Abstract
To navigate their environment, insects need to keep track of their heading direction, with some species such as the monarch butterfly able to maintain a stable direction encoding even over long migratory travels. Previous work has shown that insects encode their heading direction as a sinusoidal pattern of activity in a ring of neurons. However, it is unclear whether this sinusoidal encoding is just an evolutionary coincidence, or if it offers some particular advantage. We address this problem by establishing the basic mathematical requirements for heading integration and show that several circuits with different activity patterns can perform the same function. In this family of potential circuits, a sinusoidal activity pattern stands out as the most noise-resilient, but only when coupled with a specific connectivity pattern between neurons. Using network analysis, we compare this optimal connectivity pattern with experimental data from the locust and the fruit fly, finding a remarkably good agreement. Finally, we demonstrate that the circuit we propose can emerge naturally from a Hebbian plasticity rule, showing that the synaptic structure of our proposed network does not need to be explicitly encoded in the genetic program of the insect, but can be acquired during development.
Competing Interest Statement
The authors have declared no competing interest.