Diffusion trajectory of an asymmetric object: Information overlooked by the mean square displacement

Diffusion of an asymmetric object is characterized by its translational and rotational diffusion coefficients. Until now, anisotropic diffusion studies have been based on ensemble averages. Here we present a theoretical basis for the analysis of the trajectories of a single particle with anisotropic diffusion coefficients. We discuss the relevance of this method for motion of biomolecules in the membrane of living cells.