A model combining oscillations and attractor dynamics for generation of grid cell firing

Propofol anesthesia destabilizes neural dynamics across cortex

Every day, hundreds of thousands of people undergo general anesthesia. One hypothesis is that anesthesia disrupts dynamic stability-the ability of the brain to balance excitability with the need to be stable and controllable. To test this hypothesis, we developed a method for quantifying changes in population-level dynamic stability in complex systems: delayed linear analysis for stability estimation (DeLASE). Propofol was used to transition animals between the awake state and anesthetized unconsciousness. DeLASE was applied to macaque cortex local field potentials (LFPs). We found that neural dynamics were more unstable in unconsciousness compared with the awake state. Cortical trajectories mirrored predictions from destabilized linear systems. We mimicked the effect of propofol in simulated neural networks by increasing inhibitory tone. This in turn destabilized the networks, as observed in the neural data. Our results suggest that anesthesia disrupts dynamical stability that is required for consciousness.

Flexible coding of time or distance in hippocampal cells

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

Grid cell disruption in a mouse model of early Alzheimer's disease reflects reduced integration of self-motion cues

Converging evidence from human and rodent studies suggests that disrupted grid cell coding in the medial entorhinal cortex (MEC) underlies path integration behavioral deficits during early Alzheimer's disease (AD). However, grid cell firing relies on both self-motion cues and environmental features, and it remains unclear whether disrupted grid coding can account for specific path integration deficits reported during early AD. Here, we report in the J20 transgenic amyloid beta (Aβ) mouse model of early AD that grid cells were spatially unstable toward the center of the arena, had qualitatively different spatial components that aligned parallel to the borders of the environment, and exhibited impaired integration of distance traveled via reduced theta phase precession. Our results suggest that disrupted early AD grid coding reflects reduced integration of self-motion cues but not environmental information via geometric boundaries, providing evidence that grid cell impairments underlie path integration deficits during early AD.

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.

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.

A Framework for Intelligence and Cortical Function Based on Grid Cells in the Neocortex

How the neocortex works is a mystery. In this paper we propose a novel framework for understanding its function. Grid cells are neurons in the entorhinal cortex that represent the location of an animal in its environment. Recent evidence suggests that grid cell-like neurons may also be present in the neocortex. We propose that grid cells exist throughout the neocortex, in every region and in every cortical column. They define a location-based framework for how the neocortex functions. Whereas grid cells in the entorhinal cortex represent the location of one thing, the body relative to its environment, we propose that cortical grid cells simultaneously represent the location of many things. Cortical columns in somatosensory cortex track the location of tactile features relative to the object being touched and cortical columns in visual cortex track the location of visual features relative to the object being viewed. We propose that mechanisms in the entorhinal cortex and hippocampus that evolved for learning the structure of environments are now used by the neocortex to learn the structure of objects. Having a representation of location in each cortical column suggests mechanisms for how the neocortex represents object compositionality and object behaviors. It leads to the hypothesis that every part of the neocortex learns complete models of objects and that there are many models of each object distributed throughout the neocortex. The similarity of circuitry observed in all cortical regions is strong evidence that even high-level cognitive tasks are learned and represented in a location-based framework.

Spatial synchronization codes from coupled rate-phase neurons

During spatial navigation, the frequency and timing of spikes from spatial neurons including place cells in hippocampus and grid cells in medial entorhinal cortex are temporally organized by continuous theta oscillations (6-11 Hz). The theta rhythm is regulated by subcortical structures including the medial septum, but it is unclear how spatial information from place cells may reciprocally organize subcortical theta-rhythmic activity. Here we recorded single-unit spiking from a constellation of subcortical and hippocampal sites to study spatial modulation of rhythmic spike timing in rats freely exploring an open environment. Our analysis revealed a novel class of neurons that we termed 'phaser cells,' characterized by a symmetric coupling between firing rate and spike theta-phase. Phaser cells encoded space by assigning distinct phases to allocentric isocontour levels of each cell's spatial firing pattern. In our dataset, phaser cells were predominantly located in the lateral septum, but also the hippocampus, anteroventral thalamus, lateral hypothalamus, and nucleus accumbens. Unlike the unidirectional late-to-early phase precession of place cells, bidirectional phase modulation acted to return phaser cells to the same theta-phase along a given spatial isocontour, including cells that characteristically shifted to later phases at higher firing rates. Our dynamical models of intrinsic theta-bursting neurons demonstrated that experience-independent temporal coding mechanisms can qualitatively explain (1) the spatial rate-phase relationships of phaser cells and (2) the observed temporal segregation of phaser cells according to phase-shift direction. In open-field phaser cell simulations, competitive learning embedded phase-code entrainment maps into the weights of downstream targets, including path integration networks. Bayesian phase decoding revealed error correction capable of resetting path integration at subsecond timescales. Our findings suggest that phaser cells may instantiate a subcortical theta-rhythmic loop of spatial feedback. We outline a framework in which location-dependent synchrony reconciles internal idiothetic processes with the allothetic reference points of sensory experience.

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.

Phosphorylation of Tau protein correlates with changes in hippocampal theta oscillations and reduces hippocampal excitability in Alzheimer's model

Tau hyperphosphorylation at several sites, including those close to the microtubule domain region (MDr), is considered a key pathological event in the development of Alzheimer's disease (AD). Recent studies indicate that at the very early stage of this disease, increased phosphorylation in Tau's MDr domain correlates with reduced levels of neuronal excitability. Mechanistically, we show that pyramidal neurons and some parvalbumin-positive interneurons in 1-month-old triple-transgenic AD mice accumulate hyperphosphorylated Tau protein and that this accumulation correlates with changes in theta oscillations in hippocampal neurons. Pyramidal neurons from young triple-transgenic AD mice exhibited less spike accommodation and power increase in subthreshold membrane oscillations. Furthermore, triple-transgenic AD mice challenged with the potassium channel blocker 4-aminopyridine had reduced theta amplitude compared with 4-aminopyridine-treated control mice and, unlike these controls, displayed no seizure-like activity after this challenge. Collectively, our results provide new insights into AD pathogenesis and suggest that increases in Tau phosphorylation at the initial stages of the disease represent neuronal responses that compensate for brain circuit overexcitation.

Neural mechanisms of navigation involving interactions of cortical and subcortical structures

Animals must perform spatial navigation for a range of different behaviors, including selection of trajectories toward goal locations and foraging for food sources. To serve this function, a number of different brain regions play a role in coding different dimensions of sensory input important for spatial behavior, including the entorhinal cortex, the retrosplenial cortex, the hippocampus, and the medial septum. This article will review data concerning the coding of the spatial aspects of animal behavior, including location of the animal within an environment, the speed of movement, the trajectory of movement, the direction of the head in the environment, and the position of barriers and objects both relative to the animal's head direction (egocentric) and relative to the layout of the environment (allocentric). The mechanisms for coding these important spatial representations are not yet fully understood but could involve mechanisms including integration of self-motion information or coding of location based on the angle of sensory features in the environment. We will review available data and theories about the mechanisms for coding of spatial representations. The computation of different aspects of spatial representation from available sensory input requires complex cortical processing mechanisms for transformation from egocentric to allocentric coordinates that will only be understood through a combination of neurophysiological studies and computational modeling.

Probabilistic Learning by Rodent Grid Cells

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

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

Potential roles of cholinergic modulation in the neural coding of location and movement speed

Behavioral data suggest that cholinergic modulation may play a role in certain aspects of spatial memory, and neurophysiological data demonstrate neurons that fire in response to spatial dimensions, including grid cells and place cells that respond on the basis of location and running speed. These neurons show firing responses that depend upon the visual configuration of the environment, due to coding in visually-responsive regions of the neocortex. This review focuses on the physiological effects of acetylcholine that may influence the sensory coding of spatial dimensions relevant to behavior. In particular, the local circuit effects of acetylcholine within the cortex regulate the influence of sensory input relative to internal memory representations via presynaptic inhibition of excitatory and inhibitory synaptic transmission, and the modulation of intrinsic currents in cortical excitatory and inhibitory neurons. In addition, circuit effects of acetylcholine regulate the dynamics of cortical circuits including oscillations at theta and gamma frequencies. These effects of acetylcholine on local circuits and network dynamics could underlie the role of acetylcholine in coding of spatial information for the performance of spatial memory tasks.

Multiple Running Speed Signals in Medial Entorhinal Cortex

Grid cells in medial entorhinal cortex (MEC) can be modeled using oscillatory interference or attractor dynamic mechanisms that perform path integration, a computation requiring information about running direction and speed. The two classes of computational models often use either an oscillatory frequency or a firing rate that increases as a function of running speed. Yet it is currently not known whether these are two manifestations of the same speed signal or dissociable signals with potentially different anatomical substrates. We examined coding of running speed in MEC and identified these two speed signals to be independent of each other within individual neurons. The medial septum (MS) is strongly linked to locomotor behavior, and removal of MS input resulted in strengthening of the firing rate speed signal, while decreasing the strength of the oscillatory speed signal. Thus, two speed signals are present in MEC that are differentially affected by disrupted MS input.

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.

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.

Sensory feedback in a bump attractor model of path integration

Mammalian spatial navigation systems utilize several different sensory information channels. This information is converted into a neural code that represents the animal's current position in space by engaging place cell, grid cell, and head direction cell networks. In particular, sensory landmark (allothetic) cues can be utilized in concert with an animal's knowledge of its own velocity (idiothetic) cues to generate a more accurate representation of position than path integration provides on its own (Battaglia et al. The Journal of Neuroscience 24(19):4541-4550 (2004)). We develop a computational model that merges path integration with feedback from external sensory cues that provide a reliable representation of spatial position along an annular track. Starting with a continuous bump attractor model, we explore the impact of synaptic spatial asymmetry and heterogeneity, which disrupt the position code of the path integration process. We use asymptotic analysis to reduce the bump attractor model to a single scalar equation whose potential represents the impact of asymmetry and heterogeneity. Such imperfections cause errors to build up when the network performs path integration, but these errors can be corrected by an external control signal representing the effects of sensory cues. We demonstrate that there is an optimal strength and decay rate of the control signal when cues appear either periodically or randomly. A similar analysis is performed when errors in path integration arise from dynamic noise fluctuations. Again, there is an optimal strength and decay of discrete control that minimizes the path integration error.

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.

Speed cells in the medial entorhinal cortex

Grid cells in the medial entorhinal cortex have spatial firing fields that repeat periodically in a hexagonal pattern. When animals move, activity is translated between grid cells in accordance with the animal's displacement in the environment. For this translation to occur, grid cells must have continuous access to information about instantaneous running speed. However, a powerful entorhinal speed signal has not been identified. Here we show that running speed is represented in the firing rate of a ubiquitous but functionally dedicated population of entorhinal neurons distinct from other cell populations of the local circuit, such as grid, head-direction and border cells. These 'speed cells' are characterized by a context-invariant positive, linear response to running speed, and share with grid cells a prospective bias of ∼50-80 ms. Our observations point to speed cells as a key component of the dynamic representation of self-location in the medial entorhinal cortex.

If I had a million neurons: Potential tests of cortico-hippocampal theories

Considerable excitement surrounds new initiatives to develop techniques for simultaneous recording of large populations of neurons in cortical structures. This chapter focuses on the potential value of large-scale simultaneous recording for advancing research on current issues in the function of cortical circuits, including the interaction of the hippocampus with cortical and subcortical structures. The review describes specific research questions that could be answered using large-scale population recording, including questions about the circuit dynamics underlying coding of dimensions of space and time for episodic memory, the role of GABAergic and cholinergic innervation from the medial septum, the functional role of spatial representations coded by grid cells, boundary cells, head direction cells, and place cells, and the fact that many models require cells coding movement direction.

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.

Principles of goal-directed spatial robot navigation in biomimetic models

Mobile robots and animals alike must effectively navigate their environments in order to achieve their goals. For animals goal-directed navigation facilitates finding food, seeking shelter or migration; similarly robots perform goal-directed navigation to find a charging station, get out of the rain or guide a person to a destination. This similarity in tasks extends to the environment as well; increasingly, mobile robots are operating in the same underwater, ground and aerial environments that animals do. Yet despite these similarities, goal-directed navigation research in robotics and biology has proceeded largely in parallel, linked only by a small amount of interdisciplinary research spanning both areas. Most state-of-the-art robotic navigation systems employ a range of sensors, world representations and navigation algorithms that seem far removed from what we know of how animals navigate; their navigation systems are shaped by key principles of navigation in 'real-world' environments including dealing with uncertainty in sensing, landmark observation and world modelling. By contrast, biomimetic animal navigation models produce plausible animal navigation behaviour in a range of laboratory experimental navigation paradigms, typically without addressing many of these robotic navigation principles. In this paper, we attempt to link robotics and biology by reviewing the current state of the art in conventional and biomimetic goal-directed navigation models, focusing on the key principles of goal-oriented robotic navigation and the extent to which these principles have been adapted by biomimetic navigation models and why.

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.

Grid cell firing properties vary as a function of theta phase locking preferences in the rat medial entorhinal cortex

Theta rhythmic fluctuations in the hippocampal–entorhinal circuit are believed to reflect rapid transitions between modes of mnemonic processing. Specifically, activity at the trough and peak of CA1 pyramidal layer theta is thought to correspond to retrieval and encoding related processing, respectively. Spatially tuned “grid cells” in layers II and III of the medial entorhinal cortex preferentially spike during the trough and peak phases of theta, respectively. Such differences suggest differential involvement of these layers to the processes of retrieval and encoding. It remains unknown, however, if the properties of grid cells that spike preferentially at the trough vs. the peak of theta differ systematically. Such putative differences would offer insights into the differential processing that occurs during these two phases. The goal of the present work was to contrast these types of grid cells. We found that significant functional dissociations do exist: trough locked grid cells carried more spatial information, had a higher degree of head direction tuning, and were more likely to phase precess. Thus, grid cells that activate during the putative retrieval phase of theta (trough) have a greater degree of location, orientation, and temporal tuning specificity relative to grid cells that activate during the putative encoding phase (peak), potentially reflecting the influence of the retrieved content. Additionally, trough locked grid cells had a lower average firing rate, were more likely to burst, and were less phase locked to high-gamma (∼80 Hz). Further analyses revealed they had different waveforms profiles and that systemic blockade of muscarinic acetylcholine receptors reduced the spatial tuning of both types, although these differences were only significant for the peak locked grid cells. These differences suggest that trough and peak locked grid cells are distinct populations of neurons.

Contribution of Ih to the relative facilitation of synaptic responses induced by carbachol in the entorhinal cortex during repetitive stimulation of the parasubiculum

Neurons in the superficial layers of the entorhinal cortex provide the hippocampus with the majority of its cortical sensory input, and also receive the major output projection from the parasubiculum. This puts the parasubiculum in a position to modulate the activity of entorhinal neurons that project to the hippocampus. These brain areas receive cholinergic projections that are active during periods of theta- and gamma-frequency electroencephalographic (EEG) activity. The purpose of this study was to investigate how cholinergic receptor activation affects the strength of repetitive synaptic responses at these frequencies in the parasubiculo-entorhinal pathway and the cellular mechanisms involved. Whole-cell patch-clamp recordings of rat layer II medial entorhinal neurons were conducted using an acute slice preparation, and responses to 5-pulse trains of stimulation at theta- and gamma-frequency delivered to the parasubiculum were recorded. The cholinergic agonist carbachol (CCh) suppressed the amplitude of single synaptic responses, but also produced a relative facilitation of synaptic responses evoked during stimulation trains. The N-methyl-d-aspartate (NMDA) glutamate receptor blocker APV did not significantly reduce the relative facilitation effect. However, the hyperpolarization-activated cationic current (Ih) channel blocker ZD7288 mimicked the relative facilitation induced by CCh, suggesting that CCh-induced inhibition of Ih could produce the effect by increasing dendritic input resistance (Rin). Inward-rectifying and leak K(+) currents are known to interact with Ih to affect synaptic excitability. Application of the K(+) channel antagonist Ba(2+) depolarized neurons and enhanced temporal summation, but did not block further facilitation of train-evoked responses by ZD7288. The Ih-dependent facilitation of synaptic responses can therefore occur during reductions in inward-rectifying potassium current (IKir) associated with dendritic depolarization. Thus, in addition to cholinergic reductions in transmitter release that are known to facilitate train-evoked responses, these findings emphasize the role of inhibition of Ih in the integration of synaptic inputs within the entorhinal cortex during cholinergically-induced oscillatory states, likely due to enhanced summation of excitatory postsynaptic potentials (EPSPs) induced by increases in dendritic Rin.

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.

Vestibular control of entorhinal cortex activity in spatial navigation

Navigation in rodents depends on both self-motion (idiothetic) and external (allothetic) information. Idiothetic information has a predominant role when allothetic information is absent or irrelevant. The vestibular system is a major source of idiothetic information in mammals. By integrating the signals generated by angular and linear accelerations during exploration, a rat is able to generate and update a vector pointing to its starting place and to perform accurate return. This navigation strategy, called path integration, has been shown to involve a network of brain structures. Among these structures, the entorhinal cortex (EC) may play a pivotal role as suggested by lesion and electrophysiological data. In particular, it has been recently discovered that some neurons in the medial EC display multiple firing fields producing a regular grid-like pattern across the environment. Such regular activity may arise from the integration of idiothetic information. This hypothesis would be strongly strengthened if it was shown that manipulation of vestibular information interferes with grid cell activity. In the present paper we review neuroanatomical and functional evidence indicating that the vestibular system influences the activity of the brain network involved in spatial navigation. We also provide new data on the effects of reversible inactivation of the peripheral vestibular system on the EC theta rhythm. The main result is that tetrodotoxin (TTX) administration abolishes velocity-controlled theta oscillations in the EC, indicating that vestibular information is necessary for EC activity. Since recent data demonstrate that disruption of theta rhythm in the medial EC induces a disorganization of grid cell firing, our findings indicate that the integration of idiothetic information in the EC is essential to form a spatial representation of the environment.

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.

Spatial coding and attractor dynamics of grid cells in the entorhinal cortex

Recent experiments support the theoretical hypothesis that recurrent connectivity plays a central role within the medial entorhinal cortex, by shaping activity of large neural populations, such that their joint activity lies within a continuous attractor. This conjecture involves dynamics within each population (module) of cells that share the same grid spacing. In addition, recent theoretical works raise a hypothesis that, taken together, grid cells from all modules maintain a sophisticated representation of position with uniquely large dynamical range, when compared with other known neural codes in the brain. To maintain such a code, activity in different modules must be coupled, within the entorhinal cortex or through the hippocampus.

Grid cell spatial tuning reduced following systemic muscarinic receptor blockade

Grid cells of the medial entorhinal cortex exhibit a periodic and stable pattern of spatial tuning that may reflect the output of a path integration system. This grid pattern has been hypothesized to serve as a spatial coordinate system for navigation and memory function. The mechanisms underlying the generation of this characteristic tuning pattern remain poorly understood. Systemic administration of the muscarinic antagonist scopolamine flattens the typically positive correlation between running speed and entorhinal theta frequency in rats. The loss of this neural correlate of velocity, an important signal for the calculation of path integration, raises the question of what influence scopolamine has on the grid cell tuning as a read out of the path integration system. To test this, the spatial tuning properties of grid cells were compared before and after systemic administration of scopolamine as rats completed laps on a circle track for food rewards. The results show that the spatial tuning of the grid cells was reduced following scopolamine administration. The tuning of head direction cells, in contrast, was not reduced by scopolamine. This is the first report to demonstrate a link between cholinergic function and grid cell tuning. This work suggests that the loss of tuning in the grid cell network may underlie the navigational disorientation observed in Alzheimer's patients and elderly individuals with reduced cholinergic tone.

Space in the brain: how the hippocampal formation supports spatial cognition

Over the past four decades, research has revealed that cells in the hippocampal formation provide an exquisitely detailed representation of an animal's current location and heading. These findings have provided the foundations for a growing understanding of the mechanisms of spatial cognition in mammals, including humans. We describe the key properties of the major categories of spatial cells: place cells, head direction cells, grid cells and boundary cells, each of which has a characteristic firing pattern that encodes spatial parameters relating to the animal's current position and orientation. These properties also include the theta oscillation, which appears to play a functional role in the representation and processing of spatial information. Reviewing recent work, we identify some themes of current research and introduce approaches to computational modelling that have helped to bridge the different levels of description at which these mechanisms have been investigated. These range from the level of molecular biology and genetics to the behaviour and brain activity of entire organisms. We argue that the neuroscience of spatial cognition is emerging as an exceptionally integrative field which provides an ideal test-bed for theories linking neural coding, learning, memory and cognition.

DC-shifts in amplitude in-field generated by an oscillatory interference model of grid cell firing

Oscillatory interference models propose a mechanism by which the spatial firing pattern of grid cells can arise from the interaction of multiple oscillators that shift in relative phase. These models produce aspects of the physiological data such as the phase precession dynamics observed in grid cells. However, existing oscillatory interference models did not predict the in-field DC shifts in the membrane potential of grid cells that have been observed during intracellular recordings in navigating animals. Here, we demonstrate that DC shifts can be generated in an oscillatory interference model when half-wave rectified oscillatory inputs are summed by a leaky integrate-and-fire neuron with a long membrane decay constant (100 ms). The non-linear mean of the half-wave rectified input signal is reproduced in the grid cell's membrane potential trace producing the DC shift within field. For shorter values of the decay constant integration is more effective if the input signal, comprising input from 6 head direction selective populations, is temporally spread during in-field epochs; this requires that the head direction selective populations act as velocity controlled oscillators with baseline oscillations that are phase offset from one another. The resulting simulated membrane potential matches several properties of the empirical intracellular recordings, including: in-field DC-shifts, theta-band oscillations, phase precession of both membrane potential oscillations and grid cell spiking activity relative to network theta and a stronger correlation between DC-shift amplitude and firing-rate than between theta-band oscillation amplitude and firing-rate. This work serves to demonstrate that oscillatory interference models can account for the DC shifts in the membrane potential observed during intracellular recordings of grid cells without the need to appeal to attractor dynamics.

Oscillatory neurocomputing with ring attractors: a network architecture for mapping locations in space onto patterns of neural synchrony

Theories of neural coding seek to explain how states of the world are mapped onto states of the brain. Here, we compare how an animal's location in space can be encoded by two different kinds of brain states: population vectors stored by patterns of neural firing rates, versus synchronization vectors stored by patterns of synchrony among neural oscillators. It has previously been shown that a population code stored by spatially tuned ‘grid cells’ can exhibit desirable properties such as high storage capacity and strong fault tolerance; here it is shown that similar properties are attainable with a synchronization code stored by rhythmically bursting ‘theta cells’ that lack spatial tuning. Simulations of a ring attractor network composed from theta cells suggest how a synchronization code might be implemented using fewer neurons and synapses than a population code with similar storage capacity. It is conjectured that reciprocal connections between grid and theta cells might control phase noise to correct two kinds of errors that can arise in the code: path integration and teleportation errors. Based upon these analyses, it is proposed that a primary function of spatially tuned neurons might be to couple the phases of neural oscillators in a manner that allows them to encode spatial locations as patterns of neural synchrony.

Neuronal rebound spiking, resonance frequency and theta cycle skipping may contribute to grid cell firing in medial entorhinal cortex

Data show a relationship of cellular resonance and network oscillations in the entorhinal cortex to the spatial periodicity of grid cells. This paper presents a model that simulates the resonance and rebound spiking properties of entorhinal neurons to generate spatial periodicity dependent upon phasic input from medial septum. The model shows that a difference in spatial periodicity can result from a difference in neuronal resonance frequency that replicates data from several experiments. The model also demonstrates a functional role for the phenomenon of theta cycle skipping in the medial entorhinal cortex.

How to build a grid cell

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

Comparison of properties of medial entorhinal cortex layer II neurons in two anatomical dimensions with and without cholinergic activation

Mechanisms underlying grid cell firing in the medial entorhinal cortex (MEC) still remain unknown. Computational modeling studies have suggested that cellular properties such as spike frequency adaptation and persistent firing might underlie the grid cell firing. Recent in vivo studies also suggest that cholinergic activation influences grid cell firing. Here we investigated the anatomical distribution of firing frequency adaptation, the medium spike after hyperpolarization potential (mAHP), subthreshold membrane potential oscillations, sag potential, input resistance and persistent firing, in MEC layer II principal cells using in vitro whole-cell patch clamp recordings in rats. Anatomical distributions of these properties were compared along both the dorso-ventral and medio-lateral axes, both with and without the cholinergic receptor agonist carbachol. We found that spike frequency adaptation is significantly stronger in ventral than in dorsal neurons both with and without carbachol. Spike frequency adaptation was significantly correlated with the duration of the mAHP, which also showed a gradient along the dorso-ventral axis. In carbachol, we found that about 50% of MEC layer II neurons show persistent firing which lasted more than 30 seconds. Persistent firing of MEC layer II neurons might contribute to grid cell firing by providing the excitatory drive. Dorso-ventral differences in spike frequency adaptation we report here are opposite from previous predictions by a computational model. We discuss an alternative mechanism as to how dorso-ventral differences in spike frequency adaptation could contribute to different scales of grid spacing.

Theta rhythm and the encoding and retrieval of space and time

Physiological data demonstrates theta frequency oscillations associated with memory function and spatial behavior. Modeling and data from animals provide a perspective on the functional role of theta rhythm, including correlations with behavioral performance and coding by timing of spikes relative to phase of oscillations. Data supports a theorized role of theta rhythm in setting the dynamics for encoding and retrieval within cortical circuits. Recent data also supports models showing how network and cellular theta rhythmicity allows neurons in the entorhinal cortex and hippocampus to code time and space as a possible substrate for encoding events in episodic memory. Here we discuss these models and relate them to current physiological and behavioral data.

Segregation of cortical head direction cell assemblies on alternating θ cycles

High-level cortical systems for spatial navigation, including entorhinal grid cells, critically depend on input from the head direction system. We examined spiking rhythms and modes of synchrony between neurons participating in head direction networks for evidence of internal processing, independent of direct sensory drive, which may be important for grid cell function. We demonstrate that head direction networks of rats are segregated into at least two populations of neurons firing on alternate theta cycles (theta cycle skipping) with fixed synchronous or anti-synchronous relationships. Pairs of anti-synchronous theta cycle skipping neurons exhibited larger differences in head direction tuning with a minimum difference of 40 degrees of head direction. Septal inactivation preserved the head direction signal but eliminated theta cycle skipping of head direction cells and grid cell spatial periodicity. We propose that internal mechanisms underlying cycle skipping in head direction networks may be critical for downstream spatial computation by grid cells.

Cellular mechanisms of spatial navigation in the medial entorhinal cortex

Neurons in the medial entorhinal cortex exhibit a grid-like spatial pattern of spike rates that has been proposed to represent a neural code for path integration. To understand how grid cell firing arises from the combination of intrinsic conductances and synaptic input in medial entorhinal stellate cells, we performed patch-clamp recordings in mice navigating in a virtual-reality environment. We found that the membrane potential signature of stellate cells during firing field crossings consisted of a slow depolarization driving spike output. This was best predicted by network models in which neurons receive sustained depolarizing synaptic input during a field crossing, such as continuous attractor network models of grid cell firing. Another key feature of the data, phase precession of intracellular theta oscillations and spiking with respect to extracellular theta oscillations, was best captured by an oscillatory interference model. Thus, these findings provide crucial new information for a quantitative understanding of the cellular basis of spatial navigation in the entorhinal cortex.