Scale-free behavior of weight distributions of connectomes

Abstract

To determine the precise link between anatomical structure and function, brain studies primarily concentrate on the anatomical wiring of the brain and its topological properties. In this work, we investigate the weighted degree and connection length distributions of the KKI-113 and KKI-18 human connectomes, the fruit fly, and the mouse retina. We find that the node strength (weighted degree) distribution behavior differs depending on the considered scale. On the global scale, the distributions are found to follow a power-law behavior, with a roughly universal exponent close to 3. However, this behavior breaks at the local scale as the node strength distributions of the KKI-18 follow a stretched exponential, and the fly and mouse retina follow the log-normal distribution, respectively, which are indicative of underlying random multiplicative processes and underpins nonlocality of learning in a brain close to the critical state. However, for the case of the KKI-113 and the H01 human (1mm3) datasets, the local weighted degree distributions follow an exponentially truncated power law, which may hint at the fact that the critical learning mechanism may have manifested at the node level too.

We are thankful for the helpful discussions with I. A. Kovács, decoding of the KKI-113 coordinates by M. T. Gastner, and the financial support from the Hungarian National Research, Development and Innovation Office NKFIH (Grant No. K146736). G.D. was supported by Grant PID2022-136216NB-I00 funded by MICIU/AEI/10.13039/501100011033 and by "ERDF A way of making Europe", ERDF, EU, Project NEurological MEchanismS of Injury, and the project Sleep-like cellular dynamics (Ministerio) (ref. 101071900) funded by the EU ERC Synergy Horizon Europe, AGAUR research support grant (ref. 2021 SGR 00917) funded by the Department of Research and Universities of the Generalitat of Catalunya.