A compartmental model was employed to investigate the electrical behavior of a dendritic spine having excitable membrane at the spine head. Here we used the Hodgkin and Huxley equations to generate excitable membrane properties; in some cases the kinetics were modified to get a longer duration action potential. Passive membrane was assumed for both the spine stem and the dendritic shaft. Synaptic input was modeled as a transient conductance increase (alpha-function) that lies in series with a battery (that corresponds to an excitatory or inhibitory synaptic equilibrium potential). 2. Threshold conditions for an action potential at the spine head membrane were found to be sensitive to the membrane properties at the spine head and to the conductance loading provided by the spine stem and the dendritic tree. Increasing either the number or the open times of the excitable channels had the effect of lowering spike threshold voltage. Increasing the spine stem resistance (RSS) or increasing the input resistance at the spinal base (RSB) also lowered the spike threshold voltage. Because a preexisting dendritic depolarization reduced the spine stem current, this lowered the spike threshold voltage, and this threshold was also shown to be sensitive to the distribution of membrane potential along the dendrite. 3. For each set of spine and dendritic parameters, there was an optimal range of RSS values for which the excitable properties at the spine head membrane resulted in maximal amplification of the dendritic excitatory postsynaptic potential (EPSP), when compared with that produced by a corresponding passive spine. This optimal range depended (with nonlinear sensitivity) on the properties of the voltage-gated channels at the spine head membrane. The maximal amplification found (for each of several sets of parameters) ranged from two to thirteen times. 4. Near this optimal range of RSS values, there was maximal (nonlinear) sensitivity of the dendritic EPSP amplitude to small changes in RSS. A minor decrease resulted in a subthreshold response at the spine head, and this resulted in a large decrease in the EPSP amplitude at the spine base. Increasing the value of RSS above this optimal range decreased the amount of spine stem current flowing to the spine base (by Ohm's law); this decreased the EPSP amplitude at the spine base. The demonstration of this optimum agrees with earlier expectations and results. 5. Excitable dendritic spines can be seen to provide an anatomical arrangement that economizes both excitable and synaptic channels. A small number of these channels (located in spine head membrane) can produce a large dendritic depolarization.(ABSTRACT TRUNCATED AT 400 WORDS)
