a) Average scale-dependent mobility of GFP 1 (Nuc: n=14 cells, Cyt: n=13 cells), GFP 3 (Nuc: n=16 cells, Cyt: n=15 cells) and GFP 5 (Nuc: n=18 cells, Cyt: n=18 cells) in the nucleus and cytoplasm. The time and length scale-dependent protein mobility is represented as the MSD (top row) or as the time-dependent diffusion coefficient D( t) in double-logarithmic representation (bottom row). Data are mean values±s.e.m. The solid lines represent a fit according to the random obstacle model in Equation (1). ( b) Time-dependent diffusion coefficients were well described by a model for diffusion in a random porous medium. On small scales, molecules diffuse freely with D 0 (left). At a characteristic distance λ, they collide with an immobile obstacle. On large scales, this collision–diffusion process can be described with a reduced diffusion coefficient D ∞. The parameters of the model function used for fitting the time-dependent diffusion coefficient in porous media are illustrated in double-logarithmic representation (right). The initial slope of the curve is related to the surface-to-volume ratio 21 S/ V (ref. 6). Extrapolation to short time scales yields the microscopic diffusion coefficient D 0 that would be measured in free solution, and extrapolation to large time scales yields the macroscopic diffusion coefficient D ∞ for translocations on large length scales. The ratio between both diffusion coefficients is referred to as retardation R. Based on these fit parameters, the correlation length λ can be calculated, which represents the length scale above which the medium appears homogeneous if it is sampled by a tracer of a given size. ( c) Parameters characterizing the cellular environment derived from the fits of the time-dependent mobility of GFP multimers are the cellular viscosity relative to water, the surface-to-volume ratio η app / η H 2 O S/ V that is a measure for the apparent obstacle concentration and the retardation R= D 0/ D ∞. The dependence of R on the molecule size can be computed for polymeric obstacles to yield estimates for the average fibre diameter d fiber and the obstacle volume fraction Φ 0 (ref. 30). Data are mean values±s.e.m. Dashed lines represent fitted model functions given by Supplementary Equation (34).