Diffusion and weak ergodicity breaking within living cells

Diffusion of single molecules and organelles in living cells has attracted considerable interest. The motion so essential for intra- and intercellular transport, regulation, and signaling, and hence for the life within cells exhibits surprising deviations from normal Brownian motion. Using optical tweezers combined with single particle tracking inside living cellular organisms we study intracellular diffusion of nano-sized organelles inside living cells. The temperature increase caused by absorption by the laser light as well as the potential physiological damage are important also to consider and will be addressed [1,2]. Lipid granules inside living S. pombe yeast cells perform anomalous diffusion, with subdiffusion being most predominant at short time-lags, and the biological functions giving motility footprints at longer time-lags [3]. At very short timescales, the subdiffusion of lipid granules is well described by the laws of continuous time random walk theory and at longer timescales the granule motion is consistent with fractional Brownian motion. Ordinary Brownian diffusion exhibits ergodicity: long time averages of a measured process for a single particle are equal to the corresponding average over a statistical ensemble. Ergodicity is also fulfilled for anomalous processes governed by fractional Brownian motion. In our analysis of the passive diffusion of liquid granules in living fission yeast cells and in endothelial cells we demonstrate that the diffusion is not only anomalous, but that ergodicity is indeed violated on biochemically relevant time scales [4,5]. Ergodicity breaking implies that time averages based on individual trajectories are random variables, such that our common wisdom associated with the picture of Brownian motion fails. While ergodicity breaking is expected in large live organisms it is surprising to find it already for a small particle essentially coupled to a thermal heat bath thus indicating that basic concepts of statistical Physics must be replaced when we analyze certain aspects of biomolecular dynamics in the cell.

1. A. Kyrsting, P.M. Bendix, D.G. Stamou, and L.B. Oddershede, Nano Letters, vol 11 p.888-892 (2011).
2. M.B. Rasmussen, L.B. Oddershede, H. Siegumfeldt, Applied and Environmental Microbiology, vol.74, no.8 (2008).
3. I.M. Tolic-Nørrelykke, E.-L. Munteanu, G. Thon, L. Oddershede, and K. Berg-Sørensen, PRL, vol.93, p.078102 (2004).
4. J.H. Jeon, V. Tejedor, S. Burov, E. Barkai, C. Selhuber, K. Berg-Sørensen, L. Oddershede, R. Metzler, PRL, vol. 106 p.048103 (2011).
5. N. Leijnse, J.-H. Jeon, S. Loft, R. Metzler, L.B. Oddershede, EPJ accepted (2012).