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Dr. Verzi
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Interdependence of structure and function in the central nervous system

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 models to explore how activity-dependent changes in spine density, shape, or intracellular free calcium may influence patterns of electrical activity; and how electrical activity due to synaptic events and excitable membrane dynamics can, over time, influence dendritic morphology. The equations governing slowly changing spine morphology comprise slow subsystems to the rapid dynamics for electrical/chemical activity, so that the systems beg for new methods in analysis and modeling for disparate time scales.