Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors

Quan Wen, Armen Stepanyants, Guy N. Elston, Alexander Y. Grosberg, Dmitri B. Chklovskii

    Research output: Contribution to journalArticlepeer-review


    The shapes of dendritic arbors are fascinating and important, yet the principles underlying these complex and diverse structures remain unclear. Here, we analyzed basal dendritic arbors of 2,171 pyramidal neurons sampled from mammalian brains and discovered 3 statistical properties: the dendritic arbor size scales with the total dendritic length, the spatial correlation of dendritic branches within an arbor has a universal functional form, and small parts of an arbor are self-similar. We proposed that these properties result from maximizing the repertoire of possible connectivity patterns between dendrites and surrounding axons while keeping the cost of dendrites low. We solved this optimization problem by drawing an analogy with maximization of the entropy for a given energy in statistical physics. The solution is consistent with the above observations and predicts scaling relations that can be tested experimentally. In addition, our theory explains why dendritic branches of pyramidal cells are distributed more sparsely than those of Purkinje cells. Our results represent a step toward a unifying view of the relationship between neuronal morphology and function.

    Original languageEnglish (US)
    Pages (from-to)12536-12541
    Number of pages6
    JournalProceedings of the National Academy of Sciences of the United States of America
    Issue number30
    StatePublished - Jul 28 2009


    • Axons
    • Entropy
    • Optimization
    • Pyramidal cell
    • Scaling

    ASJC Scopus subject areas

    • General


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