Modelling effects on grid cells of sensory input during self-motion

Tiling of large-scaled environments by grid cells requires experience

Grid cells in the medial entorhinal cortex are widely believed to provide a universal spatial metric supporting vector-based navigation irrespective of the spatial scale of an environment. However, using single unit recordings in freely behaving mice, we demonstrate that spatial periodicity in grid cell firing is substantially disrupted when transitioning from a small to a large-scale arena when the scale ratio is larger than the scale ratio of successive grid modules. Remarkably, grid patterns reemerge with experience in the large-scale arena, suggesting that grid cells can learn to represent large-scale spaces with experience.

Visual boundary cues suffice to anchor place and grid cells in virtual reality

The hippocampal formation contains neurons responsive to an animal's current location and orientation, which together provide the organism with a neural map of space.1,2,3 Spatially tuned neurons rely on external landmark cues and internally generated movement information to estimate position.4,5 An important class of landmark cue are the boundaries delimiting an environment, which can define place cell field position6,7 and stabilize grid cell firing.8 However, the precise nature of the sensory information used to detect boundaries remains unknown. We used 2-dimensional virtual reality (VR)9 to show that visual cues from elevated walls surrounding the environment are both sufficient and necessary to stabilize place and grid cell responses in VR, when only visual and self-motion cues are available. By contrast, flat boundaries formed by the edges of a textured floor did not stabilize place and grid cells, indicating only specific forms of visual boundary stabilize hippocampal spatial firing. Unstable grid cells retain internally coherent, hexagonally arranged firing fields, but these fields "drift" with respect to the virtual environment over periods >5 s. Optic flow from a virtual floor does not slow drift dynamics, emphasizing the importance of boundary-related visual information. Surprisingly, place fields are more stable close to boundaries even with floor and wall cues removed, suggesting invisible boundaries are inferred using the motion of a discrete, separate cue (a beacon signaling reward location). Subsets of place cells show allocentric directional tuning toward the beacon, with strength of tuning correlating with place field stability when boundaries are removed.

Temporal dynamics of cholinergic activity in the septo-hippocampal system

Cholinergic projection neurons in the medial septum and diagonal band of Broca are the major source of cholinergic modulation of hippocampal circuit functions that support neural coding of location and running speed. Changes in cholinergic modulation are known to correlate with changes in brain states, cognitive functions, and behavior. However, whether cholinergic modulation can change fast enough to serve as a potential speed signal in hippocampal and parahippocampal cortices and whether the temporal dynamics in such a signal depend on the presence of visual cues remain unknown. In this study, we use a fiber-photometric approach to quantify the temporal dynamics of cholinergic activity in freely moving mice as a function of the animal's movement speed and visual cues. We show that the population activity of cholinergic neurons in the medial septum and diagonal band of Broca changes fast enough to be aligned well with changes in the animal's running speed and is strongly and linearly correlated to the logarithm of the animal's running speed. Intriguingly, the cholinergic modulation remains strongly and linearly correlated to the speed of the animal's neck movements during periods of stationary activity. Furthermore, we show that cholinergic modulation is unaltered during darkness. Lastly, we identify rearing, a stereotypic behavior where the mouse stands on its hindlimbs to scan the environment from an elevated perspective, is associated with higher cholinergic activity than expected from neck movements on the horizontal plane alone. Taken together, these data show that temporal dynamics in the cholinergic modulation of hippocampal circuits are fast enough to provide a potential running speed signal in real-time. Moreover, the data show that cholinergic modulation is primarily a function of the logarithm of the animal's movement speed, both during locomotion and during stationary activity, with no significant interaction with visual inputs. These data advance our understanding of temporal dynamics in cholinergic modulation of hippocampal circuits and their functions in the context of neural coding of location and running speed.

Microcircuits for spatial coding in the medial entorhinal cortex

The hippocampal formation is critically involved in learning and memory and contains a large proportion of neurons encoding aspects of the organism's spatial surroundings. In the medial entorhinal cortex (MEC), this includes grid cells with their distinctive hexagonal firing fields as well as a host of other functionally defined cell types including head direction cells, speed cells, border cells, and object-vector cells. Such spatial coding emerges from the processing of external inputs by local microcircuits. However, it remains unclear exactly how local microcircuits and their dynamics within the MEC contribute to spatial discharge patterns. In this review we focus on recent investigations of intrinsic MEC connectivity, which have started to describe and quantify both excitatory and inhibitory wiring in the superficial layers of the MEC. Although the picture is far from complete, it appears that these layers contain robust recurrent connectivity that could sustain the attractor dynamics posited to underlie grid pattern formation. These findings pave the way to a deeper understanding of the mechanisms underlying spatial navigation and memory.

The Basis of Navigation Across Species

Animals navigate a wide range of distances, from a few millimeters to globe-spanning journeys of thousands of kilometers. Despite this array of navigational challenges, similar principles underlie these behaviors across species. Here, we focus on the navigational strategies and supporting mechanisms in four well-known systems: the large-scale migratory behaviors of sea turtles and lepidopterans as well as navigation on a smaller scale by rats and solitarily foraging ants. In lepidopterans, rats, and ants we also discuss the current understanding of the neural architecture which supports navigation. The orientation and navigational behaviors of these animals are defined in terms of behavioral error-reduction strategies reliant on multiple goal-directed servomechanisms. We conclude by proposing to incorporate an additional component into this system: the observation that servomechanisms operate on oscillatory systems of cycling behavior. These oscillators and servomechanisms comprise the basis for directed orientation and navigational behaviors. Expected final online publication date for the Annual Review of Psychology, Volume 73 is January 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A Brain-Inspired Adaptive Space Representation Model Based on Grid Cells and Place Cells

Grid cells and place cells are important neurons in the animal brain. The information transmission between them provides the basis for the spatial representation and navigation of animals and also provides reference for the research on the autonomous navigation mechanism of intelligent agents. Grid cells are important information source of place cells. The supervised learning and unsupervised learning models can be used to simulate the generation of place cells from grid cell inputs. However, the existing models preset the firing characteristics of grid cell. In this paper, we propose a united generation model of grid cells and place cells. First, the visual place cells with nonuniform distribution generate the visual grid cells with regional firing field through feedforward network. Second, the visual grid cells and the self-motion information generate the united grid cells whose firing fields extend to the whole space through genetic algorithm. Finally, the visual place cells and the united grid cells generate the united place cells with uniform distribution through supervised fuzzy adaptive resonance theory (ART) network. Simulation results show that this model has stronger environmental adaptability and can provide reference for the research on spatial representation model and brain-inspired navigation mechanism of intelligent agents under the condition of nonuniform environmental information.

Neurophysiological coding of space and time in the hippocampus, entorhinal cortex, and retrosplenial cortex

Neurophysiological recordings in behaving rodents demonstrate neuronal response properties that may code space and time for episodic memory and goal-directed behaviour. Here, we review recordings from hippocampus, entorhinal cortex, and retrosplenial cortex to address the problem of how neurons encode multiple overlapping spatiotemporal trajectories and disambiguate these for accurate memory-guided behaviour. The solution could involve neurons in the entorhinal cortex and hippocampus that show mixed selectivity, coding both time and location. Some grid cells and place cells that code space also respond selectively as time cells, allowing differentiation of time intervals when a rat runs in the same location during a delay period. Cells in these regions also develop new representations that differentially code the context of prior or future behaviour allowing disambiguation of overlapping trajectories. Spiking activity is also modulated by running speed and head direction, supporting the coding of episodic memory not as a series of snapshots but as a trajectory that can also be distinguished on the basis of speed and direction. Recent data also address the mechanisms by which sensory input could distinguish different spatial locations. Changes in firing rate reflect running speed on long but not short time intervals, and few cells code movement direction, arguing against path integration for coding location. Instead, new evidence for neural coding of environmental boundaries in egocentric coordinates fits with a modelling framework in which egocentric coding of barriers combined with head direction generates distinct allocentric coding of location. The egocentric input can be used both for coding the location of spatiotemporal trajectories and for retrieving specific viewpoints of the environment. Overall, these different patterns of neural activity can be used for encoding and disambiguation of prior episodic spatiotemporal trajectories or for planning of future goal-directed spatiotemporal trajectories.

Stellate Cells in the Medial Entorhinal Cortex Are Required for Spatial Learning

Spatial learning requires estimates of location that may be obtained by path integration or from positional cues. Grid and other spatial firing patterns of neurons in the superficial medial entorhinal cortex (MEC) suggest roles in behavioral estimation of location. However, distinguishing the contributions of path integration and cue-based signals to spatial behaviors is challenging, and the roles of identified MEC neurons are unclear. We use virtual reality to dissociate linear path integration from other strategies for behavioral estimation of location. We find that mice learn to path integrate using motor-related self-motion signals, with accuracy that decreases steeply as a function of distance. We show that inactivation of stellate cells in superficial MEC impairs spatial learning in virtual reality and in a real world object location recognition task. Our results quantify contributions of path integration to behavior and corroborate key predictions of models in which stellate cells contribute to location estimation.

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Mice learn to estimate location by path integration and cue-based strategies

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Motor-related self-motion signals are used for path integration

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Accuracy of path integration decreases with distance

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Stellate cells in medial entorhinal cortex are required for spatial learning

The Firing Rate Speed Code of Entorhinal Speed Cells Differs across Behaviorally Relevant Time Scales and Does Not Depend on Medial Septum Inputs

The firing rate of speed cells, a dedicated subpopulation of neurons in the medial entorhinal cortex (MEC), is correlated with running speed. This correlation has been interpreted as a speed code used in various computational models for path integration. These models consider firing rate to be linearly tuned by running speed in real-time. However, estimation of firing rates requires integration of spiking events over time, setting constraints on the temporal accuracy of the proposed speed code. We therefore tested whether the proposed speed code by firing rate is accurate at short time scales using data obtained from open-field recordings in male rats and mice. We applied a novel filtering approach differentiating between speed codes at multiple time scales ranging from deciseconds to minutes. In addition, we determined the optimal integration time window for firing-rate estimation using a general likelihood framework and calculated the integration time window that maximizes the correlation between firing rate and running speed. Data show that these time windows are on the order of seconds, setting constraints on real-time speed coding by firing rate. We further show that optogenetic inhibition of either cholinergic, GABAergic, or glutamatergic neurons in the medial septum/diagonal band of Broca does not affect modulation of firing rates by running speed at each time scale tested. These results are relevant for models of path integration and for our understanding of how behavioral activity states may modulate firing rates and likely information processing in the MEC.SIGNIFICANCE STATEMENT Path integration is the most basic form of navigation relying on self-motion cues. Models of path integration use medial septum/diagonal band of Broca (MSDB)-dependent MEC grid-cell firing patterns as the neurophysiological substrate of path integration. These models use a linear speed code by firing rate, but do not consider temporal constraints of integration over time for firing-rate estimation. We show that firing-rate estimation for speed cells requires integration over seconds. Using optogenetics, we show that modulation of firing rates by running speed is independent of MSDB inputs. These results enhance our understanding of path integration mechanisms and the role of the MSDB for information processing in the MEC.

A Framework for Intelligence and Cortical Function Based on Grid Cells in the Neocortex

How the neocortex works is a mystery. In this paper we propose a novel framework for understanding its function. Grid cells are neurons in the entorhinal cortex that represent the location of an animal in its environment. Recent evidence suggests that grid cell-like neurons may also be present in the neocortex. We propose that grid cells exist throughout the neocortex, in every region and in every cortical column. They define a location-based framework for how the neocortex functions. Whereas grid cells in the entorhinal cortex represent the location of one thing, the body relative to its environment, we propose that cortical grid cells simultaneously represent the location of many things. Cortical columns in somatosensory cortex track the location of tactile features relative to the object being touched and cortical columns in visual cortex track the location of visual features relative to the object being viewed. We propose that mechanisms in the entorhinal cortex and hippocampus that evolved for learning the structure of environments are now used by the neocortex to learn the structure of objects. Having a representation of location in each cortical column suggests mechanisms for how the neocortex represents object compositionality and object behaviors. It leads to the hypothesis that every part of the neocortex learns complete models of objects and that there are many models of each object distributed throughout the neocortex. The similarity of circuitry observed in all cortical regions is strong evidence that even high-level cognitive tasks are learned and represented in a location-based framework.

Emergent elasticity in the neural code for space

Upon encountering a novel environment, an animal must construct a consistent environmental map, as well as an internal estimate of its position within that map, by combining information from two distinct sources: self-motion cues and sensory landmark cues. How do known aspects of neural circuit dynamics and synaptic plasticity conspire to accomplish this feat? Here we show analytically how a neural attractor model that combines path integration of self-motion cues with Hebbian plasticity in synaptic weights from landmark cells can self-organize a consistent map of space as the animal explores an environment. Intriguingly, the emergence of this map can be understood as an elastic relaxation process between landmark cells mediated by the attractor network. Moreover, our model makes several experimentally testable predictions, including (i) systematic path-dependent shifts in the firing fields of grid cells toward the most recently encountered landmark, even in a fully learned environment; (ii) systematic deformations in the firing fields of grid cells in irregular environments, akin to elastic deformations of solids forced into irregular containers; and (iii) the creation of topological defects in grid cell firing patterns through specific environmental manipulations. Taken together, our results conceptually link known aspects of neurons and synapses to an emergent solution of a fundamental computational problem in navigation, while providing a unified account of disparate experimental observations.

Environmental deformations dynamically shift the grid cell spatial metric

In familiar environments, the firing fields of entorhinal grid cells form regular triangular lattices. However, when the geometric shape of the environment is deformed, these time-averaged grid patterns are distorted in a grid scale-dependent and local manner. We hypothesized that this distortion in part reflects dynamic anchoring of the grid code to displaced boundaries, possibly through border cell-grid cell interactions. To test this hypothesis, we first reanalyzed two existing rodent grid rescaling datasets to identify previously unrecognized boundary-tethered shifts in grid phase that contribute to the appearance of rescaling. We then demonstrated in a computational model that boundary-tethered phase shifts, as well as scale-dependent and local distortions of the time-averaged grid pattern, could emerge from border-grid interactions without altering inherent grid scale. Together, these results demonstrate that environmental deformations induce history-dependent shifts in grid phase, and implicate border-grid interactions as a potential mechanism underlying these dynamics.

Potential roles of cholinergic modulation in the neural coding of location and movement speed

Behavioral data suggest that cholinergic modulation may play a role in certain aspects of spatial memory, and neurophysiological data demonstrate neurons that fire in response to spatial dimensions, including grid cells and place cells that respond on the basis of location and running speed. These neurons show firing responses that depend upon the visual configuration of the environment, due to coding in visually-responsive regions of the neocortex. This review focuses on the physiological effects of acetylcholine that may influence the sensory coding of spatial dimensions relevant to behavior. In particular, the local circuit effects of acetylcholine within the cortex regulate the influence of sensory input relative to internal memory representations via presynaptic inhibition of excitatory and inhibitory synaptic transmission, and the modulation of intrinsic currents in cortical excitatory and inhibitory neurons. In addition, circuit effects of acetylcholine regulate the dynamics of cortical circuits including oscillations at theta and gamma frequencies. These effects of acetylcholine on local circuits and network dynamics could underlie the role of acetylcholine in coding of spatial information for the performance of spatial memory tasks.

Absence of Visual Input Results in the Disruption of Grid Cell Firing in the Mouse

Grid cells are spatially modulated neurons within the medial entorhinal cortex whose firing fields are arranged at the vertices of tessellating equilateral triangles [1]. The exquisite periodicity of their firing has led to the suggestion that they represent a path integration signal, tracking the organism’s position by integrating speed and direction of movement [2, 3, 4, 5, 6, 7, 8, 9, 10]. External sensory inputs are required to reset any errors that the path integrator would inevitably accumulate. Here we probe the nature of the external sensory inputs required to sustain grid firing, by recording grid cells as mice explore familiar environments in complete darkness. The absence of visual cues results in a significant disruption of grid cell firing patterns, even when the quality of the directional information provided by head direction cells is largely preserved. Darkness alters the expression of velocity signaling within the entorhinal cortex, with changes evident in grid cell firing rate and the local field potential theta frequency. Short-term (<1.5 s) spike timing relationships between grid cell pairs are preserved in the dark, indicating that network patterns of excitatory and inhibitory coupling between grid cells exist independently of visual input and of spatially periodic firing. However, we find no evidence of preserved hexagonal symmetry in the spatial firing of single grid cells at comparable short timescales. Taken together, these results demonstrate that visual input is required to sustain grid cell periodicity and stability in mice and suggest that grid cells in mice cannot perform accurate path integration in the absence of reliable visual cues.

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Grid cell firing patterns are disrupted in darkness in the mouse

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Grid cells are disrupted even when head direction cell signaling is preserved

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Absence of visual input alters movement velocity modulation of theta frequency

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Temporal firing relationships between grid cell pairs are preserved in the dark