Article19 November 2009free access Molecular crowding affects diffusion and binding of nuclear proteins in heterochromatin and reveals the fractal organization of chromatin Aurélien Bancaud Aurélien Bancaud Cell Biology and Biophysics Unit, EMBL, Heidelberg, GermanyPresent address: LAAS-CNRS; Université de Toulouse, 7, avenue du Colonel Roche, F-31077 Toulouse, France Search for more papers by this author Sébastien Huet Sébastien Huet Cell Biology and Biophysics Unit, EMBL, Heidelberg, Germany Search for more papers by this author Nathalie Daigle Nathalie Daigle Cell Biology and Biophysics Unit, EMBL, Heidelberg, Germany Search for more papers by this author Julien Mozziconacci Julien Mozziconacci Cell Biology and Biophysics Unit, EMBL, Heidelberg, Germany Search for more papers by this author Joël Beaudouin Joël Beaudouin Deutsches Krebsforschungszentrum and BioQuant, Research Group Theoretical Bioinformatics, Heidelberg, Germany Search for more papers by this author Jan Ellenberg Corresponding Author Jan Ellenberg Cell Biology and Biophysics Unit, EMBL, Heidelberg, Germany Search for more papers by this author Aurélien Bancaud Aurélien Bancaud Cell Biology and Biophysics Unit, EMBL, Heidelberg, GermanyPresent address: LAAS-CNRS; Université de Toulouse, 7, avenue du Colonel Roche, F-31077 Toulouse, France Search for more papers by this author Sébastien Huet Sébastien Huet Cell Biology and Biophysics Unit, EMBL, Heidelberg, Germany Search for more papers by this author Nathalie Daigle Nathalie Daigle Cell Biology and Biophysics Unit, EMBL, Heidelberg, Germany Search for more papers by this author Julien Mozziconacci Julien Mozziconacci Cell Biology and Biophysics Unit, EMBL, Heidelberg, Germany Search for more papers by this author Joël Beaudouin Joël Beaudouin Deutsches Krebsforschungszentrum and BioQuant, Research Group Theoretical Bioinformatics, Heidelberg, Germany Search for more papers by this author Jan Ellenberg Corresponding Author Jan Ellenberg Cell Biology and Biophysics Unit, EMBL, Heidelberg, Germany Search for more papers by this author Author Information Aurélien Bancaud1,‡, Sébastien Huet1,‡, Nathalie Daigle1, Julien Mozziconacci1, Joël Beaudouin2 and Jan Ellenberg 1 1Cell Biology and Biophysics Unit, EMBL, Heidelberg, Germany 2Deutsches Krebsforschungszentrum and BioQuant, Research Group Theoretical Bioinformatics, Heidelberg, Germany ‡These authors contributed equally to this work *Corresponding author. Cell Biology and Biophysics Unit, EMBL, Meyerhofstraße 1, Heidelberg D-69117, Germany. Tel.: +49 6221 387 8328; Fax: +49 6221 387 89328; E-mail: [email protected] The EMBO Journal (2009)28:3785-3798https://doi.org/10.1038/emboj.2009.340 Present address: LAAS-CNRS; Université de Toulouse, 7, avenue du Colonel Roche, F-31077 Toulouse, France There is a Have you seen? (January 2010) associated with this Article. PDFDownload PDF of article text and main figures. ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InMendeleyWechatReddit Figures & Info The nucleus of eukaryotes is organized into functional compartments, the two most prominent being heterochromatin and nucleoli. These structures are highly enriched in DNA, proteins or RNA, and thus thought to be crowded. In vitro, molecular crowding induces volume exclusion, hinders diffusion and enhances association, but whether these effects are relevant in vivo remains unclear. Here, we establish that volume exclusion and diffusive hindrance occur in dense nuclear compartments by probing the diffusive behaviour of inert fluorescent tracers in living cells. We also demonstrate that chromatin-interacting proteins remain transiently trapped in heterochromatin due to crowding induced enhanced affinity. The kinetic signatures of these crowding consequences allow us to derive a fractal model of chromatin organization, which explains why the dynamics of soluble nuclear proteins are affected independently of their size. This model further shows that the fractal architecture differs between heterochromatin and euchromatin, and predicts that chromatin proteins use different target-search strategies in the two compartments. We propose that fractal crowding is a fundamental principle of nuclear organization, particularly of heterochromatin maintenance. Introduction The interphase nucleus of eukaryotes is organized into discrete functional structures. These structures include heterochromatin, which remains condensed throughout the cell cycle, and mostly transcriptionally silent, euchromatin, which is decondensed during interphase and enriched in active genes, and nucleoli, where rRNA transcription and processing occur. They are well-characterized biochemically (Andersen et al, 2005), and can be observed for hours by light microscopy in living cells. Despite these stable properties, nuclear compartments are highly dynamic at the molecular level, if probed by fluorescence redistribution after using photobleach/activation techniques (Lippincott-Schwartz et al, 2001; Patterson and Lippincott-Schwartz, 2002) that showed rapid exchange of about every resident protein probed so far (Hager et al, 2002; Belmont, 2003; Phair et al, 2004; Beaudouin et al, 2006). To reconcile long-term macroscopic stability and molecular dynamics, nuclear compartments have been proposed to be self-organizing entities generated in a cooperative manner by a multitude of stereospecific short-lived interactions of their components (Misteli, 2005). Owing to the large number of components and non-linear cooperative biochemical couplings, this hypothesis is difficult to probe in vivo. As an alternative and not mutually exclusive model, macromolecular crowding has been suggested as a general driving force for self-organization of nuclear compartments on the basis of the osmotic manipulation of nucleoli in isolated nuclei (Hancock, 2004), and the use of hypertonic stress in intact cells (Richter et al, 2007). Classical molecular crowding studies (for reviews, see Zimmerman and Minton, 1993; Minton, 1995) investigate in vitro biophysical and biochemical consequences of the presence of large amounts of inert co-solutes that reduce the available volume by steric interaction in a reaction medium. Molecular crowding is relevant to cells because they contain high concentrations of biological macromolecules, including proteins and nucleic acids that will act as co-solutes for any protein of interest. The nucleus is known to contain the highest macromolecular densities in the cell and to exhibit significant variations in chromatin concentration ranging from ∼100 mg/ml in euchromatin (Daban, 2000) to ∼200–400 mg/ml in heterochromatin (Bohrmann et al, 1993). Nevertheless, a role for molecular crowding in nuclear organization and function has been rarely discussed or investigated. In vitro, molecular crowding has been shown to significantly alter the biophysical and biochemical properties of proteins. First, crowding induces volume exclusion: the volume occupied by co-solutes is inaccessible to other proteins, reducing their apparent concentration. Second, crowding slows down diffusion up to several orders of magnitude (Muramatsu and Minton, 1988): as co-solutes act as obstacles, they hinder molecular motion with a strong dependence on obstacle connectivity (Saxton, 1993b). Third, crowding shifts binding reactions towards bound states (Minton, 1995, 1998, 2006) because the reduction in available volume induced by co-solutes favours protein configurations associated with a reduction of entropy, that is, complexes rather than individual dissociated subunits. Recent studies have shown how the dynamics of nuclear proteins is governed by their diffusion and binding properties (Sprague et al, 2004, 2006; Beaudouin et al, 2006). If molecular crowding applies in the nucleus, we expect nuclear density variations to alter protein dynamics locally and to influence nuclear organization. Although the initial formation of nuclear structures probably requires stereospecific interactions, crowding-enhanced protein association could reinforce and maintain dense nuclear compartments. Molecular crowding could thus provide a driving force to maintain nuclear compartments composed of dynamic molecules without the need for membranes or other structural boundaries. This scenario seems to be particularly relevant for heterochromatin, formation of which requires specific histone modifications that create stereospecific binding sites (Rea et al, 2000), but maintenance of which could be facilitated by enhancing protein binding mediated by crowding. Several studies have shown that volume exclusion occurs in some nuclear compartments (Verschure et al, 2003; Gorisch et al, 2005) as predicted by the crowding theory, but local effects on diffusion and binding properties of nuclear proteins remain to be demonstrated in vivo. Here, we investigate the three consequences of molecular crowding within the nucleus of living cells. First, we demonstrate volume exclusion of inert tracers in dense nuclear compartments by high-resolution confocal imaging of their steady state concentrations. Second, we use fluorescence correlation spectroscopy to show that diffusion of these tracers is slowed down in dense nuclear compartments, although they remain kinetically permeable. Third, we demonstrate that binding rates are enhanced in dense nuclear compartments using local photoactivation (PA) of chromatin-interacting proteins. Having demonstrated the prevalence of molecular crowding effects in the nucleus, our quantitative analysis of molecular dynamics in live-cell nuclei allowed us to define the structural organization of the main nuclear crowding agent, chromatin. Three independent lines of evidence lead us to conclude that its organization is fractal. First, chromatin obstructs diffusion of inert tracers in a size-independent manner. Second, single particle displacements of quantum dots exhibit non-random distributions at short time scales consistent with fractal obstacles. Third, the enhanced binding kinetics of chromatin-interacting proteins in heterochromatic regions are well explained by a fractal kinetics model but cannot be explained by diffusion reaction models. Our analysis allows us to determine two structural parameters of chromatin, the anomaly parameter it imposes on diffusion and the fractal dimension, which characterize the random motion of diffusing tracers and the geometrical arrangement of chromatin, respectively. Together with previously established diffusion reaction models (Beaudouin et al, 2006), this study provides a comprehensive framework to mathematically describe nuclear protein dynamics. Results Nucleoli and heterochromatin exhibit size-dependent volume exclusion Nucleoli are the most prominent and dense nuclear sub-compartments composed, among others (Andersen et al, 2005), of rDNA and transcription complexes, rRNA processing complexes and modification machinery, as well as assembling ribosomal subunits. The volume fraction occupied by these macromolecules is not available for other species, and we expect volume exclusion to occur. Consequently, fluorescent inert probes should be partly physically excluded from nucleoli, and exclusion should be size dependent (Zimmerman and Minton, 1993). To evaluate nucleolar volume availability, we chose NRK cells for their large and easy-to-localize nucleoli (Figure 1A), and microinjected fluorescent dextrans of different molecular weights (MW) or expressed different GFP multimers. Confirming previous studies, for example, those by Gorisch et al (2003) and Handwerger et al (2005), we found that these tracers are excluded from nucleoli (Figure 1A). We quantified the relative exclusion, defined by the nucleolar-to-nucleoplasmic concentration ratio. Relative exclusion was found to be size dependent and to increase with probe size, being two-fold greater for a particle of ∼90 nm in diametre (500 kDa dextran) in comparison to a particle of ∼20 nm (25 kDa dextran, (Lenart and Ellenberg, 2006)). Figure 1.Steady state and induced volume exclusion in heterochromatin and nucleoli. (A) NRK cells were co-injected with 25 and 500 kDa fluorescently labelled dextrans. The right panel shows nucleolar versus nucleoplasmic relative exclusion of four different inert probes in NRK. (B) NIH3T3 cells were co-injected with 25 and 500 kDa fluorescently labelled dextrans, and stained with Hoechst to identify euchromatin or heterochromatin foci. It should be noted that heterochromatin concentration variations are amplified using Hoechst because of its sequence preference for AT-rich regions. Insets are two-fold magnified, pseudocoloured images of a heterochromatin focus. The green arrowhead indicates a heterochromatin focus, in which the DNA density is six-fold enriched in comparison with euchromatin. The relative concentration of dextrans in heterochromatin versus euchromatin was evaluated as a function of the local amount of heterochromatin in the confocal section. In the right plot, ‘effective’ exclusions in heterochromatin foci of density 6 (see Supplementary Figure S1 for details) are plotted for five probes of different molecular weights. (C) NRK cells expressing mRFP-2 alone or co-expressing Suv39H1–GFP were stained with Hoechst. Blue and purple arrowheads indicate exemplary heterochromatin foci in which mRFP-2 exclusion can be detected. On the right, the Hoechst channel is thresholded with pixels in the range 0–49, 50–134 and 134–255 represented in black, red and green, respectively. Download figure Download PowerPoint As heterochromatin is likely to be a compartment influenced by crowding effects, we assessed the behaviour of similar tracers in comparison with euchromatin. We used NIH3T3 cells in which large heterochromatin foci of about 1 μm diametre can be seen after vital DNA labelling. As previously observed (Gorisch et al, 2003; Verschure et al, 2003), we confirmed that exclusion occurs in heterochromatin (Figure 1B). For each tracer, the relative exclusion increased approximately linearly with heterochromatin concentration, and single-parameter linear fits were performed to deduce heterochromatin ‘exclusion rates’ (Supplementary Figure S1). Plotting tracer exclusion for heterochromatin foci for which DNA density was, for example, six times greater than euchromatin (green arrow in Figure 1B), clearly shows that the relative exclusion is size dependent, reaching ∼50% for 500 kDa dextrans (Figure 1B, right panel). These experiments show that heterochromatin and nucleoli are crowded to a degree that significantly reduces the available volume although still allowing the placement of molecules of as large as ∼90 nm diametre. Newly formed heterochromatin exhibits volume exclusion To test whether heterochromatin causes volume exclusion, we induced its formation by overexpressing Suv39H1, the enzyme known to trigger heterochromatin formation by histone H3 methylation (Rea et al, 2000), in NRK cells that normally show a rather homogeneous chromatin pattern in interphase. DNA was vitally stained with Hoechst to monitor chromatin density, and an RFP dimer was co-expressed to serve as a volume exclusion reporter (Figure 1C). To measure the effect of Suv39H1 expression on heterochromatin, we used quantitative analysis of the pixel intensity distribution in the DNA channel (see Supplementary Figure S1e for details), which allowed us to compute the fraction of heterochromatin per nucleus. In control cells, the chromatin organization was rather homogeneous with a low heterochromatin content of 12±2% (s.e., n=16) and the distribution of the volume exclusion reporter RFP dimer showed hardly any detectable region of volume exclusion (blue arrowhead in Figure 1C) apart from nucleoli. In cells overexpressing Suv39H1, many dense intra-nuclear DNA foci appeared (purple arrowheads in Figure 1C), and the heterochromatin content increased almost four-fold to 46±6% (s.e., n=16). The concentration of the RFP dimer in these newly formed foci was 65±10% that of euchromatin. Our results show that dense chromatin regions induced by the expression of Suv39H1 exhibit volume exclusion. Diffusion is slowed down in nucleoli and heterochromatin Molecular crowding predicts that nuclear compartments should hinder diffusion according to their density. To test this, we probed the local diffusion by fluorescence correlation spectroscopy (FCS) with a spatial precision of ∼300 nm, sufficient to discriminate euchromatin, heterochromatin and nucleoli. To first compare nucleoli with euchromatin, we again used NRK cells and assayed the single molecule fluctuations of a GFP pentamer through the focused laser beam. The autocorrelation function (see Materials and methods section) was shifted towards longer time scales in nucleoli (Figure 2A, orange data set in right panel), indicating an increased residence time in the measurement volume due to slower diffusion in this compartment. Fitting the autocorrelation function with an anomalous diffusion model, we determined nucleoplasmic and nucleolar diffusion coefficients of the GFP pentamer as 7.7±1.3 and 2.9±0.5 μm2/s, respectively, showing that nucleolar diffusion was slowed down by a factor of ∼3. Figure 2.The nuclear rheology is heterogeneous. (A) NRK cell transiently expressing H2b-mRFP and mEGFP-5 were subjected to FCS measurements. Crosses on the H2b image indicate positions at which measurements were performed. The graph shows normalized auto correlation functions (ACF) obtained in the nucleoplasm (red) and the nucleolus (orange). Fits were performed with an anomalous diffusion model (solid curves), and we deduced residence times of 1050 and 3650 μs, and anomalous coefficients of 0.78 and 0.65 in nucleoplasm and nucleolus, respectively. The inset shows count rates, that is, intensities measured by FCS in the nucleoplasm (red) and nucleolus (orange). (B) Similar experiments performed with NIH3T3 cells. The green cross indicates the position of heterochromatin measurements, which was always quality controlled taking advantage of H2B–mRFP bleaching during FCS (Supplementary Figure S2). Graphs show normalized ACFs obtained in euchromatin (red), heterochromatin (green) and nucleoli (orange). Fits (solid curves) show more pronounced diffusion slow down in nucleoli than in heterochromatin, as inferred from the mEGFP-5 residence times of 3570 μs (α=0.70) and 1410 μs (α=0.80) in nucleoli and heterochromatin, respectively, in comparison to 790 μs (α=0.77) in euchromatin (bottom). Inset shows count rates measured in euchromatin (red), heterochromatin (green) and nucleoli (orange). (C) Selected frames of mPAGFP-2 half-nucleus PA time lapse imaging with the photoactivated region represented by the polygon on the pre-activation image. To visualize entry kinetics within nuclear compartments, 1.2-μm confocal slices were grabbed. High-quality images of mPAGFP-2 steady state and Hoechst distribution were acquired 60 s after PA (lower panel). Rings on the steady-state image correspond to regions in which the intensity redistribution was measured over time. Graphs at the left compare nucleolar (orange) and heterochromatin (green) fluorescence intensity measured over time in the regions highlighted with the corresponding coloured circles in the steady-state image to the intensity in a neighbouring nucleoplasmic area (red and purple regions). Graphs at the right display the same curves after steady-state renormalization. Scale bars 10 μm. Download figure Download PowerPoint To compare the diffusion in heterochromatin with euchromatin, we again used NIH3T3 cells. The GFP pentamer diffusion coefficient was decreased by a factor of 1.6 from 9.2±1.0 μm2/s in euchromatin to 5.9±0.6 μm2/s in heterochromatin (Figure 2B, green data set in right panel). For reference, we also recorded diffusion in NIH3T3 nucleoli, in which GFP pentamer diffusion was reduced by three-fold to 2.3 μm2/s, consistent with the data from NRK cells (Figure 2B, red and orange data sets in lower panel, respectively). Our results show that crowding predictions for diffusion are relevant in the nucleus, and that diffusion is slowed down two- to three-fold in dense nuclear compartments. Dense nuclear compartments are readily accessible for diffusing proteins Although the concentrations of inert probes, such as GFP multimers and dextrans, were reduced in dense regions by volume exclusion, we observed only moderate diffusive hindrances in nuclear compartments, which suggest that uptake kinetics of diffusive tracers into dense compartments should not be dramatically impeded, allowing a dynamic exchange between them. To test this, we photoactivated PAGFP dimer in one-half of the nucleus and measured its fluorescence redistribution kinetics in heterochromatin or nucleoli relative to an adjacent euchromatin region (Figure 2C). As expected from our volume exclusion observations, PAGFP dimer reached lower steady state levels in nucleoli and heterochromatin (Figure 2C, left graphs). However, after steady-state normalization, all uptake kinetics seemed very similar at this temporal resolution (Figure 2C, right graphs). Thus, even the densest nuclear compartments are highly permeable, and readily accessible to diffusing proteins. Binding to nucleosomes and DNA is enhanced in heterochromatin The consequences of crowding on chemical reactions have been studied theoretically (Minton, 1992, 1995, 2006) and confirmed experimentally in vitro (e.g. Rivas et al, 1999, 2001). If crowding predictions apply in vivo, most reactions are expected to exhibit enhanced binding rates when their ligands are found in a crowded heterochromatin focus compared with less-crowded euchromatin. To test this, we assayed the behaviour of three generic chromatin-interacting proteins, the guanine nucleotide exchange factor RCC1 (Nemergut et al, 2001; Beaudouin et al, 2006), which interacts with H2A and H2B core histones; the linker histone isoform H1.1 (Brown, 2003; Beaudouin et al, 2006), which interacts with nucleosome entry–exit DNAs (Hamiche et al, 1996); and the C-terminal tail of H1.1 (H1t), which is a highly positively charged protein with an unspecific affinity for DNA (Subirana, 1990). These proteins were fused to PAGFP, and local PA in either euchromatin or heterochromatin was performed in volumes ∼900 nm in diametre and ∼3.1 μm in extension (Supplementary Figure S3a). Consistent with our previous observations (Beaudouin et al, 2006), we observed a rapid and complete fluorescence redistribution of H1.1, RCC1 and H1t in euchromatin (Figure 3A, red data sets in Figure 3B), accompanied by smoothing of the local fluorescence gradient over time, which indicates a contribution of diffusion in the relaxation (Beaudouin et al, 2006). Using a previously established spatial diffusion reaction model (Beaudouin et al, 2006), we analysed our data (Supplementary data). Fitting diffusive and binding parameters to the experimental data showed that the dynamics of all three proteins in euchromatin was well explained by a diffusion-limited model (Figure 3C, red data sets and their corresponding black fitting curves). The observed redistribution kinetics are, therefore, limited by the low amount of unbound proteins in steady state rather than by the residence time on chromatin (Sprague et al, 2004; Beaudouin et al, 2006). Thus, one parameter, the fraction of unbound proteins (see Materials and methods section), suffices to describe the dynamics of these proteins and we obtained 0.2±0.1% (n=13), 0.9±0.1% (n=13) and 4.1±0.4% (n=13) as the free fraction for H1.1, RCC1 and H1t respectively. As binding of H1.1, RCC1 and H1t to euchromatin is short lived, we could only estimate upper limits for their residence times of ∼2, ∼0.2 and ∼0.1 s, respectively. Figure 3.Binding of chromatin-interacting proteins is enhanced in heterochromatin. (A) Pseudocoloured images of NIH3T3 cells transiently expressing H1.1–mPAGFP, RCC1–mPAGFP and H1t–PAGFP. Images are selected frames of PA time lapse with the photoactivated region represented by circles in euchromatin (red) or in heterochromatin (green) on the pre-activation image. The inserts outlined in red and green correspond to two higher magnifications of photoactivated areas in euchromatin and heterochromatin, respectively. Two lookup tables associated to heterochromatin PA and nuclei, or to euchromatin PA are defined in the middle and lower panel, respectively. Experiments with RCC1–mPAGFP and H1t–mPAGFP were carried out at 26°C. Confocal section thickness values were set to 1.0 μm, that is, three times less than the photoactivated spot size. Scale bar 10 μm. (B) Graphs representing normalized intensities measured during relaxation in the circled regions of the experiment displayed in (A) (red: euchromatin, green: heterochromatin). Euchromatin responses are accurately fitted with a diffusion limited model (see Materials and methods section, lower solid line), but this model fails to reproduce heterochromatin response curves (upper solid lines) especially at short time scales, showing that chromatin protein dynamics are associated with a longer residence in heterochromatin right after PA. Insets represent average early time points responses measured in euchromatin and heterochromatin (red and green data sets, respectively) to emphasize on the initial plateau in heterochromatin. Download figure Download PowerPoint As all three proteins interact with chromatin with low specificity independent of histone modifications or DNA sequence, the same diffusion-limited approximation should be applicable to heterochromatin (green data sets in Figure 3B). As heterochromatin is enriched in nucleosomes and DNA, the binding sites for H1.1, RCC1 and H1t, we would expect to observe slowed-down kinetics linearly dependent on the heterochromatin-to-euchromatin concentration ratio. Surprisingly, all three proteins exhibited biphasic kinetics in heterochromatin with a plateau at short time scales, which indicates trapping of H1.1, RCC1 and H1t in heterochromatin. However, taking into account the higher local concentration of binding sites, the diffusion reaction model (Figure 3B, upper black curves) could not fit the redistribution kinetics observed in heterochromatin, and even further refinement by implementing the two-fold diffusion slow down and a possible enhancement of association rates in heterochromatin failed to fit the data (Supplementary Figure S3). To explicitly model crowding, we therefore turned to molecular dynamics simulations (Supplementary data) defining chromatin structure as a network of randomly distributed obstacles and binding sites with a constant binding site-to-obstacle ratio (Supplementary Figure S4). Although increasing obstacle density in heterochromatin could simulate a delayed redistribution, the random crowding model also failed to explain the biphasic kinetics observed in heterochromatin (Supplementary Figure S4). So far, our experiments show that all three predictions of molecular crowding are fulfilled in dense nuclear compartments such as heterochromatin in living cells. Crowding leads to volume exclusion and diffusion slow down of inert macromolecules, and locally increases the binding of chromatin-interacting proteins. Interestingly, our observations that random crowding models cannot explain the kinetics of binding enhancement suggested that a non-random organization of the crowding agent underlies these effects. We therefore decided to investigate the structural organization of euchromatin and heterochromatin in more detail. Diffusion properties are size-independent in chromatin We first studied chromatin structure by analysing the diffusive behaviour of GFP multimers composed of 1, 2, 5 or 10 GFPs in euchromatin in more detail using FCS. All GFP multimers exhibited sub-diffusive behaviours (e.g. Figure 4A) in agreement with previous studies (Wachsmuth et al, 2000; Guigas et al, 2007). Fitting the autocorrelation functions with an anomalous diffusion model, we found that the FCS anomaly parameter was independent of the size of the GFP multimer, with a value of 0.79±0.02 (Figure 4B). The degree of diffusive hindrance as compared with aqueous solution was also size independent for euchromatin; we measured by FCS that GFP and GFP dimer were slowed down from 87±7 to 29.1±1.5 and 55±4 to 17±1 μm2/s, respectively, by about three-fold. The size-independent nucleoplasmic diffusive hindrance is consistent with earlier studies performed with dextrans, ficolls and GFP multimers spanning a broad range of MWs (Seksek et al, 1997; Pack et al, 2006). Diffusion was also probed in heterochromatin in comparison with euchromatin, and similar diffusional hindrances of 1.7±0.2 and anomaly parameters of 0.75±0.07 were observed between GFP decamers, pentamers and dimers (Supplementary Figure S2), suggesting that diffusion properties were also size independent in heterochromatin. Conversely, diffusive properties were not size independent in nucleoli, in which chromatin is not the main structural component, as the anomaly parameter and the diffusive hindrance tended to decrease and increase, respectively, with MW (Supplementary Figure S2). Figure 4.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 equation (7)), 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 les