Phase coding by grid cells in unconstrained environments: two-dimensional phase precession

Grid cells: the missing link in understanding Parkinson's disease?

The mechanisms underlying Parkinson's disease (PD) are complex and not fully understood, and the box-and-arrow model among other current models present significant challenges. This paper explores the potential role of the allocentric brain and especially its grid cells in several PD motor symptoms, including bradykinesia, kinesia paradoxa, freezing of gait, the bottleneck phenomenon, and their dependency on cueing. It is argued that central hubs, like the locus coeruleus and the pedunculopontine nucleus, often narrowly interpreted in the context of PD, play an equally important role in governing the allocentric brain as the basal ganglia. Consequently, the motor and secondary motor (e.g., spatially related) symptoms of PD linked with dopamine depletion may be more closely tied to erroneous computation by grid cells than to the basal ganglia alone. Because grid cells and their associated central hubs introduce both spatial and temporal information to the brain influencing velocity perception they may cause bradykinesia or hyperkinesia as well. In summary, PD motor symptoms may primarily be an allocentric disturbance resulting from virtual faulty computation by grid cells revealed by dopamine depletion in PD.

Disrupted hippocampal synchrony following maternal immune activation in a rat model

Maternal immune activation (MIA) is a risk factor for schizophrenia and other neurodevelopmental disorders. MIA in rats models a number of the brain and behavioral changes that are observed in schizophrenia, including impaired memory. Recent studies in the MIA model have shown that the firing of the hippocampal place cells that are involved in memory processes appear relatively normal, but with abnormalities in the temporal ordering of firing. In this study, we re-analyzed data from prior hippocampal electrophysiological recordings of MIA and control animals to determine whether temporal dysfunction was evident. We find that there is a decreased ratio of slow to fast gamma power, resulting from an increase in fast gamma power and a tendency toward reduced slow gamma power in MIA rats. Moreover, we observe a robust reduction in spectral coherence between hippocampal theta and both fast and slow gamma rhythms, as well as changes in the phase of theta at which fast gamma occurs. We also find the phasic organization of place cell phase precession on the theta wave to be abnormal in MIA rats. Lastly, we observe that the local field potential of MIA rats contains more frequent sharp-wave ripple events, and that place cells were more likely to fire spikes during ripples in these animals than control. These findings provide further evidence of desynchrony in MIA animals and may point to circuit-level changes that underlie failures to integrate and encode information in schizophrenia.

Septo-hippocampal dynamics and the encoding of space and time

Encoding an event in memory requires neural activity to represent multiple dimensions of behavioral experience in space and time. Recent experiments have explored the influence of neural dynamics regulated by the medial septum on the functional encoding of space and time by neurons in the hippocampus and associated structures. This review addresses these dynamics, focusing on the role of theta rhythm, the differential effects of septal inactivation and activation on the functional coding of space and time by individual neurons, and the influence on phase coding that appears as phase precession. We also discuss data indicating that theta rhythm plays a role in timing the internal dynamics of memory encoding and retrieval, as well as the behavioral influences of these neuronal manipulations with regard to memory function.

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.

Gated transformations from egocentric to allocentric reference frames involving retrosplenial cortex, entorhinal cortex, and hippocampus

This paper reviews the recent experimental finding that neurons in behaving rodents show egocentric coding of the environment in a number of structures associated with the hippocampus. Many animals generating behavior on the basis of sensory input must deal with the transformation of coordinates from the egocentric position of sensory input relative to the animal, into an allocentric framework concerning the position of multiple goals and objects relative to each other in the environment. Neurons in retrosplenial cortex show egocentric coding of the position of boundaries in relation to an animal. These neuronal responses are discussed in relation to existing models of the transformation from egocentric to allocentric coordinates using gain fields and a new model proposing transformations of phase coding that differ from current models. The same type of transformations could allow hierarchical representations of complex scenes. The responses in rodents are also discussed in comparison to work on coordinate transformations in humans and non-human primates.

Frequency matters: how changes in hippocampal theta frequency can influence temporal coding, anxiety-reduction, and memory

Hippocampal theta frequency is a somewhat neglected topic relative to theta power, phase, coherence, and cross-frequency coupling. Accordingly, here we review and present new data on variation in hippocampal theta frequency, focusing on functional associations (temporal coding, anxiety reduction, learning, and memory). Taking the rodent hippocampal theta frequency to running-speed relationship as a model, we identify two doubly-dissociable frequency components: (a) the slope component of the theta frequency-to-stimulus-rate relationship ("theta slope"); and (b) its y-intercept frequency ("theta intercept"). We identify three tonic determinants of hippocampal theta frequency. (1) Hotter temperatures increase theta frequency, potentially consistent with time intervals being judged as shorter when hot. Initial evidence suggests this occurs via the "theta slope" component. (2) Anxiolytic drugs with widely-different post-synaptic and pre-synaptic primary targets share the effect of reducing the "theta intercept" component, supporting notions of a final common pathway in anxiety reduction involving the hippocampus. (3) Novelty reliably decreases, and familiarity increases, theta frequency, acting upon the "theta slope" component. The reliability of this latter finding, and the special status of novelty for learning, prompts us to propose a Novelty Elicits Slowing of Theta frequency (NEST) hypothesis, involving the following elements: (1) Theta frequency slowing in the hippocampal formation is a generalised response to novelty of different types and modalities; (2) Novelty-elicited theta slowing is a hippocampal-formation-wide adaptive response functioning to accommodate the additional need for learning entailed by novelty; (3) Lengthening the theta cycle enhances associativity; (4) Even part-cycle lengthening may boost associativity; and (5) Artificial theta stimulation aimed at enhancing learning should employ low-end theta frequencies.

Phase coding of spatial representations in the human entorhinal cortex

The grid-like activity pattern of cells in the mammalian entorhinal cortex provides an internal reference frame for allocentric self-localization. The same neurons maintain robust phase couplings with local field oscillations. We found that neurons of the human entorhinal cortex display consistent spatial and temporal phase locking between spikes and slow gamma band local field potentials (LFPs) during virtual navigation. The phase locking maintained an environment-specific map over time. The phase tuning of spikes to the slow gamma band LFP revealed spatially periodic phase grids with environment-dependent scaling and consistent alignment with the environment. Using a Bayesian decoding model, we could predict the avatar's position with near perfect accuracy and, to a lesser extent, that of heading direction as well. These results imply that the phase of spikes relative to spatially modulated gamma oscillations encode allocentric spatial positions. We posit that a joint spatiotemporal phase code can implement the combined neural representation of space and time in the human entorhinal cortex.

Neural circuits and symbolic processing

The ability to use symbols is a defining feature of human intelligence. However, neuroscience has yet to explain the fundamental neural circuit mechanisms for flexibly representing and manipulating abstract concepts. This article will review the research on neural models for symbolic processing. The review first focuses on the question of how symbols could possibly be represented in neural circuits. The review then addresses how neural symbolic representations could be flexibly combined to meet a wide range of reasoning demands. Finally, the review assesses the research on program synthesis and proposes that the most flexible neural representation of symbolic processing would involve the capacity to rapidly synthesize neural operations analogous to lambda calculus to solve complex cognitive tasks.

Ripple band phase precession of place cell firing during replay

Neuronal “replay,” in which place cell firing during rest recapitulates recently experienced trajectories, is thought to mediate the transmission of information from hippocampus to neocortex, but the mechanism for this transmission is unknown. Here, we show that replay uses a phase code to represent spatial trajectories by the phase of firing relative to the 150- to 250-Hz “ripple” oscillations that accompany replay events. This phase code is analogous to the theta phase precession of place cell firing during navigation, in which place cells fire at progressively earlier phases of the 6- to 12-Hz theta oscillation as their place field is traversed, providing information about self-location that is additional to the rate code and a necessary precursor of replay. Thus, during replay, each ripple cycle contains a “forward sweep” of decoded locations along the recapitulated trajectory. Our results indicate a novel encoding of trajectory information during replay and implicates phase coding as a general mechanism by which the hippocampus transmits experienced and replayed sequential information to downstream targets.

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Place cells fire at successively earlier ripple band phases during replay

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Ripple band firing phase during replay encodes location within the place field

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This produces forward sweeps of place cell activity during each ripple cycle

Information Theoretic Approaches to Deciphering the Neural Code with Functional Fluorescence Imaging

Information theoretic metrics have proven useful in quantifying the relationship between behaviorally relevant parameters and neuronal activity with relatively few assumptions. However, these metrics are typically applied to action potential (AP) recordings and were not designed for the slow timescales and variable amplitudes typical of functional fluorescence recordings (e.g., calcium imaging). The lack of research guidelines on how to apply and interpret these metrics with fluorescence traces means the neuroscience community has yet to realize the power of information theoretic metrics. Here, we used computational methods to create mock AP traces with known amounts of information. From these, we generated fluorescence traces and examined the ability of different information metrics to recover the known information values. We provide guidelines for how to use information metrics when applying them to functional fluorescence and demonstrate their appropriate application to GCaMP6f population recordings from mouse hippocampal neurons imaged during virtual navigation.

Signalling pathways contributing to learning and memory deficits in the Ts65Dn mouse model of Down syndrome

Down syndrome (DS) is a genetic trisomic disorder that produces life-long changes in physiology and cognition. Many of the changes in learning and memory seen in DS are reminiscent of disorders involving the hippocampal/entorhinal circuit. Mouse models of DS typically involve trisomy of murine chromosome 16 is homologous for many of the genes triplicated in human trisomy 21, and provide us with good models of changes in, and potential pharmacotherapy for, human DS. Recent careful dissection of the Ts65Dn mouse model of DS has revealed differences in key signalling pathways from the basal forebrain to the hippocampus and associated rhinal cortices, as well as changes in the microstructure of the hippocampus itself. In vivo behavioural and electrophysiological studies have shown that Ts65Dn animals have difficulties in spatial memory that mirror hippocampal deficits, and have changes in hippocampal electrophysiological phenomenology that may explain these differences, and align with expectations generated from in vitro exploration of this model. Finally, given the existing data, we will examine the possibility for pharmacotherapy for DS, and outline the work that remains to be done to fully understand this system.

Episodic Memories: How do the Hippocampus and the Entorhinal Ring Attractors Cooperate to Create Them?

The brain is capable of registering a constellation of events, encountered only once, as an episodic memory that can last for a lifetime. As evidenced by the clinical case of the patient HM, memories preserving their episodic nature still depend on the hippocampal formation, several years after being created, while semantic memories are thought to reside in neocortical areas. The neurobiological substrate of one-time learning and life-long storing in the brain, that must exist at the cellular and circuit level, is still undiscovered. The breakthrough is delayed by the fact that studies jointly investigating the rodent hippocampus and entorhinal cortex are mostly targeted at understanding the spatial aspect of learning. Here, we present the concept of an entorhinal cortical module, termed EPISODE module, that could explain how the representations of different elements constituting episodic memories can be linked together at the stage of encoding. The new model that we propose here reconciles the structural and functional observations made in the entorhinal cortex and explains how the downstream hippocampal processing organizes the representations into meaningful sequences.

Altered Hippocampal Place Cell Representation and Theta Rhythmicity following Moderate Prenatal Alcohol Exposure

Prenatal alcohol exposure (PAE) leads to profound deficits in spatial memory and synaptic and cellular alterations to the hippocampus that last into adulthood. Neurons in the hippocampus called place cells discharge as an animal enters specific places in an environment, establish distinct ensemble codes for familiar and novel places, and are modulated by local theta rhythms. Spatial memory is thought to critically depend on the integrity of hippocampal place cell firing. Therefore, we tested the hypothesis that hippocampal place cell firing is impaired after PAE by performing in vivo recordings from the hippocampi (CA1 and CA3) of moderate PAE and control adult rats. Our results show that hippocampal CA3 neurons from PAE rats have reduced spatial tuning. Second, CA1 and CA3 neurons from PAE rats are less likely to orthogonalize their firing between directions of travel on a linear track and between changes in contextual stimuli in an open arena compared to control neurons. Lastly, reductions in the number of hippocampal place cells exhibiting significant theta rhythmicity and phase precession were observed, which may suggest changes to hippocampal microcircuit function. Together, the reduced spatial tuning and sensitivity to contextual changes provide a neural systems-level mechanism to explain spatial memory impairment after moderate PAE.

Advantages and detection of phase coding in the absence of rhythmicity

The encoding of information in spike phase relative to local field potential (LFP) oscillations offers several theoretical advantages over equivalent firing rate codes. One notable example is provided by place and grid cells in the rodent hippocampal formation, which exhibit phase precession-firing at progressively earlier phases of the 6-12 Hz movement-related theta rhythm as their spatial firing fields are traversed. It is often assumed that such phase coding relies on a high amplitude baseline oscillation with relatively constant frequency. However, sustained oscillations with fixed frequency are generally absent in LFP and spike train recordings from the human brain. Hence, we examine phase coding relative to LFP signals with broadband low-frequency (2-20 Hz) power but without regular rhythmicity. We simulate a population of grid cells that exhibit phase precession against a baseline oscillation recorded from depth electrodes in human hippocampus. We show that this allows grid cell firing patterns to multiplex information about location, running speed and movement direction, alongside an arbitrary fourth variable encoded in LFP frequency. This is of particular importance given recent demonstrations that movement direction, which is essential for path integration, cannot be recovered from head direction cell firing rates. In addition, we investigate how firing phase might reduce errors in decoded location, including those arising from differences in firing rate across grid fields. Finally, we describe analytical methods that can identify phase coding in the absence of high amplitude LFP oscillations with approximately constant frequency, as in single unit recordings from the human brain and consistent with recent data from the flying bat. We note that these methods could also be used to detect phase coding outside of the spatial domain, and that multi-unit activity can substitute for the LFP signal. In summary, we demonstrate that the computational advantages offered by phase coding are not contingent on, and can be detected without, regular rhythmicity in neural activity.

Overview of computational models of hippocampus and related structures: Introduction to the special issue

Extensive computational modeling has focused on the hippocampal formation and associated cortical structures. This overview describes some of the factors that have motivated the strong focus on these structures, including major experimental findings and their impact on computational models. This overview provides a framework for describing the topics addressed by individual articles in this special issue of the journal Hippocampus.

An uncertainty principle for neural coding: Conjugate representations of position and velocity are mapped onto firing rates and co-firing rates of neural spike trains

The hippocampal system contains neural populations that encode an animal's position and velocity as it navigates through space. Here, we show that such populations can embed two codes within their spike trains: a firing rate code (R) conveyed by within‐cell spike intervals, and a co‐firing rate code (R˙) conveyed by between‐cell spike intervals. These two codes behave as conjugates of one another, obeying an analog of the uncertainty principle from physics: information conveyed in R comes at the expense of information in R˙, and vice versa. An exception to this trade‐off occurs when spike trains encode a pair of conjugate variables, such as position and velocity, which do not compete for capacity across R and R˙. To illustrate this, we describe two biologically inspired methods for decoding R and R˙, referred to as sigma and sigma‐chi decoding, respectively. Simulations of head direction and grid cells show that if firing rates are tuned for position (but not velocity), then position is recovered by sigma decoding, whereas velocity is recovered by sigma‐chi decoding. Conversely, simulations of oscillatory interference among theta‐modulated “speed cells” show that if co‐firing rates are tuned for position (but not velocity), then position is recovered by sigma‐chi decoding, whereas velocity is recovered by sigma decoding. Between these two extremes, information about both variables can be distributed across both channels, and partially recovered by both decoders. These results suggest that populations with different spatial and temporal tuning properties—such as speed versus grid cells—might not encode different information, but rather, distribute similar information about position and velocity in different ways across R and R˙. Such conjugate coding of position and velocity may influence how hippocampal populations are interconnected to form functional circuits, and how biological neurons integrate their inputs to decode information from firing rates and spike correlations.

Neurophysiological coding of space and time in the hippocampus, entorhinal cortex, and retrosplenial cortex

Neurophysiological recordings in behaving rodents demonstrate neuronal response properties that may code space and time for episodic memory and goal-directed behaviour. Here, we review recordings from hippocampus, entorhinal cortex, and retrosplenial cortex to address the problem of how neurons encode multiple overlapping spatiotemporal trajectories and disambiguate these for accurate memory-guided behaviour. The solution could involve neurons in the entorhinal cortex and hippocampus that show mixed selectivity, coding both time and location. Some grid cells and place cells that code space also respond selectively as time cells, allowing differentiation of time intervals when a rat runs in the same location during a delay period. Cells in these regions also develop new representations that differentially code the context of prior or future behaviour allowing disambiguation of overlapping trajectories. Spiking activity is also modulated by running speed and head direction, supporting the coding of episodic memory not as a series of snapshots but as a trajectory that can also be distinguished on the basis of speed and direction. Recent data also address the mechanisms by which sensory input could distinguish different spatial locations. Changes in firing rate reflect running speed on long but not short time intervals, and few cells code movement direction, arguing against path integration for coding location. Instead, new evidence for neural coding of environmental boundaries in egocentric coordinates fits with a modelling framework in which egocentric coding of barriers combined with head direction generates distinct allocentric coding of location. The egocentric input can be used both for coding the location of spatiotemporal trajectories and for retrieving specific viewpoints of the environment. Overall, these different patterns of neural activity can be used for encoding and disambiguation of prior episodic spatiotemporal trajectories or for planning of future goal-directed spatiotemporal trajectories.

Replay as wavefronts and theta sequences as bump oscillations in a grid cell attractor network

Grid cells fire in sequences that represent rapid trajectories in space. During locomotion, theta sequences encode sweeps in position starting slightly behind the animal and ending ahead of it. During quiescence and slow wave sleep, bouts of synchronized activity represent long trajectories called replays, which are well-established in place cells and have been recently reported in grid cells. Theta sequences and replay are hypothesized to facilitate many cognitive functions, but their underlying mechanisms are unknown. One mechanism proposed for grid cell formation is the continuous attractor network. We demonstrate that this established architecture naturally produces theta sequences and replay as distinct consequences of modulating external input. Driving inhibitory interneurons at the theta frequency causes attractor bumps to oscillate in speed and size, which gives rise to theta sequences and phase precession, respectively. Decreasing input drive to all neurons produces traveling wavefronts of activity that are decoded as replays.

The Neurobiology of Mammalian Navigation

Mammals have evolved specialized brain systems to support efficient navigation within diverse habitats and over varied distances, but while navigational strategies and sensory mechanisms vary across species, core spatial components appear to be widely shared. This review presents common elements found in mammalian spatial mapping systems, focusing on the cells in the hippocampal formation representing orientational and locational spatial information, and 'core' mammalian hippocampal circuitry. Mammalian spatial mapping systems make use of both allothetic cues (space-defining cues in the external environment) and idiothetic cues (cues derived from self-motion). As examples of each cue type, we discuss: environmental boundaries, which control both orientational and locational neuronal activity and behaviour; and 'path integration', a process that allows the estimation of linear translation from velocity signals, thought to depend upon grid cells in the entorhinal cortex. Building cognitive maps entails sampling environments: we consider how the mapping system controls exploration to acquire spatial information, and how exploratory strategies may integrate idiothetic with allothetic information. We discuss how 'replay' may act to consolidate spatial maps, and simulate trajectories to aid navigational planning. Finally, we discuss grid cell models of vector navigation.

Hippocampal Sequences During Exploration: Mechanisms and Functions

Although the hippocampus plays a critical role in spatial and episodic memories, the mechanisms underlying memory formation, stabilization, and recall for adaptive behavior remain relatively unknown. During exploration, within single cycles of the ongoing theta rhythm that dominates hippocampal local field potentials, place cells form precisely ordered sequences of activity. These neural sequences result from the integration of both external inputs conveying sensory-motor information, and intrinsic network dynamics possibly related to memory processes. Their endogenous replay during subsequent sleep is critical for memory consolidation. The present review discusses possible mechanisms and functions of hippocampal theta sequences during exploration. We present several lines of evidence suggesting that these neural sequences play a key role in information processing and support the formation of initial memory traces, and discuss potential functional distinctions between neural sequences emerging during theta vs. awake sharp-wave ripples.

Place cell assemblies remain intact, despite reduced phase precession, after cholinergic disruption

The hippocampal theta rhythm is frequently viewed as a clocking mechanism that coordinates the spiking activity of neurons across the hippocampus to form coherent neural assemblies. Phase precession is a form of temporal coding evidencing this mechanism and is degraded following systemic pharmacological disruption of cholinergic signaling. However, whether neural assemblies are commensurately degraded, as would be predicted from a clocking mechanism hypothesis, remains unknown. To address this, we recorded the spiking activity of hippocampal place cells as rats completed laps on a circle track for chocolate drink before versus during the influence of a systemic muscarinic acetylcholine receptor antagonist. We compared the integrity of hippocampal ensembles using three approaches. The first approach used cross-correlogram (CCG) analyses to ask if the relative spike-timing between pairs of cells became less reliable. The second used a general linear model based analysis to ask whether the activity of simultaneously recorded neurons became any less predictive of the spiking activity of single neurons. Finally, the third approach used a reconstruction analysis to ask if the population activity was any less informative regarding the environmental position of the animal and whether theta sequences were impaired. The results of all three analyses paint a consistent picture: systemic cholinergic disruption did not degrade assembly integrity. These data demonstrate that place cell assemblies do not depend upon high quality phase precession.

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.

Distinct Functional Groups Emerge from the Intrinsic Properties of Molecularly Identified Entorhinal Interneurons and Principal Cells

Inhibitory interneurons are an important source of synaptic inputs that may contribute to network mechanisms for coding of spatial location by entorhinal cortex (EC). The intrinsic properties of inhibitory interneurons in the EC of the mouse are mostly undescribed. Intrinsic properties were recorded from known cell types, such as, stellate and pyramidal cells and 6 classes of molecularly identified interneurons (regulator of calcineurin 2, somatostatin, serotonin receptor 3a, neuropeptide Y neurogliaform (NGF), neuropeptide Y non-NGF, and vasoactive intestinal protein) in acute brain slices. We report a broad physiological diversity between and within cell classes. We also found differences in the ability to produce postinhibitory rebound spikes and in the frequency and amplitude of incoming EPSPs. To understand the source of this intrinsic variability we applied hierarchical cluster analysis to functionally classify neurons. These analyses revealed physiologically derived cell types in EC that mostly corresponded to the lines identified by biomarkers with a few unexpected and important differences. Finally, we reduced the complex multidimensional space of intrinsic properties to the most salient five that predicted the cellular biomolecular identity with 81.4% accuracy. These results provide a framework for the classification of functional subtypes of cortical neurons by their intrinsic membrane properties.

Inferring oscillatory modulation in neural spike trains

Oscillations are observed at various frequency bands in continuous-valued neural recordings like the electroencephalogram (EEG) and local field potential (LFP) in bulk brain matter, and analysis of spike-field coherence reveals that spiking of single neurons often occurs at certain phases of the global oscillation. Oscillatory modulation has been examined in relation to continuous-valued oscillatory signals, and independently from the spike train alone, but behavior or stimulus triggered firing-rate modulation, spiking sparseness, presence of slow modulation not locked to stimuli and irregular oscillations with large variability in oscillatory periods, present challenges to searching for temporal structures present in the spike train. In order to study oscillatory modulation in real data collected under a variety of experimental conditions, we describe a flexible point-process framework we call the Latent Oscillatory Spike Train (LOST) model to decompose the instantaneous firing rate in biologically and behaviorally relevant factors: spiking refractoriness, event-locked firing rate non-stationarity, and trial-to-trial variability accounted for by baseline offset and a stochastic oscillatory modulation. We also extend the LOST model to accommodate changes in the modulatory structure over the duration of the experiment, and thereby discover trial-to-trial variability in the spike-field coherence of a rat primary motor cortical neuron to the LFP theta rhythm. Because LOST incorporates a latent stochastic auto-regressive term, LOST is able to detect oscillations when the firing rate is low, the modulation is weak, and when the modulating oscillation has a broad spectral peak.

Oscillatory modulation of neural activity in the brain is widely observed under conditions associated with a variety of cognitive tasks and mental states. Within individual neurons, oscillations may be uncovered in the moment-to-moment variation in neural firing rate. This, however, is often challenging because many factors may affect fluctuations in neural firing rate and, in addition, neurons fire irregular sets of action potentials, or spike trains, due to an unknown combination of meaningful signals and extraneous noise. We have devised a statistical Latent Oscillatory Spike Train (LOST) model with accompanying model-fitting technology, that is able to detect subtle oscillations in spike trains by taking into account both spiking noise and temporal variation in the oscillation itself. The method couples two techniques developed for other purposes in the literature on Bayesian analysis. Using data simulated from theoretical neurons and real data recorded from cortical motor neurons, we demonstrate the method’s ability to track changes in the modulatory structure of the oscillation across experimental trials.

Systemic administration of two different anxiolytic drugs decreases local field potential theta frequency in the medial entorhinal cortex without affecting grid cell firing fields

Neurons coding spatial location (grid cells) are found in medial entorhinal cortex (MEC) and demonstrate increasing size of firing fields and spacing between fields (grid scale) along the dorsoventral axis. This change in grid scale correlates with differences in theta frequency, a 6-10Hz rhythm in the local field potential (LFP) and rhythmic firing of cells. A relationship between theta frequency and grid scale can be found when examining grid cells recorded in different locations along the dorsoventral axis of MEC. When describing the relationship between theta frequency and grid scale, it is important to account for the strong positive correlation between theta frequency and running speed. Plotting LFP theta frequency across running speeds dissociates two components of this relationship: slope and intercept of the linear fit. Change in theta frequency through a change in the slope component has been modeled and shown experimentally to affect grid scale, but the prediction that change in the intercept component would not affect grid scale has not been tested experimentally. This prediction about the relationship of intercept to grid scale is the primary hypothesis tested in the experiments presented here. All known anxiolytic drugs decrease hippocampal theta frequency despite their differing mechanisms of action. Specifically, anxiolytics decrease the intercept of the theta frequency-running speed relationship in the hippocampus. Here we demonstrate that anxiolytics decrease the intercept of the theta frequency-running speed relationship in the MEC, similar to hippocampus, and the decrease in frequency through this change in intercept does not affect grid scale.

Phase precession: a neural code underlying episodic memory?

In the hippocampal formation, the sequential activation of place-specific cells represents a conceptual model for the spatio-temporal events that assemble episodic memories. The imprinting of behavioral sequences in hippocampal networks might be achieved via spike-timing-dependent plasticity and phase precession of the spiking activity of neurons. It is unclear, however, whether phase precession plays an active role by enabling sequence learning via synaptic plasticity or whether phase precession passively reflects retrieval dynamics. Here we examine these possibilities in the context of potential mechanisms generating phase precession. Knowledge of these mechanisms would allow to selectively alter phase precession and test its role in episodic memory. We finally review the few successful approaches to degrade phase precession and the resulting impact on behavior.

Flexible theta sequence compression mediated via phase precessing interneurons

Encoding of behavioral episodes as spike sequences during hippocampal theta oscillations provides a neural substrate for computations on events extended across time and space. However, the mechanisms underlying the numerous and diverse experimentally observed properties of theta sequences remain poorly understood. Here we account for theta sequences using a novel model constrained by the septo-hippocampal circuitry. We show that when spontaneously active interneurons integrate spatial signals and theta frequency pacemaker inputs, they generate phase precessing action potentials that can coordinate theta sequences in place cell populations. We reveal novel constraints on sequence generation, predict cellular properties and neural dynamics that characterize sequence compression, identify circuit organization principles for high capacity sequential representation, and show that theta sequences can be used as substrates for association of conditioned stimuli with recent and upcoming events. Our results suggest mechanisms for flexible sequence compression that are suited to associative learning across an animal’s lifespan.

DOI:http://dx.doi.org/10.7554/eLife.20349.001

Nerve cells in the brain exchange information via electrical impulses. In a given brain area, the electrical impulses at any particular moment can be thought of as forming a code that represents an aspect of the outside world. For example, groups of nerve cells in the hippocampus generate a type of code called a theta sequence, which represents a series of recent and upcoming events. The specific timing of electrical impulses within a theta sequence is crucial in creating certain types of memory.

There are two major classes of nerve cell in the brain: excitatory cells activate impulses in neighbouring cells, while inhibitory cells act to temporarily block impulses from other nerve cells. Many groups, or “circuits”, of nerve cells contain combinations of both cell types to control how and when they communicate. Previous studies show that both types of cell are active within theta sequences, but it is not known precisely how they contribute to creating the sequences.

Chadwick et al. developed a new mathematical model that simulates how theta sequences can emerge from circuits of both excitatory and inhibitory nerve cells. The connections between these simulated cells are based on experimental data from real nerve cells in the hippocampus. The model predicts that inhibitory cells play an important role in generating theta sequences by interacting with groups of excitatory cells to coordinate the timing of electrical impulses. Furthermore, the model shows how memory capacity depends on these connections.

The next step following on from this work is to carry out experiments to test the model’s predictions. This will include monitoring the same group of nerve cells in multiple different situations to find out how their theta sequences change, and recording electrical events in individual nerve cells during theta sequences. If the theory’s predictions are confirmed this would lead to a deeper understanding of how our brains remember sequences of events.

DOI:http://dx.doi.org/10.7554/eLife.20349.002

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.

Grid Cells and Place Cells: An Integrated View of their Navigational and Memory Function

Much has been learned about the hippocampal/entorhinal system, but an overview of how its parts work in an integrated way is lacking. One question regards the function of entorhinal grid cells. We propose here that their fundamental function is to provide a coordinate system for producing mind-travel in the hippocampus, a process that accesses associations with upcoming positions. We further propose that mind-travel occurs during the second half of each theta cycle. By contrast, the first half of each theta cycle is devoted to computing current position using sensory information from the lateral entorhinal cortex (LEC) and path integration information from the medial entorhinal cortex (MEC). This model explains why MEC lesions can abolish hippocampal phase precession but not place fields.

Using Grid Cells for Navigation

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

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

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

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

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We simulate various neural implementations and make testable experimental predictions

Rebound spiking in layer II medial entorhinal cortex stellate cells: Possible mechanism of grid cell function

Rebound spiking properties of medial entorhinal cortex (mEC) stellate cells induced by inhibition may underlie their functional properties in awake behaving rats, including the temporal phase separation of distinct grid cells and differences in grid cell firing properties. We investigated rebound spiking properties using whole cell patch recording in entorhinal slices, holding cells near spiking threshold and delivering sinusoidal inputs, superimposed with realistic inhibitory synaptic inputs to test the capacity of cells to selectively respond to specific phases of inhibitory input. Stellate cells showed a specific phase range of hyperpolarizing inputs that elicited spiking, but non-stellate cells did not show phase specificity. In both cell types, the phase range of spiking output occurred between the peak and subsequent descending zero crossing of the sinusoid. The phases of inhibitory inputs that induced spikes shifted earlier as the baseline sinusoid frequency increased, while spiking output shifted to later phases. Increases in magnitude of the inhibitory inputs shifted the spiking output to earlier phases. Pharmacological blockade of h-current abolished the phase selectivity of hyperpolarizing inputs eliciting spikes. A network computational model using cells possessing similar rebound properties as found in vitro produces spatially periodic firing properties resembling grid cell firing when a simulated animal moves along a linear track. These results suggest that the ability of mEC stellate cells to fire rebound spikes in response to a specific range of phases of inhibition could support complex attractor dynamics that provide completion and separation to maintain spiking activity of specific grid cell populations.

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.

Independent theta phase coding accounts for CA1 population sequences and enables flexible remapping

Hippocampal place cells encode an animal's past, current, and future location through sequences of action potentials generated within each cycle of the network theta rhythm. These sequential representations have been suggested to result from temporally coordinated synaptic interactions within and between cell assemblies. Instead, we find through simulations and analysis of experimental data that rate and phase coding in independent neurons is sufficient to explain the organization of CA1 population activity during theta states. We show that CA1 population activity can be described as an evolving traveling wave that exhibits phase coding, rate coding, spike sequences and that generates an emergent population theta rhythm. We identify measures of global remapping and intracellular theta dynamics as critical for distinguishing mechanisms for pacemaking and coordination of sequential population activity. Our analysis suggests that, unlike synaptically coupled assemblies, independent neurons flexibly generate sequential population activity within the duration of a single theta cycle.

DOI:http://dx.doi.org/10.7554/eLife.03542.001

When we explore a new place, we naturally create a mental map of the location as we go. This mental map is stored in a region of the brain called the hippocampus, which contains cells called place cells. These cells can carry information about our past, present, and future location in the form of electrical signals. They connect to each other to form networks and it has been proposed that these connections can store the information needed for the mental maps.

Real-time maps are represented in the information carried by the electrical signals themselves. A physical location is specified by the individual place cell that is activated, and by the timing of the electrical signal it produces relative to a ‘brain wave’ called the theta rhythm. Brain waves are patterns of electrical signals activated in sets of brain cells and the theta rhythm is produced in the hippocampus of an animal as it explores its surroundings.

Previous experiments suggested that when a rat explores an area, several sets of brain cells in the hippocampus are activated in sequence within each cycle of the theta rhythm. As the rat moves forward, the sequence shifts to different sets of cells to reflect the upcoming locations ahead of the rat. It has been thought that these sequences are triggered by the individual connections between the place cells.

Here, Chadwick et al. developed mathematical models of the electrical activity in the brains of rats as they explored. They used these models to analyze data from previous experiments and found that the sequences of electrical activity arise from the timing of each cell's activity relative to the theta rhythm, rather than from the connections between the cells.

Chadwick et al.'s findings suggest that the mental map may be highly flexible, allowing vast numbers of distinct memories to be stored within the same network of place cells without interference. Future studies will involve investigating the role of brain waves in the forming new mental maps and creating new memories.

DOI:http://dx.doi.org/10.7554/eLife.03542.002

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.

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.

Modeling inheritance of phase precession in the hippocampal formation

Spatial information about the environment is encoded by the activity of place and grid cells in the hippocampal formation. As an animal traverses a cell's firing field, action potentials progressively shift to earlier phases of the theta oscillation (6-10 Hz). This "phase precession" is observed also in the prefrontal cortex and the ventral striatum, but mechanisms for its generation are unknown. However, once phase precession exists in one region, it might also propagate to downstream regions. Using a computational model, we analyze such inheritance of phase precession, for example, from the entorhinal cortex to CA1 and from CA3 to CA1. We find that distinctive subthreshold and suprathreshold features of the membrane potential of CA1 pyramidal cells (Harvey et al., 2009; Mizuseki et al., 2012; Royer et al., 2012) can be explained by inheritance and that excitatory input is essential. The model explains how inhibition modulates the slope and range of phase precession and provides two main testable predictions. First, theta-modulated inhibitory input to a CA1 pyramidal cell is not necessary for phase precession. Second, theta-modulated inhibitory input on its own generates membrane potential peaks that are in phase with peaks of the extracellular field. Furthermore, we suggest that the spatial distribution of field centers of a population of phase-precessing input cells determines, not only the place selectivity, but also the characteristics of phase precession of the targeted output cell. The inheritance model thus can explain why phase precession is observed throughout the hippocampal formation and other areas of the brain.

Movement dependence and layer specificity of entorhinal phase precession in two-dimensional environments

As a rat moves, grid cells in its entorhinal cortex (EC) discharge at multiple locations of the external world, and the firing fields of each grid cell span a hexagonal lattice. For movements on linear tracks, spikes tend to occur at successively earlier phases of the theta-band filtered local field potential during the traversal of a firing field - a phenomenon termed phase precession. The complex movement patterns observed in two-dimensional (2D) open-field environments may fundamentally alter phase precession. To study this question at the behaviorally relevant single-run level, we analyzed EC spike patterns as a function of the distance traveled by the rat along each trajectory. This analysis revealed that cells across all EC layers fire spikes that phase-precess; indeed, the rate and extent of phase precession were the same, only the correlation between spike phase and path length was weaker in EC layer III. Both slope and correlation of phase precession were surprisingly similar on linear tracks and in 2D open-field environments despite strong differences in the movement statistics, including running speed. While the phase-precession slope did not correlate with the average running speed, it did depend on specific properties of the animal's path. The longer a curving path through a grid-field in a 2D environment, the shallower was the rate of phase precession, while runs that grazed a grid field tangentially led to a steeper phase-precession slope than runs through the field center. Oscillatory interference models for grid cells do not reproduce the observed phenomena.

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.