Head Direction System Research Articles

Maintaining and updating accurate internal representations of continuous variables with a handful of neurons.

Many animals rely on persistent internal representations of continuous variables for working memory, navigation, and motor control. Existing theories typically assume that large networks of neurons are required to maintain such representations accurately; networks with few neurons are thought to generate discrete representations. However, analysis of two-photon calcium imaging data from tethered flies walking in darkness suggests that their small head-direction system can maintain a surprisingly continuous and accurate representation. We thus ask whether it is possible for a small network to generate a continuous, rather than discrete, representation of such a variable. We show analytically that even very small networks can be tuned to maintain continuous internal representations, but this comes at the cost of sensitivity to noise and variations in tuning. This work expands the computational repertoire of small networks, and raises the possibility that larger networks could represent more and higher-dimensional variables than previously thought.

Transforming a head direction signal into a goal-oriented steering command.

To navigate, we must continuously estimate the direction we are headed in, and we must correct deviations from our goal1. Direction estimation is accomplished by ring attractor networks in the head direction system2,3. However, we do not fully understand how the sense of direction is used to guide action. Drosophila connectome analyses4,5 reveal three cell populations (PFL3R, PFL3L and PFL2) that connect the head direction system to the locomotor system. Here we use imaging, electrophysiology and chemogenetic stimulation during navigation to show how these populations function. Each population receives a shifted copy of the head direction vector, such that their three reference frames are shifted approximately 120° relative to each other. Each cell type then compares its own head direction vector with a common goal vector; specifically, it evaluates the congruence of these vectors via a nonlinear transformation. The output of all three cell populations is then combined to generate locomotor commands. PFL3R cells are recruited when the fly is oriented to the left of its goal, and their activity drives rightward turning; the reverse is true for PFL3L. Meanwhile, PFL2 cells increase steering speed, and are recruited when the fly is oriented far from its goal. PFL2 cells adaptively increase the strength of steering as directional error increases, effectively managing the tradeoff between speed and accuracy. Together, our results show how a map of space in the brain can be combined with an internal goal to generate action commands, via a transformation from world-centric coordinates to body-centric coordinates.

RPM: An open-source Rotation Platform for open- and closed-loop vestibular stimulation in head-fixed Mice

Head fixation allows the recording and presentation of controlled stimuli and is used to study neural processes underlying spatial navigation. However, it disrupts the head direction system because of the lack of vestibular stimulation. To overcome this limitation, we developed a novel rotation platform which can be driven by the experimenter (open-loop) or by animal movement (closed-loop). The platform is modular, affordable, easy to build and open source. Additional modules presented here include cameras for monitoring eye movements, visual virtual reality, and a micro-manipulator for positioning various probes for recording or optical interference. We demonstrate the utility of the platform by recording eye movements and showing the robust activation of head-direction cells. This novel experimental apparatus combines the advantages of head fixation and intact vestibular activity in the horizontal plane. The open-loop mode can be used to study e.g., vestibular sensory representation and processing, while the closed-loop mode allows animals to navigate in rotational space, providing a better substrate for 2-D navigation in virtual environments. The full build documentation is maintained at https://ranczlab.github.io/RPM/.

Angular Head Velocity Cells within Brainstem Nuclei Projecting to the Head Direction Circuit.

The sense of orientation of an animal is derived from the head direction (HD) system found in several limbic structures and depends on an intact vestibular labyrinth. However, how the vestibular system influences the generation and updating of the HD signal remains poorly understood. Anatomical and lesion studies point toward three key brainstem nuclei as key components for generating the HD signal-nucleus prepositus hypoglossi, supragenual nucleus, and dorsal paragigantocellularis reticular nuclei. Collectively, these nuclei are situated between the vestibular nuclei and the dorsal tegmental and lateral mammillary nuclei, which are thought to serve as the origin of the HD signal. To determine the types of information these brain areas convey to the HD network, we recorded neurons from these regions while female rats actively foraged in a cylindrical enclosure or were restrained and rotated passively. During foraging, a large subset of cells in all three nuclei exhibited activity that correlated with the angular head velocity (AHV) of the rat. Two fundamental types of AHV cells were observed; (1) symmetrical AHV cells increased or decreased their firing with increases in AHV regardless of the direction of rotation, and (2) asymmetrical AHV cells responded differentially to clockwise and counterclockwise head rotations. When rats were passively rotated, some AHV cells remained sensitive to AHV, whereas firing was attenuated in other cells. In addition, a large number of AHV cells were modulated by linear head velocity. These results indicate the types of information conveyed from the vestibular nuclei that are responsible for generating the HD signal.SIGNIFICANCE STATEMENT Extracellular recording of brainstem nuclei (nucleus prepositus hypoglossi, supragenual nucleus, and dorsal paragigantocellularis reticular nucleus) that project to the head direction circuit identified different types of AHV cells while rats freely foraged in a cylindrical environment. The firing of many cells was also modulated by linear velocity. When rats were restrained and passively rotated, some cells remained sensitive to AHV, whereas others had attenuated firing. These brainstem nuclei provide critical information about the rotational movement of the head of the rat in the azimuthal plane.

PtNPs/PEDOT:PSS-Modified Microelectrode Arrays for Detection of the Discharge of Head Direction Cells in the Retrosplenial Cortex of Rats under Dissociation between Visual and Vestibular Inputs

The electrophysiological activities of head direction (HD) cells under visual and vestibular input dissociation are important to understanding the formation of the sense of direction in animals. In this paper, we fabricated a PtNPs/PEDOT:PSS-modified MEA to detect changes in the discharge of HD cells under dissociated sensory conditions. The electrode shape was customized for the retrosplenial cortex (RSC) and was conducive to the sequential detection of neurons at different depths in vivo when combined with a microdriver. The recording sites of the electrode were modified with PtNPs/PEDOT:PSS to form a three-dimensional convex structure, leading to closer contact with neurons and improving the detection performance and signal-to-noise ratio of the MEA. We designed a rotating cylindrical arena to separate the visual and vestibular information of the rats and detected the changes in the directional tuning of the HD cells in the RSC. The results showed that after visual and vestibular sensory dissociation, HD cells used visual information to establish newly discharged directions which differed from the original direction. However, with the longer time required to process inconsistent sensory information, the function of the HD system gradually degraded. After recovery, the HD cells reverted to their newly established direction rather than the original direction. The research based on our MEAs revealed how HD cells process dissociated sensory information and contributes to the study of the spatial cognitive navigation mechanism.

Population dynamics of head-direction neurons during drift and reorientation

The head direction (HD) system functions as the brain’s internal compass1,2, classically formalized as a one-dimensional ring attractor network3,4. In contrast to a globally consistent magnetic compass, the HD system does not have a universal reference frame. Instead, it anchors to local cues, maintaining a stable offset when cues rotate5–8 and drifting in the absence of referents5,8–10. However, questions about the mechanisms that underlie anchoring and drift remain unresolved and are best addressed at the population level. For example, the extent to which the one-dimensional description of population activity holds under conditions of reorientation and drift is unclear. Here we performed population recordings of thalamic HD cells using calcium imaging during controlled rotations of a visual landmark. Across experiments, population activity varied along a second dimension, which we refer to as network gain, especially under circumstances of cue conflict and ambiguity. Activity along this dimension predicted realignment and drift dynamics, including the speed of network realignment. In the dark, network gain maintained a ‘memory trace’ of the previously displayed landmark. Further experiments demonstrated that the HD network returned to its baseline orientation after brief, but not longer, exposures to a rotated cue. This experience dependence suggests that memory of previous associations between HD neurons and allocentric cues is maintained and influences the internal HD representation. Building on these results, we show that continuous rotation of a visual landmark induced rotation of the HD representation that persisted in darkness, demonstrating experience-dependent recalibration of the HD system. Finally, we propose a computational model to formalize how the neural compass flexibly adapts to changing environmental cues to maintain a reliable representation of HD. These results challenge classical one-dimensional interpretations of the HD system and provide insights into the interactions between this system and the cues to which it anchors.

Cerebellar control of a unitary head direction sense

The head-direction (HD) system, a key neural circuit for navigation, consists of several anatomical structures containing neurons selective to the animal's head direction. HD cells exhibit ubiquitous temporal coordination across brain regions, independently of the animal's behavioral state or sensory inputs. Such temporal coordination mediates a single, stable, and persistent HD signal, which is essential for intact orientation. However, the mechanistic processes behind the temporal organization of HD cells are unknown. By manipulating the cerebellum, we identify pairs of HD cells recorded from two brain structures (anterodorsal thalamus and retrosplenial cortex) that lose their temporal coordination, specifically during the removal of the external sensory inputs. Further, we identify distinct cerebellar mechanisms that participate in the spatial stability of the HD signal depending on sensory signals. We show that while cerebellar protein phosphatase 2B-dependent mechanisms facilitate the anchoring of the HD signal on the external cues, the cerebellar protein kinase C-dependent mechanisms are required for the stability of the HD signal by self-motion cues. These results indicate that the cerebellum contributes to the preservation of a single and stable sense of direction.

Bayesian inference in ring attractor networks

Working memories are thought to be held in attractor networks in the brain. These attractors should keep track of the uncertainty associated with each memory, so as to weigh it properly against conflicting new evidence. However, conventional attractors do not represent uncertainty. Here, we show how uncertainty could be incorporated into an attractor, specifically a ring attractor that encodes head direction. First, we introduce a rigorous normative framework (the circular Kalman filter) for benchmarking the performance of a ring attractor under conditions of uncertainty. Next, we show that the recurrent connections within a conventional ring attractor can be retuned to match this benchmark. This allows the amplitude of network activity to grow in response to confirmatory evidence, while shrinking in response to poor-quality or strongly conflicting evidence. This "Bayesian ring attractor" performs near-optimal angular path integration and evidence accumulation. Indeed, we show that a Bayesian ring attractor is consistently more accurate than a conventional ring attractor. Moreover, near-optimal performance can be achieved without exact tuning of the network connections. Finally, we use large-scale connectome data to show that the network can achieve near-optimal performance even after we incorporate biological constraints. Our work demonstrates how attractors can implement a dynamic Bayesian inference algorithm in a biologically plausible manner, and it makes testable predictions with direct relevance to the head direction system as well as any neural system that tracks direction, orientation, or periodic rhythms.

Global inhibition in head-direction neural circuits: a systematic comparison between connectome-based spiking neural circuit models

The recent discovery of the head-direction (HD) system in fruit flies has provided unprecedented insights into the neural mechanisms of spatial orientation. Despite the progress, the neural substance of global inhibition, an essential component of the HD circuits, remains controversial. Some studies suggested that the ring neurons provide global inhibition, while others suggested the Δ7 neurons. In the present study, we provide evaluations from the theoretical perspective by performing systematic analyses on the computational models based on the ring-neuron (R models) and Δ7-neurons (Delta models) hypotheses with modifications according to the latest connectomic data. We conducted four tests: robustness, persistency, speed, and dynamical characteristics. We discovered that the two models led to a comparable performance in general, but each excelled in different tests. The R Models were more robust, while the Delta models were better in the persistency test. We also tested a hybrid model that combines both inhibitory mechanisms. While the performances of the R and Delta models in each test are highly parameter-dependent, the Hybrid model performed well in all tests with the same set of parameters. Our results suggest the possibility of combined inhibitory mechanisms in the HD circuits of fruit flies.

The Neural Correlates of Spatial Disorientation in Head Direction Cells.

While the brain has evolved robust mechanisms to counter spatial disorientation, their neural underpinnings remain unknown. To explore these underpinnings, we monitored the activity of anterodorsal thalamic head direction (HD) cells in rats while they underwent unidirectional or bidirectional rotation at different speeds and under different conditions (light vs dark, freely-moving vs head-fixed). Under conditions that promoted disorientation, HD cells did not become quiescent but continued to fire, although their firing was no longer direction specific. Peak firing rates, burst frequency, and directionality all decreased linearly with rotation speed, consistent with previous experiments where rats were inverted or climbed walls/ceilings in zero gravity. However, access to visual landmarks spared the stability of preferred firing directions (PFDs), indicating that visual landmarks provide a stabilizing signal to the HD system while vestibular input likely maintains direction-specific firing. In addition, we found evidence that the HD system underestimated angular velocity at the beginning of head-fixed rotations, consistent with the finding that humans often underestimate rotations. When head-fixed rotations in the dark were terminated HD cells fired in bursts that matched the frequency of rotation. This postrotational bursting shared several striking similarities with postrotational "nystagmus" in the vestibulo-ocular system, consistent with the interpretation that the HD system receives input from a vestibular velocity storage mechanism that works to reduce spatial disorientation following rotation. Thus, the brain overcomes spatial disorientation through multisensory integration of different motor-sensory inputs.

Attractor-like Dynamics in the Subicular Complex.

Distinct computations are performed at multiple brain regions during the encoding of spatial environments. Neural representations in the hippocampal, entorhinal, and head direction (HD) networks during spatial navigation have been clearly documented, while the representational properties of the subicular complex (SC) are relatively underexplored, although it has extensive anatomic connections with various brain regions involved in spatial information processing. We simultaneously recorded single units from different subregions of the SC in male rats while they ran clockwise on a centrally placed textured circular track (four different textures, each covering a quadrant), surrounded by six distal cues. The neural activity was monitored in standard sessions by maintaining the same configuration between the cues, while in cue manipulation sessions, the distal and local cues were either rotated in opposite directions to create a mismatch between them or the distal cues were removed. We report a highly coherent neural representation of the environment and a robust coupling between the HD cells and the spatial cells in the SC, strikingly different from previous reports of coupling between cells from co-recorded sites. Neural representations were (1) originally governed by the distal cues under local-distal cue-conflict conditions, (2) controlled by the local cues in the absence of distal cues, and (3) governed by the cues that are perceived to be stable. We propose that such attractor-like dynamics in the SC might play a critical role in the orientation of spatial representations, thus providing a "reference map" of the environment for further processing by other networks.SIGNIFICANCE STATEMENT The subicular complex (SC) receives major inputs from the entorhinal cortex and the hippocampus, and head direction (HD) information directly from the HD system. Using cue-conflict experiments, we studied the hierarchical representation of the local and distal cues in the SC to understand its role in the cognitive map, and report a highly coherent neural representation with robust coupling between the HD cells and the spatial cells in different subregions of the SC exhibiting attractor-like dynamics unaffected by the cue manipulations, strikingly different from previous reports of coupling between cells from co-recorded sites. This unique feature may allow the SC to function as a single computational unit during the representation of space, which may serve as a reference map of the environment.

A cognitive process occurring during sleep is revealed by rapid eye movements.

Since the discovery of rapid eye movement (REM) sleep, the nature of the eye movements that characterize this sleep phase has remained elusive. Do they reveal gaze shifts in the virtual environment of dreams or simply reflect random brainstem activity? We harnessed the head direction (HD) system of the mouse thalamus, a neuronal population whose activity reports, in awake mice, their actual HD as they explore their environment and, in sleeping mice, their virtual HD. We discovered that the direction and amplitude of rapid eye movements during REM sleep reveal the direction and amplitude of the ongoing changes in virtual HD. Thus, rapid eye movements disclose gaze shifts in the virtual world of REM sleep, thereby providing a window into the cognitive processes of the sleeping brain.

Learning accurate path integration in ring attractor models of the head direction system.

Ring attractor models for angular path integration have received strong experimental support. To function as integrators, head direction circuits require precisely tuned connectivity, but it is currently unknown how such tuning could be achieved. Here, we propose a network model in which a local, biologically plausible learning rule adjusts synaptic efficacies during development, guided by supervisory allothetic cues. Applied to the Drosophila head direction system, the model learns to path-integrate accurately and develops a connectivity strikingly similar to the one reported in experiments. The mature network is a quasi-continuous attractor and reproduces key experiments in which optogenetic stimulation controls the internal representation of heading in flies, and where the network remaps to integrate with different gains in rodents. Our model predicts that path integration requires self-supervised learning during a developmental phase, and proposes a general framework to learn to path-integrate with gain-1 even in architectures that lack the physical topography of a ring.

Plasticity between visual input pathways and the head direction system.

Animals can maintain a stable sense of direction even when they navigate in novel environments, but how the animal's brain interprets and encodes unfamiliar sensory information in its navigation system to maintain a stable sense of direction is a mystery. Recent studies have suggested that distinct brain structures of mammals and insects have evolved to solve this common problem with strategies that share computational principles; specifically, a network structure called a ring attractor maintains the sense of direction. Initially, in a novel environment, the animal's sense of direction relies on self-motion cues. Over time, the mapping from visual inputs to head direction cells, responsible for the sense of direction, is established via experience-dependent plasticity. Yet the mechanisms that facilitate acquiring a world-centered sense of direction, how many environments can be stored in memory, and what visual features are selected, all remain unknown. Thanks to recent advances in large scale physiological recording, genetic tools, and theory, these mechanisms may soon be revealed.

Automated long-term two-photon imaging in head-fixed walking Drosophila

BackgroundThe brain of Drosophila shows dynamics at multiple timescales, from the millisecond range of fast voltage or calcium transients to functional and structural changes occurring over multiple days. To relate such dynamics to behavior requires monitoring neural circuits across these multiple timescales in behaving animals. New methodHere, we develop a technique for automated long-term two-photon imaging in fruit flies, during wakefulness and extended bouts of immobility, as typically observed during sleep, navigating in virtual reality over up to seven days. The method is enabled by laser surgery, a microrobotic arm for controlling forceps for dissection assistance, an automated feeding robot, as well as volumetric, simultaneous multiplane imaging. ResultsThe approach is validated in the fly’s head direction system and walking behavior as well a neural activity are recorded. The head direction system tracks the fly’s walking direction over multiple days. Comparison with existing methodsIn comparison with previous head-fixed preparations, the time span over which tethered behavior and neural activity can be recorded at the same time is extended from hours to days. Additionally, the reproducibility and ease of dissections are improved compared with manual approaches. Different from previous laser surgery approaches, only continuous wave lasers are required. Lastly, an automated feeding system allows continuously maintaining the fly for several days in the virtual reality setup without user intervention. ConclusionsImaging in behaving flies over multiple timescales will be useful for understanding circadian activity, learning and long-term memory, or sleep.

Integration of sleep homeostasis and navigation in Drosophila.

During sleep, the brain undergoes dynamic and structural changes. In Drosophila, such changes have been observed in the central complex, a brain area important for sleep control and navigation. The connectivity of the central complex raises the question about how navigation, and specifically the head direction system, can operate in the face of sleep related plasticity. To address this question, we develop a model that integrates sleep homeostasis and head direction. We show that by introducing plasticity, the head direction system can function in a stable way by balancing plasticity in connected circuits that encode sleep pressure. With increasing sleep pressure, the head direction system nevertheless becomes unstable and a sleep phase with a different plasticity mechanism is introduced to reset network connectivity. The proposed integration of sleep homeostasis and head direction circuits captures features of their neural dynamics observed in flies and mice.

The Neuroanatomical Ultrastructure and Function of a Biological Ring Attractor

Neural representations of head direction (HD) have been discovered in many species. Theoretical work has proposed that the dynamics associated with these representations are generated, maintained, and updated by recurrent network structures called ring attractors. We evaluated this theorized structure-function relationship by performing electron-microscopy-based circuit reconstruction and RNA profiling of identified cell types in the HD system of Drosophila melanogaster. We identified motifs that have been hypothesized to maintain the HD representation in darkness, update it when the animal turns, and tether it to visual cues. Functional studies provided support for the proposed roles of individual excitatory or inhibitory circuit elements in shaping activity. We also discovered recurrent connections between neuronal arbors with mixed pre- and postsynaptic specializations. Our results confirm that the Drosophila HD network contains the core components of a ring attractor while also revealing unpredicted structural features that might enhance the network's computational power.

Precise coupling of the thalamic head-direction system to hippocampal ripples

The anterior thalamus is a key relay of neuronal signals within the limbic system. During sleep, the occurrence of hippocampal sharp wave-ripples (SWRs), believed to mediate consolidation of explicit memories, is modulated by thalamocortical network activity, yet how information is routed around SWRs and how this communication depends on neuronal dynamics remains unclear. Here, by simultaneously recording ensembles of neurons in the anterior thalamus and local field potentials in the CA1 area of the hippocampus, we show that the head-direction (HD) cells of the anterodorsal nucleus are set in stable directions immediately before SWRs. This response contrasts with other thalamic cells that exhibit diverse couplings to the hippocampus related to their intrinsic dynamics but independent of their anatomical location. Thus, our data suggest a specific and homogeneous contribution of the HD signal to hippocampal activity and a diverse and cell-specific coupling of non-HD neurons.

Vision and Locomotion Combine to Drive Path Integration Sequences in Mouse Retrosplenial Cortex.

The retrosplenial cortex (RSC) is involved in a broad range of cognitive functions, integrating rich sensory, motor, and spatial signals from multiple brain areas, including the hippocampal system. RSC neurons show hippocampus-dependent activity reminiscent of place cell sequences. Using cellular calcium imaging in a virtual reality (VR)-based locomotion task, we investigate how the integration of visual and locomotor inputs may give rise to such activity in RSC. A substantial population shows neural sequences that track position in the VR environment. This activity is driven by the conjunction of visual stimuli sequences and active movement, which is suggestive of path integration. The activity is anchored to a reference point and predominantly follows the VR upon manipulations of optic flow against locomotion. Thus, locomotion-gated optic flow, combined with the presence of contextual cues at the start of each trial, is sufficient to drive the sequential activity. A subpopulation shows landmark-related visual responses that are modulated by animal's position in the VR. Thus, rather than fragmenting the spatial representationinto equivalent locomotion-based ensemble versus optic-flow-based ensemble, in RSC, optic flow appears to override locomotion signals coherently in the population, when the gain betweenthe two signals is altered.

Equilibrium States and Their Stability in the Head-Direction Ring Network.

Head-direction cells have been found in several areas in the mammalian brains. The firing rate of an ideal head-direction cell reaches its peak value only when the animal's head points in a specific direction, and this preferred direction stays the same regardless of spatial location. In this paper we combine mathematical analytical techniques and numerical simulations to fully analyze the equilibrium states of a generic ring attractor network, which is a widely used modeling framework for the head-direction system. Under specific conditions, all solutions of the ring network are bounded, and there exists a Lyapunov function that guarantees the stability of the network for any given inputs, which may come from multiple sources in the biological system, including self-motion information for inertially based updating and landmark information for calibration. We focus on the first few terms of the Fourier series of the ring network to explicitly solve for all possible equilibrium states, followed by a stability analysis based on small perturbations. In particular, these equilibrium states include the standard single-peaked activity pattern as well as double-peaked activity pattern, whose existence is unknown but has testable experimental implications. To our surprise, we have also found an asymmetric equilibrium activity profile even when the network connectivity is strictly symmetric. Finally we examine how these different equilibrium solutions depend on the network parameters and obtain the phase diagrams in the parameter space of the ring network.