Skip to main content
SpringerLink
Log in

Modelling Dendrite Shape from Wiring Principles

  • Chapter
  • First Online:
The Computing Dendrite

Part of the book series: Springer Series in Computational Neuroscience ((NEUROSCI,volume 11))

  • 2183 Accesses

Abstract

The primary function of a dendrite is to connect a neuron to its inputs. In this chapter, I describe a model that captures the general features of dendritic trees as a function of the connectivity they implement. This model is based on locally optimising connections by weighing costs for total wiring length and conduction times. The model was used to generate synthetic dendrites that are visually indistinguishable from their real counterparts for all dendrite types tested so far. Dendrites of different cell types vary only in the shape of the volume that they span and in the weight between costs for wiring length versus conduction times. Using the model, an equation was derived that relates total dendrite length, number of branch points, spanning volume and the number of synapses, measures that are among the most commonly employed in the study of the molecular and genetic background of dendrite morphology and growth. This equation holds true for all neurons measured so far and confines the possible computations a dendrite is capable of. Finally, beyond the consequences for neuronal morphology and computation, an outlook is given on a number of ways to scale up the single cell model to study the formation of larger neural circuits.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Acebes A, Ferrús A (2000) Cellular and molecular features of axon collaterals and dendrites. Trends Neurosci 23:557–565

    Article  PubMed  CAS  Google Scholar 

  • Ascoli GA (1999) Progress and perspectives in computational neuroanatomy. Anat Rec 257:195–207

    Article  PubMed  CAS  Google Scholar 

  • Ascoli GA (2006) Mobilizing the base of neuroscience data: the case of neuronal morphologies. Nat Rev Neurosci 7:318–324

    Article  PubMed  CAS  Google Scholar 

  • Ascoli GA, Krichmar JL, Nasuto SJ, Senft SL (2001) Generation, description and storage of dendritic morphology data. Philos Trans R Soc Lond B Biol Sci 356:1131–1145

    Article  PubMed  CAS  Google Scholar 

  • Beardwood J, Halton JH, Hammersley JM (1958) The shortest path through many points. Math Proc Cambridge 55:299–327

    Article  Google Scholar 

  • Bentivoglio M, Swanson LW (2001) On the fine structure of the pes Hippocampi major (with plates XIII–XXIII) by Camillo Golgi. Brain Res Bull 54:461–483

    Article  PubMed  Google Scholar 

  • Branco T, Clark BA, Häusser M (2010) Dendritic discrimination of temporal input sequences in cortical neurons. Science 329:1671–1675

    Article  PubMed  CAS  Google Scholar 

  • Branco T, Häusser M (2010) The single dendritic branch as a fundamental functional unit in the nervous system. Curr Opin Neurobiol 20:494–502

    Article  PubMed  CAS  Google Scholar 

  • Budd JML, Kovács K, Ferecskó AS et al (2010) Neocortical axon arbors trade-off material and conduction delay conservation. PLoS Comput Biol 6:e1000711

    Article  PubMed  Google Scholar 

  • Cannon RC, Wheal HV, Turner DA (1999) Dendrites of classes of hippocampal neurons differ in structural complexity and branching patterns. J Comp Neurol 633:619–633

    Article  Google Scholar 

  • Cherniak C (1992) Local optimization of neuron arbors. Biol Cybern 66:503–510

    Article  PubMed  CAS  Google Scholar 

  • Chklovskii DB (2004) Synaptic connectivity and neuronal morphology: two sides of the same coin. Neuron 43:609–617

    PubMed  CAS  Google Scholar 

  • Chklovskii DB, Koulakov AA (2004) Maps in the brain: what can we learn from them? Annu Rev Neurosci 27:369–392

    Article  PubMed  CAS  Google Scholar 

  • Cline HT (2001) Dendritic arbor development and synaptogenesis. Curr Opin Neurobiol 11:118–126

    Article  PubMed  CAS  Google Scholar 

  • Cuntz H (2012) The dendritic density field of a cortical pyramidal cell. Front Neuroanat 6:2

    Article  PubMed  Google Scholar 

  • Cuntz H, Borst A, Segev I (2007) Optimization principles of dendritic structure. Theor Biol Med Model 4:21

    Article  PubMed  Google Scholar 

  • Cuntz H, Forstner F, Borst A, Häusser M (2010) One rule to grow them all: a general theory of neuronal branching and its practical application. PLoS Comput Biol 6:e1000877

    Article  PubMed  Google Scholar 

  • Cuntz H, Forstner F, Haag J, Borst A (2008) The morphological identity of insect dendrites. PLoS Comput Biol 4:e1000251

    Article  PubMed  Google Scholar 

  • Cuntz H, Mathy A, Häusser M (2012) A scaling law derived from optimal dendritic wiring. Proc Natl Acad Sci USA 109:11014–11018

    Article  PubMed  CAS  Google Scholar 

  • DeFelipe J (2010) Cajal’s butterflies of the soul: science and art. Oxford University Press, New York

    Google Scholar 

  • Grueber WB, Jan Y-N (2004) Dendritic development: lessons from Drosophila and related branches. Curr Opin Neurobiol 14:74–82

    Article  PubMed  CAS  Google Scholar 

  • Gulledge AT, Kampa BM, Stuart GJ (2005) Synaptic integration in dendritic trees. J Neurobiol 64:75–90

    Article  PubMed  CAS  Google Scholar 

  • Häusser M, Mel BW (2003) Dendrites: bug or feature? Curr Opin Neurobiol 13:372–383

    Article  PubMed  Google Scholar 

  • Hillman DE (1979) Neuronal shape parameters and substructures as a basis of neuronal form. In: S F (ed) The neuroscience, fourth study program. The MIT Press, Cambridge, MA, pp 477–498

    Google Scholar 

  • Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and ecitation in nerve. J Physiol 117:500–544

    PubMed  CAS  Google Scholar 

  • Jan Y-N, Jan LY (2010) Branching out: mechanisms of dendritic arborization. Nat Rev Neurosci 11:316–328

    Article  PubMed  CAS  Google Scholar 

  • Jan Y-N, Jan LY (2003) The control of dendrite development. Neuron 40:229–242

    Article  PubMed  CAS  Google Scholar 

  • Janson S (2005) Asymptotic degree distribution in random recursive trees. Random Struct Algor 26:69–83

    Article  Google Scholar 

  • Klyachko VA, Stevens CF (2003) Connectivity optimization and the positioning of cortical areas. Proc Natl Acad Sci USA 100:7937–7941

    Article  PubMed  CAS  Google Scholar 

  • Koch C, Poggio TA, Torre V (1983) Nonlinear interactions in a dendritic tree: localization, timing, and role in information processing. Proc Natl Acad Sci USA 80:2799–2802

    Article  PubMed  CAS  Google Scholar 

  • Koene RA, Tijms B, Van Hees P et al (2009) NETMORPH: a framework for the stochastic generation of large scale neuronal networks with realistic neuron morphologies. Neuroinformatics 7:195–210

    Article  PubMed  Google Scholar 

  • Livneh Y, Feinstein N, Klein M, Mizrahi A (2009) Sensory input enhances synaptogenesis of adult-born neurons. J Neurosci 29:86–97

    Article  PubMed  CAS  Google Scholar 

  • London M, Häusser M (2005) Dendritic computation. Annu Rev Neurosci 28:503–532

    Article  PubMed  CAS  Google Scholar 

  • Luczak A (2006) Spatial embedding of neuronal trees modeled by diffusive growth. J Neurosci Methods 157:132–141

    Article  PubMed  Google Scholar 

  • Mainen ZF, Sejnowski TJ (1996) Influence of dendritic structure on firing pattern in model neocortical neurons. Nature 382:363–366

    Article  PubMed  CAS  Google Scholar 

  • Mizrahi A (2007) Dendritic development and plasticity of adult-born neurons in the mouse olfactory bulb. Nat Neurosci 10:444–452

    PubMed  CAS  Google Scholar 

  • Oberlaender M, De Kock CPJ, Bruno RM et al (2011) Cell type-specific three-dimensional structure of thalamocortical circuits in a column of rat vibrissal cortex. Cereb Cortex 22:2375–2391

    Article  PubMed  Google Scholar 

  • Parrish JZ, Emoto K, Kim MD, Jan Y-N (2007) Mechanisms that regulate establishment, maintenance, and remodeling of dendritic fields. Annu Rev Neurosci 30:399–423

    Article  PubMed  CAS  Google Scholar 

  • Van Pelt J, Van Ooyen A, Uylings HBM (2001) The need for integrating neuronal morphology databases and computational environments in exploring neuronal structure and function. Anat Embryol 204:255–265

    Article  PubMed  Google Scholar 

  • Van Pelt J, Uylings HBM (2002) Branching rates and growth functions in the outgrowth of dendritic branching patterns. Network 13:261–281

    Article  PubMed  Google Scholar 

  • Poirazi P, Brannon T, Mel BW (2003) Pyramidal neuron as two-layer neural network. Neuron 37:989–999

    Article  PubMed  CAS  Google Scholar 

  • Polsky A, Mel BW, Schiller J (2004) Computational subunits in thin dendrites of pyramidal cells. Nat Neurosci 7:621–627

    Article  PubMed  CAS  Google Scholar 

  • Prim RC (1957) Shortest connection networks and some generalizations. Bell Syst Tech J 36:1389–1401

    Article  Google Scholar 

  • Rall W (1959) Branching dendritic trees and motoneuron membrane resistivity. Exp Neurol 527:491–527

    Article  Google Scholar 

  • Rall W, Burke RE, Smith TG et al (1967) Dendritic location of synapses and possible mechanisms for the monosynaptic EPSP in motoneurons. J Neurophysiol 30:1169–1193

    PubMed  CAS  Google Scholar 

  • Rall W, Rinzel J (1973) Branch input resistance and steady attenuation for input to one branch of a dendritic neuron model. Biophys J 13:648–687

    Article  PubMed  CAS  Google Scholar 

  • Ramón y Cajal S (1995) Histology of the nervous system of man and vertebrates. Oxford University Press, New York

    Google Scholar 

  • Rihn LL, Claiborne BJ (1990) Dendritic growth and regression in rat dentate granule cells during late postnatal development. Brain Res Dev Brain Res 54:115–124

    Article  PubMed  CAS  Google Scholar 

  • Samsonovich AV, Ascoli GA (2003) Statistical morphological analysis of hippocampal principal neurons indicates cell-specific repulsion of dendrites from their own cell. J Neurosci Res 71:173–187

    Article  PubMed  CAS  Google Scholar 

  • Segev I, London M (2000) Untangling dendrites with quantitative models. Science 290:744–750

    Article  PubMed  CAS  Google Scholar 

  • Shepherd GMG, Stepanyants A, Bureau I et al (2005) Geometric and functional organization of cortical circuits. Nat Neurosci 8:782–790

    Article  PubMed  CAS  Google Scholar 

  • Sholl DA (1959) A comparative study of the neuronal packing density in the cerebral cortex. J Anat 93:143–158

    PubMed  CAS  Google Scholar 

  • Snider J, Pillai A, Stevens CF (2010) A universal property of axonal and dendritic arbors. Neuron 66:45–56

    Article  PubMed  CAS  Google Scholar 

  • Steele JM, Shepp LA, Eddy WF (1987) On the number of leaves of a Euclidean minimal spanning tree. J Appl Probab 24:809–826

    Article  Google Scholar 

  • Stuart GJ, Spruston N, Häusser M (2007) Dendrites. Oxford University Press, USA

    Book  Google Scholar 

  • Teeter CM, Stevens CF (2011) A general principle of neural arbor branch density. Curr Biol 21:2105–2108

    Article  PubMed  CAS  Google Scholar 

  • Torben-Nielsen B, Stiefel KM (2010) An inverse approach for elucidating dendritic function. Front Comput Neurosci 4:128

    Article  PubMed  Google Scholar 

  • Torben-Nielsen B, Vanderlooy S, Postma EO (2008) Non-parametric algorithmic generation of neuronal morphologies. Neuroinformatics 6:257–277

    Article  PubMed  Google Scholar 

  • Uylings HBM, Van Pelt J (2002) Measures for quantifying dendritic arborizations. Network 13:397–414

    Article  PubMed  Google Scholar 

  • Wang Y, Gupta A, Toledo-rodriguez M, Wu CZ (2002) Anatomical, physiological, molecular and circuit properties of nest basket cells in the developing somatosensory cortex. Cereb Cortex 395–410

    Google Scholar 

  • Wen Q, Chklovskii DB (2008) A cost-benefit analysis of neuronal morphology. J Neurophys 99:2320–2328

    Article  Google Scholar 

  • Wen Q, Stepanyants A, Elston GN et al (2009) Maximization of the connectivity repertoire as a statistical principle governing the shapes of dendritic arbors. Proc Natl Acad Sci USA 106:12536–12541

    Article  PubMed  CAS  Google Scholar 

  • Williams SR, Stuart GJ (2002) Dependence of EPSP efficacy on synapse location in neocortical pyramidal neurons. Science 295:1907–1910

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgments

The work presented here was a collaborative effort together with Alexander Borst, Friedrich Förstner, Jürgen Haag, Michael Häusser, Alexandre Mathy and Idan Segev. I would like to thank Peter Jedlicka for constructive criticism on this manuscript.

Author information

Authors and Affiliations

  1. Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society, Frankfurt/Main, Germany

    Hermann Cuntz

  2. Institute of Clinical Neuroanatomy, Goethe University, Theodor-Stern-Kai 7, Frankfurt/Main, D-60590, Germany

    Hermann Cuntz

Authors
  1. Hermann Cuntz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hermann Cuntz .

Editor information

Editors and Affiliations

  1. Institute of Clinical Neuroanatomy, Ernst Strüngmann Institute (ESI) for Neuroscience in Cooperation with Max Planck Society & Goethe-University, Frankfurt, Germany

    Hermann Cuntz

  2. Institute for Theoretical Biology, Humboldt-Universität zu Berlin, Berlin, Germany

    Michiel W.H. Remme

  3. Department of Neurobiology, Hebrew University of Jerusalem, Jerusalem, Israel

    Benjamin Torben-Nielsen

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this chapter

Cite this chapter

Cuntz, H. (2014). Modelling Dendrite Shape from Wiring Principles. In: Cuntz, H., Remme, M., Torben-Nielsen, B. (eds) The Computing Dendrite. Springer Series in Computational Neuroscience, vol 11. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8094-5_6

Download citation

Publish with us

Policies and ethics

Search

Navigation