Theoretical study on electrical properties of dendritic spines.

In most parts of mammalian central nervous system the majority of synapses are located on dendritic spines. Several suggestions have been made about the functional significance of the dendritic spines. We investigate electrical properties of dendritic spines in the neurons with arbitrary dendritic geometry. Following Butz & Cowan (1974), all dendritic branches, including spines, are treated as cylinders of uniform passive membrane. We show that the postsynaptic potential due to the synapse on the spine is represented as a convolution integral of the following two functions. The first is the postsynaptic potential caused by the same synapse on the branching point where the spine stalk is attached to the main dendritic trunk. The second function is determined mainly by the morphological and electrical properties of the spine and it represents the attenuation effect of the spine. On the assumption that the diameter of the spine stalk is sufficiently small compared to that of the parent dendrite to which the spine stem is attached, we obtain an approximation of the second function and conclude that morphological change of the spine does not produce an effective change of the postsynaptic potential, hence does not provide the neural basis for learning or memory simply by changing cable properties of dendrites. Moreover, we show that synapses on the dendritic spine are not effectively isolated from other synapses on the same assumption.