POSTER PRESENTATION Open Access Modeling the effects of anomalous diffusion on synaptic plasticity

The diffusion of cytosolic intracellular signals in spiny dendrites is anomalous due to spine trapping [1]. During anomalous diffusion the mean square displacement (MSD) of diffusing molecules follows a power law, MSD ~ ta, with a called the anomalous exponent. We have shown that a depends on the density and structure of spines and could be a general property of all spiny dendrites [2]. Anomalous diffusion affects the spatial spread and tem-poral concentration profiles of cytosolic molecules, thus potentially affecting the specificity and reliability of synap-tic plasticity. Here we study the effect of anomalous diffu-sion 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 acti-vates MAPK or phosphorylates AMPARs, which are then removed from the synapse [3]. We use the fractional diffusion formulation of anoma-lous diffusion. In such a framework the diffusion-reac-tion equation for a given reactant is