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 journalArticle

    Abstract

    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
    Volume106
    Issue number30
    DOIs
    StatePublished - Jul 28 2009

    Fingerprint

    Pyramidal Cells
    Dendrites
    Purkinje Cells
    Physics
    Entropy
    Axons
    Costs and Cost Analysis
    Brain

    Keywords

    • Axons
    • Entropy
    • Optimization
    • Pyramidal cell
    • Scaling

    ASJC Scopus subject areas

    • General

    Cite this

    Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors. / Wen, Quan; Stepanyants, Armen; Elston, Guy N.; Grosberg, Alexander Y.; Chklovskii, Dmitri B.

    In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 106, No. 30, 28.07.2009, p. 12536-12541.

    Research output: Contribution to journalArticle

    Wen, Quan ; Stepanyants, Armen ; Elston, Guy N. ; Grosberg, Alexander Y. ; Chklovskii, Dmitri B. / Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors. In: Proceedings of the National Academy of Sciences of the United States of America. 2009 ; Vol. 106, No. 30. pp. 12536-12541.
    @article{20a70ae025524a5fb0ba6a3223fcee93,
    title = "Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors",
    abstract = "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.",
    keywords = "Axons, Entropy, Optimization, Pyramidal cell, Scaling",
    author = "Quan Wen and Armen Stepanyants and Elston, {Guy N.} and Grosberg, {Alexander Y.} and Chklovskii, {Dmitri B.}",
    year = "2009",
    month = "7",
    day = "28",
    doi = "10.1073/pnas.0901530106",
    language = "English (US)",
    volume = "106",
    pages = "12536--12541",
    journal = "Proceedings of the National Academy of Sciences of the United States of America",
    issn = "0027-8424",
    number = "30",

    }

    TY - JOUR

    T1 - Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors

    AU - Wen, Quan

    AU - Stepanyants, Armen

    AU - Elston, Guy N.

    AU - Grosberg, Alexander Y.

    AU - Chklovskii, Dmitri B.

    PY - 2009/7/28

    Y1 - 2009/7/28

    N2 - 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.

    AB - 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.

    KW - Axons

    KW - Entropy

    KW - Optimization

    KW - Pyramidal cell

    KW - Scaling

    UR - http://www.scopus.com/inward/record.url?scp=68149170901&partnerID=8YFLogxK

    UR - http://www.scopus.com/inward/citedby.url?scp=68149170901&partnerID=8YFLogxK

    U2 - 10.1073/pnas.0901530106

    DO - 10.1073/pnas.0901530106

    M3 - Article

    VL - 106

    SP - 12536

    EP - 12541

    JO - Proceedings of the National Academy of Sciences of the United States of America

    JF - Proceedings of the National Academy of Sciences of the United States of America

    SN - 0027-8424

    IS - 30

    ER -