Bat and rat neurons differ in theta-frequency resonance despite similar coding of space

The Role of the Posterior Hypothalamus in the Modulation and Production of Rhythmic Theta Oscillations

Theta rhythm recorded as an extracellular synchronous field potential is generated in a number of brain sites including the hippocampus. The physiological occurrence of hippocampal theta rhythm is associated with the activation of a number of structures forming the ascending brainstem-hippocampal synchronizing pathway. Experimental evidence indicates that the supramammillary nucleus and posterior hypothalamic nuclei, considered as the posterior hypothalamic area, comprise a critical node of this ascending pathway. The posterior hypothalamic area plays an important role in movement control, place-learning, memory processing, emotion and arousal. In the light of multiplicity of functions of the posterior hypothalamic area and the influence of theta field oscillations on a number of neural processes, it is the authors' intent to summarize the data concerning the involvement of the supramammillary nucleus and posterior hypothalamic nuclei in the modulation of limbic theta rhythmicity as well as the ability of these brain structures to independently generate theta rhythmicity.

The Autism Palette: Combinations of Impairments Explain the Heterogeneity in ASD

Autism spectrum disorder (ASD) is a heterogeneous neuropsychiatric condition traditionally defined by core symptoms in social behavior, speech/communication, repetitive behavior, and restricted interests. Beyond the core symptoms, autism has strong association with other disorders such as intellectual disability (ID), epilepsy, schizophrenia among many others. This paper outlines a theory of ASD with capacity to connect heterogeneous "core" symptoms, medical and psychiatric comorbidities as well as other etiological theories of autism in a unifying cognitive framework rooted in neuroscience and genetics. Cognition is embedded into an ever-developing structure modified by experiences, including the outcomes of environment influencing behaviors. The key constraint of cognition is that the brain can handle only 7±2 relevant variables at a time, whereas sensory variables, i.e., the number of sensory neurons is orders of magnitude larger. As a result, (a) the extraction, (b) the encoding, and (c) the capability for the efficient cognitive manipulation of the relevant variables, and (d) the compensatory mechanisms that counteract computational delays of the distributed components are critical. We outline our theoretical model to describe a Cartesian Factor (CF) forming, autoencoder-like cognitive mechanism which breaks combinatorial explosion and is accelerated by internal reinforcing machineries and discuss the neural processes that support CF formation. Impairments in any of these aspects may disrupt learning, cognitive manipulation, decisions on interactions, and execution of decisions. We suggest that social interactions are the most susceptible to combinations of diverse small impairments and can be spoiled in many ways that pile up. Comorbidity is experienced, if any of the many potential impairments is relatively strong. We consider component spoiling impairments as the basic colors of autism, whereas the combinations of individual impairments make the palette of autism. We put forth arguments on the possibility of dissociating the different main elements of the impairments that can appear together. For example, impairments of generalization (domain general learning) and impairments of dealing with many variable problems, such as social situations may appear independently and may mutually enhance their impacts. We also consider mechanisms that may lead to protection.

A computational model for grid maps in neural populations

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

The face of animal cognition

As an increasing number of researchers investigate the cognitive abilities of an ever-wider range of animals, animal cognition is currently among the most exciting fields within animal behavior. Tinbergen would be proud: all four of his approaches are being pursued and we are learning much about how animals collect information and how they use that information to make decisions for their current and future states as well as what animals do not perceive or choose to ignore. Here I provide an overview of this productivity, alighting only briefly on any single example, to showcase the diversity of species, of approaches and the sheer mass of research effort currently under way. We are getting closer to understanding the minds of other animals and the evolution of cognition at an increasingly rapid rate.

Spike Time Synchrony in the Absence of Continuous Oscillations

Eliav et al., (2018) recently reported hippocampal-entorhinal spiking in bats occurring preferentially at specific phases of nonrhythmic extracellular voltage fluctuations. This disentanglement of phase coding from continuous oscillations raises new questions about the importance of rhythms for neuronal coordination.

Three-dimensional tuning of head direction cells in rats

Head direction (HD) cells fire when the animal faces that cell's preferred firing direction (PFD) in the horizontal plane. The PFD response when the animal is oriented outside the earth-horizontal plane could result from cells representing direction in the plane of locomotion or as a three-dimensional (3D), global-referenced direction anchored to gravity. To investigate these possibilities, anterodorsal thalamic HD cells were recorded from restrained rats while they were passively positioned in various 3D orientations. Cell responses were unaffected by pitch or roll up to ~90° from the horizontal plane. Firing was disrupted once the animal was oriented >90° away from the horizontal plane and during inversion. When rolling the animal around the earth-vertical axis, cells were active when the animal's ventral surface faced the cell's PFD. However, with the rat rolled 90° in an ear-down orientation, pitching the rat and rotating it around the vertical axis did not produce directionally tuned responses. Complex movements involving combinations of yaw-roll, but usually not yaw-pitch, resulted in reduced directional tuning even at the final upright orientation when the rat had full visual view of its environment and was pointing in the cell's PFD. Directional firing was restored when the rat's head was moved back-and-forth. There was limited evidence indicating that cells contained conjunctive firing with pitch or roll positions. These findings suggest that the brain's representation of directional heading is derived primarily from horizontal canal information and that the HD signal is a 3D gravity-referenced signal anchored to a direction in the horizontal plane. NEW & NOTEWORTHY This study monitored head direction cell responses from rats in three dimensions using a series of manipulations that involved yaw, pitch, roll, or a combination of these rotations. Results showed that head direction responses are consistent with the use of two reference frames simultaneously: one defined by the surrounding environment using primarily visual landmarks and a second defined by the earth's gravity vector.

Nonoscillatory Phase Coding and Synchronization in the Bat Hippocampal Formation

Hippocampal theta oscillations were proposed to be important for multiple functions, including memory and temporal coding of position. However, previous findings from bats have questioned these proposals by reporting absence of theta rhythmicity in bat hippocampal formation. Does this mean that temporal coding is unique to rodent hippocampus and does not generalize to other species? Here, we report that, surprisingly, bat hippocampal neurons do exhibit temporal coding similar to rodents, albeit without any continuous oscillations at the 1-20 Hz range. Bat neurons exhibited very strong locking to the non-rhythmic fluctuations of the field potential, such that neurons were synchronized together despite the absence of oscillations. Further, some neurons exhibited "phase precession" and phase coding of the bat's position-with spike phases shifting earlier as the animal moved through the place field. This demonstrates an unexpected type of neural coding in the mammalian brain-nonoscillatory phase coding-and highlights the importance of synchrony and temporal coding for hippocampal function across species.

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

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

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

Cincinnati water maze: A review of the development, methods, and evidence as a test of egocentric learning and memory

Advantageous maneuvering through the environment to find food and avoid or escape danger is central to survival of most animal species. The ability to do so depends on learning and remembering different locations, especially home-base. This capacity is encoded in the brain by two systems: one using cues outside the organism (distal cues), allocentric navigation, and one using self-movement, internal cues (proximal cues), for egocentric navigation. Whereas allocentric navigation involves the hippocampus, entorhinal cortex, and surrounding structures, egocentric navigation involves the dorsal striatum and connected structures; in humans this system encodes routes and integrated paths and when over-learned, becomes procedural memory. Allocentric assessment methods have been extensively reviewed elsewhere. The purpose of this paper is to review one specific method for assessing egocentric, route-based navigation in rats: the Cincinnati water maze (CWM). The test is an asymmetric multiple-T maze arranged in such a way that rats must learn to find path openings along walls rather at ends in order to reach the goal. Failing to do this leads to cul-de-sacs and repeated errors. The task may be learned in the light or dark, but in the dark, wherein distal cues are eliminated, provides the best assessment of egocentric navigation. When used in conjunction with tests of other types of learning, such as allocentric navigation, the CWM provides a balanced approach to assessing the two major forms of navigational learning and memory found in mammals.

Physiological Properties of Neurons in Bat Entorhinal Cortex Exhibit an Inverse Gradient along the Dorsal-Ventral Axis Compared to Entorhinal Neurons in Rat

Medial entorhinal cortex (MEC) grid cells exhibit firing fields spread across the environment on the vertices of a regular tessellating triangular grid. In rodents, the size of the firing fields and the spacing between the firing fields are topographically organized such that grid cells located more ventrally in MEC exhibit larger grid fields and larger grid-field spacing compared with grid cells located more dorsally. Previous experiments in brain slices from rodents have shown that several intrinsic cellular electrophysiological properties of stellate cells in layer II of MEC change systematically in neurons positioned along the dorsal-ventral axis of MEC, suggesting that these intrinsic cellular properties might control grid-field spacing. In the bat, grid cells in MEC display a functional topography in terms of grid-field spacing, similar to what has been reported in rodents. However, it is unclear whether neurons in bat MEC exhibit similar gradients of cellular physiological properties, which may serve as a conserved mechanism underlying grid-field spacing in mammals. To test whether entorhinal cortex (EC) neurons in rats and bats exhibit similar electrophysiological gradients, we performed whole-cell patch recordings along the dorsal-ventral axis of EC in bats. Surprisingly, our data demonstrate that the sag response properties and the resonance properties recorded in layer II neurons of entorhinal cortex in the Egyptian fruit bat demonstrate an inverse relationship along the dorsal-ventral axis compared with the rat.

SIGNIFICANCE STATEMENT

As animals navigate, neurons in medial entorhinal cortex (MEC), termed grid cells, discharge at regular spatial intervals. In bats and rats, the spacing between the firing fields of grid cells changes systematically along the dorsal-ventral axis of MEC. It has been proposed that these changes could be generated by systematic differences in the intrinsic cellular physiology of neurons distributed along the dorsal-ventral axis of MEC. The results from our study show that key intrinsic physiological properties of neurons in entorhinal cortex of the bat and rat change in the opposite direction along the dorsal-ventral axis of entorhinal cortex, suggesting that these intrinsic physiological properties cannot account in the same way across species for the change in grid-field spacing shown along the dorsal-ventral axis.

Gamma Oscillations and Their Cross-frequency Coupling in the Primate Hippocampus during Sleep

STUDY OBJECTIVES

The mechanism by which sleep consolidates memory is unclear. Based on the two-stage model of memory consolidation, different functions for slow wave sleep (SWS) and rapid eye movement (REM) sleep have been proposed; thus, state-dependent changes of neural oscillations in the hippocampus might clarify this fundamental question.

METHODS

We recorded hippocampal local field potentials from freely behaving monkeys via telemetry and analyzed their nonstationary oscillations using Hilbert-Huang transform.

RESULTS

By applying a recently developed empirical mode decomposition analysis, we found strong cross-frequency coupling between high-frequency and slow wave oscillations during SWS and a prominent increase of gamma band activity in short bursts during REM sleep in unanesthetized primates' hippocampus.

CONCLUSION

Spatiotemporal integration through coupled oscillations during slow wave sleep might be a physiological basis of system consolidation, whereas gamma bursts during rapid eye movement sleep might be related to synaptic consolidation in the local hippocampal neural circuit.

Grid cells in 3-D: Reconciling data and models

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

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.

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

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

Examination of rhythmicity of extracellularly recorded neurons in the entorhinal cortex

A number of studies have examined the theta-rhythmic modulation of neuronal firing in the hippocampal circuit. For extracellular recordings, this is often done by examining spectral properties of the spike-time autocorrelogram, most significantly, for validating the presence or absence of theta modulation across species. These techniques can show significant rhythmicity for high firing rate, highly rhythmic neurons; however, they are substantially biased by several factors including the peak firing rate of the neuron, the amount of time spent in the neuron's receptive field, and other temporal properties of the rhythmicity such as cycle-skipping. These limitations make it difficult to examine rhythmic modulation in neurons with low firing rates or when an animal has short dwell times within the firing field and difficult to compare rhythmicity under disparate experimental conditions when these factors frequently differ. Here, we describe in detail the challenges that researchers face when using these techniques and apply our findings to recent recordings from bat entorhinal grid cells, suggesting that they may have lacked enough data to examine theta rhythmicity robustly. We describe a more sensitive and statistically rigorous method using maximum likelihood estimation (MLE) of a parametric model of the lags within the autocorrelation window, which helps to alleviate some of the problems of traditional methods and was also unable to detect rhythmicity in bat grid cells. Using large batteries of simulated data, we explored the boundaries for which the MLE technique and the theta index can detect rhythmicity. The MLE technique is less sensitive to many features of the autocorrelogram and provides a framework for statistical testing to detect rhythmicity as well as changes in rhythmicity in individual sessions providing a substantial improvement over previous methods.

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.

Has a fully three-dimensional space map never evolved in any species? A comparative imperative for studies of spatial cognition

I propose that it is premature to assert that a fully three-dimensional map has never evolved in any species, as data are lacking to show that space coding in all animals is the same. Instead, I hypothesize that three-dimensional representation is tied to an animal's mode of locomotion through space. Testing this hypothesis requires a large body of comparative data.

Value of water mazes for assessing spatial and egocentric learning and memory in rodent basic research and regulatory studies

Maneuvering safely through the environment is central to survival of all animals. The ability to do this depends on learning and remembering locations. This capacity is encoded in the brain by two systems: one using cues outside the organism (distal cues), allocentric navigation, and one using self-movement, internal cues and sometimes proximal cues, egocentric navigation. Allocentric navigation involves the hippocampus, entorhinal cortex, and surrounding structures (e.g., subiculum); in humans this system encodes declarative memory (allocentric, semantic, and episodic, i.e., memory for people, places, things, and events). This form of memory is assessed in laboratory animals by many methods, but predominantly the Morris water maze (MWM). Egocentric navigation involves the dorsal striatum and connected structures; in humans this system encodes routes and integrated paths and when over-learned becomes implicit or procedural memory. Several allocentric methods for rodents are reviewed and compared with the MWM with particular focus on the Cincinnati water maze (CWM). MWM advantages include minimal training, no food deprivation, ease of testing, reliable learning, insensitivity to differences in body weight and appetite, absence of non-performers, control methods for performance effects, repeated testing capability and other factors that make this test well-suited for regulatory studies. MWM limitations are also reviewed. Evidence-based MWM design and testing methods are presented. On balance, the MWM is arguably the preferred test for assessing learning and memory in basic research and regulatory studies and the CWM is recommended if two tests can be accommodated so that both allocentric (MWM) and egocentric (CWM) learning and memory can be effectively and efficiently assessed.

Membrane potential-dependent integration of synaptic inputs in entorhinal stellate neurons

Stellate cells (SCs) of the medial entorhinal cortex exhibit robust spontaneous membrane-potential oscillations (MPOs) in the theta (4-12 Hz) frequency band as well as theta-frequency resonance in their membrane impedance spectra. Past experimental and modeling work suggests that these features may contribute to the phase-locking of SCs to the entorhinal theta rhythm and may be important for forming the hexagonally tiled grid cell place fields exhibited by these neurons in vivo. Among the major biophysical mechanisms contributing to MPOs is a population of persistent (non-inactivating or slowly inactivating) sodium channels. The resulting persistent sodium conductance (GNaP ) gives rise to an apparent increase in input resistance as the cell approaches threshold. In this study, we used dynamic clamp to test the hypothesis that this increased input resistance gives rise to voltage-dependent, and thus MPO phase-dependent, changes in the amplitude of excitatory and inhibitory post-synaptic potential (PSP) amplitudes. We find that PSP amplitude depends on membrane potential, exhibiting a 5-10% increase in amplitude per mV depolarization. The effect is larger than-and sums quasi-linearly with-the effect of the synaptic driving force, V - Esyn . Given that input-driven MPOs 10 mV in amplitude are commonly observed in MEC stellate cells in vivo, this voltage- and phase-dependent synaptic gain is large enough to modulate PSP amplitude by over 50% during theta-frequency MPOs. Phase-dependent synaptic gain may therefore impact the phase locking and phase precession of grid cells in vivo to ongoing network oscillations. © 2014 Wiley Periodicals, Inc.

Controlling phase noise in oscillatory interference models of grid cell firing

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

Grid cells and cortical representation

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

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.

Three-dimensional space: locomotory style explains memory differences in rats and hummingbirds

While most animals live in a three-dimensional world, they move through it to different extents depending on their mode of locomotion: terrestrial animals move vertically less than do swimming and flying animals. As nearly everything we know about how animals learn and remember locations in space comes from two-dimensional experiments in the horizontal plane, here we determined whether the use of three-dimensional space by a terrestrial and a flying animal was correlated with memory for a rewarded location. In the cubic mazes in which we trained and tested rats and hummingbirds, rats moved more vertically than horizontally, whereas hummingbirds moved equally in the three dimensions. Consistent with their movement preferences, rats were more accurate in relocating the horizontal component of a rewarded location than they were in the vertical component. Hummingbirds, however, were more accurate in the vertical dimension than they were in the horizontal, a result that cannot be explained by their use of space. Either as a result of evolution or ontogeny, it appears that birds and rats prioritize horizontal versus vertical components differently when they remember three-dimensional space.

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.

Assessing spatial learning and memory in rodents

Maneuvering safely through the environment is central to survival of almost all species. The ability to do this depends on learning and remembering locations. This capacity is encoded in the brain by two systems: one using cues outside the organism (distal cues), allocentric navigation, and one using self-movement, internal cues and nearby proximal cues, egocentric navigation. Allocentric navigation involves the hippocampus, entorhinal cortex, and surrounding structures; in humans this system encodes allocentric, semantic, and episodic memory. This form of memory is assessed in laboratory animals in many ways, but the dominant form of assessment is the Morris water maze (MWM). Egocentric navigation involves the dorsal striatum and connected structures; in humans this system encodes routes and integrated paths and, when overlearned, becomes procedural memory. In this article, several allocentric assessment methods for rodents are reviewed and compared with the MWM. MWM advantages (little training required, no food deprivation, ease of testing, rapid and reliable learning, insensitivity to differences in body weight and appetite, absence of nonperformers, control methods for proximal cue learning, and performance effects) and disadvantages (concern about stress, perhaps not as sensitive for working memory) are discussed. Evidence-based design improvements and testing methods are reviewed for both rats and mice. Experimental factors that apply generally to spatial navigation and to MWM specifically are considered. It is concluded that, on balance, the MWM has more advantages than disadvantages and compares favorably with other allocentric navigation tasks.

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.

Hippocampal theta oscillations are slower in humans than in rodents: implications for models of spatial navigation and memory

The theta oscillation is a neuroscience enigma. When a rat runs through an environment, large-amplitude theta oscillations (4-10 Hz) reliably appear in the hippocampus's electrical activity. The consistency of this pattern led to theta playing a central role in theories on the neural basis of mammalian spatial navigation and memory. However, in fact, hippocampal oscillations at 4-10 Hz are rare in humans and in some other species. This presents a challenge for theories proposing theta as an essential component of the mammalian brain, including models of place and grid cells. Here, I examine this issue by reviewing recent research on human hippocampal oscillations using direct brain recordings from neurosurgical patients. This work indicates that the human hippocampus does indeed exhibit rhythms that are functionally similar to theta oscillations found in rodents, but that these signals have a slower frequency of approximately 1-4 Hz. I argue that oscillatory models of navigation and memory derived from rodent data are relevant for humans, but that they should be modified to account for the slower frequency of the human theta rhythm.

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.

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.

Mechanisms and functions of theta rhythms

The theta rhythm is one of the largest and most sinusoidal activity patterns in the brain. Here I survey progress in the field of theta rhythms research. I present arguments supporting the hypothesis that theta rhythms emerge owing to intrinsic cellular properties yet can be entrained by several theta oscillators throughout the brain. I review behavioral correlates of theta rhythms and consider how these correlates inform our understanding of theta rhythms' functions. I discuss recent work suggesting that one function of theta is to package related information within individual theta cycles for more efficient spatial memory processing. Studies examining the role of theta phase precession in spatial memory, particularly sequence retrieval, are also summarized. Additionally, I discuss how interregional coupling of theta rhythms facilitates communication across brain regions. Finally, I conclude by summarizing how theta rhythms may support cognitive operations in the brain, including learning.