The Fokker-Planck equation of the superstatistical fractional Brownian motion with application to passive tracers inside cytoplasm

Abstract

By collecting from literature data the experimental evidences of anomalous diffusion of passive tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live E. coli cells, we get the probability density function of molecules' displacement and we derive the corresponding Fokker-Planck equation. Molecules' distribution emerges to be related to the Kr\"atzel function and its Fokker-Planck equation be a fractional diffusion equation in the Erd\'elyi-Kober sense. The irreducibility of the derived Fokker-Planck equation to those of other literature models is also discussed.