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The spread of electrical activity in a dendritic tree is shaped, in part, by its morphology. Conversely, experimental evidence is growing that electrical and chemical activity can slowly shape the morphology of the dendrite. In this theoretical study, we view dendritic spines as dynamic elements, with biophysical properties that change in response to patterns of chemical and/or electrical activity. We are motivated by recent experiments and diagrammatic models suggesting that activity-dependent processes can regulate structural modifications in dendritic spines as well as the density of spines. We formulate a nonlinear cable model to explore how activity-dependent changes in spine density (minutes to hours) can influence patterns of electrical activity; and how electrical activity due to synaptic events and excitable membrane dynamics can, over time, influence the spine distribution and hence the morphology of the dendrite. The equations governing slowly changing spine morphology and intraspine calcium dynamics comprise a slow subsystem to the cable model. We derive slow subsystems for two specific diagrammatic models: Structural synaptic plasticity associated with LTP, proposed by Geinisman (1996), and spine elongation and shortening depending on different levels of intraspine calcium, proposed by Harris (1999).