Biologically Inert Particles Anomalous Diffusion

The transport of inert particles, fluorescein dextran, in spiny dendrites of cerebellar Purkinje cells is subdiffusive [375], i.e., (x t)), where 0 y 1. 

The model formulated in Sect. 8.3.1 predicts this subdiffusive behavior. For simplicity we assume that the waiting time PDF for the dendrite (pyit) is exponential. Experimental evidence suggests a power-law distribution for the waiting time PDF 2(0 as i 00, which reads in Laplace space 2 s) = 1 - (tj)  

---

Santamaria et al. [375] found that the transport of biologically inert particles, fluorescein dextran, in spiny dendrites is very slow compared with standard diffusion. The mean-square displacement is x t)) with y < 1 [298, 379]. The anomalous diffusion appears to be caused by the dendritic spines acting as the traps for the particles. We present here a mesoscopic model for the transport and biochemical reactions inside a population of spines and dendrites [122]. The morphology of spiny dendrites is very complex the distances between the spines and their sizes and shapes are randomly distributed [179, 362]. The model allows us to deal with the morphological diversity of dendritic spines via the transparent formalism of waiting time distributions. 

---