Theoretical principles explain the structure of the insect head direction circuit.

To navigate their environment, insects need to keep track of their orientation. Previous work has shown that insects encode their head direction as a sinusoidal activity pattern around a ring of neurons arranged in an eight-column structure. However, it is unclear whether this sinusoidal encoding of head direction is just an evolutionary coincidence or if it offers a particular functional advantage. To address this question, we establish the basic mathematical requirements for direction encoding and show that it can be performed by many circuits, all with different activity patterns. Among these activity patterns, we prove that the sinusoidal one is the most noise-resilient, but only when coupled with a sinusoidal connectivity pattern between the encoding neurons. We compare this predicted optimal connectivity pattern with anatomical data from the head direction circuits of the locust and the fruit fly, finding that our theory agrees with experimental evidence. Furthermore, we demonstrate that our predicted circuit can emerge using Hebbian plasticity, implying that the neural connectivity does not need to be explicitly encoded in the genetic program of the insect but rather can emerge during development. Finally, we illustrate that in our theory, the consistent presence of the eight-column organisation of head direction circuits across multiple insect species is not a chance artefact but instead can be explained by basic evolutionary principles.

Insects, including fruit flies and locusts, move throughout their environment to find food, interact with each other or escape danger. To navigate their surroundings, insects need to be able to keep track of their orientation. This tracking is achieved through visual cues and integrating information about their movements whilst flying so they know which direction their head is facing. The set of neurons responsible for relaying information about the direction of the head (also known as heading) are connected together in a ring made up of eight columns of cells. Previous studies showed that the level of activity across this ring of neurons resembles a sinusoid shape: a smooth curve with one peak which encodes the animal's heading. Neurons downstream from this eight-column ring, which relay velocity information, also display this sinusoidal pattern of activation. Aceituno, Dall'Osto and Pisokas wanted to understand whether this sinusoidal pattern was an evolutionary coincidence, or whether it offers a particular advantage to insects. To answer this question, they established the mathematical criteria required for neurons in the eight-column ring to encode information about the heading of the animal. This revealed that these conditions can be satisfied by many different patterns of activation, not just the sinusoidal shape. However, Aceituno, Dall'Osto and Pisokas show that the sinusoidal shape is the most resilient to variations in neuronal activity which may impact the encoded information. Further experiments revealed that this resilience only occurred if neurons in the circuit were connected together in a certain pattern. Aceituno, Dall'Osto and Pisokas then compared this circuit with experimental data from locusts and fruit flies and found that both insects exhibit the predicted connection pattern. They also discovered that animals do not have to be born with this neuronal connection pattern, but can develop it during their lifetime. These findings provide fresh insights into how insects relay information about the direction of their head as they fly. They suggest that the structure of the neuronal circuit responsible for encoding head direction was not formed by chance but instead arose due to the evolutionary benefits it provided.

Anesthesia disrupts distance, but not direction, of path integration memory.

Solitary foraging insects, such as ants, maintain an estimate of the direction and distance to their starting location as they move away from it, in a process known as path integration. This estimate, commonly known as the "home vector," is updated continuously as the ant moves1-4 and is reset as soon as it enters its nest,5 yet ants prevented from returning to their nest can still use their home vector when released several hours later.6,7 This conjunction of fast update and long persistence of the home vector memory does not directly map to existing accounts of short-, mid-, and long-term memory;2,8-12 hence, the substrate of this memory remains unknown. Chill-coma anesthesia13-15 has previously been shown to affect associative memory retention in fruit flies14,16 and honeybees.9,17,18 We investigate the nature of path integration memory by anesthetizing ants after they have accumulated home vector information and testing if the memory persists on recovery. We show that after anesthesia the memory of the distance ants have traveled is degraded, but the memory of the direction is retained. We also show that this is consistent with models of path integration that maintain the memory in a redundant Cartesian coordinate system and with the hypothesis that chill-coma produces a proportional reduction of the memory, rather than a subtractive reduction or increase of noise. The observed effect is not compatible with a memory based on recurrent circuit activity and points toward an activity-dependent molecular process as the basis of path integration memory.

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.

Reverse Engineering and Robotics as Tools for Analyzing Neural Circuits.

Understanding neuronal circuits that have evolved over millions of years to control adaptive behavior may provide us with alternative solutions to problems in robotics. Recently developed genetic tools allow us to study the connectivity and function of the insect nervous system at the single neuron level. However, neuronal circuits are complex, so the question remains, can we unravel the complex neuronal connectivity to understand the principles of the computations it embodies? Here, I illustrate the plausibility of incorporating reverse engineering to analyze part of the central complex, an insect brain structure essential for navigation behaviors such as maintaining a specific compass heading and path integration. I demonstrate that the combination of reverse engineering with simulations allows the study of both the structure and function of the underlying circuit, an approach that augments our understanding of both the computation performed by the neuronal circuit and the role of its components.