Propagation of CaMKII translocation waves in heterogeneous spiny dendrites
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Accepted version
Author(s)
Bressloff, Paul C
Type
Journal Article
Abstract
CaMKII (Ca2+-calmodulin-dependent protein kinase II) is a key regulator of glutamatergic synapses and plays an essential role in many forms of synaptic plasticity. It has recently been observed experimentally that stimulating a local region of dendrite not only induces the local translocation of CaMKII from the dendritic shaft to synaptic targets within spines, but also initiates a wave of CaMKII translocation that spreads distally through the dendrite with an average speed of order 1μm/s. We have previously developed a simple reaction–diffusion model of CaMKII translocation waves that can account for the observed wavespeed and predicts wave propagation failure if the density of spines is too high. A major simplification of our previous model was to treat the distribution of spines as spatially uniform. However, there are at least two sources of heterogeneity in the spine distribution that occur on two different spatial scales. First, spines are discrete entities that are joined to a dendritic branch via a thin spine neck of submicron radius, resulting in spatial variations in spine density at the micron level. The second source of heterogeneity occurs on a much longer length scale and reflects the experimental observation that there is a slow proximal to distal variation in the density of spines. In this paper, we analyze how both sources of heterogeneity modulate the speed of CaMKII translocation waves along a spiny dendrite. We adapt methods from the study of the spread of biological invasions in heterogeneous environments, including homogenization theory of pulsating fronts and Hamilton–Jacobi dynamics of sharp interfaces.
Date Issued
2013-06
Date Acceptance
2012-04-18
Citation
Journal of Mathematical Biology, 2013, 66 (7), pp.1499-1525
ISSN
0303-6812
Publisher
Springer Science and Business Media LLC
Start Page
1499
End Page
1525
Journal / Book Title
Journal of Mathematical Biology
Volume
66
Issue
7
Copyright Statement
Copyright © 2013 Springer-Verlag. This version of the article has been accepted for publication, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: http://dx.doi.org/10.1007/s00285-012-0542-9
Identifier
http://dx.doi.org/10.1007/s00285-012-0542-9
Publication Status
Published
Date Publish Online
2012-05-16