Optimal Population Codes for Space: Grid Cells Outperform Place Cells

Rodents use two distinct neuronal coordinate systems to estimate their position: place fields in the hippocampus and grid fields in the entorhinal cortex. Whereas place cells spike at only one particular spatial location, grid cells fire at multiple sites that correspond to the points of an imaginary hexagonal lattice. We study how to best construct place and grid codes, taking the probabilistic nature of neural spiking into account. Which spatial encoding properties of individual neurons confer the highest resolution when decoding the animal’s position from the neuronal population response? A priori, estimating a spatial position from a grid code could be ambiguous, as regular periodic lattices possess translational symmetry. The solution to this problem requires lattices for grid cells with different spacings; the spatial resolution crucially depends on choosing the right ratios of these spacings across the population. We compute the expected error in estimating the position in both the asymptotic limit, using Fisher information, and for low spike counts, using maximum likelihood estimation. Achieving high spatial resolution and covering a large range of space in a grid code leads to a trade-off: the best grid code for spatial resolution is built of nested modules with different spatial periods, one inside the other, whereas maximizing the spatial range requires distinct spatial periods that are pairwisely incommensurate. Optimizing the spatial resolution predicts two grid cell properties that have been experimentally observed. First, short lattice spacings should outnumber long lattice spacings. Second, the grid code should be self-similar across different lattice spacings, so that the grid field always covers a fixed fraction of the lattice period. If these conditions are satisfied and the spatial “tuning curves” for each neuron span the same range of firing rates, then the resolution of the grid code easily exceeds that of the best possible place code with the same number of neurons

Cortical-hippocampal processing: prefrontal-hippocampal contributions to the spatiotemporal relationship of events

The hippocampus and prefrontal cortex play distinct roles in the generation and retrieval of episodic memory. The hippocampus is crucial for binding inputs across behavioral timescales, whereas the prefrontal cortex is found to influence retrieval. Spiking of hippocampal principal neurons contains environmental information, including information about the presence of specific objects and their spatial or temporal position relative to environmental and behavioral cues. Neural activity in the prefrontal cortex is found to map behavioral sequences that share commonalities in sensory input, movement, and reward valence. Here I conducted a series of four experiments to test the hypothesis that external inputs from cortex update cell assemblies that are organized within the hippocampus. I propose that cortical inputs coordinate with CA3 to rapidly integrate information at fine timescales. Extracellular tetrode recordings of neurons in the orbitofrontal cortex were performed in rats during a task where object valences were dictated by the spatial context in which they were located. Orbitofrontal ensembles, during object sampling, were found to organize all measured task elements in inverse rank relative to the rank previously observed in the hippocampus, whereby orbitofrontal ensembles displayed greater differentiation for object valence and its contextual identity than spatial position. Using the same task, a follow-up experiment assessed coordination between prefrontal and hippocampal networks by simultaneously recording medial prefrontal and hippocampal activity. The circuit was found to coordinate at theta frequencies, whereby hippocampal theta engaged prefrontal signals during contextual sampling, and the order of engagement reversed during object sampling. Two additional experiments investigated hippocampal temporal representations. First, hippocampal patterns were found to represent conjunctions of time and odor during a head-fixed delayed match-to-sample task. Lastly, I assessed the dependence of hippocampal firing patterns on intrinsic connectivity during the delay period versus active navigation of spatial routes, as rats performed a delayed-alternation T-maze. Stimulation of the ventral hippocampal commissure induced remapping of hippocampal activity during the delay period selectively. Despite temporal reorganization, different hippocampal populations emerged to predict temporal position. These results show hippocampal representations are guided by stable cortical signals, but also, coordination between cortical and intrinsic circuitry stabilizes flexible CA1 temporal representations

Slow Inhibition and Inhibitory Recruitment in the Hippocampal Dentate Gyrus

L’hippocampe joue un rôle central dans la navigation spatiale, la mémoire et l’organisation spatio-temporelle des souvenirs. Ces fonctions sont maintenues par la capacité du gyrus denté (GD) de séparation des patrons d'activité neuronales. Le GD est situé à l’entrée de la formation hippocampique où il reconnaît la présence de nouveaux motifs parmi la densité de signaux afférant arrivant par la voie entorhinale (voie perforante). Le codage parcimonieux est la marque distinctive du GD. Ce type de codage est le résultat de la faible excitabilité intrinsèque des cellules granulaires (CGs) en combinaison avec une inhibition locale prédominante. En particulier, l’inhibition de type « feedforward » ou circuit inhibiteur antérograde, est engagée par la voie perforante en même temps que les CGs. Ainsi les interneurones du circuit antérograde fournissent des signaux GABAergique aux CGs de manière presque simultanée qu’elles reçoivent les signaux glutamatergiques. Cette thèse est centrée sur l’étude des interactions entre ces signaux excitateurs de la voie entorhinale et les signaux inhibiteurs provenant des interneurones résidant dans le GD et ceci dans le contexte du codage parcimonieux et le patron de décharge en rafale caractéristique des cellules granulaires. Nous avons adressé les relations entre les projections entorhinales et le réseau inhibitoire antérograde du GD en faisant des enregistrements électrophysiologiques des CG pendant que la voie perforante est stimulée de manière électrique ou optogénétique. Nous avons découvert un nouvel mécanisme d’inhibition qui apparait à délais dans les CGs suite à une stimulation dans les fréquences gamma. Ce mécanisme induit une hyperpolarisation de longue durée (HLD) et d’une amplitude prononce. Cette longue hyperpolarisation est particulièrement prolongée et dépasse la durée d’autres types d’inhibition transitoire lente décrits chez les CGs. L’induction de HLD crée une fenêtre temporaire de faible excitabilité suite à laquelle le patron de décharge des CGs et l’intégration d’autres signaux excitateurs sont altérés de manière transitoire. Nous avons donc conclu que l’activité inhibitrice antérograde joue un rôle central dans les processus de codage dans le GD. Cependant, alors qu’il existe une multitude d’études décrivant les interneurones qui font partie de ce circuit inhibiteur, la question de comment ces cellules sont recrutées par la voie entorhinale reste quelque peu explorée. Pour apprendre plus à ce sujet, nous avons enregistré des interneurones résidant iii dans la couche moléculaire du GD tout en stimulant la voie perforante de manière optogénétique. Cette méthode de stimulation nous a permis d’induire la libération de glutamate endogène des terminales entorhinales et ainsi d’observer le recrutement purement synaptique d’interneurones. De manière surprenante, les résultats de cette expérience démontrent un faible taux d’activation des interneurones, accompagné d’un tout aussi faible nombre total de potentiels d’action émis en réponse à la stimulation même à haute fréquence. Ce constat semble contre-intuitif étant donné qu’en générale on assume qu’une forte activité inhibitrice est requise pour le maintien du codage parcimonieux. Tout de même, l’analyse des patrons de décharge des interneurones qui ont été activés a fait ressortir la prééminence de trois grands types: décharge précoce, retardée ou régulière par rapport le début des pulses lumineux. Les résultats obtenus durant cette thèse mettent la lumière sur l’important conséquences fonctionnelles des interactions synaptique et polysynaptique de nature transitoire dans les réseaux neuronaux. Nous aimerions aussi souligner l’effet prononcé de l’inhibition à court terme du type prolongée sur l’excitabilité des neurones et leurs capacités d’émettre des potentiels d’action. De plus que cet effet est encore plus prononcé dans le cas de HLD dont la durée dépasse souvent la seconde et altère l’intégration d’autres signaux arrivants simultanément. Donc on croit que les effets de HLD se traduisent au niveau du réseaux neuronal du GD comme une composante cruciale pour le codage parcimonieux. En effet, ce type de codage semble être la marque distinctive de cette région étant donné que nous avons aussi observé un faible niveau d’activation chez les interneurones. Cependant, le manque d’activité accrue du réseau inhibiteur antérograde peut être compensé par le maintien d’un gradient GABAergique constant à travers le GD via l’alternance des trois modes de décharges des interneurones. En conclusion, il semble que le codage parcimonieux dans le GD peut être préservé même en absence d’activité soutenue du réseau inhibiteur antérograde et ceci grâce à des mécanismes alternatives d’inhibition prolongée à court terme.The hippocampus is implicated in spatial navigation, the generation and recall of memories, as well as their spatio-temporal organization. These functions are supported by the processes of pattern separation that occurs in the dentate gyrus (DG). Situated at the entry of the hippocampal formation, the DG is well placed to detect and sort novelty patterns amongst the high-density excitatory signals that arrive via the entorhinal cortex (EC). A hallmark of the DG is sparse encoding that is enabled by a combination of low intrinsic excitability of the principal cells and local inhibition. Feedforward inhibition (FFI) is recruited directly by the EC and simultaneously with the granule cells (GCs). Therefore, FFI provides fast GABA release and shapes input integration at the millisecond time scale. This thesis aimed to investigate the interplay of entorhinal excitatory signals with GCs and interneurons, from the FFI in the DG, in the framework of sparse encoding and GC’s characteristic burst firing. We addressed the long-range excitation – local inhibitory network interactions using electrophysiological recordings of GCs – while applying an electrical or optogenetic stimulation of the perforant path (PP) in the DG. We discovered and described a novel delayed-onset inhibitory post synaptic potential (IPSP) in GCs, following PP stimulation in the gamma frequency range. Most importantly, the IPSP was characterized by a large amplitude and prolonged decay, outlasting previously described slow inhibitory events in GCs. The long-lasting hyperpolarization (LLH) caused by the slow IPSPs generates a low excitability time window, alters the GCs firing pattern, and interferes with other stimuli that arrive simultaneously. FFI is therefore a key player in the computational processes that occurs in the DG. However, while many studies have been dedicated to the description of the various types of the interneurons from the FFI, the question of how these cells are synaptically recruited by the EC remains not entirely elucidated. We tackled this problem by recording from interneurons in the DG molecular layer during PP-specific optogenetic stimulation. Light-driven activation of the EC terminals enabled a purely synaptic recruitment of interneurons via endogenous glutamate release. We found that this method of stimulation recruits only a subset of interneurons. In addition, the total number of action potentials (AP) was surprisingly low even at high frequency stimulation. This result is counterintuitive, as strong and persistent inhibitory signals are assumed to restrict GC v activation and maintain sparseness. However, amongst the early firing interneurons, late and regular spiking patterns were clearly distinguishable. Interestingly, some interneurons expressed LLH similar to the GCs, arguing that it could be a commonly used mechanism for regulation of excitability across the hippocampal network. In summary, we show that slow inhibition can result in a prolonged hyperpolarization that significantly alters concurrent input’s integration. We believe that these interactions contribute to important computational processes such as sparse encoding. Interestingly, sparseness seems to be the hallmark of the DG, as we observed a rather low activation of the interneuron network as well. However, the alternating firing of ML-INs could compensate the lack of persistent activity by the continuous GABA release across the DG. Taken together these results offer an insight into a mechanism of feedforward inhibition serving as a sparse neural code generator in the DG

Temporal coding in the hippocampus

There is a large body of evidence that the hippocampus is involved in temporal aspects of memory. It remains unclear what neural processes within the hippocampus contribute to this ability. The following experiments aim to quantify and qualify these neural processes while rats perform temporal memory tasks. First we examined the firing of neurons in the hippocampus while rats compared a current series of odors to a learned sequence of odors. We found evidence of neural correlates which might represent whether a stimulus odor was in the correct ordinal sequence or not. Next we examined the delay intervals in between learned sequences of events with the goal of identifying the origin of “time cells” in the hippocampus. We used a delayed alternating T-maze task that our lab has used before to record time cells in area CA1 of the hippocampus. We found time cells in CA3, one of the major inputs to CA1 and demonstrated that they behave in many ways like place cells previously observed in these two regions. Time cells had previously been reported to occur only when an animal is engaged in a task with memory load. We demonstrated that memory load isn't necessary to observe time cells. Our observations of the similarities between place and time cells led us to conjecture that the hippocampus might process space and time similarly. In a final study I examined time vii cell firing properties with an aim at constraining models of time cells. We defined time cells in several ways including a new methodology that is promising as a future unbiased selection criteria. All of our findings help further elucidate several different ways that neural coding in the hippocampus contributes to temporal processing

Neural ensemble interactions underlying memory consolidation

Episodic memory formation and spatial navigation are core functions of the hippocampus. Embedded in a path integration based navigational system, the hippocampus generates orthogonal codes for different environments. To separate events within the same spatial map, the magnitude of individual place cell firing is modulated by external sensory information. The rate differences are also expressed to separate different running directions within an environment. Previous work suggested that the maps can be perturbed by external cues, but that the rate perturbations are not associatively stored. The present result shows that the rate code is reinstated offline and thus likely associatively stored, which fits well with the theory that describes the hippocampus as generating an index code for episodic memories to assist in retrieval of distributed information stored in the cortex. Lastly, this thesis addresses the methodological challenges of current electrophysiological techniques in detecting excitatory local connectivity on the example of the prefrontal cortex.AI-HS scholarship to CDS and Polaris Award to BL

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

The role of medial entorhinal cortex activity in hippocampal CA1 spatiotemporally correlated sequence generation and object selectivity for memory function

The hippocampus is crucial for episodic memory and certain forms of spatial navigation. Firing activity of hippocampal principal neurons contains environmental information, including the presence of specific objects, as well as the animal’s spatial and temporal position relative to environmental and behavioral cues. The organization of these firing correlates may allow the formation of memory traces through the integration of object and event information onto a spatiotemporal framework of cell assemblies. Characterizing how external inputs guide internal dynamics in the hippocampus to enable this process across different experiences is crucial to understanding hippocampal function. A body of literature implicates the medial entorhinal cortex (MEC) in supplying spatial and temporal information to the hippocampus. Here we develop a protocol utilizing bilaterally implanted custom designed triple fiber optic arrays and the red-shifted inhibitory opsin JAWS to transiently inactivate large volumes of MEC in freely behaving rats. This was coupled with extracellular tetrode recording of ensembles in CA1 of the hippocampus during a novel memory task involving temporal, spatial and object related epochs, in order to assess the importance of MEC activity for hippocampal feature selectivity during a rich and familiar experience. We report that inactivation of MEC during a mnemonic temporal delay disrupts the existing temporal firing field sequence in CA1 both during and following the inactivation period. Neurons with firing fields prior to the inactivation on each trial remained relatively stable. The disruption of CA1 temporal firing field sequences was accompanied by a behavioral deficit implicating MEC activity and hippocampal temporal field sequences in effective memory across time. Inactivating MEC during the object or spatial epochs of the task did not significantly alter CA1 object selective or spatial firing fields and behavioral performance remained stable. Our findings suggest that MEC is crucial specifically for temporal field organization and expression during a familiar and rich experience. These results support a role for MEC in guiding hippocampal cell assembly sequences in the absence of salient changing stimuli, which may extend to the navigation of cognitive organization in humans and support memory formation and retrieval