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

Abstract

By collecting from literature data experimental evidence of anomalous diffusion of passive tracers inside cytoplasm, and in particular of subdiffusion of mRNA molecules inside live Escherichia coli cells, we obtain the probability density function of molecules’ displacement and we derive the corresponding Fokker–Planck equation. Molecules’ distribution emerges to be related to the Krätzel function and its Fokker–Planck equation to be a fractional diffusion equation in the Erdélyi–Kober sense. The irreducibility of the derived Fokker–Planck equation to those of other literature models is also discussed.

Keywords

• anomalous diffusion
• Fokker–Planck equation
• Erdélyi–Kober fractional equation
• Krätzel function
• mRNA molecules
• Escherichia coli cells