A dual-axis rotation rule for updating the head direction cell reference frame during movement in three dimensions

The mosaic structure of the mammalian cognitive map

The cognitive map, proposed by Tolman in the 1940s, is a hypothetical internal representation of space constructed by the brain to enable an animal to undertake flexible spatial behaviors such as navigation. The subsequent discovery of place cells in the hippocampus of rats suggested that such a map-like representation does exist, and also provided a tool with which to explore its properties. Single-neuron studies in rodents conducted in small singular spaces have suggested that the map is founded on a metric framework, preserving distances and directions in an abstract representational format. An open question is whether this metric structure pertains over extended, often complexly structured real-world space. The data reviewed here suggest that this is not the case. The emerging picture is that instead of being a single, unified construct, the map is a mosaic of fragments that are heterogeneous, variably metric, multiply scaled, and sometimes laid on top of each other. Important organizing factors within and between fragments include boundaries, context, compass direction, and gravity. The map functions not to provide a comprehensive and precise rendering of the environment but rather to support adaptive behavior, tailored to the species and situation.

Adaptive cognitive maps for curved surfaces in the 3D world

Terrains in a 3D world can be undulating. Yet, most prior research has exclusively investigated spatial representations on a flat surface, leaving a 2D cognitive map as the dominant model in the field. Here, we investigated whether humans represent a curved surface by building a dimension-reduced flattened 2D map or a full 3D map. Participants learned the location of objects positioned on a flat and curved surface in a virtual environment by driving on the concave side of the surface (Experiment 1), driving and looking vertically (Experiment 2), or flying (Experiment 3). Subsequently, they were asked to retrieve either the path distance or the 3D Euclidean distance between the objects. Path distance estimation was good overall, but we found a significant underestimation bias for the path distance on the curve, suggesting an influence of potential 3D shortcuts, even though participants were only driving on the surface. Euclidean distance estimation was better when participants were exposed more to the global 3D structure of the environment by looking and flying. These results suggest that the representation of the 2D manifold, embedded in a 3D world, is neither purely 2D nor 3D. Rather, it is flexible and dependent on the behavioral experience and demand.

Thalamocortical interactions in cognition and disease: the mediodorsal and anterior thalamic nuclei

The mediodorsal thalamus (MD) and anterior thalamic nuclei (ATN) are two adjacent brain nodes that support our ability to make decisions, learn, update information, form and retrieve memories, and find our way around. The MD and PFC work in partnerships to support cognitive processes linked to successful learning and decision-making, while the ATN and extended hippocampal system together coordinate the encoding and retrieval of memories and successful spatial navigation. Yet, while these distinctions may appear to be segregated, both the MD and ATN together support our higher cognitive functions as they regulate and are influenced by interconnected fronto-temporal neural networks and subcortical inputs. Our review focuses on recent studies in animal models and in humans. This evidence is re-shaping our understanding of the importance of MD and ATN cortico-thalamocortical pathways in influencing complex cognitive functions. Given the evidence from clinical settings and neuroscience research labs, the MD and ATN should be considered targets for effective treatments in neuropsychiatric diseases and disorders and neurodegeneration.

Modeling the grid cell activity on non-horizontal surfaces based on oscillatory interference modulated by gravity

Internal representation of the space is a fundamental and crucial function of the animal's brain. Grid cells in the medial entorhinal cortex are thought to provide an environment-invariant metric system for the navigation of the animal. Most experimental and theoretical studies have focused on the horizontal planar codes of grid cell, while how this metric coordinate system is configured in the actual three-dimensional space remains unclear. Evidence has implied the spatial cognition may not be fully volumetric. We proposed an oscillatory interference model with a novel gravity and body plane modulation to simulate grid cell activity in complex space for rodents. The animal can perceive the rotation of its body plane along the local surface by sensing the gravity, causing the modulation to the dendritic oscillations. The results not only reproduce the firing patterns of the grid cell recorded from known experiments, but also predict the grid codes in novel environments. It further demonstrates that the gravity signal is indispensable for the animal's navigation, and supports the hypothesis that the periodic firing of the grid cell is intrinsically not a volumetric code in three-dimensional space. This will provide new insights to understand the spatial representation of the actual world in the brain.

Irregular distribution of grid cell firing fields in rats exploring a 3D volumetric space

We investigated how entorhinal grid cells encode volumetric space. On a horizontal surface, grid cells usually produce multiple, spatially focal, approximately circular firing fields that are evenly sized and spaced to form a regular, close-packed, hexagonal array. This spatial regularity has been suggested to underlie navigational computations. In three dimensions, theoretically the equivalent firing pattern would be a regular, hexagonal close packing of evenly sized spherical fields. In the present study, we report that, in rats foraging in a cubic lattice, grid cells maintained normal temporal firing characteristics and produced spatially stable firing fields. However, although most grid fields were ellipsoid, they were sparser, larger, more variably sized and irregularly arranged, even when only fields abutting the lower surface (equivalent to the floor) were considered. Thus, grid self-organization is shaped by the environment's structure and/or movement affordances, and grids may not need to be regular to support spatial computations.

Volumetric spatial behaviour in rats reveals the anisotropic organisation of navigation

We investigated how access to the vertical dimension influences the natural exploratory and foraging behaviour of rats. Using high-accuracy three-dimensional tracking of position in two- and three-dimensional environments, we sought to determine (i) how rats navigated through the environments with respect to gravity, (ii) where rats chose to form their home bases in volumetric space, and (iii) how they navigated to and from these home bases. To evaluate how horizontal biases may affect these behaviours, we compared a 3D maze where animals preferred to move horizontally to a different 3D configuration where all axes were equally energetically costly to traverse. Additionally, we compared home base formation in two-dimensional arenas with and without walls to the three-dimensional climbing mazes. We report that many behaviours exhibited by rats in horizontal spaces naturally extend to fully volumetric ones, such as home base formation and foraging excursions. We also provide further evidence for the strong differentiation of the horizontal and vertical axes: rats showed a horizontal movement bias, they formed home bases mainly in the bottom layers of both mazes and they generally solved the vertical component of return trajectories before and faster than the horizontal component. We explain the bias towards horizontal movements in terms of energy conservation, while the locations of home bases are explained from an information gathering view as a method for correcting self-localisation.

On the absence or presence of 3D tuned head direction cells in rats: a review and rebuttal

A major question in the field of spatial cognition is how animals represent three-dimensional (3D) space. Different results have been obtained across various species and may depend on whether the species inhabits a 3D environment or is terrestrial (land dwelling). The head direction (HD) cell system is an attractive candidate to study in terms of 3D representations. HD cells fire as a function of the animal's directional heading in the horizontal plane, independent of the animal's location and on-going behavior. Another issue concerns whether HD cells are tuned in 3D space or tuned to the 2D horizontal plane. Shinder and Taube (Shinder ME, Taube JS. J Neurophysiol 121: 4-37, 2019) addressed this issue by manipulating a rat's orientation in 3D space while monitoring responses from classic HD cells in the rat anterodorsal thalamus. They reported that HD cells did not display conjunctive firing with pitch or roll orientations. Direction-specific firing was primarily derived from horizontal semicircular canal information and that the gravity vector played an important role in influencing the cell's firing rate and its preferred firing direction. Laurens and Angelaki (Laurens J, Angelaki DE. J Neurophysiol 122: 1274-1287, 2019) challenged this view by performing a mathematical analysis on the Shinder and Taube data and concluded that they would not have seen 3D tuning based on their experimental approach. We provide a historical review of these issues followed by a summary of the experiments, which includes additional analyses. We then define what it means for a HD cell to be tuned in 3D and finish by rebutting the reanalyses performed by Laurens and Angelaki.

A gravity-based three-dimensional compass in the mouse brain

Gravity sensing provides a robust verticality signal for three-dimensional navigation. Head direction cells in the mammalian limbic system implement an allocentric neuronal compass. Here we show that head-direction cells in the rodent thalamus, retrosplenial cortex and cingulum fiber bundle are tuned to conjunctive combinations of azimuth and tilt, i.e. pitch or roll. Pitch and roll orientation tuning is anchored to gravity and independent of visual landmarks. When the head tilts, azimuth tuning is affixed to the head-horizontal plane, but also uses gravity to remain anchored to the allocentric bearings in the earth-horizontal plane. Collectively, these results demonstrate that a three-dimensional, gravity-based, neural compass is likely a ubiquitous property of mammalian species, including ground-dwelling animals.

Head direction neurons constitute the brain’s compass, and are classically known to indicate head orientation in the horizontal plane. Here, the authors show that head direction neurons form a three-dimensional compass that can also indicate head tilt, and anchors to gravity.

Commutative Properties of Head Direction Cells during Locomotion in 3D: Are All Routes Equal?

Navigation often requires movement in three-dimensional (3D) space. Recent studies have postulated two different models for how head direction (HD) cells encode 3D space: the rotational plane hypothesis and the dual-axis model. To distinguish these models, we recorded HD cells in female rats while they traveled different routes along both horizontal and vertical surfaces from an elevated platform to the top of a cuboidal apparatus. We compared HD cell preferred firing directions (PFDs) in different planes and addressed the issue of whether HD cell firing is commutative-does the order of the animal's route affect the final outcome of the cell's PFD? Rats locomoted a direct or indirect route from the floor to the cube top via one, two, or three vertical walls. Whereas the rotational plane hypothesis accounted for PFD shifts when the animal traversed horizontal corners, the cell's PFD was better explained by the dual-axis model when the animal traversed vertical corners. Responses also followed the dual-axis model (1) under dark conditions, (2) for passive movement of the rat, (3) following apparatus rotation, (4) for movement around inside vertical corners, and (5) across a 45° outside vertical corner. The order in which the animal traversed the different planes did not affect the outcome of the cell's PFD, indicating that responses were commutative. HD cell peak firing rates were generally equivalent along each surface. These findings indicate that the animal's orientation with respect to gravity plays an important role in determining a cell's PFD, and that vestibular and proprioceptive cues drive these computations.SIGNIFICANCE STATEMENT Navigating in a three-dimensional (3D) world is a complex task that requires one to maintain a proper sense of orientation relative to both local and global cues. Rodent head direction (HD) cells have been suggested to subserve this sense of orientation, but most HD cell studies have focused on navigation in 2D environments. We investigated the responses of HD cells as rats moved between multiple vertically and horizontally oriented planar surfaces, demonstrating that HD cells align their directional representations to both local (current plane of locomotion) and global (gravity) cues across several experimental conditions, including darkness and passive movement. These findings offer critical insights into the processing of 3D space in the mammalian brain.

The place-cell representation of volumetric space in rats

Place cells are spatially modulated neurons found in the hippocampus that underlie spatial memory and navigation: how these neurons represent 3D space is crucial for a full understanding of spatial cognition. We wirelessly recorded place cells in rats as they explored a cubic lattice climbing frame which could be aligned or tilted with respect to gravity. Place cells represented the entire volume of the mazes: their activity tended to be aligned with the maze axes, and when it was more difficult for the animals to move vertically the cells represented space less accurately and less stably. These results demonstrate that even surface-dwelling animals represent 3D space and suggests there is a fundamental relationship between environment structure, gravity, movement and spatial memory.

The head direction cell network: attractor dynamics, integration within the navigation system, and three-dimensional properties

Knowledge of head direction cell function has progressed remarkably in recent years. The predominant theory that they form an attractor has been confirmed by several experiments. Candidate pathways that may convey visual input have been identified. The pre-subicular circuitry that conveys head direction signals to the medial entorhinal cortex, potentially sustaining path integration by grid cells, has been resolved. Although the neuronal substrate of the attractor remains unknown in mammals, a simple head direction network, whose structure is astoundingly similar to neuronal models theorized decades earlier, has been identified in insects. Finally, recent experiments have revealed that these cells do not encode head direction in the horizontal plane only, but also in vertical planes, thus providing a 3D orientation signal.

Mechanisms Underlying the Neural Computation of Head Direction

Many animals use an internal sense of direction to guide their movements through the world. Neurons selective to head direction are thought to support this directional sense and have been found in a diverse range of species, from insects to primates, highlighting their evolutionary importance. Across species, most head-direction networks share four key properties: a unique representation of direction at all times, persistent activity in the absence of movement, integration of angular velocity to update the representation, and the use of directional cues to correct drift. The dynamics of theorized network structures called ring attractors elegantly account for these properties, but their relationship to brain circuits is unclear. Here, we review experiments in rodents and flies that offer insights into potential neural implementations of ring attractor networks. We suggest that a theory-guided search across model systems for biological mechanisms that enable such dynamics would uncover general principles underlying head-direction circuit function.

NeuroSLAM: a brain-inspired SLAM system for 3D environments

Roboticists have long drawn inspiration from nature to develop navigation and simultaneous localization and mapping (SLAM) systems such as RatSLAM. Animals such as birds and bats possess superlative navigation capabilities, robustly navigating over large, three-dimensional environments, leveraging an internal neural representation of space combined with external sensory cues and self-motion cues. This paper presents a novel neuro-inspired 4DoF (degrees of freedom) SLAM system named NeuroSLAM, based upon computational models of 3D grid cells and multilayered head direction cells, integrated with a vision system that provides external visual cues and self-motion cues. NeuroSLAM's neural network activity drives the creation of a multilayered graphical experience map in a real time, enabling relocalization and loop closure through sequences of familiar local visual cues. A multilayered experience map relaxation algorithm is used to correct cumulative errors in path integration after loop closure. Using both synthetic and real-world datasets comprising complex, multilayered indoor and outdoor environments, we demonstrate NeuroSLAM consistently producing topologically correct three-dimensional maps.

"It's all in their head": hierarchical exploration of a three-dimensional layered pyramid in rats

Wayfinding in a three-dimensional (3D) environment is intricate, and surface-bounded animals may overcome this complexity by breaking it down into horizontal layers along with the vertical location of each layer. Here, we examined how rats explored a layered pyramid placed in a large open field. We found that exploration presented a hierarchical (or fractal) shape of three types of roundtrips: (1) from the primary home-base to the open-field floor; (2) from the floor up and down the pyramid levels; and (3) from local home-base on each pyramid level. Ascent was slow and interrupted, whereas descent was fast. This difference was a result of level altitude, remaining after data were normalized proportionally to level area. In contrast, the time spent and the distance traveled on each level were dependent on level area, not on level altitude. This structure of spatial behavior accords with multilevel exploration, presenting a relatively independent exploration of each level. The vertical dimension in this experiment thus did not alter the typical spatiotemporal behavior, and the 3D environment was explored by application of the same spatiotemporal approach as that of a horizontal open field. We suggest that this lack of alteration is due to the horizontal posture of the animal's head and trunk during progression on the pyramid. This behavior also seems to fit the bicoding hypothesis, in which the vertical information is virtually contextual (non-metric), and so, when the rat progresses to a new level, it explores it as a newly accessed horizontal floor area.

A model-based reassessment of the three-dimensional tuning of head direction cells in rats

In a recent study, Shinder and Taube (Shinder ME, Taube JS. J Neurophysiol 121: 4-37, 2019) concluded that head direction cells in the anterior thalamus of rats are tuned to one-dimensional (1D, yaw-only) motion, in contrast to recent findings in bats, mice, and rats. Here we reinterpret the author's experimental results using model comparison and demonstrate that, contrary to their conclusions, experimental data actually supports the dual-axis rule (lson JJ, Jeffery KJ. JNeurophysiol 119: 192-208, 2018) and tilted azimuth model (Laurens J, Angelaki DE. Neuron 97: 275-289, 2018), where head direction cells use gravity to integrate 3D rotation signals about all cardinal axes of the head. We further show that the Shinder and Taube study is inconclusive regarding the presence of vertical orientation tuning; i.e., whether head direction cells encode 3D orientation in the horizontal and vertical planes conjunctively. Using model simulations, we demonstrate that, even if 3D tuning existed, the experimental protocol and data analyses used by Shinder and Taube would not have revealed it. We conclude that the actual experimental data of Shinder and Taube are compatible with the 3D properties of head direction cells discovered by other groups, yet incorrect conclusions were reached because of incomplete and qualitative analyses.NEW & NOTEWORTHY We conducted a model-based analysis previously published data where rat head direction cells were recorded during three-dimensional motion (Shinder ME, Taube JS. J Neurophysiol 121: 4-37, 2019). We found that these data corroborate previous models ("dual-axis rule," Page HJI, Wilson JJ, Jeffery KJ. J Neurophysiol 119: 192-208, 2018; and "tilted azimuth model," Laurens J, Angelaki DE. Neuron 97: 275-289, 2018) where head direction cells integrate rotations along all three head axes to encode head orientation in a gravity-anchored reference frame.

Space and Memory (Far) Beyond the Hippocampus: Many Subcortical Structures Also Support Cognitive Mapping and Mnemonic Processing

Memory research remains focused on just a few brain structures-in particular, the hippocampal formation (the hippocampus and entorhinal cortex). Three key discoveries promote this continued focus: the striking demonstrations of enduring anterograde amnesia after bilateral hippocampal damage; the realization that synapses in the hippocampal formation are plastic e.g., when responding to short bursts of patterned stimulation ("long-term potentiation" or LTP); and the discovery of a panoply of spatially-tuned cells, principally surveyed in the hippocampal formation (place cells coding for position; head-direction cells, providing compass-like information; and grid cells, providing a metric for 3D space). Recent anatomical, behavioral, and electrophysiological work extends this picture to a growing network of subcortical brain structures, including the anterior thalamic nuclei, rostral midline thalamic nuclei, and the claustrum. There are, for example, spatially-tuned cells in all of these regions, including cells with properties similar to place cells of the hippocampus proper. These findings add new perspectives to what had been originally been proposed-but often overlooked-half a century ago: that damage to an extended network of structures connected to the hippocampal formation results in diencephalic amnesia. We suggest these new findings extend spatial signaling in the brain far beyond the hippocampal formation, with profound implications for theories of the neural bases of spatial and mnemonic functions.

The Brain Compass: A Perspective on How Self-Motion Updates the Head Direction Cell Attractor

Head direction cells form an internal compass signaling head azimuth orientation even without visual landmarks. This property is generated by a neuronal ring attractor that is updated using rotation velocity cues. The properties and origin of this velocity drive remain, however, unknown. We propose a quantitative framework whereby this drive represents a multisensory self-motion estimate computed through an internal model that uses sensory prediction errors of vestibular, visual, and somatosensory cues to improve on-line motor drive. We show how restraint-dependent strength of recurrent connections within the attractor can explain differences in head direction cell firing between free foraging and restrained passive rotation. We also summarize recent findings on how gravity influences azimuth coding, indicating that the velocity drive is not purely egocentric. Finally, we show that the internal compass may be three-dimensional and hypothesize that the additional vertical degrees of freedom use global allocentric gravity cues.

Encoding of 3D head direction information in the human brain

Head direction cells are critical for navigation because they convey information about which direction an animal is facing within an environment. To date, most studies on head direction encoding have been conducted on a horizontal two-dimensional (2D) plane, and little is known about how three-dimensional (3D) direction information is encoded in the brain despite humans and other animals living in a 3D world. Here, we investigated head direction encoding in the human brain while participants moved within a virtual 3D "spaceship" environment. Movement was not constrained to planes and instead participants could move along all three axes in volumetric space as if in zero gravity. Using functional magnetic resonance imaging (fMRI) multivoxel pattern similarity analysis, we found evidence that the thalamus, particularly the anterior portion, and the subiculum encoded the horizontal component of 3D head direction (azimuth). In contrast, the retrosplenial cortex was significantly more sensitive to the vertical direction (pitch) than to the azimuth. Our results also indicated that vertical direction information in the retrosplenial cortex was significantly correlated with behavioral performance during a direction judgment task. Our findings represent the first evidence showing that the "classic" head direction system that has been identified on a horizontal 2D plane also seems to encode vertical and horizontal heading in 3D space in the human brain.

Three-dimensional tuning of head direction cells in rats

Head direction (HD) cells fire when the animal faces that cell's preferred firing direction (PFD) in the horizontal plane. The PFD response when the animal is oriented outside the earth-horizontal plane could result from cells representing direction in the plane of locomotion or as a three-dimensional (3D), global-referenced direction anchored to gravity. To investigate these possibilities, anterodorsal thalamic HD cells were recorded from restrained rats while they were passively positioned in various 3D orientations. Cell responses were unaffected by pitch or roll up to ~90° from the horizontal plane. Firing was disrupted once the animal was oriented >90° away from the horizontal plane and during inversion. When rolling the animal around the earth-vertical axis, cells were active when the animal's ventral surface faced the cell's PFD. However, with the rat rolled 90° in an ear-down orientation, pitching the rat and rotating it around the vertical axis did not produce directionally tuned responses. Complex movements involving combinations of yaw-roll, but usually not yaw-pitch, resulted in reduced directional tuning even at the final upright orientation when the rat had full visual view of its environment and was pointing in the cell's PFD. Directional firing was restored when the rat's head was moved back-and-forth. There was limited evidence indicating that cells contained conjunctive firing with pitch or roll positions. These findings suggest that the brain's representation of directional heading is derived primarily from horizontal canal information and that the HD signal is a 3D gravity-referenced signal anchored to a direction in the horizontal plane. NEW & NOTEWORTHY This study monitored head direction cell responses from rats in three dimensions using a series of manipulations that involved yaw, pitch, roll, or a combination of these rotations. Results showed that head direction responses are consistent with the use of two reference frames simultaneously: one defined by the surrounding environment using primarily visual landmarks and a second defined by the earth's gravity vector.

A hierarchical anti-Hebbian network model for the formation of spatial cells in three-dimensional space

Three-dimensional (3D) spatial cells in the mammalian hippocampal formation are believed to support the existence of 3D cognitive maps. Modeling studies are crucial to comprehend the neural principles governing the formation of these maps, yet to date very few have addressed this topic in 3D space. Here we present a hierarchical network model for the formation of 3D spatial cells using anti-Hebbian network. Built on empirical data, the model accounts for the natural emergence of 3D place, border, and grid cells, as well as a new type of previously undescribed spatial cell type which we call plane cells. It further explains the plausible reason behind the place and grid-cell anisotropic coding that has been observed in rodents and the potential discrepancy with the predicted periodic coding during 3D volumetric navigation. Lastly, it provides evidence for the importance of unsupervised learning rules in guiding the formation of higher-dimensional cognitive maps.

Neurons in the hippocampal formation encode diverse spatial properties. Here, the authors present a hierarchical network model for 3D spatial navigation that accounts for the observed neuronal representations and predict as yet unreported cell types with planar selectivity.

Three-Dimensional Representation of Motor Space in the Mouse Superior Colliculus

From the act of exploring an environment to that of grasping a cup of tea, animals must put in register their motor acts with their surrounding space. In the motor domain, this is likely to be defined by a register of three-dimensional (3D) displacement vectors, whose recruitment allows motion in the direction of a target. One such spatially targeted action is seen in the head reorientation behavior of mice, yet the neural mechanisms underlying these 3D behaviors remain unknown. Here, by developing a head-mounted inertial sensor for studying 3D head rotations and combining it with electrophysiological recordings, we show that neurons in the mouse superior colliculus are either individually or conjunctively tuned to the three Eulerian components of head rotation. The average displacement vectors associated with motor-tuned colliculus neurons remain stable over time and are unaffected by changes in firing rate or the duration of spike trains. Finally, we show that the motor tuning of collicular neurons is largely independent from visual or landmark cues. By describing the 3D nature of motor tuning in the superior colliculus, we contribute to long-standing debate on the dimensionality of collicular motor decoding; furthermore, by providing an experimental paradigm for the study of the metric of motor tuning in mice, this study also paves the way to the genetic dissection of the circuits underlying spatially targeted motion.

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Development of inertial sensor system for monitoring 3D head movements in real time

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Neurons in the superior colliculus code for the full dimensionality of head rotations

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Firing rate correlates with velocity, but not head displacement angle

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The spatial tuning of collicular units is largely independent of visual or landmark cues

A dual-axis rotation rule for updating the head direction cell reference frame during movement in three dimensions

In the mammalian brain, allocentric (Earth-referenced) head direction, called azimuth, is encoded by head direction (HD) cells, which fire according to the facing direction of the animal's head. On a horizontal surface, rotations of the head around the dorsoventral (D-V) axis, called yaw, correspond to changes in azimuth and elicit appropriate updating of the HD "compass" signal to enable large-scale navigation. However, if the animal moves through three-dimensional (3D) space then there is no longer a simple relationship between yaw rotations and azimuth changes, and so processing of 3D rotations is needed. Construction of a global 3D compass would require complex integration of 3D rotations, and also a large neuronal population, most neurons of which would be silent most of the time since animals rarely sample all available 3D orientations. We propose that, instead, the HD system treats the 3D space as a set of interrelated 2D surfaces. It could do this by updating activity according to both yaw rotations around the D-V axis and rotations of the D-V axis around the gravity-defined vertical axis. We present preliminary data to suggest that this rule operates when rats move between walls of opposing orientations. This dual-axis rule, which we show is straightforward to implement using the classic one-dimensional "attractor" architecture, allows consistent representation of azimuth even in volumetric space and thus may be a general feature of mammalian directional computations even for animals that swim or fly. NEW & NOTEWORTHY Maintaining a sense of direction is complicated when moving in three-dimensional (3D) space. Head direction cells, which update the direction sense based on head rotations, may accommodate 3D movement by processing both rotations of the head around the axis of the animal's body and rotations of the head/body around gravity. With modeling we show that this dual-axis rule works in principle, and we present preliminary data to support its operation in rats.

Gravity orientation tuning in macaque anterior thalamus

Gravity may provide a ubiquitous allocentric reference to the brain's spatial orientation circuits. Here we describe neurons in the macaque anterior thalamus tuned to pitch and roll orientation relative to gravity, independently of visual landmarks. We show that individual cells exhibit two-dimensional tuning curves, with peak firing rates at a preferred vertical orientation. These results identify a thalamic pathway for gravity cues to influence perception, action and spatial cognition.