The input-output transformation of the hippocampal granule cells: from grid cells to place fields

The structure of networks that produce the transformation from grid cells to place cells

Since grid cells were discovered in the medial entorhinal cortex, several models have been proposed for the transformation from periodic grids to the punctate place fields of hippocampal place cells. These prior studies have each focused primarily on a particular model structure. By contrast, the goal of this study is to understand the general nature of the solutions that generate the grids-to-places transformation, and to exploit this insight to solve problems that were previously unsolved. First, we derive a family of feedforward networks that generate the grids-to-places transformations. These networks have in common an inverse relationship between the synaptic weights and a grid property that we call the normalized offset. Second, we analyze the solutions of prior models in terms of this novel measure and found to our surprise that almost all prior models yield solutions that can be described by this family of networks. The one exception is a model that is unrealistically sensitive to noise. Third, with this insight into the structure of the solutions, we then construct explicitly solutions for the grids-to-places transformation with multiple spatial maps, that is, with place fields in arbitrary locations either within the same (multiple place fields) or in different (global remapping) enclosures. These multiple maps are possible because the weights are learned or assigned in such a way that a group of weights contributes to spatial specificity in one context but remains spatially unstructured in another context. Fourth, we find parameters such that global remapping solutions can be found by synaptic learning in spiking neurons, despite previous suggestions that this might not be possible. In conclusion, our results demonstrate the power of understanding the structure of the solutions and suggest that we may have identified the structure that is common to all robust solutions of the grids-to-places transformation.

Modular realignment of entorhinal grid cell activity as a basis for hippocampal remapping

Hippocampal place fields, the local regions of activity recorded from place cells in exploring rodents, can undergo large changes in relative location during remapping. This process would appear to require some form of modulated global input. Grid-cell responses recorded from layer II of medial entorhinal cortex in rats have been observed to realign concurrently with hippocampal remapping, making them a candidate input source. However, this realignment occurs coherently across colocalized ensembles of grid cells (Fyhn et al., 2007). The hypothesized entorhinal contribution to remapping depends on whether this coherence extends to all grid cells, which is currently unknown. We study whether dividing grid cells into small numbers of independently realigning modules can both account for this localized coherence and allow for hippocampal remapping. To do this, we construct a model in which place-cell responses arise from network competition mediated by global inhibition. We show that these simulated responses approximate the sparsity and spatial specificity of hippocampal activity while fully representing a virtual environment without learning. Place-field locations and the set of active place cells in one environment can be independently rearranged by changes to the underlying grid-cell inputs. We introduce new measures of remapping to assess the effectiveness of grid-cell modularity and to compare shift realignments with other geometric transformations of grid-cell responses. Complete hippocampal remapping is possible with a small number of shifting grid modules, indicating that entorhinal realignment may be able to generate place-field randomization despite substantial coherence.

Intracellular determinants of hippocampal CA1 place and silent cell activity in a novel environment

For each environment a rodent has explored, its hippocampus contains a map consisting of a unique subset of neurons, called place cells, that have spatially tuned spiking there, with the remaining neurons being essentially silent. Using whole-cell recording in freely moving rats exploring a novel maze, we observed differences in intrinsic cellular properties and input-based subthreshold membrane potential levels underlying this division into place and silent cells. Compared to silent cells, place cells had lower spike thresholds and peaked versus flat subthreshold membrane potentials as a function of animal location. Both differences were evident from the beginning of exploration. Additionally, future place cells exhibited higher burst propensity before exploration. Thus, internal settings appear to predetermine which cells will represent the next novel environment encountered. Furthermore, place cells fired spatially tuned bursts with large, putatively calcium-mediated depolarizations that could trigger plasticity and stabilize the new map for long-term storage. Our results provide new insight into hippocampal memory formation.

Head direction cells in the postsubiculum do not show replay of prior waking sequences during sleep

During slow-wave sleep (SWS) and rapid eye movement (REM) sleep, hippocampal place cells in the rat show replay of sequences previously observed during waking. We tested the hypothesis from computational modeling that the temporal structure of REM sleep replay could arise from an interplay of place cells with head direction cells in the postsubiculum. Physiological single-unit recording was performed simultaneously from five or more head direction or place by head direction cells in the postsubiculum during running on a circular track allowing sampling of a full range of head directions, and during sleep periods before and after running on the circular track. Data analysis compared the spiking activity during individual REM periods with waking as in previous analysis procedures for REM sleep. We also used a new procedure comparing groups of similar runs during waking with REM sleep periods. There was no consistent evidence for a statistically significant correlation of the temporal structure of spiking during REM sleep with spiking during waking running periods. Thus, the spiking activity of head direction cells during REM sleep does not show replay of head direction cell activity occurring during a previous waking period of running on the task. In addition, we compared the spiking of postsubiculum neurons during hippocampal sharp wave ripple events. We show that head direction cells are not activated during sharp wave ripples, whereas neurons responsive to place in the postsubiculum show reliable spiking at ripple events.

Hippocampal microcircuit dynamics probed using optical imaging approaches

Mammalian cortical structures are endowed with the capacity for plasticity, which emerges from a combination of the dynamics of circuit connectivity and function, and the intrinsic function of the neurons within the circuit. However, this capacity is accompanied by a significant risk: the capability to generate seizure discharges is also a property of all mammalian cortices. How do cortical circuits reconcile the requirement to maintain plasticity, but at the same time control seizure initiation? These issues come into particular focus in the hippocampus. The hippocampus is one of the main plasticity engines in the brain, and is also a structure frequently implicated in the generation of epileptic seizures, with temporal lobe epilepsy constituting the most prevalent form of epilepsy in the adult population. One aspect of hippocampal circuitry that is particularly prominent is its intimate interconnections with the entorhinal cortex. These interconnections create a number of excitatory synaptic loops within the limbic system, which, in addition to being important in cognitive function, can support reentrant activation and seizure generation. In the present review, using optical imaging approaches to elucidate circuit processing at high temporal and spatial resolution, we examine how two targets of entorhinal cortical input within the hippocampus, the dentate gyrus and area CA1, regulate these synaptic pathways in ways that can maintain functions important in generation of normal activity patterns, but that dampen the ability of these inputs to generate seizure discharges.

The mechanism of rate remapping in the dentate gyrus

Rate remapping is a recently revealed neural code in which sensory information modulates the firing rate of hippocampal place cells. The mechanism underlying rate remapping is unknown. Its characteristic modulation, however, must arise from the interaction of the two major inputs to the hippocampus, the medial entorhinal cortex (MEC), in which grid cells represent the spatial position of the rat, and the lateral entorhinal cortex (LEC), in which cells represent the sensory properties of the environment. We have used computational methods to elucidate the mechanism by which this interaction produces rate remapping. We show that the convergence of LEC and MEC inputs, in conjunction with a competitive network process mediated by feedback inhibition, can account quantitatively for this phenomenon. The same principle accounts for why different place fields of the same cell vary independently as sensory information is altered. Our results show that rate remapping can be explained in terms of known mechanisms.

Formation of the non-functional and functional pools of granule cells in the dentate gyrus: role of neurogenesis, LTP and LTD

Some aspects of the function of the dentate gyrus (DG) and CA3 regions of the hippocampus are beginning to be understood, notably the way that grid cell inputs from the medial entorhinal cortex (MEC) are processed to form place cells in the dentate/CA3. However, one aspect of DG function remains very puzzling: more than 95% of the cells do not fire in any environment. Here, I propose a possible explanation for these non-functional cells. Because of the competition mediated by feedback inhibition, only the most excited DG cells fire. Cells that do not spike nevertheless receive excitatory input from the grid cells of the MEC (these cells fire nearly continuously because they represent a property (space) that is always being processed). Experiments suggest that synapses on such cells will undergo long-term depression (LTD). Cells that have their synapses weakened in this way are less likely to be winners in subsequent competitions. There may thus be a downward spiral in which losers eventually have no chance of winning and thus become non-functional. On the other hand, cells that fire get stronger synapses, making them more likely to be subsequent winners. Because the long-term potentiation (LTP) in these cells balances ongoing LTD, these cells will be relatively stable members of the functional pool. Although these pools are relatively stable, there will nevertheless be some chance that LTD converts a functional cell to a non-functional one; in contrast, the probability of a reverse transition is near zero. Thus, without additional processes, there would be a slow reduction in the size of the functional pool. I suggest that the ongoing generation of new cells by neurogenesis may be a solution to this problem. These cells are highly excitable and may thus win the competition to fire. In this way, the functional pool will be replenished. To test this and other theories about the DG requires an understanding of the role of the DG in memory. Recent experimental and theoretical work is providing a better understanding of the unique memory functions of the DG/CA3 unit. This will provide a behavioural framework for testing the ideas proposed here.

A manifold of spatial maps in the brain

Two neural systems are known to encode self-location in the brain: Place cells in the hippocampus encode unique locations in unique environments, whereas grid cells, border cells and head-direction cells in the parahippocampal cortex provide a universal metric for mapping positions and directions in all environments. These systems have traditionally been studied in very simple environments; however, natural environments are compartmentalized, nested and variable in time. Recent studies indicate that hippocampal and entorhinal spatial maps reflect this complexity. The maps fragment into interconnected, rapidly changing and tightly coordinated submaps. Plurality, fast dynamics and dynamic grouping are optimal for a brain system thought to exploit large pools of stored information to guide behavior on a second-by-second time frame in the animal's natural habitat.

The single place fields of CA3 cells: a two-stage transformation from grid cells

Granule cells of the dentate gyrus (DG) generally have multiple place fields, whereas CA3 cells, which are second order, have only a single place field. Here, we explore the mechanisms by which the high selectivity of CA3 cells is achieved. Previous work showed that the multiple place fields of DG neurons could be quantitatively accounted for by a model based on the number and strength of grid cell inputs and a competitive network interaction in the DG that is mediated by gamma frequency feedback inhibition. We have now built a model of CA3 based on similar principles. CA3 cells receive input from an average of one active DG cell and from 1,400 cortical grid cells. Based on experimental findings, we have assumed a linear interaction of the two pathways. The results show that simulated CA3 cells generally have a single place field, as observed experimentally. Thus, a two-step process based on simple rules (and that can occur without learning) is able to explain how grid cell inputs to the hippocampus give rise to cells having ultimate spatial selectivity. The CA3 processes that produce a single place depend critically on the competitive network processes and do not require the direct cortical inputs to CA3, which are therefore likely to perform some other unknown function.

Hebbian analysis of the transformation of medial entorhinal grid-cell inputs to hippocampal place fields

The discovery of grid cells in the medial entorhinal cortex (MEC) permits the characterization of hippocampal computation in much greater detail than previously possible. The present study addresses how an integrate-and-fire unit driven by grid-cell spike trains may transform the multipeaked, spatial firing pattern of grid cells into the single-peaked activity that is typical of hippocampal place cells. Previous studies have shown that in the absence of network interactions, this transformation can succeed only if the place cell receives inputs from grids with overlapping vertices at the location of the place cell's firing field. In our simulations, the selection of these inputs was accomplished by fast Hebbian plasticity alone. The resulting nonlinear process was acutely sensitive to small input variations. Simulations differing only in the exact spike timing of grid cells produced different field locations for the same place cells. Place fields became concentrated in areas that correlated with the initial trajectory of the animal; the introduction of feedback inhibitory cells reduced this bias. These results suggest distinct roles for plasticity of the perforant path synapses and for competition via feedback inhibition in the formation of place fields in a novel environment. Furthermore, they imply that variability in MEC spiking patterns or in the rat's trajectory is sufficient for generating a distinct population code in a novel environment and suggest that recalling this code in a familiar environment involves additional inputs and/or a different mode of operation of the network.

Parallel computational subunits in dentate granule cells generate multiple place fields

A fundamental question in understanding neuronal computations is how dendritic events influence the output of the neuron. Different forms of integration of neighbouring and distributed synaptic inputs, isolated dendritic spikes and local regulation of synaptic efficacy suggest that individual dendritic branches may function as independent computational subunits. In the present paper, we study how these local computations influence the output of the neuron. Using a simple cascade model, we demonstrate that triggering somatic firing by a relatively small dendritic branch requires the amplification of local events by dendritic spiking and synaptic plasticity. The moderately branching dendritic tree of granule cells seems optimal for this computation since larger dendritic trees favor local plasticity by isolating dendritic compartments, while reliable detection of individual dendritic spikes in the soma requires a low branch number. Finally, we demonstrate that these parallel dendritic computations could contribute to the generation of multiple independent place fields of hippocampal granule cells.

Neurons were originally divided into three morphologically distinct compartments: the dendrites receive the synaptic input, the soma integrates it and communicates the output of the cell to other neurons via the axon. Although several lines of evidence challenged this oversimplified view, neurons are still considered to be the basic information processing units of the nervous system as their output reflects the computations performed by the entire dendritic tree. In the present study, the authors build a simplified computational model and calculate that, in certain neurons, relatively small dendritic branches are able to independently trigger somatic firing. Therefore, in these cells, an action potential mirrors the activity of a small dendritic subunit rather than the input arriving to the whole dendritic tree. These neurons can be regarded as a network of a few independent integrator units connected to a common output unit. The authors demonstrate that a moderately branched dendritic tree of hippocampal granule cells may be optimized for these parallel computations. Finally the authors show that these parallel dendritic computations could explain some aspects of the location dependent activity of hippocampal granule cells.

A second function of gamma frequency oscillations: an E%-max winner-take-all mechanism selects which cells fire

The role of gamma oscillations in producing synchronized firing of groups of principal cells is well known. Here, we argue that gamma oscillations have a second function: they select which principal cells fire. This selection process occurs through the interaction of excitation with gamma frequency feedback inhibition. We sought to understand the rules that govern this process. One possibility is that a constant fraction of cells fire. Our analysis shows, however, that the fraction is not robust because it depends on the distribution of excitation to different cells. A robust description is termed E%-max: cells fire if they have suprathreshold excitation (E) within E% of the cell that has maximum excitation. The value of E%-max is approximated by the ratio of the delay of feedback inhibition to the membrane time constant. From measured values, we estimate that E%-max is 5-15%. Thus, an E%-max winner-take-all process can discriminate between groups of cells that have only small differences in excitation. To test the utility of this framework, we analyzed the role of oscillations in V1, one of the few systems in which both spiking and intracellular excitation have been directly measured. We show that an E%-max winner-take-all process provides a simple explanation for why the orientation tuning of firing is narrower than that of the excitatory input and why this difference is not affected by increasing excitation. Because gamma oscillations occur in many brain regions, the framework we have developed for understanding the second function of gamma is likely to have wide applicability.