Analytical description of anomalous diffusion in living cells

We propose a stochastic model for intracellular transport processes associated with the activity of molecular motors. This out-of-equilibrium model, based on a generalized Langevin equation, considers a particle immersed in a viscoelastic environment and simultaneously driven by an external random force that models the motors activity. An analytical expression for the mean square displacement is derived, which exhibits a subdiffusive to superdiffusive transition. We show that the experimentally accessible statistical properties of the diffusive particle motion can be reproduced by this model.

💡 Research Summary

The paper presents a comprehensive stochastic framework for describing intracellular transport that incorporates both the viscoelastic nature of the cytoplasmic environment and the active, out‑of‑equilibrium forces generated by molecular motors. Starting from a generalized Langevin equation (GLE), the authors model the particle’s motion as being subjected to a memory kernel K(t)∝t⁻ᵅ (0 < α < 1) that captures the long‑time viscoelastic response of the crowded cytoskeleton, and an internal thermal noise ξ(t) linked to K(t) by the fluctuation‑dissipation theorem (FDT). To account for motor activity, they introduce an additional random force F_ext(t) with zero mean and a power‑law autocorrelation ⟨F_ext(t)F_ext(0)⟩∝t⁻ᵞ (0 < γ < 1). This “colored” noise represents the persistent, ATP‑driven fluctuations generated by motor stepping and cargo binding/unbinding events.

By applying Laplace transforms, the authors solve the GLE analytically and obtain explicit expressions for the particle’s velocity and position. The mean‑square displacement (MSD) follows a sum of two scaling contributions: \