A stage-structured population model for activity-dependent dendritic spines.

Here we present a novel application of stage-structured population modelling to explore the properties of neuronal dendrites with spines. Dendritic spines are small protrusions that emanate from the dendritic shaft of several functionally important neurons in the cerebral cortex. They are the postsynaptic sites of over 90% of excitatory synapses in the mammalian brain. Here, we formulate a stage-structured population model of a passive dendrite with activity-dependent spines using a continuum approach. This computational study models three dynamic populations of activity-dependent spine types, corresponding to the anatomical categories of stubby, mushroom, and thin spines. In this stage-structured population model, transitions between spine type populations are driven by calcium levels that depend on local electrical activity. We explore the influence of the changing spine populations and spine types on the development of electrical propagation pathways in response to repetitive synaptic input, and which input frequencies are best for facilitating these pathways.