, and self-organizing map (SOM) models. Recent experiments revealing the in vivo intracellular signatures of grid cells (Domnisoru et al., 2013; Schmidt-Heiber and Hausser, 2013), the primarily inhibitory recurrent connectivity of grid cells (Couey et al., 2013; Pastoll et al., 2013), and the topographic organization of grid cells within anatomically overlapping modules of multiple spatial scales along the dorsoventral axis of MEC (Stensola et al., 2012) provide strong constraints and challenges to existing grid cell models. This article provides a computational explanation for how MEC cells can emerge through learning with grid cell properties in modular structures. Within this SOM model, grid cells with different rates of temporal integration learn modular properties with different spatial scales. Model grid cells learn in response to inputs from multiple scales of directionally-selective stripe cells (Krupic et al., 2012; Mhatre et al., 2012) that perform path integration of the linear velocities that are experienced during navigation. Slower rates of grid cell temporal integration support learned associations with stripe cells of larger scales. The explanatory and predictive capabilities of the three types of grid cell models are comparatively analyzed in light of recent data to illustrate how the SOM model overcomes problems that other types of models have not yet handled.

A hybrid oscillatory interference/continuous attractor network model of grid cell firing

Grid cells in the rodent medial entorhinal cortex exhibit remarkably regular spatial firing patterns that tessellate all environments visited by the animal. Two theoretical mechanisms that could generate this spatially periodic activity pattern have been proposed: oscillatory interference and continuous attractor dynamics. Although a variety of evidence has been cited in support of each, some aspects of the two mechanisms are complementary, suggesting that a combined model may best account for experimental data. The oscillatory interference model proposes that the grid pattern is formed from linear interference patterns or "periodic bands" in which velocity-controlled oscillators integrate self-motion to code displacement along preferred directions. However, it also allows the use of symmetric recurrent connectivity between grid cells to provide relative stability and continuous attractor dynamics. Here, we present simulations of this type of hybrid model, demonstrate that it generates intracellular membrane potential profiles that closely match those observed in vivo, addresses several criticisms aimed at pure oscillatory interference and continuous attractor models, and provides testable predictions for future empirical studies.

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.