The insect compass system: From theory to circuitry

Abstract

AbstractTo 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. We address this question by establishing the basic mathematical requirements for direction encoding and show that several potential circuits with different activity patterns can perform the same function. We prove that among these activity patterns, the sinusoidal one is the most noise-resilient, but only when coupled with a specific connectivity pattern between the encoding neurons. We compare this optimal connectivity pattern with experimental data from the head direction circuits of the locust and the fruit fly, finding a remarkable agreement between our theory and experimental evidence. Furthermore, we demonstrate that our predicted circuit can emerge naturally using Hebbian plasticity, which means 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.