A model of head direction and landmark coding in complex environments

Distinct cortical spatial representations learned along disparate visual pathways

Recent experimental studies have discovered diverse spatial properties, such as head direction tuning and egocentric tuning, of neurons in the postrhinal cortex (POR) and revealed how the POR spatial representation is distinct from the retrosplenial cortex (RSC). However, how these spatial properties of POR neurons emerge is unknown, and the cause of distinct cortical spatial representations is also unclear. Here, we build a learning model of POR based on the pathway from the superior colliculus (SC) that has been shown to have motion processing within the visual input. Our designed SC-POR model demonstrates that diverse spatial properties of POR neurons can emerge from a learning process based on visual input that incorporates motion processing. Moreover, combining SC-POR model with our previously proposed V1-RSC model, we show that distinct cortical spatial representations in POR and RSC can be learnt along disparate visual pathways (originating in SC and V1), suggesting that the varying features encoded in different visual pathways contribute to the distinct spatial properties in downstream cortical areas.

Distinct codes for environment structure and symmetry in postrhinal and retrosplenial cortices

Complex sensory information arrives in the brain from an animal's first-person ('egocentric') perspective. However, animals can efficiently navigate as if referencing map-like ('allocentric') representations. The postrhinal (POR) and retrosplenial (RSC) cortices are thought to mediate between sensory input and internal maps, combining egocentric representations of physical cues with allocentric head direction (HD) information. Here we show that neurons in the POR and RSC of female Long-Evans rats are tuned to distinct but complementary aspects of local space. Egocentric bearing (EB) cells recorded in square and L-shaped environments reveal that RSC cells encode local geometric features, while POR cells encode a more global account of boundary geometry. Additionally, POR HD cells can incorporate egocentric information to fire in two opposite directions with two oppositely placed identical visual landmarks, while only a subset of RSC HD cells possess this property. Entorhinal grid and HD cells exhibit consistently allocentric spatial firing properties. These results reveal significant regional differences in the neural encoding of spatial reference frames.

Continuous Bump Attractor Networks Require Explicit Error Coding for Gain Recalibration

Representations of continuous variables are crucial to create internal models of the external world. A prevailing model of how the brain maintains these representations is given by continuous bump attractor networks (CBANs) in a broad range of brain functions across different areas, such as spatial navigation in hippocampal/entorhinal circuits and working memory in prefrontal cortex. Through recurrent connections, a CBAN maintains a persistent activity bump, whose peak location can vary along a neural space, corresponding to different values of a continuous variable. To track the value of a continuous variable changing over time, a CBAN updates the location of its activity bump based on inputs that encode the changes in the continuous variable (e.g., movement velocity in the case of spatial navigation)-a process akin to mathematical integration. This integration process is not perfect and accumulates error over time. For error correction, CBANs can use additional inputs providing ground-truth information about the continuous variable's correct value (e.g., visual landmarks for spatial navigation). These inputs enable the network dynamics to automatically correct any representation error. Recent experimental work on hippocampal place cells has shown that, beyond correcting errors, ground-truth inputs also fine-tune the gain of the integration process, a crucial factor that links the change in the continuous variable to the updating of the activity bump's location. However, existing CBAN models lack this plasticity, offering no insights into the neural mechanisms and representations involved in the recalibration of the integration gain. In this paper, we explore this gap by using a ring attractor network, a specific type of CBAN, to model the experimental conditions that demonstrated gain recalibration in hippocampal place cells. Our analysis reveals the necessary conditions for neural mechanisms behind gain recalibration within a CBAN. Unlike error correction, which occurs through network dynamics based on ground-truth inputs, gain recalibration requires an additional neural signal that explicitly encodes the error in the network's representation via a rate code. Finally, we propose a modified ring attractor network as an example CBAN model that verifies our theoretical findings. Combining an error-rate code with Hebbian synaptic plasticity, this model achieves recalibration of integration gain in a CBAN, ensuring accurate representation for continuous variables.

Continuous Bump Attractor Networks Require Explicit Error Coding for Gain Recalibration

Representations of continuous variables are crucial to create internal models of the external world. A prevailing model of how the brain maintains these representations is given by continuous bump attractor networks (CBANs) in a broad range of brain functions across different areas, such as spatial navigation in hippocampal/entorhinal circuits and working memory in prefrontal cortex. Through recurrent connections, a CBAN maintains a persistent activity bump, whose peak location can vary along a neural space, corresponding to different values of a continuous variable. To track the value of a continuous variable changing over time, a CBAN updates the location of its activity bump based on inputs that encode the changes in the continuous variable (e.g., movement velocity in the case of spatial navigation)-a process akin to mathematical integration. This integration process is not perfect and accumulates error over time. For error correction, CBANs can use additional inputs providing ground-truth information about the continuous variable's correct value (e.g., visual landmarks for spatial navigation). These inputs enable the network dynamics to automatically correct any representation error. Recent experimental work on hippocampal place cells has shown that, beyond correcting errors, ground-truth inputs also fine-tune the gain of the integration process, a crucial factor that links the change in the continuous variable to the updating of the activity bump's location. However, existing CBAN models lack this plasticity, offering no insights into the neural mechanisms and representations involved in the recalibration of the integration gain. In this paper, we explore this gap by using a ring attractor network, a specific type of CBAN, to model the experimental conditions that demonstrated gain recalibration in hippocampal place cells. Our analysis reveals the necessary conditions for neural mechanisms behind gain recalibration within a CBAN. Unlike error correction, which occurs through network dynamics based on ground-truth inputs, gain recalibration requires an additional neural signal that explicitly encodes the error in the network's representation via a rate code. Finally, we propose a modified ring attractor network as an example CBAN model that verifies our theoretical findings. Combining an error-rate code with Hebbian synaptic plasticity, this model achieves recalibration of integration gain in a CBAN, ensuring accurate representation for continuous variables.

Coordinated head direction representations in mouse anterodorsal thalamic nucleus and retrosplenial cortex

The sense of direction is critical for survival in changing environments and relies on flexibly integrating self-motion signals with external sensory cues. While the anatomical substrates involved in head direction (HD) coding are well known, the mechanisms by which visual information updates HD representations remain poorly understood. Retrosplenial cortex (RSC) plays a key role in forming coherent representations of space in mammals and it encodes a variety of navigational variables, including HD. Here, we use simultaneous two-area tetrode recording to show that RSC HD representation is nearly synchronous with that of the anterodorsal nucleus of thalamus (ADn), the obligatory thalamic relay of HD to cortex, during rotation of a prominent visual cue. Moreover, coordination of HD representations in the two regions is maintained during darkness. We further show that anatomical and functional connectivity are consistent with a strong feedforward drive of HD information from ADn to RSC, with anatomically restricted corticothalamic feedback. Together, our results indicate a concerted global HD reference update across cortex and thalamus.

The Anterior Thalamus Preferentially Drives Allocentric But Not Egocentric Orientation Tuning in Postrhinal Cortex

Navigating a complex world requires integration of multiple spatial reference frames, including information about one's orientation in both allocentric and egocentric coordinates. Combining these two information sources can provide additional information about one's spatial location. Previous studies have demonstrated that both egocentric and allocentric spatial signals are reflected by the firing of neurons in the rat postrhinal cortex (POR), an area that may serve as a hub for integrating allocentric head direction (HD) cell information with egocentric information from center-bearing and center-distance cells. However, we have also demonstrated that POR HD cells are uniquely influenced by the visual properties and locations of visual landmarks, bringing into question whether the POR HD signal is truly allocentric as opposed to simply being a response to visual stimuli. To investigate this issue, we recorded HD cells from the POR of female rats while bilaterally inactivating the anterior thalamus (ATN), a region critical for expression of the "classic" HD signal in cortical areas. We found that ATN inactivation led to a significant decrease in both firing rate and tuning strength for POR HD cells, as well as a disruption in the encoding of allocentric location by conjunctive HD/egocentric cells. In contrast, POR egocentric cells without HD tuning were largely unaffected in a consistent manner by ATN inactivation. These results indicate that the POR HD signal originates at least partially from projections from the ATN and supports the view that the POR acts as a hub for the integration of egocentric and allocentric spatial representations.

Coregistration of heading to visual cues in retrosplenial cortex

Spatial cognition depends on an accurate representation of orientation within an environment. Head direction cells in distributed brain regions receive a range of sensory inputs, but visual input is particularly important for aligning their responses to environmental landmarks. To investigate how population-level heading responses are aligned to visual input, we recorded from retrosplenial cortex (RSC) of head-fixed mice in a moving environment using two-photon calcium imaging. We show that RSC neurons are tuned to the animal's relative orientation in the environment, even in the absence of head movement. Next, we found that RSC receives functionally distinct projections from visual and thalamic areas and contains several functional classes of neurons. While some functional classes mirror RSC inputs, a newly discovered class coregisters visual and thalamic signals. Finally, decoding analyses reveal unique contributions to heading from each class. Our results suggest an RSC circuit for anchoring heading representations to environmental visual landmarks.

Symmetries and asymmetries in the neural encoding of 3D space

The neural coding of space centres on three foundational cell types: place cells, head direction cells and grid cells. One notable characteristic of these neurons is the symmetry properties of their spatial firing patterns. In symmetric environments, firing patterns are often also symmetric: for example, place cells show translational symmetry in aligned sub-compartments of a multi-compartment environment. A single head direction cell has a mirror-symmetric firing pattern, while a sub-class of head direction cells can show multi-fold rotational symmetries in multi-compartment environments, matching the symmetry of the recently experienced environment. The entorhinal grid cells are notable for the symmetry of their firing patterns in both rotational and translational domains. However, these symmetries are broken in a variety of situations. These symmetry-making and -breaking observations shed light on the underlying computations that generate these firing patterns, and also invite speculation as to whether they may have a functional role. This article outlines these findings and speculates on the consequences of the resultant firing symmetries and asymmetries for spatial coding and cognition. This article is part of a discussion meeting issue 'New approaches to 3D vision'.

Environment Symmetry Drives a Multidirectional Code in Rat Retrosplenial Cortex

We investigated how environment symmetry shapes the neural processing of direction by recording directionally tuned retrosplenial neurons in male Lister hooded rats exploring multicompartment environments that had different levels of global rotational symmetry. Our hypothesis built on prior observations of twofold symmetry in the directional tuning curves of rats in a globally twofold-symmetric environment. To test whether environment symmetry was the relevant factor shaping the directional responses, here we deployed the same apparatus (two connected rectangular boxes) plus one with fourfold symmetry (a 2 × 2 array of connected square boxes) and one with onefold symmetry (a circular open-field arena). Consistent with our hypothesis we found many neurons with tuning curve symmetries that mirrored these environment symmetries, having twofold, fourfold, or onefold symmetric tuning, respectively. Some cells expressed this pattern only globally (across the whole environment), maintaining singular tuning curves in each subcompartment. However, others also expressed it locally within each subcompartment. Because multidirectionality has not been reported in naive rats in single environmental compartments, this suggests an experience-dependent effect of global environment symmetry on local firing symmetry. An intermingled population of directional neurons were classic head direction cells with globally referenced directional tuning. These cells were electrophysiologically distinct, with narrower tuning curves and a burstier firing pattern. Thus, retrosplenial directional neurons can simultaneously encode overall head direction and local head direction (relative to compartment layout). Furthermore, they can learn about global environment symmetry and express this locally. This may be important for the encoding of environment structure beyond immediate perceptual reach.SIGNIFICANCE STATEMENT We investigated how environment symmetry shapes the neural code for space by recording directionally tuned neurons from the retrosplenial cortex of rats exploring single- or multicompartment environments having onefold, twofold, or fourfold rotational symmetry. We found that many cells expressed a symmetry in their head direction tuning curves that matched the corresponding global environment symmetry, indicating plasticity of their directional tuning. They were also electrophysiologically distinct from canonical head directional cells. Notably, following exploration of the global space, many multidirectionally tuned neurons encoded global environment symmetry, even in local subcompartments. Our results suggest that multidirectional head direction codes contribute to the cognitive mapping of the complex structure of multicompartmented spaces.

Neural basis of topographical disorientation in the primate posterior cingulate gyrus based on a labeled graph

Patients with lesions in the posterior cingulate gyrus (PCG), including the retrosplenial cortex (RSC) and posterior cingulate cortex (PCC), cannot navigate in familiar environments, nor draw routes on a 2D map of the familiar environments. This suggests that the topographical knowledge of the environments (i.e., cognitive map) to find the right route to a goal is represented in the PCG, and the patients lack such knowledge. However, theoretical backgrounds in neuronal levels for these symptoms in primates are unclear. Recent behavioral studies suggest that human spatial knowledge is constructed based on a labeled graph that consists of topological connections (edges) between places (nodes), where local metric information, such as distances between nodes (edge weights) and angles between edges (node labels), are incorporated. We hypothesize that the population neural activity in the PCG may represent such knowledge based on a labeled graph to encode routes in both 3D environments and 2D maps. Since no previous data are available to test the hypothesis, we recorded PCG neuronal activity from a monkey during performance of virtual navigation and map drawing-like tasks. The results indicated that most PCG neurons responded differentially to spatial parameters of the environments, including the place, head direction, and reward delivery at specific reward areas. The labeled graph-based analyses of the data suggest that the population activity of the PCG neurons represents the distance traveled, locations, movement direction, and navigation routes in the 3D and 2D virtual environments. These results support the hypothesis and provide a neuronal basis for the labeled graph-based representation of a familiar environment, consistent with PCG functions inferred from the human clinicopathological studies.

A Spiking Neural Network Model of Rodent Head Direction Calibrated With Landmark Free Learning

Maintaining a stable estimate of head direction requires both self-motion (idiothetic) information and environmental (allothetic) anchoring. In unfamiliar or dark environments idiothetic drive can maintain a rough estimate of heading but is subject to inaccuracy, visual information is required to stabilize the head direction estimate. When learning to associate visual scenes with head angle, animals do not have access to the 'ground truth' of their head direction, and must use egocentrically derived imprecise head direction estimates. We use both discriminative and generative methods of visual processing to learn these associations without extracting explicit landmarks from a natural visual scene, finding all are sufficiently capable at providing a corrective signal. Further, we present a spiking continuous attractor model of head direction (SNN), which when driven by idiothetic input is subject to drift. We show that head direction predictions made by the chosen model-free visual learning algorithms can correct for drift, even when trained on a small training set of estimated head angles self-generated by the SNN. We validate this model against experimental work by reproducing cue rotation experiments which demonstrate visual control of the head direction signal.

Spatial context and the functional role of the postrhinal cortex

The postrhinal cortex (POR) serves as a key input area to the hippocampal system. It receives highly processed information from the ventral visual stream and other limbic areas including the retrosplenial cortex, parahippocampal areas, and portions of the limbic thalamus. The POR was studied early on by David Bucci and colleagues who first postulated that the POR plays a major role in contextual learning. Here we review a number of approaches and experimental studies that have explored POR's role in contextual processing. We discuss POR lesion studies that monitored deficits in fear conditioning tasks and the effects that these lesions had on processing visual landmark information. We then review the types of spatial correlates encoded by POR cells. A large number of head direction (HD) cells are present, although recent findings suggest that many of them are more accurately characterized as landmark modulated-HD cells as opposed to classic HD cells. A significant number of POR cells are also tuned to egocentric properties of the environment, such as the spatial relationship of the animal to the center of its environment, or the distance between the animal and either the environment's center or its boundaries. We suggest potential frameworks through which these functional cell types might support contextual processing. We then discuss deficits seen in humans who have damage to the homologous parahippocampal cortex, and we finish by reviewing functional imaging studies that found activation of this area while human subjects performed various tasks. A preponderance of evidence suggests that the POR, along with its interactions with retrosplenial cortex, plays a key role in contextual information processing.

Landmark-modulated directional coding in postrhinal cortex

Visual landmarks can anchor an animal's internal sense of orientation to the external world. The rodent postrhinal cortex (POR) may facilitate this processing. Here, we demonstrate that, in contrast to classic head direction (HD) cells, which have a single preferred orientation, POR HD cells develop a second preferred orientation when an established landmark cue is duplicated along another environmental wall. We therefore refer to these cells as landmark-modulated-HD (LM-HD) cells. LM-HD cells discriminate between landmarks in familiar and novel locations, discriminate between visually disparate landmarks, and continue to respond to the previous location of a familiar landmark following its removal. Rats initially exposed to different stable landmark configurations show LM-HD tuning that may reflect the integration of visual landmark information into an allocentric HD signal. These results provide insight into how visual landmarks are integrated into a framework that supports the neural encoding of landmark-based orientation.