Learning place cells, grid cells and invariances with excitatory and inhibitory plasticity

Robust variability of grid cell properties within individual grid modules enhances encoding of local space

Although grid cells are one of the most well studied functional classes of neurons in the mammalian brain, the assumption that there is a single grid orientation and spacing per grid module has not been carefully tested. We investigate and analyze a recent large-scale recording of medial entorhinal cortex to characterize the presence and degree of heterogeneity of grid properties within individual modules. We find evidence for small, but robust, variability and hypothesize that this property of the grid code could enhance the ability of encoding local spatial information. Performing analysis on synthetic populations of grid cells, where we have complete control over the amount heterogeneity in grid properties, we demonstrate that variability, of a similar magnitude to the analyzed data, leads to significantly decreased decoding error, even when restricted to activity from a single module. Our results highlight how the heterogeneity of the neural response properties may benefit coding and opens new directions for theoretical and experimental analysis of grid cells.

A miniaturized mesoscope for the large-scale single-neuron-resolved imaging of neuronal activity in freely behaving mice

Exploring the relationship between neuronal dynamics and ethologically relevant behaviour involves recording neuronal-population activity using technologies that are compatible with unrestricted animal behaviour. However, head-mounted microscopes that accommodate weight limits to allow for free animal behaviour typically compromise field of view, resolution or depth range, and are susceptible to movement-induced artefacts. Here we report a miniaturized head-mounted fluorescent mesoscope that we systematically optimized for calcium imaging at single-neuron resolution, for increased fields of view and depth of field, and for robustness against motion-generated artefacts. Weighing less than 2.5 g, the mesoscope enabled recordings of neuronal-population activity at up to 16 Hz, with 4 μm resolution over 300 μm depth-of-field across a field of view of 3.6 × 3.6 mm2 in the cortex of freely moving mice. We used the mesoscope to record large-scale neuronal-population activity in socially interacting mice during free exploration and during fear-conditioning experiments, and to investigate neurovascular coupling across multiple cortical regions.

CA3 Circuit Model Compressing Sequential Information in Theta Oscillation and Replay

The hippocampus plays a critical role in the compression and retrieval of sequential information. During wakefulness, it achieves this through theta phase precession and theta sequences. Subsequently, during periods of sleep or rest, the compressed information reactivates through sharp-wave ripple events, manifesting as memory replay. However, how these sequential neuronal activities are generated and how they store information about the external environment remain unknown. We developed a hippocampal cornu ammonis 3 (CA3) computational model based on anatomical and electrophysiological evidence from the biological CA3 circuit to address these questions. The model comprises theta rhythm inhibition, place input, and CA3-CA3 plastic recurrent connection. The model can compress the sequence of the external inputs, reproduce theta phase precession and replay, learn additional sequences, and reorganize previously learned sequences. A gradual increase in synaptic inputs, controlled by interactions between theta-paced inhibition and place inputs, explained the mechanism of sequence acquisition. This model highlights the crucial role of plasticity in the CA3 recurrent connection and theta oscillational dynamics and hypothesizes how the CA3 circuit acquires, compresses, and replays sequential information.

A consistent map in the medial entorhinal cortex supports spatial memory

The medial entorhinal cortex (MEC) is hypothesized to function as a cognitive map for memory-guided navigation. How this map develops during learning and influences memory remains unclear. By imaging MEC calcium dynamics while mice successfully learned a novel virtual environment over ten days, we discovered that the dynamics gradually became more spatially consistent and then stabilized. Additionally, grid cells in the MEC not only exhibited improved spatial tuning consistency, but also maintained stable phase relationships, suggesting a network mechanism involving synaptic plasticity and rigid recurrent connectivity to shape grid cell activity during learning. Increased c-Fos expression in the MEC in novel environments further supports the induction of synaptic plasticity. Unsuccessful learning lacked these activity features, indicating that a consistent map is specific for effective spatial memory. Finally, optogenetically disrupting spatial consistency of the map impaired memory-guided navigation in a well-learned environment. Thus, we demonstrate that the establishment of a spatially consistent MEC map across learning both correlates with, and is necessary for, successful spatial memory.

A consistent map in the medial entorhinal cortex supports spatial memory

The medial entorhinal cortex (MEC) is hypothesized to function as a cognitive map for memory-guided navigation. How this map develops during learning and influences memory remains unclear. By imaging MEC calcium dynamics while mice successfully learned a novel virtual environment over ten days, we discovered that the dynamics gradually became more spatially consistent and then stabilized. Additionally, grid cells in the MEC not only exhibited improved spatial tuning consistency, but also maintained stable phase relationships, suggesting a network mechanism involving synaptic plasticity and rigid recurrent connectivity to shape grid cell activity during learning. Increased c-Fos expression in the MEC in novel environments further supports the induction of synaptic plasticity. Unsuccessful learning lacked these activity features, indicating that a consistent map is specific for effective spatial memory. Finally, optogenetically disrupting spatial consistency of the map impaired memory-guided navigation in a well-learned environment. Thus, we demonstrate that the establishment of a spatially consistent MEC map across learning both correlates with, and is necessary for, successful spatial memory.

Are grid cells used for navigation? On local metrics, subjective spaces, and black holes

The symmetric, lattice-like spatial pattern of grid-cell activity is thought to provide a neuronal global metric for space. This view is compatible with grid cells recorded in empty boxes but inconsistent with data from more naturalistic settings. We review evidence arguing against the global-metric notion, including the distortion and disintegration of the grid pattern in complex and three-dimensional environments. We argue that deviations from lattice symmetry are key for understanding grid-cell function. We propose three possible functions for grid cells, which treat real-world grid distortions as a feature rather than a bug. First, grid cells may constitute a local metric for proximal space rather than a global metric for all space. Second, grid cells could form a metric for subjective action-relevant space rather than physical space. Third, distortions may represent salient locations. Finally, we discuss mechanisms that can underlie these functions. These ideas may transform our thinking about grid cells.

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.

Excitatory-inhibitory recurrent dynamics produce robust visual grids and stable attractors

Spatially modulated grid cells have been recently found in the rat secondary visual cortex (V2) during active navigation. However, the computational mechanism and functional significance of V2 grid cells remain unknown. To address the knowledge gap, we train a biologically inspired excitatory-inhibitory recurrent neural network to perform a two-dimensional spatial navigation task with multisensory input. We find grid-like responses in both excitatory and inhibitory RNN units, which are robust with respect to spatial cues, dimensionality of visual input, and activation function. Population responses reveal a low-dimensional, torus-like manifold and attractor. We find a link between functional grid clusters with similar receptive fields and structured excitatory-to-excitatory connections. Additionally, multistable torus-like attractors emerged with increasing sparsity in inter- and intra-subnetwork connectivity. Finally, irregular grid patterns are found in recurrent neural network (RNN) units during a visual sequence recognition task. Together, our results suggest common computational mechanisms of V2 grid cells for spatial and non-spatial tasks.

Place cells dynamically refine grid cell activities to reduce error accumulation during path integration in a continuous attractor model

Navigation is one of the most fundamental skills of animals. During spatial navigation, grid cells in the medial entorhinal cortex process speed and direction of the animal to map the environment. Hippocampal place cells, in turn, encode place using sensory signals and reduce the accumulated error of grid cells for path integration. Although both cell types are part of the path integration system, the dynamic relationship between place and grid cells and the error reduction mechanism is yet to be understood. We implemented a realistic model of grid cells based on a continuous attractor model. The grid cell model was coupled to a place cell model to address their dynamic relationship during a simulated animal's exploration of a square arena. The grid cell model processed the animal's velocity and place field information from place cells. Place cells incorporated salient visual features and proximity information with input from grid cells to define their place fields. Grid cells had similar spatial phases but a diversity of spacings and orientations. To determine the role of place cells in error reduction for path integration, the animal's position estimates were decoded from grid cell activities with and without the place field input. We found that the accumulated error was reduced as place fields emerged during the exploration. Place fields closer to the animal's current location contributed more to the error reduction than remote place fields. Place cells' fields encoding space could function as spatial anchoring signals for precise path integration by grid cells.

Regulation of circuit organization and function through inhibitory synaptic plasticity

Diverse inhibitory neurons in the mammalian brain shape circuit connectivity and dynamics through mechanisms of synaptic plasticity. Inhibitory plasticity can establish excitation/inhibition (E/I) balance, control neuronal firing, and affect local calcium concentration, hence regulating neuronal activity at the network, single neuron, and dendritic level. Computational models can synthesize multiple experimental results and provide insight into how inhibitory plasticity controls circuit dynamics and sculpts connectivity by identifying phenomenological learning rules amenable to mathematical analysis. We highlight recent studies on the role of inhibitory plasticity in modulating excitatory plasticity, forming structured networks underlying memory formation and recall, and implementing adaptive phenomena and novelty detection. We conclude with experimental and modeling progress on the role of interneuron-specific plasticity in circuit computation and context-dependent learning.

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.

Toroidal topology of population activity in grid cells

The medial entorhinal cortex is part of a neural system for mapping the position of an individual within a physical environment1. Grid cells, a key component of this system, fire in a characteristic hexagonal pattern of locations2, and are organized in modules3 that collectively form a population code for the animal's allocentric position1. The invariance of the correlation structure of this population code across environments4,5 and behavioural states6,7, independent of specific sensory inputs, has pointed to intrinsic, recurrently connected continuous attractor networks (CANs) as a possible substrate of the grid pattern1,8-11. However, whether grid cell networks show continuous attractor dynamics, and how they interface with inputs from the environment, has remained unclear owing to the small samples of cells obtained so far. Here, using simultaneous recordings from many hundreds of grid cells and subsequent topological data analysis, we show that the joint activity of grid cells from an individual module resides on a toroidal manifold, as expected in a two-dimensional CAN. Positions on the torus correspond to positions of the moving animal in the environment. Individual cells are preferentially active at singular positions on the torus. Their positions are maintained between environments and from wakefulness to sleep, as predicted by CAN models for grid cells but not by alternative feedforward models12. This demonstration of network dynamics on a toroidal manifold provides a population-level visualization of CAN dynamics in grid cells.

Self-organization of a doubly asynchronous irregular network state for spikes and bursts

Cortical pyramidal cells (PCs) have a specialized dendritic mechanism for the generation of bursts, suggesting that these events play a special role in cortical information processing. In vivo, bursts occur at a low, but consistent rate. Theory suggests that this network state increases the amount of information they convey. However, because burst activity relies on a threshold mechanism, it is rather sensitive to dendritic input levels. In spiking network models, network states in which bursts occur rarely are therefore typically not robust, but require fine-tuning. Here, we show that this issue can be solved by a homeostatic inhibitory plasticity rule in dendrite-targeting interneurons that is consistent with experimental data. The suggested learning rule can be combined with other forms of inhibitory plasticity to self-organize a network state in which both spikes and bursts occur asynchronously and irregularly at low rate. Finally, we show that this network state creates the network conditions for a recently suggested multiplexed code and thereby indeed increases the amount of information encoded in bursts.

Memories in a network with excitatory and inhibitory plasticity are encoded in the spiking irregularity

Cell assemblies are thought to be the substrate of memory in the brain. Theoretical studies have previously shown that assemblies can be formed in networks with multiple types of plasticity. But how exactly they are formed and how they encode information is yet to be fully understood. One possibility is that memories are stored in silent assemblies. Here we used a computational model to study the formation of silent assemblies in a network of spiking neurons with excitatory and inhibitory plasticity. We found that even though the formed assemblies were silent in terms of mean firing rate, they had an increased coefficient of variation of inter-spike intervals. We also found that this spiking irregularity could be read out with support of short-term plasticity, and that it could contribute to the longevity of memories.

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.

The grid code for ordered experience

Entorhinal cortical grid cells fire in a periodic pattern that tiles space, which is suggestive of a spatial coordinate system. However, irregularities in the grid pattern as well as responses of grid cells in contexts other than spatial navigation have presented a challenge to existing models of entorhinal function. In this Perspective, we propose that hippocampal input provides a key informative drive to the grid network in both spatial and non-spatial circumstances, particularly around salient events. We build on previous models in which neural activity propagates through the entorhinal-hippocampal network in time. This temporal contiguity in network activity points to temporal order as a necessary characteristic of representations generated by the hippocampal formation. We advocate that interactions in the entorhinal-hippocampal loop build a topological representation that is rooted in the temporal order of experience. In this way, the structure of grid cell firing supports a learned topology rather than a rigid coordinate frame that is bound to measurements of the physical world.

Locally ordered representation of 3D space in the entorhinal cortex

As animals navigate on a two-dimensional surface, neurons in the medial entorhinal cortex (MEC) known as grid cells are activated when the animal passes through multiple locations (firing fields) arranged in a hexagonal lattice that tiles the locomotion surface¹. However, although our world is three-dimensional, it is unclear how the MEC represents 3D space². Here we recorded from MEC cells in freely flying bats and identified several classes of spatial neurons, including 3D border cells, 3D head-direction cells, and neurons with multiple 3D firing fields. Many of these multifield neurons were 3D grid cells, whose neighbouring fields were separated by a characteristic distance-forming a local order-but lacked any global lattice arrangement of the fields. Thus, whereas 2D grid cells form a global lattice-characterized by both local and global order-3D grid cells exhibited only local order, creating a locally ordered metric for space. We modelled grid cells as emerging from pairwise interactions between fields, which yielded a hexagonal lattice in 2D and local order in 3D, thereby describing both 2D and 3D grid cells using one unifying model. Together, these data and model illuminate the fundamental differences and similarities between neural codes for 3D and 2D space in the mammalian brain.

The functional organization of excitatory synaptic input to place cells

Hippocampal place cells contribute to mammalian spatial navigation and memory formation. Numerous models have been proposed to explain the location-specific firing of this cognitive representation, but the pattern of excitatory synaptic input leading to place firing is unknown, leaving no synaptic-scale explanation of place coding. Here we used resonant scanning two-photon microscopy to establish the pattern of synaptic glutamate input received by CA1 place cells in behaving mice. During traversals of the somatic place field, we found increased excitatory dendritic input, mainly arising from inputs with spatial tuning overlapping the somatic field, and functional clustering of this input along the dendrites over ~10 µm. These results implicate increases in total excitatory input and co-activation of anatomically clustered synaptic input in place firing. Since they largely inherit their fields from upstream synaptic partners with similar fields, many CA1 place cells appear to be part of multi-brain-region cell assemblies forming representations of specific locations.

Learning excitatory-inhibitory neuronal assemblies in recurrent networks

Understanding the connectivity observed in the brain and how it emerges from local plasticity rules is a grand challenge in modern neuroscience. In the primary visual cortex (V1) of mice, synapses between excitatory pyramidal neurons and inhibitory parvalbumin-expressing (PV) interneurons tend to be stronger for neurons that respond to similar stimulus features, although these neurons are not topographically arranged according to their stimulus preference. The presence of such excitatory-inhibitory (E/I) neuronal assemblies indicates a stimulus-specific form of feedback inhibition. Here, we show that activity-dependent synaptic plasticity on input and output synapses of PV interneurons generates a circuit structure that is consistent with mouse V1. Computational modeling reveals that both forms of plasticity must act in synergy to form the observed E/I assemblies. Once established, these assemblies produce a stimulus-specific competition between pyramidal neurons. Our model suggests that activity-dependent plasticity can refine inhibitory circuits to actively shape cortical computations.

Complementary Inhibitory Weight Profiles Emerge from Plasticity and Allow Flexible Switching of Receptive Fields

Cortical areas comprise multiple types of inhibitory interneurons, with stereotypical connectivity motifs that may follow specific plasticity rules. Yet, their combined effect on postsynaptic dynamics has been largely unexplored. Here, we analyze the response of a single postsynaptic model neuron receiving tuned excitatory connections alongside inhibition from two plastic populations. Synapses from each inhibitory population change according to distinct plasticity rules. We tested different combinations of three rules: Hebbian, anti-Hebbian, and homeostatic scaling. Depending on the inhibitory plasticity rule, synapses become unspecific (flat), anticorrelated to, or correlated with excitatory synapses. Crucially, the neuron's receptive field (i.e., its response to presynaptic stimuli) depends on the modulatory state of inhibition. When both inhibitory populations are active, inhibition balances excitation, resulting in uncorrelated postsynaptic responses regardless of the inhibitory tuning profiles. Modulating the activity of a given inhibitory population produces strong correlations to either preferred or nonpreferred inputs, in line with recent experimental findings that show dramatic context-dependent changes of neurons' receptive fields. We thus confirm that a neuron's receptive field does not follow directly from the weight profiles of its presynaptic afferents. Our results show how plasticity rules in various cell types can interact to shape cortical circuit motifs and their dynamics.SIGNIFICANCE STATEMENT Neurons in sensory areas of the cortex are known to respond to specific features of a given input (e.g., specific sound frequencies), but recent experimental studies show that such responses (i.e., their receptive fields) depend on context. Inspired by the cortical connectivity, we built models of excitatory and inhibitory inputs onto a single neuron, to study how receptive fields may change on short and long time scales. We show how various synaptic plasticity rules allow for the emergence of diverse connectivity profiles and, moreover, how their dynamic interaction creates a mechanism by which postsynaptic responses can quickly change. Our work emphasizes multiple roles of inhibition in cortical processing and provides a first mechanistic model for flexible receptive fields.

Recurrent amplification of grid-cell activity

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

A Generalized Linear Model of a Navigation Network

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

A Brain-Inspired Adaptive Space Representation Model Based on Grid Cells and Place Cells

Grid cells and place cells are important neurons in the animal brain. The information transmission between them provides the basis for the spatial representation and navigation of animals and also provides reference for the research on the autonomous navigation mechanism of intelligent agents. Grid cells are important information source of place cells. The supervised learning and unsupervised learning models can be used to simulate the generation of place cells from grid cell inputs. However, the existing models preset the firing characteristics of grid cell. In this paper, we propose a united generation model of grid cells and place cells. First, the visual place cells with nonuniform distribution generate the visual grid cells with regional firing field through feedforward network. Second, the visual grid cells and the self-motion information generate the united grid cells whose firing fields extend to the whole space through genetic algorithm. Finally, the visual place cells and the united grid cells generate the united place cells with uniform distribution through supervised fuzzy adaptive resonance theory (ART) network. Simulation results show that this model has stronger environmental adaptability and can provide reference for the research on spatial representation model and brain-inspired navigation mechanism of intelligent agents under the condition of nonuniform environmental information.

A theory of joint attractor dynamics in the hippocampus and the entorhinal cortex accounts for artificial remapping and grid cell field-to-field variability

The representation of position in the mammalian brain is distributed across multiple neural populations. Grid cell modules in the medial entorhinal cortex (MEC) express activity patterns that span a low-dimensional manifold which remains stable across different environments. In contrast, the activity patterns of hippocampal place cells span distinct low-dimensional manifolds in different environments. It is unknown how these multiple representations of position are coordinated. Here, we develop a theory of joint attractor dynamics in the hippocampus and the MEC. We show that the system exhibits a coordinated, joint representation of position across multiple environments, consistent with global remapping in place cells and grid cells. In addition, our model accounts for recent experimental observations that lack a mechanistic explanation: variability in the firing rate of single grid cells across firing fields, and artificial remapping of place cells under depolarization, but not under hyperpolarization, of layer II stellate cells of the MEC.

The interplay between somatic and dendritic inhibition promotes the emergence and stabilization of place fields

During the exploration of novel environments, place fields are rapidly formed in hippocampal CA1 neurons. Place cell firing rate increases in early stages of exploration of novel environments but returns to baseline levels in familiar environments. Although similar in amplitude and width, place fields in familiar environments are more stable than in novel environments. We propose a computational model of the hippocampal CA1 network, which describes the formation, dynamics and stabilization of place fields. We show that although somatic disinhibition is sufficient to form place fields, dendritic inhibition along with synaptic plasticity is necessary for place field stabilization. Our model suggests that place cell stability can be attributed to strong excitatory synaptic weights and strong dendritic inhibition. We show that the interplay between somatic and dendritic inhibition balances the increased excitatory weights, such that place cells return to their baseline firing rate after exploration. Our model suggests that different types of interneurons are essential to unravel the mechanisms underlying place field plasticity. Finally, we predict that artificially induced dendritic events can shift place fields even after place field stabilization.

Inhibitory Plasticity: From Molecules to Computation and Beyond

Synaptic plasticity is the cellular and molecular counterpart of learning and memory and, since its first discovery, the analysis of the mechanisms underlying long-term changes of synaptic strength has been almost exclusively focused on excitatory connections. Conversely, inhibition was considered as a fixed controller of circuit excitability. Only recently, inhibitory networks were shown to be finely regulated by a wide number of mechanisms residing in their synaptic connections. Here, we review recent findings on the forms of inhibitory plasticity (IP) that have been discovered and characterized in different brain areas. In particular, we focus our attention on the molecular pathways involved in the induction and expression mechanisms leading to changes in synaptic efficacy, and we discuss, from the computational perspective, how IP can contribute to the emergence of functional properties of brain circuits.

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.

Velocity coupling of grid cell modules enables stable embedding of a low dimensional variable in a high dimensional neural attractor

Grid cells in the medial entorhinal cortex (MEC) encode position using a distributed representation across multiple neural populations (modules), each possessing a distinct spatial scale. The modular structure of the representation confers the grid cell neural code with large capacity. Yet, the modularity poses significant challenges for the neural circuitry that maintains the representation, and updates it based on self motion. Small incompatible drifts in different modules, driven by noise, can rapidly lead to large, abrupt shifts in the represented position, resulting in catastrophic readout errors. Here, we propose a theoretical model of coupled modules. The coupling suppresses incompatible drifts, allowing for a stable embedding of a two-dimensional variable (position) in a higher dimensional neural attractor, while preserving the large capacity. We propose that coupling of this type may be implemented by recurrent synaptic connectivity within the MEC with a relatively simple and biologically plausible structure.

Modeling grid fields instead of modeling grid cells : An effective model at the macroscopic level and its relationship with the underlying microscopic neural system

A neuron's firing correlates are defined as the features of the external world to which its activity is correlated. In many parts of the brain, neurons have quite simple such firing correlates. A striking example are grid cells in the rodent medial entorhinal cortex: their activity correlates with the animal's position in space, defining 'grid fields' arranged with a remarkable periodicity. Here, we show that the organization and evolution of grid fields relate very simply to physical space. To do so, we use an effective model and consider grid fields as point objects (particles) moving around in space under the influence of forces. We reproduce several observations on the geometry of grid patterns. This particle-like behavior is particularly salient in a recent experiment in which two separate grid patterns merge. We discuss pattern formation in the light of known results from physics of two-dimensional colloidal systems. Notably, we study the limitations of the widely used 'gridness score' and show how physics of 2d systems could be a source of inspiration, both for data analysis and computational modeling. Finally, we draw the relationship between our 'macroscopic' model for grid fields and existing 'microscopic' models of grid cell activity and discuss how a description at the level of grid fields allows to put constraints on the underlying grid cell network.

Origin and role of path integration in the cognitive representations of the hippocampus: computational insights into open questions

Path integration is a straightforward concept with varied connotations that are important to different disciplines concerned with navigation, such as ethology, cognitive science, robotics and neuroscience. In studying the hippocampal formation, it is fruitful to think of path integration as a computation that transforms a sense of motion into a sense of location, continuously integrated with landmark perception. Here, we review experimental evidence that path integration is intimately involved in fundamental properties of place cells and other spatial cells that are thought to support a cognitive abstraction of space in this brain system. We discuss hypotheses about the anatomical and computational origin of path integration in the well-characterized circuits of the rodent limbic system. We highlight how computational frameworks for map-building in robotics and cognitive science alike suggest an essential role for path integration in the creation of a new map in unfamiliar territory, and how this very role can help us make sense of differences in neurophysiological data from novel versus familiar and small versus large environments. Similar computational principles could be at work when the hippocampus builds certain non-spatial representations, such as time intervals or trajectories defined in a sensory stimulus space.

Hexagonal Grid Fields Optimally Encode Transitions in Spatiotemporal Sequences

Grid cells of the rodent entorhinal cortex are essential for spatial navigation. Although their function is commonly believed to be either path integration or localization, the origin or purpose of their hexagonal firing fields remains disputed. Here they are proposed to arise as an optimal encoding of transitions in sequences. First, storage requirements for transitions in general episodic sequences are examined using propositional logic and graph theory. Subsequently, transitions in complete metric spaces are considered under the assumption of an ideal sampling of an input space. It is shown that memory capacity of neurons that have to encode multiple feasible spatial transitions is maximized by a hexagonal pattern. Grid cells are proposed to encode spatial transitions in spatiotemporal sequences, with the entorhinal-hippocampal loop forming a multitransition system.