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

The Weber-Fechner law proposes that our perceived sensory input increases with physical input on a logarithmic scale. Hippocampal ‘time cells’ carry a record of recent experience by firing sequentially during a circumscribed period of time after a triggering stimulus. Different cells have ‘time fields’ at different delays up to at least tens of seconds. Past studies suggest that time cells represent a compressed timeline by demonstrating that fewer time cells fire late in the delay and their time fields are wider. This paper asks whether the compression of time cells obeys the Weber-Fechner Law. Time cells were studied with a hierarchical Bayesian model that simultaneously accounts for the firing pattern at the trial level, cell level, and population level. This procedure allows separate estimates of the within-trial receptive field width and the across-trial variability. After isolating across-trial variability, time field width increased linearly with delay. Further, the time cell population was distributed evenly along a logarithmic time axis. These findings provide strong quantitative evidence that the neural temporal representation in rodent hippocampus is logarithmically compressed and obeys a neural Weber-Fechner Law.

Neuronal representations of spatial location and movement speed in the medial entorhinal cortex during the ‘active’ theta state of the brain are important for memory-guided navigation and rely on visual inputs. However, little is known about how visual inputs change neural dynamics as a function of running speed and time. By manipulating visual inputs in mice, we demonstrate that changes in spatial stability of grid cell firing correlate with changes in a proposed speed signal by local field potential theta frequency. In contrast, visual inputs do not alter the running speed-dependent gain in neuronal firing rates. Moreover, we provide evidence that sensory inputs other than visual inputs can support grid cell firing, though less accurately, in complete darkness. Finally, changes in spatial accuracy of grid cell firing on a 10 s time scale suggest that grid cell firing is a function of velocity signals integrated over past time.

While memories are often thought of as flashbacks to a previous experience, they do not simply conserve veridical representations of the past but must continually integrate new information to ensure survival in dynamic environments. Therefore, ‘drift’ in neural firing patterns, typically construed as disruptive ‘instability’ or an undesirable consequence of noise, may actually be useful for updating memories. In our view, continual modifications in memory representations reconcile classical theories of stable memory traces with neural drift. Here we review how memory representations are updated through dynamic recruitment of neuronal ensembles on the basis of excitability and functional connectivity at the time of learning. Overall, we emphasize the importance of considering memories not as static entities, but instead as flexible network states that reactivate and evolve across time and experience.

The relationship between grid cells and two types of neurons found in the medial entorhinal cortex has been clarified.

Oscillations are ubiquitous features of brain dynamics that undergo task-related changes in synchrony, power, and frequency. The impact of those changes on target networks is poorly understood. In this work, we used a biophysically detailed model of prefrontal cortex (PFC) to explore the effects of varying the spike rate, synchrony, and waveform of strong oscillatory inputs on the behavior of cortical networks driven by them. Interacting populations of excitatory and inhibitory neurons with strong feedback inhibition are inhibition-based network oscillators that exhibit resonance (i.e., larger responses to preferred input frequencies). We quantified network responses in terms of mean firing rates and the population frequency of network oscillation; and characterized their behavior in terms of the natural response to asynchronous input and the resonant response to oscillatory inputs. We show that strong feedback inhibition causes the PFC to generate internal (natural) oscillations in the beta/gamma frequency range (>15 Hz) and to maximize principal cell spiking in response to external oscillations at slightly higher frequencies. Importantly, we found that the fastest oscillation frequency that can be relayed by the network maximizes local inhibition and is equal to a frequency even higher than that which maximizes the firing rate of excitatory cells; we call this phenomenon population frequency resonance. This form of resonance is shown to determine the optimal driving frequency for suppressing responses to asynchronous activity. Lastly, we demonstrate that the natural and resonant frequencies can be tuned by changes in neuronal excitability, the duration of feedback inhibition, and dynamic properties of the input. Our results predict that PFC networks are tuned for generating and selectively responding to beta- and gamma-rhythmic signals due to the natural and resonant properties of inhibition-based oscillators. They also suggest strategies for optimizing transcranial stimulation and using oscillatory networks in neuromorphic engineering.

Firing fields of grid cells in medial entorhinal cortex show compression or expansion after manipulations of the location of environmental barriers. This compression or expansion could be selective for individual grid cell modules with particular properties of spatial scaling. We present a model for differences in the response of modules to barrier location that arise from different mechanisms for the influence of visual features on the computation of location that drives grid cell firing patterns. These differences could arise from differences in the position of visual features within the visual field. When location was computed from the movement of visual features on the ground plane (optic flow) in the ventral visual field, this resulted in grid cell spatial firing that was not sensitive to barrier location in modules modeled with small spacing between grid cell firing fields. In contrast, when location was computed from static visual features on walls of barriers, i.e. in the more dorsal visual field, this resulted in grid cell spatial firing that compressed or expanded based on the barrier locations in modules modeled with large spacing between grid cell firing fields. This indicates that different grid cell modules might have differential properties for computing location based on visual cues, or the spatial radius of sensitivity to visual cues might differ between modules.

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 versus 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.

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 alternating 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.

Single unit recordings in the rat hippocampus have demonstrated shifts in the specificity of spiking activity during learning of a contextual item-reward association task. In this task, rats received reward for responding to different items dependent upon the context an item appeared in, but not dependent upon the location an item appears at. Initially, neurons in the rat hippocampus primarily show firing based on place, but as the rat learns the task this firing became more selective for items. We simulated this effect using a simple circuit model with discrete inputs driving spiking activity representing place and item followed sequentially by a discrete representation of the motor actions involving a response to an item (digging for food) or the movement to a different item (movement to a different pot for food). We implemented spiking replay in the network representing neural activity observed during sharp-wave ripple events, and modified synaptic connections based on a simple representation of spike-timing dependent synaptic plasticity. This simple network was able to consistently learn the context-dependent responses, and transitioned from dominant coding of place to a gradual increase in specificity to items consistent with analysis of the experimental data. In addition, the model showed an increase in specificity toward context. The increase of selectivity in the model is accompanied by an increase in binariness of the synaptic weights for cells that are part of the functional network.

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

With the goal of understanding behavioral mechanisms of generalization, we analyzed the ability of neural networks to generalize across context. We modeled a behavioral task where the correct responses to a set of specific sensory stimuli varied systematically across different contexts. The correct response depended on the stimulus (A,B,C,D) and context quadrant (1,2,3,4). The possible 16 stimulus-context combinations were associated with one of two responses (X,Y), one of which was correct for half of the combinations. The correct responses varied symmetrically across contexts. This allowed responses to previously unseen stimuli (probe stimuli) to be generalized from stimuli that had been presented previously. By testing the simulation on two or more stimuli that the network had never seen in a particular context, we could test whether the correct response on the novel stimuli could be generated based on knowledge of the correct responses in other contexts. We tested this generalization capability with a Deep Belief Network (DBN), Multi-Layer Perceptron (MLP) network, and the combination of a DBN with a linear perceptron (LP). Overall, the combination of the DBN and LP had the highest success rate for generalization.

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

The entorhinal cortex receives prominent cholinergic innervation from the medial septum and the vertical limb of the diagonal band of Broca (MSDB). To understand how cholinergic neurotransmission can modulate behavior, research has been directed towards identification of the specific cellular mechanisms in entorhinal cortex that can be modulated through cholinergic activity. This review focuses on intrinsic cellular properties of neurons in entorhinal cortex that may underlie functions such as working memory, spatial processing and episodic memory. In particular, the study of stellate cells in medial entorhinal has resulted in discovery of correlations between physiological properties of these neurons and properties of the unique spatial representation that is demonstrated through unit recordings of neurons in medial entorhinal cortex from awake-behaving animals. A separate line of investigation has demonstrated persistent firing behavior among neurons in entorhinal cortex that is enhanced by cholinergic activity and could underlie working memory. There is also evidence that acetylcholine plays a role in modulation of synaptic transmission that could also enhance mnemonic function in entorhinal cortex. Finally, the local circuits of entorhinal cortex demonstrate a variety of interneuron physiology, which is also subject to cholinergic modulation. Together these effects alter the dynamics of entorhinal cortex to underlie the functional role of acetylcholine in memory.

Acetylcholine plays an important role in cognitive function, as shown by pharmacological manipulations that impact working memory, attention, episodic memory and spatial memory function. Acetylcholine also shows striking modulatory influences on the cellular physiology of hippocampal and cortical neurons. Modeling of neural circuits provides a framework for understanding how the cognitive functions may arise from the influence of acetylcholine on neural and network dynamics. We review the influences of cholinergic manipulations on behavioral performance in working memory, attention, episodic memory and spatial memory tasks, the physiological effects of acetylcholine on neural and circuit dynamics, and the computational models that provide insight into the functional relationships between the physiology and behavior. Specifically, we discuss the important role of acetylcholine in governing mechanisms of active maintenance in working memory tasks and in regulating network dynamics important for effective processing of stimuli in attention and episodic memory tasks. We also propose that theta rhythm play a crucial role as an intermediary between the physiological influences of acetylcholine and behavior in episodic and spatial memory tasks. We conclude with a synthesis of the existing modeling work and highlight future directions that are likely to be rewarding given the existing state of the literature for both empiricists and modelers.

Different models have been able to account for different features of the data on grid cell firing properties, including the relationship of grid cells to cellular properties and network oscillations. This paper describes a model that combines elements of two major classes of models of grid cells: models using interference of oscillations and models using attractor dynamics. This model includes a population of units with oscillatory input representing input from the medial septum. These units are termed heading angle cells because their connectivity depends upon heading angle in the environment as well as the spatial phase coded by the cell. These cells project to a population of grid cells. The sum of the heading angle input results in standing waves of circularly symmetric input to the grid cell population. Feedback from the grid cell population increases the activity of subsets of the heading angle cells, resulting in the network settling into activity patterns that resemble the patterns of firing fields in a population of grid cells. The properties of heading angle cells firing as conjunctive grid-by-head-direction cells can shift the grid cell firing according to movement velocity. The pattern of interaction of oscillations requires use of separate populations that fire on alternate cycles of the net theta rhythmic input to grid cells, similar to recent neurophysiological data on theta cycle skipping in medial entorhinal cortex.

Pharmacological and lesion data indicate that acetylcholine plays an important role in memory formation. Increased levels of acetylcholine in the hippocampal formation are associated with successful encoding while disruption of the cholinergic system leads to impairments on a range of mnemonic tasks. Cholinergic signalling from the medial septum also plays a central role in generating and pacing theta-band oscillations throughout the hippocampal formation. New results suggest a potential link between these distinct phenomena. Environmental novelty, a condition associated with strong cholinergic drive, has been shown to induce an expansion in the firing pattern of entorhinal grid cells and a reduction in the frequency of theta measured from the LFP. Computational modelling suggests the spatial activity of grid cells is produced by interference between neuronal oscillators; scale being determined by theta-band oscillations in entorhinal stellate cells, the frequency of which are modulated by acetylcholine. We propose a causal link: increased cholinergic signalling in response to environmental novelty triggers grid expansion. Cholinergic induced grid expansion may enhance, or even induce, encoding by producing a mismatch between spatial inputs to the hippocampus, such as barrier cells and grids cell with different scales.

Boundary vector cells in entorhinal cortex fire when a rat is in locations at a specific distance from walls of an environment. This firing may originate from memory of the barrier location combined with path integration, or the firing may depend upon the apparent visual input image stream. The modeling work presented here investigates the role of optic flow, the apparent change of patterns of light on the retina, as input for boundary vector cell firing. Analytical spherical flow is used by a template model to segment walls from the ground, to estimate self-motion and the distance and allocentric direction of walls, and to detect drop-offs. Distance estimates of walls in an empty circular or rectangular box have a mean error of less than or equal to two centimeters. Integrating these estimates into a visually driven boundary vector cell model leads to the firing patterns characteristic for boundary vector cells. This suggests that optic flow can influence the firing of boundary vector cells.

Performance of memory tasks is impaired by lesions to either the medial prefrontal cortex (mPFC) or the hippocampus (HPC); although how these two areas contribute to successful performance is not well understood. mPFC unit activity is temporally affected by hippocampal theta oscillations, with almost half the mPFC population entrained to theta in behaving animals, pointing to theta interactions as the mechanism enabling collaborations between these two areas. mPFC neurons respond to sensory stimuli and responses in working memory tasks, though the function of these correlated firing rate changes remains unclear because similar responses are reported during mPFC dependent and independent tasks. Using a DNMS task we compared error trials vs. correct trials and found almost all mPFC cells fired at similar rates during both error and correct trials (92%), however theta-entrainment of mPFC neurons declined during error performance as only 17% of cells were theta-entrained (during correct trials 46% of the population was theta-entrained). Across the population, error and correct trials did not differ in firing rate, but theta-entrainment was impaired. Periods of theta-entrainment and firing rate changes appeared to be independent variables, and only theta-entrainment was correlated with successful performance, indicating mPFC-HPC theta range interactions are the key to successful DNMS performance.

Models of the hexagonally arrayed spatial activity pattern of grid cell firing in the literature generally fall into two main categories: continuous attractor models or oscillatory interference models. Burak and Fiete (2009, PLoS Comput Biol) recently examined noise in two continuous attractor models, but did not consider oscillatory interference models in detail. Here we analyze an oscillatory interference model to examine the effects of noise on its stability and spatial firing properties. We show analytically that the square of the drift in encoded position due to noise is proportional to time and inversely proportional to the number of oscillators. We also show there is a relatively fixed breakdown point, independent of many parameters of the model, past which noise overwhelms the spatial signal. Based on this result, we show that a pair of oscillators are expected to maintain a stable grid for approximately t = 5mu(3)/(4pisigma)(2) seconds where mu is the mean period of an oscillator in seconds and sigma(2) its variance in seconds(2). We apply this criterion to recordings of individual persistent spiking neurons in postsubiculum (dorsal presubiculum) and layers III and V of entorhinal cortex, to subthreshold membrane potential oscillation recordings in layer II stellate cells of medial entorhinal cortex and to values from the literature regarding medial septum theta bursting cells. All oscillators examined have expected stability times far below those seen in experimental recordings of grid cells, suggesting the examined biological oscillators are unfit as a substrate for current implementations of oscillatory interference models. However, oscillatory interference models can tolerate small amounts of noise, suggesting the utility of circuit level effects which might reduce oscillator variability. Further implications for grid cell models are discussed.

Behavioral tasks are often used to study the different memory systems present in humans and animals. Such tasks are usually designed to isolate and measure some aspect of a single memory system. However, it is not necessarily clear that any given task actually does isolate a system or that the strategy used by a subject in the experiment is the one desired by the experimenter. We have previously shown that when tasks are written mathematically as a form of partially-observable Markov decision processes, the structure of the tasks provide information regarding the possible utility of certain memory systems. These previous analyses dealt with the disambiguation problem: given a specific ambiguous observation of the environment, is there information provided by a given memory strategy that can disambiguate that observation to allow a correct decisionµ Here we extend this approach to cases where multiple memory systems can be strategically combined in different ways. Specifically, we analyze the disambiguation arising from three ways by which episodic-like memory retrieval might be cued (by another episodic-like memory, by a semantic association, or by working memory for some earlier observation). We also consider the disambiguation arising from holding earlier working memories, episodic-like memories or semantic associations in working memory. From these analyses we can begin to develop a quantitative hierarchy among memory systems in which stimulus-response memories and semantic associations provide no disambiguation while the episodic memory system provides the most flexible

Researchers use a variety of behavioral tasks to analyze the effect of biological manipulations on memory function. This research will benefit from a systematic mathematical method for analyzing memory demands in behavioral tasks. In the framework of reinforcement learning theory, these tasks can be mathematically described as partially-observable Markov decision processes. While a wealth of evidence collected over the past 15 years relates the basal ganglia to the reinforcement learning framework, only recently has much attention been paid to including psychological concepts such as working memory or episodic memory in these models. This paper presents an analysis that provides a quantitative description of memory states sufficient for correct choices at specific decision points. Using information from the mathematical structure of the task descriptions, we derive measures that indicate whether working memory (for one or more cues) or episodic memory can provide strategically useful information to an agent. In particular, the analysis determines which observed states must be maintained in or retrieved from memory to perform these specific tasks. We demonstrate the analysis on three simplified tasks as well as eight more complex memory tasks drawn from the animal and human literature (two alternation tasks, two sequence disambiguation tasks, two non-matching tasks, the 2-back task, and the 1-2-AX task). The results of these analyses agree with results from quantitative simulations of the task reported in previous publications and provide simple indications of the memory demands of the tasks which can require far less computation than a full simulation of the task. This may provide a basis for a quantitative behavioral stoichiometry of memory tasks.

Recent advances in single-neuron biophysics have enhanced our understanding of information processing on the cellular level, but how the detailed properties of individual neurons give rise to large-scale behavior remains unclear. Here, we present a model of the hippocampal network based on observed biophysical properties of hippocampal and entorhinal cortical neurons. We assembled our model to simulate spatial alternation, a task that requires memory of the previous path through the environment for correct selection of the current path to a reward site. The convergence of inputs from entorhinal cortex and hippocampal region CA3 onto CA1 pyramidal cells make them potentially important for integrating information about place and temporal context on the network level. Our model shows how place and temporal context information might be combined in CA1 pyramidal neurons to give rise to splitter cells, which fire selectively based on a combination of place and temporal context. The model leads to a number of experimentally testable predictions that may lead to a better understanding of the biophysical basis of information processing in the hippocampus.