Populations of dendritic spines can change in number and shape quite rapidly as a result of synaptic activity. Here, we explore the consequences of such changes on the input-output properties of a dendritic branch. We consider two models: one for activity-dependent spine densities and the other for calcium-mediated spine-stem restructuring. In the activity-dependent density model we find that for repetitive synaptic input to passive spines, changes in spine density remain local to the input site. For excitable spines, the spine density increases both inside and outside the input region. When the spine stem resistances are relatively high, the transition to higher dendritic output is abrupt; when low, the rate of increase is gradual and resembles long-term potentiation. In the second model, spine density is held constant, but the stem dimensions are allowed to change as a result of stimulation-induced calcium influxes. The model is formulated so that a moderate amount of synaptic activation results in spine stem elongation, whereas high levels of activation result in stem shortening. Under these conditions, passive spines receiving modest stimulation progressively increase their spine stem resistance and head potentials, but little change occurs in the dendritic output. For excitable spines, modest stimulation frequencies cause a lengthening of both stimulated and neighboring spines and the stimulus eventually propagates. High-frequency stimulation that causes spines to shorten in the stimulated region decreases the amplitude of the dendritic output slightly or drastically, depending on initial spine densities and stem resistances.
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