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Heavy-tailed neuronal connectivity arises from Hebbian self-organization

Nature Physics volume 20, pages 484–491 (2024)Cite this article

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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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Fig. 1: Heavy-tailed connectivity in neuronal connectomes.
Fig. 2: Preferential growth produces scale-free connection strengths.
Fig. 3: Activity-dependent dynamics give rise to network clustering.
Fig. 4: Capturing heavy-tailed and clustered connectivity in real connectomes.

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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).

Author information

Authors and Affiliations

  1. Initiative for the Theoretical Sciences, Graduate Center, City University of New York, New York, NY, USA

    Christopher W. Lynn

  2. Department of Physics, Princeton University, Princeton, NJ, USA

    Christopher W. Lynn & Caroline M. Holmes

  3. Department of Physics, Yale University, New Haven, CT, USA

    Christopher W. Lynn

  4. Quantitative Biology Institute, Yale University, New Haven, CT, USA

    Christopher W. Lynn

  5. Wu Tsai Institute, Yale University, New Haven, CT, USA

    Christopher W. Lynn

  6. Department of Organismic & Evolutionary Biology, Harvard University, Cambridge, MA, USA

    Caroline M. Holmes

  7. Department of Organismal Biology & Anatomy, University of Chicago, Chicago, IL, USA

    Stephanie E. Palmer

  8. Department of Physics, University of Chicago, Chicago, IL, USA

    Stephanie E. Palmer

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  1. Christopher W. Lynn
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Contributions

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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Correspondence to Christopher W. Lynn.

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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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