Calibration of the head direction network: a role for symmetric angular head velocity cells

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.

Angular head velocity cells within brainstem nuclei projecting to the head direction circuit

An animal's perceived sense of orientation depends upon the head direction (HD) system found in several limbic structures and depends upon an intact peripheral vestibular labyrinth. However, how the vestibular system influences the generation, maintenance, and updating of the HD signal remains poorly understood. Anatomical and lesion studies point towards three key brainstem nuclei as being potential critical components in generating the HD signal: nucleus prepositus hypoglossi (NPH), supragenual nucleus (SGN), and dorsal paragigantocellularis reticular nuclei (PGRNd). 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 test this hypothesis, extracellular recordings were made in these areas while rats either freely foraged in a cylindrical environment or were restrained and rotated passively. During foraging, a large subset of cells in all three nuclei exhibited activity that correlated with changes in the rat's angular head velocity (AHV). Two fundamental types of AHV cells were observed: 1) symmetrical AHV cells increased or decreased their neural firing with increases in AHV regardless of the direction of rotation; 2) asymmetrical AHV cells responded differentially to clockwise (CW) and counter-clockwise (CCW) head rotations. When rats were passively rotated, some AHV cells remained sensitive to AHV whereas others had attenuated firing. In addition, a large number of AHV cells were modulated by linear head velocity. These results indicate the types of information conveyed in the ascending vestibular pathways 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 angular head velocity (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 rat's head in the azimuthal plane.

Sharp Tuning of Head Direction and Angular Head Velocity Cells in the Somatosensory Cortex

Head direction (HD) cells form a fundamental component in the brain's spatial navigation system and are intricately linked to spatial memory and cognition. Although HD cells have been shown to act as an internal neuronal compass in various cortical and subcortical regions, the neural substrate of HD cells is incompletely understood. It is reported that HD cells in the somatosensory cortex comprise regular-spiking (RS, putative excitatory) and fast-spiking (FS, putative inhibitory) neurons. Surprisingly, somatosensory FS HD cells fire in bursts and display much sharper head-directionality than RS HD cells. These FS HD cells are nonconjunctive, rarely theta rhythmic, sparsely connected and enriched in layer 5. Moreover, sharply tuned FS HD cells, in contrast with RS HD cells, maintain stable tuning in darkness; FS HD cells' coexistence with RS HD cells and angular head velocity (AHV) cells in a layer-specific fashion through the somatosensory cortex presents a previously unreported configuration of spatial representation in the neocortex. Together, these findings challenge the notion that FS interneurons are weakly tuned to sensory stimuli, and offer a local circuit organization relevant to the generation and transmission of HD signaling in the brain.

A model of head direction and landmark coding in complex environments

Environmental information is required to stabilize estimates of head direction (HD) based on angular path integration. However, it is unclear how this happens in real-world (visually complex) environments. We present a computational model of how visual feedback can stabilize HD information in environments that contain multiple cues of varying stability and directional specificity. We show how combinations of feature-specific visual inputs can generate a stable unimodal landmark bearing signal, even in the presence of multiple cues and ambiguous directional specificity. This signal is associated with the retrosplenial HD signal (inherited from thalamic HD cells) and conveys feedback to the subcortical HD circuitry. The model predicts neurons with a unimodal encoding of the egocentric orientation of the array of landmarks, rather than any one particular landmark. The relationship between these abstract landmark bearing neurons and head direction cells is reminiscent of the relationship between place cells and grid cells. Their unimodal encoding is formed from visual inputs via a modified version of Oja's Subspace Algorithm. The rule allows the landmark bearing signal to disconnect from directionally unstable or ephemeral cues, incorporate newly added stable cues, support orientation across many different environments (high memory capacity), and is consistent with recent empirical findings on bidirectional HD firing reported in the retrosplenial cortex. Our account of visual feedback for HD stabilization provides a novel perspective on neural mechanisms of spatial navigation within richer sensory environments, and makes experimentally testable predictions.

The head direction circuit of two insect species

Recent studies of the Central Complex in the brain of the fruit fly have identified neurons with activity that tracks the animal’s heading direction. These neurons are part of a neuronal circuit with dynamics resembling those of a ring attractor. The homologous circuit in other insects has similar topographic structure but with significant structural and connectivity differences. We model the connectivity patterns of two insect species to investigate the effect of these differences on the dynamics of the circuit. We illustrate that the circuit found in locusts can also operate as a ring attractor but differences in the inhibition pattern enable the fruit fly circuit to respond faster to heading changes while additional recurrent connections render the locust circuit more tolerant to noise. Our findings demonstrate that subtle differences in neuronal projection patterns can have a significant effect on circuit performance and illustrate the need for a comparative approach in neuroscience.

An On-chip Spiking Neural Network for Estimation of the Head Pose of the iCub Robot

In this work, we present a neuromorphic architecture for head pose estimation and scene representation for the humanoid iCub robot. The spiking neuronal network is fully realized in Intel's neuromorphic research chip, Loihi, and precisely integrates the issued motor commands to estimate the iCub's head pose in a neuronal path-integration process. The neuromorphic vision system of the iCub is used to correct for drift in the pose estimation. Positions of objects in front of the robot are memorized using on-chip synaptic plasticity. We present real-time robotic experiments using 2 degrees of freedom (DoF) of the robot's head and show precise path integration, visual reset, and object position learning on-chip. We discuss the requirements for integrating the robotic system and neuromorphic hardware with current technologies.

Self-Organized Attractor Dynamics in the Developing Head Direction Circuit

Head direction (HD) cells are neurons found in an extended cortical and subcortical network that signal the orientation of an animal’s head relative to its environment [1, 2, 3]. They are a fundamental component of the wider circuit of spatially responsive hippocampal formation neurons that make up the neural cognitive map of space [4]. During post-natal development, HD cells are the first among spatially modulated neurons in the hippocampal circuit to exhibit mature firing properties [5, 6], but before eye opening, HD cell responses in rat pups have low directional information and are directionally unstable [7, 8]. Using Bayesian decoding of HD cell ensemble activity recorded in the anterodorsal thalamic nucleus (ADN), we characterize this instability and identify its source: under-signaling of angular head velocity, which incompletely shifts the directional signal in proportion to head turns. We find evidence that geometric cues (the corners of a square environment) can be used to mitigate this under-signaling and, thereby, stabilize the directional signal even before eye opening. Crucially, even when directional firing cannot be stabilized, ensembles of unstable HD cells show short-timescale (1–10 s) temporal and spatial couplings consistent with an adult-like HD network. The HD network is widely modeled as a continuous attractor whose output is one coherent activity peak, updated during movement by angular head velocity signals and anchored by landmark cues [9, 10, 11]. Our findings present strong evidence for this model, and they demonstrate that the required network circuitry is in place and functional early during development, independent of reference to landmark information.

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Non-visual cues can anchor head direction (HD) cells in pre-eye-opening rat pups

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Internal network dynamics are preserved even when the HD representation is unstable

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Angular velocity under-signaling drives instability, which is mitigated by corners

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Circuit architecture develops even before any landmarks can stabilize HD responses

Coupled symmetric and asymmetric circuits underlying spatial orientation in fruit flies

Maintaining spatial orientation when carrying out goal-directed movements requires an animal to perform angular path integration. Such functionality has been recently demonstrated in the ellipsoid body (EB) of fruit flies, though the precise circuitry and underlying mechanisms remain unclear. We analyze recently published cellular-level connectomic data and identify the unique characteristics of the EB circuitry, which features coupled symmetric and asymmetric rings. By constructing a spiking neural circuit model based on the connectome, we reveal that the symmetric ring initiates a feedback circuit that sustains persistent neural activity to encode information regarding spatial orientation, while the asymmetric rings are capable of integrating the angular path when the body rotates in the dark. The present model reproduces several key features of EB activity and makes experimentally testable predictions, providing new insight into how spatial orientation is maintained and tracked at the cellular level.

Ellipsoid body (EB) neurons in the fruit fly represent the animal heading through a bump-like activity dynamics. Here the authors report a connectome-driven spiking neural circuit model of the EB and the protocerebral bridge (PB) that can maintain and update an activity bump related to the spatial orientation.

Environmental Anchoring of Head Direction in a Computational Model of Retrosplenial Cortex

Allocentric (world-centered) spatial codes driven by path integration accumulate error unless reset by environmental sensory inputs that are necessarily egocentric (body-centered). Previous models of the head direction system avoided the necessary transformation between egocentric and allocentric reference frames by placing visual cues at infinity. Here we present a model of head direction coding that copes with exclusively proximal cues by making use of a conjunctive representation of head direction and location in retrosplenial cortex. Egocentric landmark bearing of proximal cues, which changes with location, is mapped onto this retrosplenial representation. The model avoids distortions due to parallax, which occur in simple models when a single proximal cue card is used, and can also accommodate multiple cues, suggesting how it can generalize to arbitrary sensory environments. It provides a functional account of the anatomical distribution of head direction cells along Papez' circuit, of place-by-direction coding in retrosplenial cortex, the anatomical connection from the anterior thalamic nuclei to retrosplenial cortex, and the involvement of retrosplenial cortex in navigation. In addition to parallax correction, the same mechanism allows for continuity of head direction coding between connected environments, and shows how a head direction representation can be stabilized by a single within arena cue. We also make predictions for drift during exploration of a new environment, the effects of hippocampal lesions on retrosplenial cells, and on head direction coding in differently shaped environments.

SIGNIFICANCE STATEMENT

The activity of head direction cells signals the direction of an animal's head relative to landmarks in the world. Although driven by internal estimates of head movements, head direction cells must be kept aligned to the external world by sensory inputs, which arrive in the reference frame of the sensory receptors. We present a computational model, which proposes that sensory inputs are correctly associated to head directions by virtue of a conjunctive representation of place and head directions in the retrosplenial cortex. The model allows for a stable head direction signal, even when the sensory input from nearby cues changes dramatically whenever the animal moves to a different location, and enables stable representations of head direction across connected environments.

Neural mechanisms of self-location

The ability to self-localise and to navigate to remembered goals in complex and changeable environments is crucial to the survival of many mobile species. Electrophysiological investigations of the mammalian hippocampus and associated brain structures have identified several classes of neurons which represent information about an organism's position and orientation. These include place cells, grid cells, head direction cells, and boundary vector cells, as well as cells representing aspects of self-motion. Understanding how these neural representations are formed and updated from environmental sensory information and from information relating to self-motion is an important topic attracting considerable current interest. Here we review the computational mechanisms thought to underlie the formation of these different spatial representations, the interactions between them, and their use in guiding behaviour. These include some of the clearest examples of computational mechanisms of general interest to neuroscience, such as attractor dynamics, temporal coding and multi-modal integration. We also discuss the close relationships between computational modelling and experimental research which are driving progress in this area.

Path integration of head direction: updating a packet of neural activity at the correct speed using axonal conduction delays

The head direction cell system is capable of accurately updating its current representation of head direction in the absence of visual input. This is known as the path integration of head direction. An important question is how the head direction cell system learns to perform accurate path integration of head direction. In this paper we propose a model of velocity path integration of head direction in which the natural time delay of axonal transmission between a linked continuous attractor network and competitive network acts as a timing mechanism to facilitate the correct speed of path integration. The model effectively learns a “look-up” table for the correct speed of path integration. In simulation, we show that the model is able to successfully learn two different speeds of path integration across two different axonal conduction delays, and without the need to alter any other model parameters. An implication of this model is that, by learning look-up tables for each speed of path integration, the model should exhibit a degree of robustness to damage. In simulations, we show that the speed of path integration is not significantly affected by degrading the network through removing a proportion of the cells that signal rotational velocity.

Maintaining a cognitive map in darkness: the need to fuse boundary knowledge with path integration

Spatial navigation requires the processing of complex, disparate and often ambiguous sensory data. The neurocomputations underpinning this vital ability remain poorly understood. Controversy remains as to whether multimodal sensory information must be combined into a unified representation, consistent with Tolman's “cognitive map”, or whether differential activation of independent navigation modules suffice to explain observed navigation behaviour. Here we demonstrate that key neural correlates of spatial navigation in darkness cannot be explained if the path integration system acted independently of boundary (landmark) information. In vivo recordings demonstrate that the rodent head direction (HD) system becomes unstable within three minutes without vision. In contrast, rodents maintain stable place fields and grid fields for over half an hour without vision. Using a simple HD error model, we show analytically that idiothetic path integration (iPI) alone cannot be used to maintain any stable place representation beyond two to three minutes. We then use a measure of place stability based on information theoretic principles to prove that featureless boundaries alone cannot be used to improve localization above chance level. Having shown that neither iPI nor boundaries alone are sufficient, we then address the question of whether their combination is sufficient and – we conjecture – necessary to maintain place stability for prolonged periods without vision. We addressed this question in simulations and robot experiments using a navigation model comprising of a particle filter and boundary map. The model replicates published experimental results on place field and grid field stability without vision, and makes testable predictions including place field splitting and grid field rescaling if the true arena geometry differs from the acquired boundary map. We discuss our findings in light of current theories of animal navigation and neuronal computation, and elaborate on their implications and significance for the design, analysis and interpretation of experiments.

Do animals need “cognitive maps“? One of the main difficulties in answering this question is finding a definitive scenario where having and not having a “cognitive map“ result in measurably different outcomes. Many key predictions made by models involving some sort of “cognitive map“ can also be replicated by models without a “cognitive map“. Here we consider published data on rodents navigating in darkness inside homogeneous arenas. The head direction system becomes unstable within three minutes in darkness, yet place and grid cells have been reported to fire in the same locations for thirty minutes or longer. We show firstly that it is theoretically implausible for path integration alone to maintain a stable positional representation beyond three minutes, given a drifting head direction system in darkness. Secondly, we prove that even assuming perfect boundary knowledge is insufficient to maintain a stable positional representation. Finally, we show in simulated and real arenas that a nearoptimal combination of path integration and boundary representation is sufficient to produce stable positional representations in darkness consistent with published data. The necessity for fusing path integration and landmark information for accurate localization in darkness is both consistent with, and motivates the existence of, “cognitive maps.“

Vestibular and attractor network basis of the head direction cell signal in subcortical circuits

Accurate navigation depends on a network of neural systems that encode the moment-to-moment changes in an animal's directional orientation and location in space. Within this navigation system are head direction (HD) cells, which fire persistently when an animal's head is pointed in a particular direction (Sharp et al., 2001a; Taube, 2007). HD cells are widely thought to underlie an animal's sense of spatial orientation, and research over the last 25+ years has revealed that this robust spatial signal is widely distributed across subcortical and cortical limbic areas. The purpose of the present review is to summarize some of the recent studies arguing that the origin of the HD signal resides subcortically, specifically within the reciprocal connections of the dorsal tegmental and lateral mammillary nuclei. Furthermore, we review recent work identifying "bursting" cellular activity in the HD cell circuit after lesions of the vestibular system, and relate these observations to the long held view that attractor network mechanisms underlie HD signal generation. Finally, we summarize anatomical and physiological work suggesting that this attractor network architecture may reside within the tegmento-mammillary circuit.

Using strategic movement to calibrate a neural compass: a spiking network for tracking head direction in rats and robots

The head direction (HD) system in mammals contains neurons that fire to represent the direction the animal is facing in its environment. The ability of these cells to reliably track head direction even after the removal of external sensory cues implies that the HD system is calibrated to function effectively using just internal (proprioceptive and vestibular) inputs. Rat pups and other infant mammals display stereotypical warm-up movements prior to locomotion in novel environments, and similar warm-up movements are seen in adult mammals with certain brain lesion-induced motor impairments. In this study we propose that synaptic learning mechanisms, in conjunction with appropriate movement strategies based on warm-up movements, can calibrate the HD system so that it functions effectively even in darkness. To examine the link between physical embodiment and neural control, and to determine that the system is robust to real-world phenomena, we implemented the synaptic mechanisms in a spiking neural network and tested it on a mobile robot platform. Results show that the combination of the synaptic learning mechanisms and warm-up movements are able to reliably calibrate the HD system so that it accurately tracks real-world head direction, and that calibration breaks down in systematic ways if certain movements are omitted. This work confirms that targeted, embodied behaviour can be used to calibrate neural systems, demonstrates that ‘grounding’ of modelled biological processes in the real world can reveal underlying functional principles (supporting the importance of robotics to biology), and proposes a functional role for stereotypical behaviours seen in infant mammals and those animals with certain motor deficits. We conjecture that these calibration principles may extend to the calibration of other neural systems involved in motion tracking and the representation of space, such as grid cells in entorhinal cortex.