Heading Direction
heading direction
The Secret Bayesian Life of Ring Attractor Networks
Efficient navigation requires animals to track their position, velocity and heading direction (HD). Some animals’ behavior suggests that they also track uncertainties about these navigational variables, and make strategic use of these uncertainties, in line with a Bayesian computation. Ring-attractor networks have been proposed to estimate and track these navigational variables, for instance in the HD system of the fruit fly Drosophila. However, such networks are not designed to incorporate a notion of uncertainty, and therefore seem unsuited to implement dynamic Bayesian inference. Here, we close this gap by showing that specifically tuned ring-attractor networks can track both a HD estimate and its associated uncertainty, thereby approximating a circular Kalman filter. We identified the network motifs required to integrate angular velocity observations, e.g., through self-initiated turns, and absolute HD observations, e.g., visual landmark inputs, according to their respective reliabilities, and show that these network motifs are present in the connectome of the Drosophila HD system. Specifically, our network encodes uncertainty in the amplitude of a localized bump of neural activity, thereby generalizing standard ring attractor models. In contrast to such standard attractors, however, proper Bayesian inference requires the network dynamics to operate in a regime away from the attractor state. More generally, we show that near-Bayesian integration is inherent in generic ring attractor networks, and that their amplitude dynamics can account for close-to-optimal reliability weighting of external evidence for a wide range of network parameters. This only holds, however, if their connection strengths allow the network to sufficiently deviate from the attractor state. Overall, our work offers a novel interpretation of ring attractor networks as implementing dynamic Bayesian integrators. We further provide a principled theoretical foundation for the suggestion that the Drosophila HD system may implement Bayesian HD tracking via ring attractor dynamics.
Neural mechanisms of navigation behavior
The regions of the insect brain devoted to spatial navigation are beautifully orderly, with a remarkably precise pattern of synaptic connections. Thus, we can learn much about the neural mechanisms of spatial navigation by targeting identifiable neurons in these networks for in vivo patch clamp recording and calcium imaging. Our lab has recently discovered that the "compass system" in the Drosophila brain is anchored to not only visual landmarks, but also the prevailing wind direction. Moreover, we found that the compass system can re-learn the relationship between these external sensory cues and internal self-motion cues, via rapid associative synaptic plasticity. Postsynaptic to compass neurons, we found neurons that conjunctively encode heading direction and body-centric translational velocity. We then showed how this representation of travel velocity is transformed from body- to world-centric coordinates at the subsequent layer of the network, two synapses downstream from compass neurons. By integrating this world-centric vector-velocity representation over time, it should be possible for the brain to form a stored representation of the body's path through the environment.
Extracting heading and goal through structured action
Many flexible behaviors are thought to rely on internal representations of an animal’s spatial relationship to its environment and of the consequences of its actions in that environment. While such representations—e.g. of head direction and value—have been extensively studied, how they are combined to guide behavior is not well understood. I will discuss how we are exploring these questions using a classical visual learning paradigm for the fly. I’ll begin by describing a simple policy that, when tethered to an internal representation of heading, captures structured behavioral variability in this task. I’ll describe how ambiguities in the fly’s visual surroundings affect its perception and, when coupled to this policy, manifest in predictable changes in behavior. Informed by newly-released connectomic data, I’ll then discuss how these computations might be carried out and combined within specific circuits in the fly’s central brain, and how perception and action might interact to shape individual differences in learning performance.
Vector addition in the navigational circuits of the fly
In a cross wind, the direction a fly moves through the air may differ from its heading direction, the direction defined by its body axis. I will present a model based on experimental results that reveals how a heading direction “compass” signal is combined with optic flow to compute and represent the direction that a fly is traveling. This provides a general framework for understand how flies perform vector computations.
Who can turn faster? Comparison of the head direction circuit of two species
Ants, bees and other insects have the ability to return to their nest or hive using a navigation strategy known as path integration. Similarly, fruit flies employ path integration to return to a previously visited food source. An important component of path integration is the ability of the insect to keep track of its heading relative to salient visual cues. A highly conserved brain region known as the central complex has been identified as being of key importance for the computations required for an insect to keep track of its heading. However, the similarities or differences of the underlying heading tracking circuit between species are not well understood. We sought to address this shortcoming by using reverse engineering techniques to derive the effective underlying neural circuits of two evolutionary distant species, the fruit fly and the locust. Our analysis revealed that regardless of the anatomical differences between the two species the essential circuit structure has not changed. Both effective neural circuits have the structural topology of a ring attractor with an eight-fold radial symmetry (Fig. 1). However, despite the strong similarities between the two ring attractors, there remain differences. Using computational modelling we found that two apparently small anatomical differences have significant functional effect on the ability of the two circuits to track fast rotational movements and to maintain a stable heading signal. In particular, the fruit fly circuit responds faster to abrupt heading changes of the animal while the locust circuit maintains a heading signal that is more robust to inhomogeneities in cell membrane properties and synaptic weights. We suggest that the effects of these differences are consistent with the behavioural ecology of the two species. On the one hand, the faster response of the ring attractor circuit in the fruit fly accommodates the fast body saccades that fruit flies are known to perform. On the other hand, the locust is a migratory species, so its behaviour demands maintenance of a defined heading for a long period of time. Our results highlight that even seemingly small differences in the distribution of dendritic fibres can have a significant effect on the dynamics of the effective ring attractor circuit with consequences for the behavioural capabilities of each species. These differences, emerging from morphologically distinct single neurons highlight the importance of a comparative approach to neuroscience.
A hindbrain ring attractor network that integrates heading direction in the larval zebrafish
COSYNE 2022
A hindbrain ring attractor network that integrates heading direction in the larval zebrafish
COSYNE 2022