What grid cells convey about rat location

We characterize the relationship between the simultaneously recorded quantities of rodent grid cell firing and the position of the rat. The formalization reveals various properties of grid cell activity when considered as a neural code for representing and updating estimates of the rat's location. We show that, although the spatially periodic response of grid cells appears wasteful, the code is fully combinatorial in capacity. The resulting range for unambiguous position representation is vastly greater than the ≈1–10 m periods of individual lattices, allowing for unique high-resolution position specification over the behavioral foraging ranges of rats, with excess capacity that could be used for error correction. Next, we show that the merits of the grid cell code for position representation extend well beyond capacity and include arithmetic properties that facilitate position updating. We conclude by considering the numerous implications, for downstream readouts and experimental tests, of the properties of the grid cell code

Neural systems supporting navigation

Highlights: • Recent neuroimaging and electrophysiology studies have begun to shed light on the neural dynamics of navigation systems. • Computational models have advanced theories of how entorhinal grid cells and hippocampal place cells might serve navigation. • Hippocampus and entorhinal cortex provide complementary representations of routes and vectors for navigation. Much is known about how neural systems determine current spatial position and orientation in the environment. By contrast little is understood about how the brain represents future goal locations or computes the distance and direction to such goals. Recent electrophysiology, computational modelling and neuroimaging research have shed new light on how the spatial relationship to a goal may be determined and represented during navigation. This research suggests that the hippocampus may code the path to the goal while the entorhinal cortex represents the vector to the goal. It also reveals that the engagement of the hippocampus and entorhinal cortex varies across the different operational stages of navigation, such as during travel, route planning, and decision-making at waypoints

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

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

Theta oscillations, timing and cholinergic modulation in the rodent hippocampal circuit

The medial temporal lobe (MTL) is crucial for episodic and spatial memory, and shows rhythmicity in the local field potential and neuronal spiking. Gamma oscillations (>40Hz) are mediatepd by local circuitry and interact with slower theta oscillations (6-10 Hz). Both oscillation frequencies are modulated by cholinergic input from the medial septum. Entorhinal grid cells fire when an animal visits particular locations in the environment arranged on the corners of tightly packed, equilateral triangles. Grid cells show phase precession, in which neurons fire at progressively earlier phases relative to theta oscillation as animals move through firing fields. This work focuses on the temporal organization of spiking and network rhythms, and their modulation by septal inputs, which are thought to be involved in MTL function. First, I recorded grid cells as rats explored open spaces and examined precession, previously only characterized on linear tracks, and compared it to predictions from models. I identified precession, including in conjunctive head-direction-by-grid cells and on passes that clipped the edge of the firing field. Secondly, I studied problems of measuring single neuron theta rhythmicity and developed an improved approach. Using the novel approach, I identified diverse modulation of rat medial entorhinal neurons’ rhythmic frequencies by running speed, independent from the modulation of firing rate by speed. Under pharmacological inactivation of the septum, rhythmic tuning was disrupted while rate tuning was enhanced. The approach also showed that available data is insufficient to prove that bat grid cells are arrhythmic due to low firing rates. In the final project, I optogenetically silenced cholinergic septal cells while recording from hippocampal area CA1. I identified changes in theta rhythmic currents and in theta-gamma coupling. This silencing disrupted performance when applied during the encoding phase of a delayed match to position task. These data support hypothetical roles of these rhythms in encoding and retrieval and suggest possible mechanisms for their modulation. Together, evidence from these projects suggests a role for theta in the function of spatial and episodic memory. These oscillations have important implications for communication and computation, and they can provide a substrate for efficient brain function

Memory capacity in the hippocampus

Neural assemblies in hippocampus encode positions. During rest, the hippocam- pus replays sequences of neural activity seen during awake behavior. This replay is linked to memory consolidation and mental exploration of the environment. Re- current networks can be used to model the replay of sequential activity. Multiple sequences can be stored in the synaptic connections. To achieve a high mem- ory capacity, recurrent networks require a pattern separation mechanism. Such a mechanism is global remapping, observed in place cell populations. A place cell fires at a particular position of an environment and is silent elsewhere. Multiple place cells usually cover an environment with their firing fields. Small changes in the environment or context of a behavioral task can cause global remapping, i.e. profound changes in place cell firing fields. Global remapping causes some cells to cease firing, other silent cells to gain a place field, and other place cells to move their firing field and change their peak firing rate. The effect is strong enough to make global remapping a viable pattern separation mechanism. We model two mechanisms that improve the memory capacity of recurrent net- works. The effect of inhibition on replay in a recurrent network is modeled using binary neurons and binary synapses. A mean field approximation is used to de- termine the optimal parameters for the inhibitory neuron population. Numerical simulations of the full model were carried out to verify the predictions of the mean field model. A second model analyzes a hypothesized global remapping mecha- nism, in which grid cell firing is used as feed forward input to place cells. Grid cells have multiple firing fields in the same environment, arranged in a hexagonal grid. Grid cells can be used in a model as feed forward inputs to place cells to produce place fields. In these grid-to-place cell models, shifts in the grid cell firing patterns cause remapping in the place cell population. We analyze the capacity of such a system to create sets of separated patterns, i.e. how many different spatial codes can be generated. The limiting factor are the synapses connecting grid cells to place cells. To assess their capacity, we produce different place codes in place and grid cell populations, by shuffling place field positions and shifting grid fields of grid cells. Then we use Hebbian learning to increase the synaptic weights be- tween grid and place cells for each set of grid and place code. The capacity limit is reached when synaptic interference makes it impossible to produce a place code with sufficient spatial acuity from grid cell firing. Additionally, it is desired to also maintain the place fields compact, or sparse if seen from a coding standpoint. Of course, as more environments are stored, the sparseness is lost. Interestingly, place cells lose the sparseness of their firing fields much earlier than their spatial acuity. For the sequence replay model we are able to increase capacity in a simulated recurrent network by including an inhibitory population. We show that even in this more complicated case, capacity is improved. We observe oscillations in the average activity of both excitatory and inhibitory neuron populations. The oscillations get stronger at the capacity limit. In addition, at the capacity limit, rather than observing a sudden failure of replay, we find sequences are replayed transiently for a couple of time steps before failing. Analyzing the remapping model, we find that, as we store more spatial codes in the synapses, first the sparseness of place fields is lost. Only later do we observe a decay in spatial acuity of the code. We found two ways to maintain sparse place fields while achieving a high capacity: inhibition between place cells, and partitioning the place cell population so that learning affects only a small fraction of them in each environment. We present scaling predictions that suggest that hundreds of thousands of spatial codes can be produced by this pattern separation mechanism. The effect inhibition has on the replay model is two-fold. Capacity is increased, and the graceful transition from full replay to failure allows for higher capacities when using short sequences. Additional mechanisms not explored in this model could be at work to concatenate these short sequences, or could perform more complex operations on them. The interplay of excitatory and inhibitory populations gives rise to oscillations, which are strongest at the capacity limit. The oscillation draws a picture of how a memory mechanism can cause hippocampal oscillations as observed in experiments. In the remapping model we showed that sparseness of place cell firing is constraining the capacity of this pattern separation mechanism. Grid codes outperform place codes regarding spatial acuity, as shown in Mathis et al. (2012). Our model shows that the grid-to-place transformation is not harnessing the full spatial information from the grid code in order to maintain sparse place fields. This suggests that the two codes are independent, and communication between the areas might be mostly for synchronization. High spatial acuity seems to be a specialization of the grid code, while the place code is more suitable for memory tasks. In a detailed model of hippocampal replay we show that feedback inhibition can increase the number of sequences that can be replayed. The effect of inhibition on capacity is determined using a meanfield model, and the results are verified with numerical simulations of the full network. Transient replay is found at the capacity limit, accompanied by oscillations that resemble sharp wave ripples in hippocampus. In a second model Hippocampal replay of neuronal activity is linked to memory consolidation and mental exploration. Furthermore, replay is a potential neural correlate of episodic memory. To model hippocampal sequence replay, recurrent neural networks are used. Memory capacity of such networks is of great interest to determine their biological feasibility. And additionally, any mechanism that improves capacity has explanatory power. We investigate two such mechanisms. The first mechanism to improve capacity is global, unspecific feedback inhibition for the recurrent network. In a simplified meanfield model we show that capacity is indeed improved. The second mechanism that increases memory capacity is pattern separation. In the spatial context of hippocampal place cell firing, global remapping is one way to achieve pattern separation. Changes in the environment or context of a task cause global remapping. During global remapping, place cell firing changes in unpredictable ways: cells shift their place fields, or fully cease firing, and formerly silent cells acquire place fields. Global remapping can be triggered by subtle changes in grid cells that give feed-forward inputs to hippocampal place cells. We investigate the capacity of the underlying synaptic connections, defined as the number of different environments that can be represented at a given spatial acuity. We find two essential conditions to achieve a high capacity and sparse place fields: inhibition between place cells, and partitioning the place cell population so that learning affects only a small fraction of them in each environments. We also find that sparsity of place fields is the constraining factor of the model rather than spatial acuity. Since the hippocampal place code is sparse, we conclude that the hippocampus does not fully harness the spatial information available in the grid code. The two codes of space might thus serve different purposes

Neural basis of route-planning and goal-coding during flexible navigation

Animals and humans are remarkable in their ability to flexibly adapt to changes in their surroundings. Navigational flexibility may take many forms and in this thesis we investigate its neural and behavioral underpinnings using a variety of methods and tasks tailored to each specific research aim. These methods include functional resonance magnetic imaging (fMRI), freely moving virtual reality, desktop virtual reality, large-scale online testing, and computational modelling. First, we reanalysed previously collected rodent data in the lab to better under- stand behavioural bias that may occur during goal-directed navigation tasks. Based on finding some biases we designed a new approach of simulating results on maze configurations prior to data collection to select the ideal mazes for our task. In a parallel line of methods development, we designed a freely moving navigation task using large-scale wireless virtual reality in a 10x10 space. We compared human behaviour to that of a select number of reinforcement learning agents to investigate the feasibility of computational modelling approaches to freely moving behaviour. Second, we further developed our new approach of simulating results on maze configuration to design a novel spatial navigation task used in a parallel experiment in both rats and humans. We report the human findings using desktop virtual reality and fMRI. We identified a network of regions including hippocampal, caudate nu- cleus, and lateral orbitofrontal cortex involvement in learning hidden goal locations. We also identified a positive correlation between Euclidean goal distance and brain activity in the caudate nucleus during ongoing navigation. Third, we developed a large online testing paradigm to investigate the role of home environment on wayfinding ability. We extended previous reports that street network complexity is beneficial in improving wayfinding ability as measured using a previously reported virtual navigation game, Sea Hero Quest, as well as in a novel virtual navigation game, City Hero Quest. We also report results of a navigational strategies questionnaire that highlights differences of growing up inside and outside cities in the United States and how this relates to wayfinding ability. Fourth, we investigate route planning in a group of expert navigators, licensed London taxi drivers. We designed a novel mental route planning task, probing 120 different routes throughout the extensive street network of London. We find hip- pocampal and retrosplenial involvement in route planning. We also identify the frontopolar cortex as one of several brain regions parametrically modulated by plan- ning demand. Lastly, I summarize the findings from these studies and how they all come to provide different insights into our remarkable ability to flexibly adapt to naviga- tional challenges in our environment