Encyclopedia of Computational Neuroscience

2015 Edition
| Editors: Dieter Jaeger, Ranu Jung

Dendritic Spines: Continuum Theory

  • Steven M. Baer
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-6675-8_797

Synonyms

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

Classica...

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

References

  1. Baer SM, Rinzel J (1991) Propagation of dendritic spikes mediated by excitable spines: a continuum theory. J Neurophysiol 65:874–890PubMedGoogle Scholar
  2. Bell J, Holmes M (1992) Model of the dynamics of receptor potential in a mechanoreceptor. Math Biosci 110:139–174PubMedGoogle Scholar
  3. Coombes S, Bressloff PC (2003) Saltatory waves in the spike-diffuse-spike model of active dendritic spines. Phys Rev Lett 91:028102PubMedGoogle Scholar
  4. Coutts EJ, Lord GJ (2013) Effects of noise on models of spiny dendrites. J Comput Neurosci 34:245–257PubMedGoogle Scholar
  5. 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 505:12–22PubMedGoogle Scholar
  6. Jack JJB, Noble D, Tsien RW (1975) Electric current flow in excitable cells. Clarendon, OxfordGoogle Scholar
  7. Miller JP, Rall W, Rinzel J (1985) Synaptic amplification by active membrane in dendritic spines. Brain Res 325:325–330PubMedGoogle Scholar
  8. 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 39–97Google Scholar
  9. Rall W, Rinzel J (1971a) Dendritic spines and synaptic potency explored theoretically. Proc Int Union Physiol Sci XXV Int Congr IX:466Google Scholar
  10. Rall W, Rinzel J (1971b) Dendritic spine function and synaptic attenuation calculations. Prog Abstr Soc Neurosci 1:64Google Scholar
  11. 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 605–636Google Scholar
  12. Rall W, Shepherd GM (1968) Theoretical reconstruction of field potentials and dendrodendritic synaptic interactions in olfactory bulb. J Neurophysiol 31:884–915PubMedGoogle Scholar
  13. Segev I, Rall W (1988) Computational study of an excitable dendritic spine. J Neurophysiol 60:499–523PubMedGoogle Scholar
  14. 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 82:2192–2195PubMedCentralPubMedGoogle Scholar
  15. 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 93:2073–2089PubMedGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.School of Mathematical and Statistical SciencesArizona State UniversityTempeUSA