Active transport in complex media: Relationship between persistence and superdiffusion

We study the relationship between anomalous diffusion and persistent motion of micron-sized particles moving in a viscoelastic environment and subjected to an external noise. In the framework of a generalized Langevin equation, we compare the analytical expressions of the mean square displacement and the mean cosine of the turning angle. Both magnitudes can be easily computed from the particles trajectories, and allow us to investigate the different anomalous regimes typically obtained, for instance, in single particle tracking experiments within living cells. Finally, we analyze the directional changes occurring during the motion of pigment organelles driven by molecular motors in Xenopus laevis melanocytes, as an example of application of our model.