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# A Theoretical Analysis of Electrical Properties of Spines

Koch, Christof and Poggio, Tomaso (1983) A Theoretical Analysis of Electrical Properties of Spines. Proceedings of the Royal Society of London. Series B, Biological Sciences, 218 (1213). pp. 455-477. ISSN 0962-8452. https://resolver.caltech.edu/CaltechAUTHORS:20130816-103203068

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## Abstract

The electrical properties of a cortical (spiny) pyramidal cell were analysed on the basis of passive cable theory from measurements made on histological material (C. Koch, T. Poggio & V. Torre, Phil. Trans. R. Soc. Lond. B 298, 227-264 (1982)). The basis of this analysis is the solution of the cable equation for an arbitrary branched dendritic tree. The conclusions, however, hold within a wide range of values of electrical parameters, provided that the membrane is passive. We determined the potential at the soma as a function of the synaptic input (transient conductance changes) and as a function of the spine neck dimensions, following a suggestion by W. Rall (Brain Inf. Serv. Res. Rep. 3, 13-21 (1974); Studies in neurophysiology (ed. R. Porter), pp. 203-209 (Cambridge University Press, 1978)) that the spine neck might be an important determinant in regulating the efficiency of synapses on spines. From our investigation four major points emerge. (i) Spines may effectively compress the effect of each single excitatory synapse on the soma, mapping a wide range of inputs onto a limited range of outputs (nonlinear saturation). This is also true for very fast transient inputs, in sharp contrast with the case of a synapse on a dendrite. (ii) The somatic depolarization due to an excitatory synapse on a spine is a very sensitive function of the spine neck length and diameter. Thus the spine can effectively control the attenuation of its input via the dimensions of the neck, thereby setting the shape of the resulting saturation curve. There is an optimal neck diameter for which variations of the neck are most effective in controlling the weight of the excitatory spine synapse. For reasonable parameter values this optimal value is consistent with anatomical data. This might be the basic mechanism underlying ultra-short memory, long-term potentiation in the hippocampus or learning in the cerebellum. (iii) Spines with shunting inhibitory synapses on them are ineffective in reducing the somatic depolarization due to excitatory inputs on the dendritic shaft or on other spines. Thus isolated inhibitory synapses on a spine are not expected to occur. (iv) The conjunction of an excitatory synapse with a shunting inhibitory synapse on the same spine may result in a time-discrimination circuit with a temporal resolution of around 100 $\mu$s.

Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/0.1098/rspb.1983.0051 DOIArticle
http://rspb.royalsocietypublishing.org/content/218/1213/455.abstractPublisherArticle
http://www.jstor.org/stable/35802JSTORArticle
ORCID:
AuthorORCID
Koch, Christof0000-0001-6482-8067
Additional Information:Received 1 March 1983. Weare grateful to B. B. Boycott, F.R.S., V. Braitenberg, F. H. C. Crick, F.R.S., K. Hausen, K. Nielsen and J. Rauschecker for reading various versions of the manuscript and for many comments and ideas. A. Schiiz, F. H. C. Crick, V. Braitenberg and V. Torre aroused our interest in the properties of spines. We are also indebted to V. Braitenberg, who kindly provided the histological material on which our analysis is based. T. Wiegand helped us with the figures. This work was done at the Max Planck Institut fiir biologische Kybernetik. C. K. was supported by a fellowship from the Studienstiftung des deutschen Volkes and is presently supported by the Fritz Thyssen Stiftung. Support for T.P. is provided by the Advanced Research Projects Agency of the Department of Defense under Office of Naval Research contract N00014-75-C-0643 and by the National Science Foundation grant MCS-79-23110. Travel for collaboration purposes was supported under N.A.T.O. grant number 237.81.
Group:Koch Laboratory (KLAB)
Funders:
Funding AgencyGrant Number
Studienstiftung des deutschen VolkesUNSPECIFIED
Fritz Thyssen StiftungUNSPECIFIED
Office of Naval Research (ONR)N00014-75-C-0643
NSFMCS-79-23110
North Atlantic Treaty Organization (NATO)237.81