Abstract
The connections in networks of neurons are heavy-tailed, with a small number of neurons connected much more strongly than the vast majority of pairs. However, it remains unclear whether this heavy-tailed connectivity emerges from simple underlying mechanisms. Here we propose a minimal model of synaptic self-organization: connections are pruned at random, and the synaptic strength rearranges under a mixture of preferential and random dynamics. Under these generic rules, networks evolve to produce distributions of connectivity strength that are asymptotically scale-free, with a power-law exponent that depends only on the probability of preferential (rather than random) growth. Extending our model to include neuronal activity and Hebbian plasticity, we find that clustering in the network also emerges naturally. We confirm these predictions in the connectomes of several animals, suggesting that heavy-tailed and clustered connectivity may arise from general principles of network self-organization rather than mechanisms specific to individual species or systems.
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Data availability
The neuronal data analysed in this paper are openly available at github.com/ChrisWLynn/Heavy_tailed_connectivity.
Code availability
The code used to perform the analyses in this paper is openly available at github.com/ChrisWLynn/Heavy_tailed_connectivity.
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Acknowledgements
We thank D. J. Schwab and L. Papadopoulos for discussions and feedback and P. Kratsios for help with illustrations. This work was supported in part by the National Science Foundation, through the Center for the Physics of Biological Function (PHY–1734030) and a Graduate Research Fellowship (C.M.H.); by the James S. McDonnell Foundation through a Postdoctoral Fellowship Award (C.W.L.); and by the National Institutes of Health BRAIN initiative (R01EB026943).
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C.W.L. and S.E.P. conceived the project. C.W.L. designed the models, and C.W.L. and C.M.H. performed the analysis with input from S.E.P. C.W.L. wrote the paper and Supplementary Information, and C.M.H. and S.E.P. edited the paper and Supplementary Information.
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Lynn, C.W., Holmes, C.M. & Palmer, S.E. Heavy-tailed neuronal connectivity arises from Hebbian self-organization. Nat. Phys. 20, 484–491 (2024). https://doi.org/10.1038/s41567-023-02332-9
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DOI: https://doi.org/10.1038/s41567-023-02332-9