Chromatin shows a fractal organization at length scales ⩽∼100 nm. (**A**) Average FCS response of mEGFP in bulk (pink crosses) fitted with a standard diffusion model (α=1 in ), and in the nucleoplasm (red circles) fitted with an anomalous sub-diffusive model (α=0.79, dashed line) or a standard diffusion model (solid line). (**B**) FCS behaviours of mEGFP (red), mEGFP-2 (cyan), mEGFP-5 (green) and mEGFP-10 (purple) multimers were probed in the nucleoplasm of NRK cells. As GFP decamers and to a lesser degree GFP pentamers were partially degraded in cells (), we used the residence time in the FCS volume to report their molecular weight. On the basis of anomalous sub-diffusion fits, anomalous parameters are plotted versus nucleoplasmic residence times that are assumed to be proportional to mEGFP multimers MW. (**C**) NIH3T3 cells were micro-injected with QDs. The inset shows the trajectory of one QD aggregate obtained from a time series acquired every 1.9 ms. Scale bar 5 μm. (**D**) Plot of log(MSD/(*D* × Δ*t*)) versus log(Δ*t*) averaged over 16 tracks (blue crosses), and linear fit at short time scales (black line), slope of which (γ=0.73 in equation (3)) shows the anomalous subdiffusive motion of QDs. The plateau at long time scales corresponds to a standard diffusive behaviour. (**E**) Histograms of the displacement at 1.9 ms (red) and 30.4 ms (cyan) obtained with 15 independent tracks (∼14 000 points), and their corresponding fits based on a random walk model (). In the inset, residuals show the Brownian response at 30.4 ms (cyan), and the deviation to this behaviour at 1.9 ms (red). The discrepancy to the Brownian model at 1.9 ms was neither observed in control experiments performed in free solution nor with QDs bound to chromatin (), and we show in that this anomalous behaviour cannot be explained by QDs transiently binding to chromatin. (**F**) The blue plot shows the ratio of displacement histograms at 1.9 ms versus 7.8 ms for one QD trajectory (blue data set). The solid curve corresponds to the fit obtained with the stretched exponential model (see equation (6) in Materials and methods section). Its amplitude is related to fractal dimension of chromatin, and we measure *f*=2.5 given that γ=0.73. It should be noted that *f*=3.0 in the case of free diffusion ().

## PubMed Commons