Anomalous diffusion

Anomalous relaxation and diffusion processes in biomolecular systems The internal dynamics of biomolecular systems such as proteins is characterized by a vast spectrum of time scales and most of the dynamical modes are strongly overdamped and diffusive. Their time evolution and corresponding time correlation functions can be modeled by fractional Fokker-Planck equations, which generalize the idea of Markovian, i.e. memoryless small-step diffusion processes to stochastic processes with long-time memory. The keyword “anomalous relaxation” refers here to the strongly non-exponential decay of the corresponding time correlation functions. We have successfully applied and continue to apply such concepts to model quasielastic neutron scattering spectra and NMR relaxation spectra from proteins.

Anomalous diffusion generally refers to unconstrained diffusion process where the mean square displacement exhibits a non-linear growth with time. The underlying mechanisms are the same as for anomalous relaxation, except that the dynamics of the diffusing particles, which maybe anything from single atoms to whole proteins, is not space-limited. We have studied anomalous lateral diffusion if lipid molecules in lipid bilayers and we have also developed a theoretical framework for anomalous diffusion and relaxation in general, which links such processes to the atomistic dynamics in “crowded” molecular systems. Anomalous diffusion is an ubiquitous phenomenon which is also of great importance in other domains of science, such as in solid state physics, in physical chemistry, and in financial mathematics


  • Hinsen K, Kneller GR
    Communication: A multiscale Bayesian inference approach to analyzing subdiffusion in particle trajectories
    The Journal of Chemical Physics. 2016 Oct 21;145(15):151101

  • Stachura S, Kneller GR
    Communication: Probing anomalous diffusion in frequency space
    J Chem Phys. 2015;143(19):191103

  • Kneller GR
    Communication: A scaling approach to anomalous diffusion
    J Chem Phys. 2014;141(4):41105