A Theoretical Analysis of Electrical Properties of Spines
The electrical properties of a cortical (spiny) pyramidal cell were analyzed on the basis of passive cable theory from measurements made on histological material (Koch, Poggio & Torre 1982). The basis of this analysis is the solution o the cable equation for an arbitrary branched dendritic tree. 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. From our investigation four major points emerge: 1. Spine 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. 2. 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 resulting saturation curve. This might be the basic mechanism underlying ultra-short memory, long-term potentiation in the hippocampus or learning in the cerebellum. 3. 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. 4. 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 100usec.