Deforming the hippocampal map

Remapping revisited: how the hippocampus represents different spaces

The representation of distinct spaces by hippocampal place cells has been linked to changes in their place fields (the locations in the environment where the place cells discharge strongly), a phenomenon that has been termed 'remapping'. Remapping has been assumed to be accompanied by the reorganization of subsecond cofiring relationships among the place cells, potentially maximizing hippocampal information coding capacity. However, several observations challenge this standard view. For example, place cells exhibit mixed selectivity, encode non-positional variables, can have multiple place fields and exhibit unreliable discharge in fixed environments. Furthermore, recent evidence suggests that, when measured at subsecond timescales, the moment-to-moment cofiring of a pair of cells in one environment is remarkably similar in another environment, despite remapping. Here, I propose that remapping is a misnomer for the changes in place fields across environments and suggest instead that internally organized manifold representations of hippocampal activity are actively registered to different environments to enable navigation, promote memory and organize knowledge.

A map of spatial navigation for neuroscience

Spatial navigation has received much attention from neuroscientists, leading to the identification of key brain areas and the discovery of numerous spatially selective cells. Despite this progress, our understanding of how the pieces fit together to drive behavior is generally lacking. We argue that this is partly caused by insufficient communication between behavioral and neuroscientific researchers. This has led the latter to under-appreciate the relevance and complexity of spatial behavior, and to focus too narrowly on characterizing neural representations of space-disconnected from the computations these representations are meant to enable. We therefore propose a taxonomy of navigation processes in mammals that can serve as a common framework for structuring and facilitating interdisciplinary research in the field. Using the taxonomy as a guide, we review behavioral and neural studies of spatial navigation. In doing so, we validate the taxonomy and showcase its usefulness in identifying potential issues with common experimental approaches, designing experiments that adequately target particular behaviors, correctly interpreting neural activity, and pointing to new avenues of research.

From Topological Analyses to Functional Modeling: The Case of Hippocampus

Topological data analyses are widely used for describing and conceptualizing large volumes of neurobiological data, e.g., for quantifying spiking outputs of large neuronal ensembles and thus understanding the functions of the corresponding networks. Below we discuss an approach in which convergent topological analyses produce insights into how information may be processed in mammalian hippocampus—a brain part that plays a key role in learning and memory. The resulting functional model provides a unifying framework for integrating spiking data at different timescales and following the course of spatial learning at different levels of spatiotemporal granularity. This approach allows accounting for contributions from various physiological phenomena into spatial cognition—the neuronal spiking statistics, the effects of spiking synchronization by different brain waves, the roles played by synaptic efficacies and so forth. In particular, it is possible to demonstrate that networks with plastic and transient synaptic architectures can encode stable cognitive maps, revealing the characteristic timescales of memory processing.

Replays of spatial memories suppress topological fluctuations in cognitive map

The spiking activity of the hippocampal place cells plays a key role in producing and sustaining an internalized representation of the ambient space-a cognitive map. These cells do not only exhibit location-specific spiking during navigation, but also may rapidly replay the navigated routs through endogenous dynamics of the hippocampal network. Physiologically, such reactivations are viewed as manifestations of "memory replays" that help to learn new information and to consolidate previously acquired memories by reinforcing synapses in the parahippocampal networks. Below we propose a computational model of these processes that allows assessing the effect of replays on acquiring a robust topological map of the environment and demonstrate that replays may play a key role in stabilizing the hippocampal representation of space.

Origin and role of path integration in the cognitive representations of the hippocampus: computational insights into open questions

Path integration is a straightforward concept with varied connotations that are important to different disciplines concerned with navigation, such as ethology, cognitive science, robotics and neuroscience. In studying the hippocampal formation, it is fruitful to think of path integration as a computation that transforms a sense of motion into a sense of location, continuously integrated with landmark perception. Here, we review experimental evidence that path integration is intimately involved in fundamental properties of place cells and other spatial cells that are thought to support a cognitive abstraction of space in this brain system. We discuss hypotheses about the anatomical and computational origin of path integration in the well-characterized circuits of the rodent limbic system. We highlight how computational frameworks for map-building in robotics and cognitive science alike suggest an essential role for path integration in the creation of a new map in unfamiliar territory, and how this very role can help us make sense of differences in neurophysiological data from novel versus familiar and small versus large environments. Similar computational principles could be at work when the hippocampus builds certain non-spatial representations, such as time intervals or trajectories defined in a sensory stimulus space.

Through synapses to spatial memory maps via a topological model

Various neurophysiological and cognitive functions are based on transferring information between spiking neurons via a complex system of synaptic connections. In particular, the capacity of presynaptic inputs to influence the postsynaptic outputs–the efficacy of the synapses–plays a principal role in all aspects of hippocampal neurophysiology. However, a direct link between the information processed at the level of individual synapses and the animal’s ability to form memories at the organismal level has not yet been fully understood. Here, we investigate the effect of synaptic transmission probabilities on the ability of the hippocampal place cell ensembles to produce a cognitive map of the environment. Using methods from algebraic topology, we find that weakening synaptic connections increase spatial learning times, produce topological defects in the large-scale representation of the ambient space and restrict the range of parameters for which place cell ensembles are capable of producing a map with correct topological structure. On the other hand, the results indicate a possibility of compensatory phenomena, namely that spatial learning deficiencies may be mitigated through enhancement of neuronal activity.

Topological Schemas of Memory Spaces

Hippocampal cognitive map—a neuronal representation of the spatial environment—is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework—the memory space—that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as “networks of interconnections among the representations of events,” have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature—a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure.

Transient cell assembly networks encode stable spatial memories

One of the mysteries of memory is that it can last despite changes in the underlying synaptic architecture. How can we, for example, maintain an internal spatial map of an environment over months or years when the underlying network is full of transient connections? In the following, we propose a computational model for describing the emergence of the hippocampal cognitive map in a network of transient place cell assemblies and demonstrate, using methods of algebraic topology, how such a network can maintain spatial memory over time.

Gamma Synchronization Influences Map Formation Time in a Topological Model of Spatial Learning

The mammalian hippocampus plays a crucial role in producing a cognitive map of space-an internalized representation of the animal's environment. We have previously shown that it is possible to model this map formation using a topological framework, in which information about the environment is transmitted through the temporal organization of neuronal spiking activity, particularly those occasions in which the firing of different place cells overlaps. In this paper, we discuss how gamma rhythm, one of the main components of the extracellular electrical field potential affects the efficiency of place cell map formation. Using methods of algebraic topology and the maximal entropy principle, we demonstrate that gamma modulation synchronizes the spiking of dynamical cell assemblies, which enables learning a spatial map at faster timescales.

A model of topological mapping of space in bat hippocampus

The mammalian hippocampus plays a key role in spatial learning and memory, but the exact nature of the hippocampal representation of space is still being explored. Recently, there has been a fair amount of success in modeling hippocampal spatial maps in rats, assuming a topological perspective on spatial information processing. In this article, we use the topological approach to study the formation of a 3D spatial map in bats, which produces several insights into neurophysiological mechanisms of the hippocampal spatial leaning. First, we demonstrate that, in order to produce accurate maps of the environment, place cell should be organized into functional groups, which can be interpreted as cell assemblies. Second, the model suggests that the readout neurons in these cell assemblies should function as integrators of synaptic inputs, rather than detectors of place cells' coactivity, which allows estimating the integration time window. Lastly, the model suggests that, in contrast with relatively slow moving rats, suppressing θ-precession in bats improves the place cells capacity to encode spatial maps, which is consistent with the experimental observations. © 2016 Wiley Periodicals, Inc.

Topological Schemas of Cognitive Maps and Spatial Learning

Spatial navigation in mammals is based on building a mental representation of their environment-a cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains vague. A key difficulty is that these maps are collective, emergent phenomena that cannot be reduced to a simple combination of inputs provided by individual neurons. In this paper we suggest computational frameworks for integrating the spiking signals of individual cells into a spatial map, which we call schemas. We provide examples of four schemas defined by different types of topological relations that may be neurophysiologically encoded in the brain and demonstrate that each schema provides its own large-scale characteristics of the environment-the schema integrals. Moreover, we find that, in all cases, these integrals are learned at a rate which is faster than the rate of complete training of neural networks. Thus, the proposed schema framework differentiates between the cognitive aspect of spatial learning and the physiological aspect at the neural network level.

Reconceiving the hippocampal map as a topological template

The role of the hippocampus in spatial cognition is incontrovertible yet controversial. Place cells, initially thought to be location-specifiers, turn out to respond promiscuously to a wide range of stimuli. Here we test the idea, which we have recently demonstrated in a computational model, that the hippocampal place cells may ultimately be interested in a space's topological qualities (its connectivity) more than its geometry (distances and angles); such higher-order functioning would be more consistent with other known hippocampal functions. We recorded place cell activity in rats exploring morphing linear tracks that allowed us to dissociate the geometry of the track from its topology. The resulting place fields preserved the relative sequence of places visited along the track but did not vary with the metrical features of the track or the direction of the rat's movement. These results suggest a reinterpretation of previous studies and new directions for future experiments.

Independence of landmark and self-motion-guided navigation: a different role for grid cells

Recent interest in the neural bases of spatial navigation stems from the discovery of neuronal populations with strong, specific spatial signals. The regular firing field arrays of medial entorhinal grid cells suggest that they may provide place cells with distance information extracted from the animal's self-motion, a notion we critically review by citing new contrary evidence. Next, we question the idea that grid cells provide a rigid distance metric. We also discuss evidence that normal navigation is possible using only landmarks, without self-motion signals. We then propose a model that supposes that information flow in the navigational system changes between light and dark conditions. We assume that the true map-like representation is hippocampal and argue that grid cells have a crucial navigational role only in the dark. In this view, their activity in the light is predominantly shaped by landmarks rather than self-motion information, and so follows place cell activity; in the dark, their activity is determined by self-motion cues and controls place cell activity. A corollary is that place cell activity in the light depends on non-grid cells in ventral medial entorhinal cortex. We conclude that analysing navigational system changes between landmark and no-landmark conditions will reveal key functional properties.

Attractor dynamics of spatially correlated neural activity in the limbic system

Attractor networks are a popular computational construct used to model different brain systems. These networks allow elegant computations that are thought to represent a number of aspects of brain function. Although there is good reason to believe that the brain displays attractor dynamics, it has proven difficult to test experimentally whether any particular attractor architecture resides in any particular brain circuit. We review models and experimental evidence for three systems in the rat brain that are presumed to be components of the rat's navigational and memory system. Head-direction cells have been modeled as a ring attractor, grid cells as a plane attractor, and place cells both as a plane attractor and as a point attractor. Whereas the models have proven to be extremely useful conceptual tools, the experimental evidence in their favor, although intriguing, is still mostly circumstantial.

Sensory feedback, error correction, and remapping in a multiple oscillator model of place-cell activity

Mammals navigate by integrating self-motion signals ("path integration") and occasionally fixing on familiar environmental landmarks. The rat hippocampus is a model system of spatial representation in which place cells are thought to integrate both sensory and spatial information from entorhinal cortex. The localized firing fields of hippocampal place cells and entorhinal grid-cells demonstrate a phase relationship with the local theta (6-10 Hz) rhythm that may be a temporal signature of path integration. However, encoding self-motion in the phase of theta oscillations requires high temporal precision and is susceptible to idiothetic noise, neuronal variability, and a changing environment. We present a model based on oscillatory interference theory, previously studied in the context of grid cells, in which transient temporal synchronization among a pool of path-integrating theta oscillators produces hippocampal-like place fields. We hypothesize that a spatiotemporally extended sensory interaction with external cues modulates feedback to the theta oscillators. We implement a form of this cue-driven feedback and show that it can retrieve fixed points in the phase code of position. A single cue can smoothly reset oscillator phases to correct for both systematic errors and continuous noise in path integration. Further, simulations in which local and global cues are rotated against each other reveal a phase-code mechanism in which conflicting cue arrangements can reproduce experimentally observed distributions of "partial remapping" responses. This abstract model demonstrates that phase-code feedback can provide stability to the temporal coding of position during navigation and may contribute to the context-dependence of hippocampal spatial representations. While the anatomical substrates of these processes have not been fully characterized, our findings suggest several signatures that can be evaluated in future experiments.

Learning in a geometric model of place cell firing

Following Hartley et al. (Hartley et al. (2000) Hippocampus 10:369-379), we present a simple feed-forward model of place cell (PC) firing predicated on neocortical information regarding the environmental geometry surrounding the animal. Incorporating the idea of boundaries with distinct sensory qualities, we show that synaptic plasticity mediated by a BCM-like rule (Bienenstock et al. (1982) J Neurosci 2:32-48) produces PCs that encode position relative to specific extended landmarks. In an unchanging environment the model is shown to undergo an initial phase of learning, resulting in the formation of stable place fields. In familiar environments, perturbation of environmental cues produces graded changes in the firing rate and position of place fields. Model simulations are compared favorably with three sets of experimental data: (1) Results published by Barry et al. (Barry et al. (2006) Rev Neurosci 17:71-97) showing the slow disappearance of duplicate place fields produced when a barrier is placed into a familiar environment. (2) Rivard et al.'s (Rivard et al. (2004) J Gen Physiol 124:9-25) study showing a graded response in PC firing such that fields near to a centrally placed object encode space relative to the object, whereas more distant fields respond to the surrounding environment. (3) Fenton et al.'s (Fenton et al. (2000a) J Gen Physiol 116:191-209) observation that inconsistent rotation of cue cards produces parametric changes in place field positions. The merits of the model are discussed in terms of its extensibility and biological plausibility.

Characterization of inhibitory circuits in the malformed hippocampus of Lis1 mutant mice

Heterozygous mutation or deletion of a lissencephaly gene (Lis1) in humans is associated with a severe disruption of cortical and hippocampal lamination, cognitive deficit, and severe seizures. Mice with one null allele of Lis1 (Lis1(+/-) mice) exhibit significant brain malformations and slowed migration of interneuron precursors. Although hyperexcitability was demonstrated in dysplastic hippocampal slices from Lis1(+/-) mice, little is known about synaptic function in these animals. Here we analyzed GABA-mediated synaptic inhibition. We recorded isolated whole cell inhibitory postsynaptic currents (IPSCs) on visually identified pyramidal neurons in disorganized CA1 regions of hippocampal slices prepared from Lis1(+/-) mice. We observed a 32% increase in spontaneous IPSC frequency in Lis1(+/-) mice compared with normotopic CA1 pyramidal neurons in age-matched controls. This increase was not associated with a change in spontaneous IPSC decay or miniature IPSC frequency. Mean IPSC amplitude was increased, and event histograms indicated a greater number of large (>125 pA) events. Tonic inhibition, response to paired-pulse stimulation and evoked IPSC decay kinetics were not altered. Consistent with increased synaptic inhibition, Lis1(+/-) interneurons also exhibited more spontaneous firing in cell-attached recordings and increased excitation as measured by voltage-clamp recording of spontaneous excitatory postsynaptic currents (EPSCs) onto interneurons. Our results reveal a significant alteration in the function of inhibitory circuits within the malformed Lis1(+/-) hippocampus. Given that precisely coordinated GABAergic activity is vital to generation of oscillatory activity and place field precision in hippocampus, these alterations in synaptic inhibition may contribute to seizures and altered cognitive function in type I Lissencephaly.

The boundary vector cell model of place cell firing and spatial memory

We review evidence for the boundary vector cell model of the environmental determinants of the firing of hippocampal place cells. Preliminary experimental results are presented concerning the effects of addition or removal of environmental boundaries on place cell firing and evidence that boundary vector cells may exist in the subiculum. We review and update computational simulations predicting the location of human search within a virtual environment of variable geometry, assuming that boundary vector cells provide one of the input representations of location used in mammalian spatial memory. Finally, we extend the model to include experience-dependent modification of connection strengths through a BCM-like learning rule - the size and sign of strength change is influenced by historic activity of the postsynaptic cell. Simulations are compared to experimental data on the firing of place cells under geometrical manipulations to their environment. The relationship between neurophysiological results in rats and spatial behaviour in humans is discussed.

A spin glass model of path integration in rat medial entorhinal cortex

Electrophysiological recording studies in the dorsocaudal region of medial entorhinal cortex (dMEC) of the rat reveal cells whose spatial firing fields show a remarkably regular hexagonal grid pattern (Fyhn et al., 2004; Hafting et al., 2005). We describe a symmetric, locally connected neural network, or spin glass model, that spontaneously produces a hexagonal grid of activity bumps on a two-dimensional sheet of units. The spatial firing fields of the simulated cells closely resemble those of dMEC cells. A collection of grids with different scales and/or orientations forms a basis set for encoding position. Simulations show that the animal's location can easily be determined from the population activity pattern. Introducing an asymmetry in the model allows the activity bumps to be shifted in any direction, at a rate proportional to velocity, to achieve path integration. Furthermore, information about the structure of the environment can be superimposed on the spatial position signal by modulation of the bump activity levels without significantly interfering with the hexagonal periodicity of firing fields. Our results support the conjecture of Hafting et al. (2005) that an attractor network in dMEC may be the source of path integration information afferent to hippocampus.