Modeling the effects of anomalous diffusion on synaptic plasticity
© Marinov and Santamaria; licensee BioMed Central Ltd. 2013
Published: 8 July 2013
The diffusion of cytosolic intracellular signals in spiny dendrites is anomalous due to spine trapping . During anomalous diffusion the mean square displacement (MSD) of diffusing molecules follows a power law, MSD ~ tα, with α called the anomalous exponent. We have shown that α depends on the density and structure of spines and could be a general property of all spiny dendrites . Anomalous diffusion affects the spatial spread and temporal concentration profiles of cytosolic molecules, thus potentially affecting the specificity and reliability of synaptic plasticity. Here we study the effect of anomalous diffusion on the spatial and the temporal distribution of signals involved in the expression of long term depression (LTD) in Purkinje cells (PCs). LTD depends on the PKC-MAPK positive feedback cascade. Increased [Ca2+] activates PKC, which in turn activates MAPK. Activated MAPK and [Ca2+] results in production of arachidonic acid which then activates PKC. The activated PKC either further activates MAPK or phosphorylates AMPARs, which are then removed from the synapse .
where α depends on the spine density along the dendrite, γ(t) is the generalized transport coefficient, CRi(t) is the concentration of the reactant Ri and f(CRi, CRj) defines the reaction terms of the specific biochemical reaction. Solving a system of coupled fractional diffusion-reaction equations for [Ca2+], PKC and MAPK is computationally expensive. To address this problem we recently developed a Fractional Integration Toolbox (FIT) .
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