Non-Markovian model for transport and reactions of particles in spiny dendrites

Abstract

Motivated by the experiments [Santamaria et al., Neuron 52, 635 (2006)] that indicated the possibility of subdiffusive transport of molecules along dendrites of cerebellar Purkinje cells, we develop a mesoscopic model for transport and chemical reactions of particles in spiny dendrites. The communication between spines and a parent dendrite is described by a non-Markovian random process and, as a result, the overall movement of particles can be subdiffusive. A system of integrodifferential equations is derived for the particles densities in dendrites and spines. This system involves the spine-dendrite interaction term which describes the memory effects and nonlocality in space. We consider the impact of power-law waiting time distributions on the transport of biochemical signals and mechanism of the accumulation of plasticity-inducing signals inside spines.