Comment to the article by Michael J. Saxton: A biological interpretation of transient anomalous subdiffusion. I. qualitative model.

In a recent paper (1), Michael J. Saxton proposes to interpret as anomalous diffusion the occurrence of apparent transient sub-diffusive regimes in mean-squared displacements (MSD) plots, calculated from trajectories of molecules diffusing in living cells, acquired by Single Particle (or Molecule) Tracking techniques (SPT or SMT). The demonstration relies on the analysis of both three-dimensional diffusion by Platani and co-workers (2) and two-dimensional diffusion by Murase and co-workers (3). In particular, the data reported by Murase et al. cover extremely large time scales and experimental conditions: video rate but also high-speed SPT and single fluorescence molecule imaging. This is an exciting opportunity to address the question of anomalous diffusion because the experiments cover time scales ranging from 33 µs up to 5 s, i.e. more than five decades (see Fig. 1(b)). As pointed out by M.J. Saxton, anomalous diffusion (4) arises from an infinite hierarchy of space or energy scales hindering normal diffusion. The normal diffusion law MSD(t) = 4D µ t, where D µ is the microscopic diffusion coefficient, becomes MSD(t) ≈ Ωt α , where Ω is some coefficient and α is the anomalous diffusion exponent. In the case of sub-diffusive behavior, α < 1. However, in cellular processes, the hierarchy is always finite, since there is a short distance cutoff , larger than the molecular scale, and a large distance one, typically the cell size. Therefore one can expect anomalous diffusion regime on a transient time interval only, and crosses-over to normal diffusion at short and long time scales. It is precisely what is observed by Platani et al. (2) and Murase et al. (3). In Fig. 1, the experimental apparent sub-diffusive regimes can cover up to three decades.