Abstract
The central complex (CX), which consists of four neuropils located in the central brain of insects, is characterized by a complex but highly organized and repetitive circuit architecture. Furthermore, CX has been suggested to participate in a range of functions including spatial working memory, sensory-motor transformation and motor control. However, how these functions are implemented and realized by the complex neural circuits in CX remains unclear. As a first step toward understanding of the functions of the CX neural circuits, we mathematically analyzed connectivity of 662 Drosophila neurons which innervate one of the CX neuropils, the protocerebral bridge. Specifically, each neuron is represented as a high-dimensional innervation vector with each dimension corresponding to a subregion of CX. We found that the seemly complex innervation patterns of the neurons are highly structured and the whole network can be generated or even predicted by applying a generator matrix on a small set of initial neurons. The result implies that the development of the complex CX neural network can be highly efficient because it can be driven by a small set of genes that encode the simple rules, or the generator matrices. We further investigated a small set of observed neurons with innervation patterns that cannot be generated from the generator matrices. To determine whether these “special” neurons play specific roles in information transduction, we compared the network constructed by neurons from observed data and the network generated from the mathematical model (the generator matrices). Specifically, we studied how signals propagate from a given input neuron to a given output neuron through multiple intermediate neurons. We found that the observed network is characterized by large pathway numbers that are several folds larger than that of the model network for specific input-output neuron pairs. We further identified that only two specific neurons in EIP class are responsible for the major changes in the pathway numbers which greatly increase the complexity of network computation. Further analysis indicated that the unique innervation pattern of these neurons plays a key role in maximizing the processing complexity. The result suggests that a small number of specially designed neurons can greatly improve the processing complexity of network. Therefore, our work provides insights into the complex organization of CX neural circuits and may generate specific predictions that can be tested experimentally.