The study demonstrates that the exponential distance rule (EDR), which has been observed in the brain networks of mammals, also holds true for the Drosophila fruit fly. By analyzing the available neuron tree structures, the researchers measured the decay rate of the EDR using both real axonal lengths and Euclidean distances. They estimated the decay rate to be in the range of 15.6-19.8 mm^-1 for real axonal paths and 31.1-35.0 mm^-1 for Euclidean distances.
The researchers then studied the network of neuropils (brain regions) in Drosophila and applied the EDR-based network model, similar to previous studies on mammals. They found that the EDR model accurately predicts most binary properties of the network, such as degree distributions, uni- and bi-directional links, clustering coefficient, average path length, and triangular motifs. However, the model underestimates the large number of completely connected subgraphs (cliques) observed in the real network.
For weighted network properties, the model reproduces the qualitative behavior well, including the communication efficiency as a function of network density. However, there are some quantitative differences in the link weight and out-strength distributions, which the researchers attribute to potential imprecisions in the connection weights determined by convolutional neural networks and the applied 5-neuron threshold.
An interesting property that the geometrical model fails to reproduce is the asymmetry of connection weights between brain regions. While the model predicts more symmetric weights, the real network exhibits a pronounced asymmetry, which the researchers suggest is likely important for the functional hierarchy of brain areas. Surprisingly, homotopic connections (links between the left and right sides of the same functional areas) are much more symmetric and align well with the model predictions.
The researchers argue that the EDR-based model is an appropriate null model for analyzing structural brain networks, as it effectively captures many topological properties that are consequences of geometry and physical structure. Comparing real networks to this null model can help identify functionally relevant features that are not solely due to geometric constraints, such as the observed asymmetry in connection weights.
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