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A Compartmental Model for Activity-Dependent Dendritic Spine Branching

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Abstract

Dendritic spines are small, mushroom-like protrusions from the arbor of a neuron in the central nervous system. Interdependent changes in the morphology, biochemistry, and activity of spines have been associated with learning and memory. Moreover, post-mortem cortices from patients with Alzheimer’s or Parkinson’s disease exhibit biochemical and physical alterations within their dendritic arbors and a reduction in the number of dendritic spines. For over a decade, experimentalists have observed perforations in postsynaptic densities on dendritic spines after induction of long-term potentiation, a sustained enhancement of response to a brief electrical or chemical stimulus, associated with learning and memory. In more recent work, some suggest that activity-dependent intraspine calcium may regulate the surface area of the spine head, and reorganization of postsynaptic densities on the surface.

In this paper, we develop a model of a dendritic spine with the ability to partition its transmission and receptor zones, as well as the entire spine head. Simulations are initially performed with fixed parameters for morphology to study electrical properties and identify parameters that increase efficacy of the synaptic connection. Equations are then introduced to incorporate calcium as a second messenger in regulating continuous changes in morphology. In the model, activity affects compartmental calcium, which regulates spine head morphology. Conversely, spine head morphology affects the level of local activity, whether the spines are modeled with passive membrane properties, or excitable membrane using Hodgkin–Huxley kinetics. Results indicate that merely separating the postsynaptic receptors on the surface of the spine may add to the diversity of circuitry, but does not change the efficacy of the synapse. However, when the surface area of the spine is a dynamic variable, efficacy of the synapse may vary continuously over time.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, San Diego State University-Imperial Valley Campus, 720 Heber Avenue, Calexico, CA, 92231, USA

    D. W. Verzi & O. Y. Noris

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  1. D. W. Verzi
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  2. O. Y. Noris
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Correspondence to D. W. Verzi.

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Verzi, D.W., Noris, O.Y. A Compartmental Model for Activity-Dependent Dendritic Spine Branching. Bull. Math. Biol. 71, 1048–1072 (2009). https://doi.org/10.1007/s11538-009-9393-y

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  • DOI: https://doi.org/10.1007/s11538-009-9393-y

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