Skip to main content
SpringerLink
Log in

Dendritic Spines: Continuum Theory

Encyclopedia of Computational Neuroscience

  • 189 Accesses

Synonyms

Baer-Rinzel (BR) continuum model; Continuum spine model; Continuum spine theory; Continuum theory for active spines

Definition

The continuum theory for dendritic spines, developed by Baer and Rinzel (1991), is an extension of classical cable theory for which the distribution of spines is treated as a continuum. The theory applies when the interspine distance is much less than the length scale of the dendrite, for example, when the dendrite is populated by a large number of spines. The formulation maintains the basic feature that there is no direct coupling between neighboring spines; voltage spread along dendrites is the only way for spines to interact. With the continuum theory, different spine morphologies, multiple populations of spines, and distributed physiological properties are represented explicitly and compactly by relatively few differential equations. The theory is general so that idealized or realistic kinetic models may be adapted.

Detailed Description

Classical...

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Baer SM, Rinzel J (1991) Propagation of dendritic spikes mediated by excitable spines: a continuum theory. J Neurophysiol 65:874–890

    CAS  PubMed  Google Scholar 

  • Bell J, Holmes M (1992) Model of the dynamics of receptor potential in a mechanoreceptor. Math Biosci 110:139–174

    Article  CAS  PubMed  Google Scholar 

  • Coombes S, Bressloff PC (2003) Saltatory waves in the spike-diffuse-spike model of active dendritic spines. Phys Rev Lett 91:028102

    Article  CAS  PubMed  Google Scholar 

  • Coutts EJ, Lord GJ (2013) Effects of noise on models of spiny dendrites. J Comput Neurosci 34:245–257

    Article  PubMed  Google Scholar 

  • Holmes WR, Woody CD (1989) Effects of uniform and non-uniform synaptic ‘activation-distributions’ on the cable properties of modeled cortical pyramidal neurons. Brain Res 505:12–22

    Article  CAS  PubMed  Google Scholar 

  • Jack JJB, Noble D, Tsien RW (1975) Electric current flow in excitable cells. Clarendon, Oxford

    Google Scholar 

  • Miller JP, Rall W, Rinzel J (1985) Synaptic amplification by active membrane in dendritic spines. Brain Res 325:325–330

    Article  CAS  PubMed  Google Scholar 

  • Rall W (1977) Core conductor theory and cable properties of neurons. In: Kandel ER, Brookhardt JM, Mountcastle VM (eds) Handbook of physiology, the nervous system, cellular biology of neurons. American Physiological Society, Bethesda, pp 39–97

    Google Scholar 

  • Rall W, Rinzel J (1971a) Dendritic spines and synaptic potency explored theoretically. Proc Int Union Physiol Sci XXV Int Congr IX:466

    Google Scholar 

  • Rall W, Rinzel J (1971b) Dendritic spine function and synaptic attenuation calculations. Prog Abstr Soc Neurosci 1:64

    Google Scholar 

  • Rall W, Segev I (1987) Functional possibilities for synapses on dendrites and on dendritic spines. In: Edelman GM, Gall WE, Cowan WM (eds) Synaptic function. Wiley, New York, pp 605–636

    Google Scholar 

  • Rall W, Shepherd GM (1968) Theoretical reconstruction of field potentials and dendrodendritic synaptic interactions in olfactory bulb. J Neurophysiol 31:884–915

    CAS  PubMed  Google Scholar 

  • Segev I, Rall W (1988) Computational study of an excitable dendritic spine. J Neurophysiol 60:499–523

    CAS  PubMed  Google Scholar 

  • Shepherd GM, Brayton RK, Miller JP, Segev I, Rinzel J, Rall W (1985) Signal enhancement in distal cortical dendrites by means of interactions between active dendritic spines. Proc Natl Acad Sci U S A 82:2192–2195

    Article  CAS  PubMed Central  PubMed  Google Scholar 

  • Verzi DW, Rheuben MB, Baer SM (2004) Impact of time-dependent changes in spine density and spine shape on the input–output properties of a dendritic branch: a computational study. J Neurophysiol 93:2073–2089

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ, USA

    Steven M. Baer

Authors
  1. Steven M. Baer
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Steven M. Baer .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this entry

Cite this entry

Baer, S.M. (2014). Dendritic Spines: Continuum Theory. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_797-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_797-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

  • eBook Packages: Springer Reference Biomedicine and Life SciencesReference Module Biomedical and Life Sciences

Publish with us

Policies and ethics

Chapter history

  1. Latest

    Dendritic Spines: Continuum Theory
    Published:
    28 July 2019

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_797-2

  2. Original

    Dendritic Spines: Continuum Theory
    Published:
    14 March 2014

    DOI: https://doi.org/10.1007/978-1-4614-7320-6_797-1

Search

Navigation