Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors
- aJanelia Farm Research Campus, Howard Hughes Medical Institute, 19700 Helix Drive, Ashburn, VA 20147;
- bDepartment of Physics and Center for Interdisciplinary Research on Complex Systems, Northeastern University, 110 Forsyth Street, Boston, MA 02115;
- cCentre for Cognitive Neuroscience, Sunshine Coast, Queensland 4562, Australia; and
- dDepartment of Physics, New York University, New York, NY 10003
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.
Footnotes
- 2To whom correspondence should be addressed. E-mail: mitya{at}janelia.hhmi.org
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Edited by Charles F. Stevens, The Salk Institute for Biological Studies, La Jolla, CA, and approved May 21, 2009
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Author contributions: Q.W., A.S., A.Y.G., and D.B.C. designed research; Q.W., A.S., G.N.E., A.Y.G., and D.B.C. performed research; Q.W., A.S., A.Y.G., and D.B.C. analyzed data; and Q.W., A.S., G.N.E., A.Y.G., and D.B.C. wrote the paper.
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↵1Present address: Department of Physics, Harvard University, 17 Oxford Street, Cambridge, MA 02138.
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The authors declare no conflict of interest.
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This article is a PNAS Direct Submission.
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Data deposition: The data reported in this paper have been deposited at http://research.janelia.org/Chklovskii/data.htm.
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This article contains supporting information online at www.pnas.org/cgi/content/full/0901530106/DCSupplemental.
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Freely available online through the PNAS open access option.
