A surging amount of experimental and simulations studies reveals persistent anomalous diffusion in both cellular membranes and the cytoplasm [1,2]. The anomalous diffusion is observed for micron-sized objects down to labelled single molecules such as green fluorescent proteins [3].
This talk will first present results from large scale computer simulations and stochastic analysis of the motion of lipids and embedded proteins in lipid bilayer model membranes [4], indicating that increased disorder leads to longer and longer lasting anomalous diffusion. In particular, the motion of lipids and proteins can become non-Gaussian [4]. In the membranes of living cells anomalous diffusion of embedded protein channels can last over several hundreds of seconds [5]. In particular, this anomalous diffusion can become non-ergodic and exhibit ageing, two topics explained and discussed in this talk [6].
The findings of anomalous diffusion in membranes will be complemented by a brief summary of anomalous diffusion in the cellular cytoplasm, referring to both subdiffusion of passive tracers and superdiffusion due to active motion in cells.

[1] K. Norregaard, R. Metzler, C. Ritter, K. Berg-Sorensen, and L. Oddershede, Chem. Rev. 117, 4342 (2017).
[2] F. Hofling and T. Franosch, Rep Progr Phys 76, 046602 (2013).
[3] C Di Rienzo, V Piazza, E Gratton, F Beltram, and F Cardarelli, Nature Comm 5, 5891 (2014).
[4] J-H Jeon, HM-S Monne, M Javanainen, and R Metzler, Phys Rev Lett 109, 188103 (2012); J-H Jeon, M Javanainen, H Martinez-Seara, R Metzler, and I Vattulainen, Phys Rev X 6, 021006 (2016).
[5] AV Weigel, B Simon, MM Tamkun, and D Krapf, Proc Natl Acad Sci USA 108, 6438 (2011).
[6] R Metzler, J-H Jeon, AG Cherstvy, E Barkai, Phys Chem Chem Phys 16 24128 (2014).