A theoretical analysis of electrical properties of spines

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 hippo­ campus 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 μs.