Spatial navigation and multiscale representation by hippocampal place cells

Hippocampal lesions are known to impair success in navigation tasks. While such tasks could be solved by memorizing complete paths from a starting location to the goal, animals still perform successfully when placed in a novel starting position. We propose a navigation algorithm to solve the latter problem by exploiting two facts about hippocampal organization: (1) The size of the place fields of hippocampal place cells varies systematically along the dorsoventral axis, with dorsal place cells having smaller place fields than ventral (Kjelstrup et. al. 2008); and (2) the theta oscillation propagates as a traveling wave from dorsal to ventral hippocampus (Lubenov and Siapas, 2009). Taken together, these observations imply that the hippocampal representation of space progresses from fine- to coarse-grained within every theta cycle. 

The algorithm assumes that place cells can be activated by the animal's imagining a goal location, in addition to physically standing in the appropriate location. In the proposed algorithm, place cell activation propagates from small scale to large scale until place cells are found which respond strongly to both the physical location and the goal location. These place fields have their centers aligned roughly in the direction of the goal, providing a crude estimate of which direction the animal should step to approach the goal. Fine-grained directional information is contained in the smaller scale place fields within these large ones. Our algorithm therefore identifies a sequence of place cells, one from each scale, whose centers lie roughly along the line to the goal. 

Simulations reveal successful navigation to the goal, even around obstacles. By minimizing the number of steps the animal takes to reach the goal, we predict the organization of the optimal place field "map"; specifically the fraction of place cells which should be allocated to each spatial scale. This prediction is, in principle, experimentally testable.

The set of place fields with centers lying along a line to the goal is used to compute a step direction by maximizing the probability that those cells will be active in the next time step, given that a particular step direction is chosen.

The proposed algorithm handles navigation around obstacles by including "border cells" (Solstad et. al. 2008) which inhibit place cells in proportion to the degree of overlap between the place field and the obstacle. Furthermore, including firing rate adaptation of place cells prevents the animal from getting stuck in one spot

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

The Importance of Forgetting: Limiting Memory Improves Recovery of Topological Characteristics from Neural Data

We develop of a line of work initiated by Curto and Itskov towards understanding the amount of information contained in the spike trains of hippocampal place cells via topology considerations. Previously, it was established that simply knowing which groups of place cells fire together in an animal's hippocampus is sufficient to extract the global topology of the animal's physical environment. We model a system where collections of place cells group and ungroup according to short-term plasticity rules. In particular, we obtain the surprising result that in experiments with spurious firing, the accuracy of the extracted topological information decreases with the persistence (beyond a certain regime) of the cell groups. This suggests that synaptic transience, or forgetting, is a mechanism by which the brain counteracts the effects of spurious place cell activity

Learning place cells, grid cells and invariances with excitatory and inhibitory plasticity

Neurons in the hippocampus and adjacent brain areas show a large diversity in their tuning to location and head direction, and the underlying circuit mechanisms are not yet resolved. In particular, it is unclear why certain cell types are selective to one spatial variable, but invariant to another. For example, place cells are typically invariant to head direction. We propose that all observed spatial tuning patterns – in both their selectivity and their invariance – arise from the same mechanism: Excitatory and inhibitory synaptic plasticity driven by the spatial tuning statistics of synaptic inputs. Using simulations and a mathematical analysis, we show that combined excitatory and inhibitory plasticity can lead to localized, grid-like or invariant activity. Combinations of different input statistics along different spatial dimensions reproduce all major spatial tuning patterns observed in rodents. Our proposed model is robust to changes in parameters, develops patterns on behavioral timescales and makes distinctive experimental predictions.BMBF, 01GQ1201, Lernen und Gedächtnis in balancierten Systeme

Linear Self-Motion Cues Support the Spatial Distribution and Stability of Hippocampal Place Cells

The vestibular system provides a crucial component of place-cell and head-direction cell activity [1-7]. Otolith signals are necessary for head-direction signal stability and associated behavior [8, 9], and the head-direction signal's contribution to parahippocampal spatial representations [10-14] suggests that place cells may also require otolithic information. Here, we demonstrate that self-movement information from the otolith organs is necessary for the development of stable place fields within and across sessions. Place cells in otoconia-deficient tilted mice showed reduced spatial coherence and formed place fields that were located closer to environmental boundaries, relative to those of control mice. These differences reveal an important otolithic contribution to place-cell functioning and provide insight into the cognitive deficits associated with otolith dysfunction

Parallel and convergent processing in grid cell, head-direction cell, boundary cell, and place cell networks.

The brain is able to construct internal representations that correspond to external spatial coordinates. Such brain maps of the external spatial topography may support a number of cognitive functions, including navigation and memory. The neuronal building block of brain maps are place cells, which are found throughout the hippocampus of rodents and, in a lower proportion, primates. Place cells typically fire in one or few restricted areas of space, and each area where a cell fires can range, along the dorsoventral axis of the hippocampus, from 30 cm to at least several meters. The sensory processing streams that give rise to hippocampal place cells are not fully understood, but substantial progress has been made in characterizing the entorhinal cortex, which is the gateway between neocortical areas and the hippocampus. Entorhinal neurons have diverse spatial firing characteristics, and the different entorhinal cell types converge in the hippocampus to give rise to a single, spatially modulated cell type-the place cell. We therefore suggest that parallel information processing in different classes of cells-as is typically observed at lower levels of sensory processing-continues up into higher level association cortices, including those that provide the inputs to hippocampus. WIREs Cogn Sci 2014, 5:207-219. doi: 10.1002/wcs.1272 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website