American Institute of Mathematical Sciences

Advanced
2007, 4(4): 617-631. doi: 10.3934/mbe.2007.4.617

A model of activity-dependent changes in dendritic spine density and spine structure

S. M. Crook 1, , M. Dur-e-Ahmad 2, and  S. M. Baer 2,

1. 

Department of Mathematics and Statistics and School of Life Sciences, Arizona State University, Tempe, Arizona 85287, United States
2. 

Department of Mathematics and Statistics, Arizona State University, Tempe, Arizona 85287, United States, United States

Received  February 2007 Revised  June 2007 Published  August 2007

Recent evidence indicates that the morphology and density of dendritic spines are regulated during synaptic plasticity. See, for instance, a review by Hayashi and Majewska [9]. In this work, we extend previous modeling studies [27] by combining a model for activity-dependent spine density with one for calcium-mediated spine stem restructuring. The model is based on the standard dimensionless cable equation, which represents the change in the membrane potential in a passive dendrite. Additional equations characterize the change in spine density along the dendrite, the current balance equation for an individual spine head, the change in calcium concentration in the spine head, and the dynamics of spine stem resistance. We use computational studies to investigate the changes in spine density and structure for differing synaptic inputs and demonstrate the effects of these changes on the input-output properties of the dendritic branch. Moderate amounts of high-frequency synaptic activation to dendritic spines result in an increase in spine stem resistance that is correlated with spine stem elongation. In addition, the spine density increases both inside and outside the input region. The model is formulated so that this long-term potentiation-inducing stimulus eventually leads to structural stability. In contrast, a prolonged low-frequency stimulation paradigm that would typically induce long-term depression results in a decrease in stem resistance (correlated with stem shortening) and an eventual decrease in spine density.
Keywords: dendritic spine, dendritic plasticity, structural plasticity., long-term potentiation.
Mathematics Subject Classification: 92D3.
Citation: S. M. Crook, M. Dur-e-Ahmad, S. M. Baer. A model of activity-dependent changes in dendritic spine density and spine structure. Mathematical Biosciences & Engineering, 2007, 4 (4) : 617-631. doi: 10.3934/mbe.2007.4.617
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