Geometric developmental principles for the emergence of brain-like weighted and directed neuronal networks

TL;DR

This study identifies geometric and attachment principles that explain the emergence of complex, brain-like network structures across multiple species, highlighting universal developmental mechanisms.

Contribution

It introduces a comprehensive model combining distance dependence, weight-preferential, and degree-preferential attachment to replicate brain network features.

Findings

Distance-dependent connectivity produces small-world networks.

Incorporating weight-preferential attachment reproduces heavy-tailed weight distributions.

Adding degree-preferential attachment generates heavy-tailed degree distributions.

Abstract

Brain networks exhibit remarkable structural properties, including high local clustering, short path lengths, and heavy-tailed weight and degree distributions. While these features are thought to enable efficient information processing with minimal wiring costs, the fundamental principles that generate such complex network architectures across species remain unclear. Here, we analyse single-neuron resolution connectomes across five species (C. Elegans, Platynereis, Drosophila M., zebrafish and mouse) to investigate the fundamental wiring principles underlying brain network formation. We show that distance-dependent connectivity alone produces small-world networks, but fails to generate heavy-tailed distributions. By incorporating weight-preferential attachment, which arises from spatial clustering of synapses along neurites, we reproduce heavy-tailed weight distributions while maintaining small-world topology. Adding degree-preferential attachment, linked to the extent of dendritic and axonal arborization, enables the generation of heavy-tailed degree distributions. Through systematic parameter exploration, we demonstrate that the combination of distance dependence, weight-preferential attachment, and degree-preferential attachment is sufficient to reproduce all characteristic properties of empirical brain networks. Our results reveal that activity-independent geometric constraints during neural development can account for the conserved architectural principles observed across evolutionarily distant species, suggesting universal mechanisms governing neural circuit assembly.