From the fly connectome to exact ring attractor dynamics

A cognitive compass enabling spatial navigation requires the neural representation of head direction (HD), yet the neural circuit architecture enabling this representation remains unclear. While various network models have been proposed to explain HD systems, these models rely on simplified circuit architectures that may be irreconcilable with empirical observations from connectomes. Here we construct a neural network model for the fruit fly HD system that satisfies both connectome-derived architectural constraints and the functional requirement of continuous head-direction representation. To achieve this, we first characterized an ensemble of continuous attractor networks where compass neurons providing local mutual excitation are coupled to inhibitory neurons. Our multipopulation model allowed us to discover a new class of ring attractor network with weaker symmetry requirements than usually assumed. For each of the four available fly connectomes, our analyses uncovered three distinct realizations of these networks. Furthermore, we found that synaptic variations among and around the fly connectomes can be compensated by cell-type-specific rescaling of synaptic weights, which could be potentially achieved through neuromodulation. The fly connectomes are ideally configured to take advantage of this mechanism, suggesting a novel design principle linking synapse-resolution connectivity to network computation.