Passive cable properties of dendritic spines and spiny neurons

A cable model of the linear properties of dendritic spines was generated using the Laplace transform technique. Analytical solutions for the voltages generated in the spine by a current impulse at the spine head were used in a numerical procedure for simulating the effect of a synaptic conductance change. The synaptic current produced by the conductance change was used as an input for evaluation of the postsynaptic potential and current injected into the dendrite at the base of the spine. The primary effect of the dendritic spine was to attenuate synaptic current. This effect was produced by the high input impedance at axospinous synapses, which resulted in giant spike-like excitatory postsynaptic potentials (EPSPs) that approached the reversal potential of the synapse and thus reduced the potential gradient driving the synaptic current. Although virtually all of the synaptic current was transferred to the dendrite, it produced much smaller EPSPs there due to the low dendritic input impedance. Very small conductance changes produced near maximal synaptic currents in dendritic spines. The current attenuating effect of the spine was accentuated with brief synaptic transients and reduced with prolonged synaptic conductance changes. The size and shape of the spine head, and the diameter and boundary conditions of the dendrite had little or no effect on current attenuation for spines in the naturally occurring size range. The diameter and length of the spine stalk and the size and location of the spine apparatus were the key morphological factors determining the synaptic currents generated by axospinous synapses. Naturally occurring size and shape differences among dendritic spines produced large differences in synaptic potency when compared in a model spiny neuron based on the neostriatal spiny projection neuron. These differences were comparable to those produced by differences in synaptic-location on the same neuron.