Correlated Spatio-Temporal Fluctuations in Chromatin Compaction States Characterize Stem Cells

Abstract

Stem cells integrate signals from the microenvironment to generate lineage-specific gene expression programs upon differentiation. Undifferentiated cell nuclei are easily deformable, with an active transcriptome, whereas differentiated cells have stiffer nuclei and condensed chromatin. Chromatin organization in the stem cell state is known to be highly dynamic but quantitative characterizations of its plasticity are lacking. Using fluorescence imaging, we study the spatio-temporal dynamics of nuclear architecture and chromatin compaction in mouse embryonic stem (ES) cells and differentiated states. Individual ES cells exhibit a relatively narrow variation in chromatin compaction, whereas primary mouse embryonic fibroblasts (PMEF) show broad distributions. However, spatial correlations in chromatin compaction exhibit an emergent length scale in PMEFs, although they are unstructured and longer ranged in ES cells. We provide evidence for correlated fluctuations with large amplitude and long intrinsic timescales, including an oscillatory component, in both chromatin compaction and nuclear area in ES cells. Such fluctuations are largely frozen in PMEF. The role of actin and Lamin A/C in modulating these fluctuations is described. A simple theoretical formulation reproduces the observed dynamics. Our results suggest that, in addition to nuclear plasticity, correlated spatio-temporal structural fluctuations of chromatin in undifferentiated cells characterize the stem cell state.

Introduction

Embryonic stem (ES) cells can differentiate into multiple lineages when exposed to soluble factors (1,2) or extracellular matrix signals (3–6). In this process, the highly active (7,8) and variable transcriptome (9–11) of ES cells must transform to generate lineage-specific gene expression patterns. Changes in epigenetic modifications and chromatin organization have been shown to influence lineage specificity (12). Functionally, stem cells possess distinct histone modifications (13–15) and a permissive chromatin structure (16–20) compared to differentiated cells. Mechanically, ES cell nuclei are softer (21,22), have a flexible nuclear organization (16,19), are devoid of nuclear scaffold protein Lamin A/C (23,24), and lack a well-defined cytoskeleton before differentiation (25,26).

Stem cell differentiation should be accompanied by nontrivial changes in the spatio-temporal dynamics of chromatin organization as well as by alterations in nuclear architecture. This is a connection that is as yet poorly understood, although previous work (16,20) highlighted the role of changes in chromatin plasticity across differentiation, arguing that plasticity of chromatin organization was an essential feature of the stem cell state. Earlier work also demonstrated a direct correlation between dynamic transitions in chromatin assembly and the onset of cellular differentiation and developmental programs.

In this work, we elucidate novel, to our knowledge, aspects of such plasticity. We quantitatively describe correlated spatio-temporal fluctuations in the chromatin compaction states of undifferentiated cells, capturing changes in these fluctuations across multiple length and timescales. In stem cells, chromatin organization exhibits strong fluctuations in both time and space. In addition, correlation lengths for chromatin compaction are large and substantial nuclear size fluctuations with an oscillatory component are seen. Such size fluctuations appear to be correlated with local fluctuations in chromatin compaction. Similar measurements in the differentiated state yield considerably suppressed dynamics, short correlation lengths for chromatin compaction, and the emergence of an intrinsic scale associated with higher order chromatin organization. Our results suggest that such correlated spatio-temporal structural fluctuations of chromatin in undifferentiated cells, and not simply their fluidity, characterize the stem cell state. Such structural fluctuations are likely to be crucial in enabling the sampling of a range of functional chromatin states by transcription factor networks during cellular differentiation.

Materials and Methods

Cell culture

R1 ES cells and H2B-EGFP ES cells were cultured on a layer of feeder cells primary mouse embryonic fibroblasts (PMEF) with DMEM-F12 supplemented with 15% knockout fetal bovine serum, 1 mM sodium pyruvate (Sigma), 0.1 mM nonessential amino acids, 2 mM L-Glutamine, 0.1 mM β-mercaptoethanol (Sigma), and 500 U/ml leukemia inhibitory factor (LIF) (Chemicon) and penicillin-streptomycin. PMEF were cultured with DMEM-F12 supplemented with 10% fetal bovine serum, penicillin-streptomycin. Cells were maintained at 37°C in a 5% CO₂ incubator. PMEF cells up to third passage were used in the experiments. (All cell culture reagents, unless otherwise indicated, are from Gibco Invitrogen.) Both cell types grown on coverslip dishes for 1 day were transfected with 500 ng of DNA using Lipofectamine 2000 and Opti-MEM. The cells were imaged 24 h later for fluorescence recovery after photobleaching (FRAP) and anisotropy experiments. For immunostaining, the following antibodies were used α-tubulin (1:200, Abcam), Lamin B1 (1:200, Abcam), and phosphor-Myosin Light Chain (1:100, Cell Signaling), Oct-4 (1:500, Abcam) and secondary antibodies were used at 1:500 (Invitrogen). ES cells were induced to differentiate by plating them on gelatin-coated dishes and LIF withdrawal. Cells were treated for ATP depletion using a cocktail of 10 mM NaN3 (Sigma) and 6 mM 2-deoxy-D-glucose (Sigma) in M1 without glucose and were left in the incubator at 37°C for 30 min. The medium was replaced by the respective culture medium. For synchronizing ES cells in G2/M and G1 phase Nocodazole (200 ng/ml for 16 h) and Aphidicholine (10 μg/ml for 12 h) was used, respectively. For differentiation of ES cells on gelatin-coated dishes, in the presence of cytoskeleton perturbation, 100 nM Cytochalasin D (Sigma) was used. For actin depolymerization in PMEFs 2 μg/ml of Cytochalasin D was added to cells in culture for 5 min at 37°C.

Cell cycle synchronization

Control and various drug-treated ES cells were trypsinized and pelleted at 4°C. The pellet was further resuspended in 300 μl of cold 1X PBS and chilled on ice. Later 700 μl of ice cold 100% ethanol was added to the resuspended cells and rapidly mixed with a pipette. The mixture with cells was incubated on ice for 1 h and the cells were pelleted by spinning and ethanol was removed. Cells were washed twice with phosphate buffered saline (PBS). 10 μl of RNase (10 mg/ml) in 125 μl of 1X PBS was added to cells and kept at 37°C for 15 min in a water bath. Next, 10 μl of Propidium iodide (1 mg/ml) was added to the samples, volume was made up to 500 μl by PBS and the mixture was incubated at room temperature for 30 min. The labeled cells were analyzed using flow cytometry using BD FACSVantage SE Cell Sorter (see Fig. S6 in the Supporting Material).

Fluorescence anisotropy

Images were captured on an Olympus microscope with 60X/1.4 NA objective using an EMCCD camera (Andor). Mercury arc source was used for the excitation light, which was then selected for vertical polarization using a sheet polarizer (Melles Griot). The emitted light was collected using a U-SIP split chip polarizing module. Images were captured using Andor software and analyzed using LabVIEW (National Instruments) as described previously (27). Anisotropy is defined as $A=I_{II}-I_{\perp }/I_{II}+2I_{\perp }$, where I_II is the parallel component of the emission intensity with respect to the excitation polarization direction and I_⊥ is the perpendicular component (Figs. S3–S5).

Confocal imaging

Zeiss (LSM510-Meta/Confocor2) and Olympus (FV1000) fluorescence microscopes were used in our experiments. Imaging and FRAP experiments on cells were carried out using C-Apochromat 63X, 1.4 N.A oil immersion objective with identical acquisition settings. Enhanced green fluorescent protein (EGFP)-tagged proteins and fluorescein isothiocyanate were excited with the 488 nm line of an Argon-ion laser (Lassos) and the emission collected with a 500–530 nm band pass filter. Fluorophores such as Cy3/Rhodamine and Alexa-647 were excited using 543 and 633nm laser line and collected using 560–615 band pass and 650 LP filters, respectively. A 405 laser line was used to excite Hoechst 33342. Confocal images (512 × 512 pixels, 8 bit images, with optimal pinhole sizes) were acquired. Z-stacks of nuclei with a step size of 0.5–1 μm were acquired. The error in confocal volume measurement was determined using FocalCheck fluorescent microspheres, 6 μm, Invitrogen mounted using ProLong Gold antifade reagent, (Invitrogen).

Data analysis

To compute the nuclear shape in ES cells, the nuclear area versus z-depth plot was fit to an ellipse, with minor axis determined from the maximum area plane and keeping the major axis as a free parameter. Heterochromatin nodes were determined from H2B EGFP intensity images of the nucleus based on a stringent intensity and area threshold: pixels with intensity more than (mean nuclear intensity + 1.5 times standard deviation) were first filtered from the nuclear image. To remove spurious signals, an area threshold was then used in which contiguous clusters of at least 10 pixels were selected. The relative nuclear area fluctuation was obtained by subtracting the mean area from the time series (a_i). This was used to deduce the dimensionless nuclear area compressibility via

$$\xi =\frac{\Delta a}{a}=\frac{\sqrt{\frac{1}{N}{\sum }_i\langle {\left(a_i-\langle a_i\rangle \right)}^2\rangle }}{\frac{1}{N}{\sum }_i\langle a_i\rangle }.$$

From the relative area fluctuation, an autocorrelation analysis was carried out to determine the dynamics of area fluctuations. To obtain characteristic length scales, the spatial correlation curve of anisotropy map, g(r) for ES was fit to the following equation y = y₀ + ae^−x/t in Origin 8.0 (OriginLab). For a pixel-wise autocorrelation analysis, the anisotropy time-series images were first centroid aligned to correct for any nuclear movement. A central region of interest from the image was then selected and a three-dimensional matrix with the 3rd dimension as time was constructed. Each linear array along the 3rd dimension was used as a signal to calculate the autocorrelation function

$$G\left(\tau \right)=\frac{\langle \left(A\left(t\right)-\overline{A}\right).\left(A\left(t+\tau \right)-\overline{A}\right)\rangle }{\langle {\left(A\left(t\right)-\overline{A}\right)}^2\rangle },$$

where A(t) is the anisotropy value at time t at point (x,y) in nucleus and $\overline{A}$ is the time average anisotropy value at (x,y). To obtain the averaged autocorrelation (G(τ)), the mean G(τ) over all points (x,y) was calculated. All the data analysis was carried out using LabVIEW 6.1 (National Instruments) and graphs were plotted in Origin 8.0 (OriginLab). The p value was obtained from Student’s t-test. ^∗ in all graphs shows a significance level below p < 0.05.

Results

Coupling of cytoskeletal architecture to nuclear morphology

We first address differences in cytoskeletal architecture between ES cells and PMEFs and their connection to nuclear shape and fluctuations. Fig. 1 A compares the organization of actin, microtubules, Lamin B1, and DNA in ES cells and PMEF. Staining for F-actin using rhodamine phalloidin shows that actin structures are localized near the plasma membrane in ES cells. In contrast, they appear as stress fibers in the cytoplasm in PMEFs. Similarly, α-tubulin staining shows enrichment between the plasma membrane and nuclear envelope in ES cells while manifesting as a bulk fibrillar pattern in PMEFs. Lamin B1 is found to be enriched at the nuclear periphery in stem cells, although it is present throughout the nucleus in PMEFs. These staining patterns indicate that cytoskeletal and nuclear lamina organizations in the two cell types are distinct.

Figure 1.

Coupling of cytoskeletal architecture to nuclear morphology. (A) Representative immunofluorescence images of ES cells (upper panel) and PMEFs (lower panel): DNA, LaminB1, F-actin, and microtubules have been stained. Merge of F-actin (red) and microtubule (green) is also shown. Scale bar is 5 μm. (B) Representative immunofluorescence images during ES cell differentiation (Day 0, Day 2, Day 4, and Day 6) on gelatin-coated dishes: F-actin (red) and phosphorylated myosin II light chain (green). Scale bar is 5 μm. (C) Normalized color-coded images of DNA intensity in nuclei of ES cells plated on gelatin-coated dishes. Scale bar is 5 μm. (D) Plot representing nuclear area as a function of Z-depth in cells at different days of differentiation and PMEFs. N = 22 (Day 0), 15 (Day 2), 9 (Day 4), 10 (Day 6), 50 (PMEF). Inset indicates nuclear volume. (E) Plot representing number of condensed chromatin nodes per cell with onset of differentiation. (F) Representative images of Actin-EGFP before and after photobleaching (0, 4, 30, and 50 s) in ES cells (upper panel) and PMEF (lower panel). White arrows indicate bleach region. (G) FRAP curves for transiently expressed Actin-EGFP in PMEF in different regions, stress fibers (black), cortical actin (gray), and in ES cells (red).

Because cytoskeletal stresses are known to regulate nuclear morphology (26,28), we next studied the temporal progression of these stresses and the associated changes in chromatin structure during stem cell differentiation. To follow these changes, ES cells were cultured on gelatin-coated dishes, with withdrawal of LIF. Induction of ES cell differentiation resulted in the appearance of actin stress fibers and myosin II localization by Day 2 in culture (Fig. 1 B). On mapping the onset of chromatin condensation, we found that distinct heterochromatin patterns emerged, as evident in color-coded intensity images (Fig. 1 C). Although intensities are relatively homogeneous in the ES cell state, differentiation is accompanied by a considerable increase in heterogeneity in such intensity. Such heterogeneity takes the form of localized bright regions, which we associate with heterochromatin (19).

The onset of differentiation was also accompanied by changes in nuclear size as well as a flattening of the nucleus (Fig. 1 D and Fig. S1, A and B). Nuclear volume and cell volume increased twofold (inset of Fig. 1 D, Fig. S1, C and D) upon differentiation, as obtained through confocal z-sections. In ES cells, the nuclear volume is smaller (∼1000 μm³) and the nucleus is an oblate ellipsoid whose major axis (along z) is twice the minor axis. In comparison, the PMEF nucleus (∼1500 μm³) is a flattened ellipsoid with major axis along x-y as seen in Fig. S1 F. With the appearance of stress fibers, the number and area fraction of heterochromatin regions also show a significant increase (Fig. 1 E and Fig. S1 E).

To further probe the coupling between cytoskeletal reorganization and differentiation, ES cells were differentiated as described previously in the presence of Cytochalasin D (Cyto D), which induces actin depolymerization. Although the differentiation of control ES cells was accompanied by nuclear and cytoskeletal reorganization, cells treated with Cyto D failed to flatten as seen by F-actin staining (Fig. S2 A). Furthermore, it is known that stem cells cultured in the presence of Blebbistatin do not differentiate (29). These results, taken together, indicate that cytoskeletal remodeling is important for cellular differentiation.

To investigate the dynamic organization of the actin cytoskeleton, Actin-EGFP was transiently transfected in both cell types. Diffuse actin patterns were seen in the cytoplasm of ES cells, whereas cortical actin and stress fibers were seen in fibroblasts (Fig. 1 F). FRAP of Actin-EGFP revealed higher fractional recovery (∼60%) in ES cells, similar to the recovery in the cortical actin regions in PMEFs. On the other hand, stress fibers in PMEFs showed a smaller recovery fraction (∼20%) as seen in Fig. 1 G and Movie S1 and Movie S2. These results indicate that actin architecture is more dynamic in ES cells in comparison to PMEF.

Heterogeneity in chromatin compaction states in ES cells

The complexation of DNA with histones and other nuclear proteins results in higher order chromatin structure. We employed fluorescence anisotropy imaging of core histone-H2B tagged to EGFP to explore the spatial heterogeneity in such structures (27). The local volume fraction of the bound chromatin, chromatin compaction, was visualized through fluorescence anisotropy maps. Fluorescence anisotropy, defined by $A=I_{II}-I_{\perp }/I_{II}+2I_{\perp }$ (see Materials and Methods), is a measure of rotational diffusion of the labeled molecule. Higher values of A indicate that the motion of labeled core histones is rotationally hindered, whereas lower values signal rotationally mobile histones. The two extreme values of the anisotropy come from histones that are in the strongly DNA-bound or unbound states. Thus, the local anisotropy A is a weighted sum of the anisotropies of the bound and unbound species of histones, with weights given by the fraction of histones in these states.

Because the local fraction of bound histones is proportional to the local fraction of tightly compacted chromatin, the spatial map of fluorescence anisotropy from labeled histones provides a direct measure of local chromatin compaction in living cells. Fig. S3, A–C shows the spatial distribution of anisotropy values and the corresponding H2B-EGFP fluorescent intensity images of a PMEF nucleus together with zoomed in regions showing heterochromatin and euchromatin. As seen in the cropped regions of interest, heterochromatin regions where anisotropy is higher also have a higher intensity, whereas euchromatin regions tend to have relatively decreased anisotropy values. Because heterochromatin regions are more compact and condensed, the rotational diffusion of core histones is hindered in such regions and they show higher anisotropy than the rest of the nucleus.

The panel of anisotropy images (Fig. 2, A–E), reveals striking differences in the compaction states of chromatin in ES cells and PMEFs. From the images, it is apparent that individual ES cells have very distinct compaction profiles compared to PMEF. This is further highlighted graphically in Fig. 2, A–E, and Fig. S3 D, where it can be seen that individual ES cell nuclei exhibit a very narrow spatial variation in chromatin compaction. Interestingly, despite the narrow distribution of anisotropy values in individual ES cells, the distribution in an ensemble of ES cells and PMEFs, obtained by plotting and normalizing pixel-wise anisotropy values across different cells, are closely similar (Fig. 2, F and G). Thus, we conclude that the chromatin compaction states of individual ES cells, averaged over a population, sample the same broad spectrum exhibited by differentiated cells.

Figure 2.

Heterogeneity in chromatin compaction states in ES cells. (A–E) Color-coded anisotropy maps of core histone H2B are shown for typical nucleus of ES cells (upper panel) and PMEFs (lower panel). Scale bar is 5 μm. The graphs at the bottom show the anisotropy distribution in individual ES cells (red) and PMEF (black). The bar to the right shows range of anisotropy values corresponding to specific colors. (F–G) The frequency distribution of anisotropy values of each nucleus in a population of ES cells (F) and PMEFs (G). Different colors represent different cells. N = 100. (H) Plot of spatial correlation of anisotropy for multiple ES cells. Inset: Mean spatial correlation g(r) computed for ES cells and solid line represents exponential fit to the curve. (I) Plot of spatial correlation of anisotropy for multiple PMEFs. Inset: Mean spatial correlation for PMEF scaled with respect to the second peak distance. Each color represents a single cell.

To compare and contrast the spatial distribution of chromatin compaction in ES cells and PMEFs, we studied the spatial correlation of the local anisotropy. The mean subtracted pixel-wise anisotropy values (pixel size = 160 nm) were obtained from the images and used to compute a coarse-grained anisotropy correlation function,

$$g\left(r\right)=\frac{\langle \Delta \mathit{A}\left({\mathit{r}}^{\text{'}}\right).\Delta \mathit{A}\left({\mathit{r}}^{\text{'}}+\mathit{r}\right)\rangle }{\langle \Delta \mathit{A}{\left({\mathit{r}}^{\text{'}}\right)}^2\rangle },$$

where ΔA(r′) = A(r′) − 〈A〉 is the anisotropy at position r′ relative to the mean.

The correlation function g(r) in each cell is plotted in Fig. 2, H and I, for ES cells and PMEF, respectively. Although g(r) in ES cells shows a monotonic decay with a broad distribution, in PMEFs this distribution is considerably narrower. Furthermore, in PMEFs, g(r) exhibits a weak peak at a characteristic length scale (r₀) that differs slightly between cells. When averaged over cells g(r) for ES cells decays exponentially with a correlation length (λ ∼2.2 μm), although correlation lengths in individual cells can be much larger or smaller (inset to Fig. 2 H).

To identify the characteristic length scale for PMEFs, individual spatial correlation plots were scaled by dividing r by the distance (r₀) at which the second peak for g(r) appears. The inset to Fig. 2 I show the collapsed plot in scaled coordinates clearly showing the increase in spatial correlation of the compaction associated with this length scale. The distribution of r₀ (with mean equal to 3 μm) is shown in Fig. S3 F and corresponds to the distribution of distances between regions of high (low) chromatin compaction (Fig. S3 E). Thus, chromatin compaction exhibits spatial correlations with a characteristic length in differentiated cells. The spectrum of such decays across stem cells is broad enough that no characteristic length scale could be identified.

Active processes regulate heterogeneity in chromatin compaction

We now examine the role of active processes (ATP dependent) in regulating heterogeneity in chromatin compaction states in ES cells. The panel of anisotropy images in Fig. 3 A shows statistically significant differences between control and ATP-depleted ES cells. Typically, the histogram of mean anisotropy of individual ES cells shows a narrower distribution with a lowered mean anisotropy upon ATP depletion (Fig. 3 B and inset to Fig. 3 B). However, for a similar treatment duration we see a relatively smaller difference in the anisotropy distributions in PMEF (panel of images in Fig. 3 C and its corresponding anisotropy distribution in Fig. 3 D and inset to Fig. 3 D), although a longer duration of ATP depletion affects anisotropy measurements in PMEF as well (Fig. S7). The correlation function g(r) in each cell is plotted in Fig. 3, E and F, for ATP-depleted ES cells and PMEF, respectively. The inset to Fig. 3 F shows a reduction by a factor of one-fourth in the spatial length scales for correlations in ES cells, whereas such length scales remain similar in PMEFs upon ATP depletion. These results are consistent with previous studies (27,30), which suggested that the maintenance of chromatin compaction states was linked to ATP-dependent active processes.

Figure 3.

Active processes regulate heterogeneity in chromatin compaction. (A) Color-coded anisotropy maps of core histone H2B are shown for typical nucleus of control ES cells (upper panel) and after ATP depletion (lower panel). (B) Representative plots with corresponding Gaussian fits indicating the distribution of mean anisotropy values in control (black) and ATP-depleted ES cells (red). Inset: The mean of anisotropy values over individual cells in population of cells in the two cases N = 60. (C) Color-coded anisotropy maps of core histone H2B of ATP-depleted PMEFs (N = 40). (D) The mean anisotropy distribution plots for control PMEFs (black) and after ATP depletion (red). Inset: The mean of anisotropy values over individual cells in the population of cells in the two cases. (E–F) Plot of spatial correlation of anisotropy for multiple ATP-depleted ES cells and ATP-depleted PMEFs, respectively. Inset: Bar graph showing spread in g(r) for all the cases.

Nuclear area fluctuations in ES cells reveal an unusual power spectrum

We next assessed the interplay between such structural plasticity in chromatin compaction and heterogeneities in the dynamics of the cell nucleus. To monitor the steady-state dynamics of nuclear shape, the confocal section with maximum nuclear area was obtained in both ES cells and PMEFs using EGFP-LaminB1 as a marker of nuclear boundary. ES cells exhibit relatively larger fluctuations with an oscillatory component in nuclear area when compared to PMEF (Fig.4 A). The inset to Fig. 4 A shows the probability distribution of nuclear area fluctuations in both ES cells and PMEFs. We quantified areal fluctuations via

$$\xi =\frac{\Delta a}{a}=\frac{\sqrt{\frac{1}{N}{\sum }_i\langle {\left(a_i-\langle a_i\rangle \right)}^2\rangle }}{\frac{1}{N}{\sum }_i\langle a_i\rangle },$$

(see Materials and Methods) finding that ES cells are softer with ξ ∼0.05, whereas PMEFs are stiffer with ξ ∼0.01, consistent with previous studies (22).

Figure 4.

Nuclear area fluctuations in ES cells and PMEFs. (A) Typical representative plots of fluctuations in residual nuclear area with time for ES cells (red) and PMEF (black). Inset: Probability histogram of residual nuclear area fluctuation for PMEF (black) and ES cells (red). (B) Plot showing power spectral density of residual nuclear area fluctuations for ES cells (red) and PMEF (black). Arrow shows characteristic frequency peak in ES cells. The inset shows the histogram of f₀ (N = 36). (C) Representative time lapse images (0, 200, and 400 s) of control PMEF (upper panel) and after actin depolymerization using Cyto D (lower panel). Arrows in white show the indentations in the nuclear boundary. (D) Relative nuclear area fluctuations for control (black) and Cyto D-treated PMEF (red). Inset: Probability histogram of residual nuclear area fluctuation for control (black) and Cyto D-treated PMEF (red). (E) Representative time lapse images (0, 200, and 400 s) of control PMEF (upper panel) and after Nocodazole treatment (lower panel). (F) Typical representative plots of fluctuations in residual nuclear area with time for control PMEF (black) and Nocodazole treated (red). Inset: Probability histogram of residual nuclear area fluctuation for the two conditions. (G) Representative time lapse images (0, 200, and 400 s) of control ES cells (upper panel) and after Lamin A/C transfection (lower panel). Scale bar is 5 μm in all images. (H) Typical representative plots of fluctuations in residual nuclear area with time for control ES cells (black) and Lamin A/C transfected (red). Inset: Probability histogram of residual nuclear area fluctuation for the two conditions.

As expected given the increased strength of fluctuations, the power spectrum of the nuclear area fluctuations shown in Fig. 4 B and Fig. S8 A and B, reveals a larger amplitude in ES cells compared to PMEF. Interestingly, both spectra decay as power laws indicating nontrivial temporal dynamics, with slopes 1.5 (PMEF) and 1.9 (ES cells). In addition, such power spectra for PMEF exhibit a weak peak at a characteristic frequency value that can be seen above the power law background. The characteristic frequency was found to have a distribution with mean at 0.007 (±0.002) Hz that corresponds to ∼137s in ES cells. The oscillation is most apparent when the frequency is scaled by the characteristic peak frequency (f₀) in each cell (Fig. 4 B and Fig. S8 A). The inset to Fig. 4 B shows the distribution of f₀.

Actin and Lamin A/C regulate nuclear area fluctuations

We further explored the role of actin, microtubules, and lamin in determining nuclear area fluctuations. Because actomyosin networks influence nuclear morphology during differentiation, we studied the dependence of nuclear area fluctuations on these networks in PMEF. Perturbations of actin stress fibers in PMEFs using Cyto D resulted in enhanced nuclear area fluctuations, confirming the role of actin in maintaining the structural stability of the cell nucleus in differentiated cells (Fig. 4, C and D, Movie S3 and Movie S4). The inset to Fig. 4 D shows the probability distribution of area fluctuations in control and Cyto D-treated PMEFs showing that the distribution is broadened upon actin depolymerization. To explore the contribution of microtubules to such fluctuations in differentiated cells, PMEFs were treated with Nocodazole (10 μM for 1 h). However, no significant change in nuclear area fluctuations was seen (Fig. 4, E and F, inset to Fig. 4 F), in contrast to enhance fluctuations obtained upon actin perturbations.

ES cells lack Lamin A/C and its expression during differentiation results in a stiffened nucleus (22,23). Interestingly, transient expression of Lamin A/C in ES cells results in a reduction in nuclear area fluctuations as seen in Fig. 4, G and H, suggesting that this nuclear structural protein is a major determinant of such fluctuations. Although the presence of exogenous Lamin A/C alters the amplitude of nuclear area fluctuations, it does not affect the stem cell status over short periods as seen by levels of a pluripotent marker, Oct-4 (Fig. S8 C).

These results indicate that actin and Lamin A/C are essential biological determinants in the stabilization of nuclear area fluctuations.

Chromatin compaction states couple to nuclear area fluctuations

Time-lapse fluorescence images of single cells were used to track temporal changes in anisotropy values as well as nuclear area fluctuations in ES cells and PMEFs. We followed individual ES cells in time (60 min) to observe changes in the mean anisotropy values. Over these timescales, we recorded fluctuations in the mean anisotropy values of the whole nucleus (Fig. S9 A), constructing the corresponding probability distribution (Fig. S9 B). Furthermore, we also explored local (Fig. 5 A) changes in anisotropy distributions within a central region (∼5 μm × 5 μm) in ES cells and PMEF. As seen in the images, the spatial distribution of the anisotropy values changes substantially over a 60 min interval in ES cells, whereas in PMEF such distributions show relatively minor variation. This observation highlights the importance of large dynamical fluctuations in the stem cell state vis-a-vis the differentiated state.

Figure 5.

Chromatin compaction states couple to nuclear area fluctuations. (A) Time lapse images of anisotropy in a small region in ES cells (upper panel) and PMEFs (lower panel) Scale bar is 2 μm. Pixel-wise anisotropy autocorrelation for single ES cell (B) and PMEF (C) Each color represents a different pixel. Inset: Representative autocorrelation curve from different spatial locations. (D) Time lapse images of thresholded nuclear area (upper panel) and corresponding anisotropy maps (lower panel) for a single ES cell nucleus. (E) Autocorrelation functions for relative nuclear area fluctuation (black) and anisotropy (red for a single ES cell nucleus.

From these images, pixel-wise autocorrelations (as described in Materials and Methods) of the anisotropy values were computed to determine the dynamics of chromatin compaction states. Fig. 5, B and C, shows the pixel-wise distribution of autocorrelations in an ES cell and PMEF, respectively. The inset to Fig. 5 B represents three characteristic correlation curves in an ES cell; namely, rapidly decaying, slow decaying, and oscillatory, each obtained from a different spatial location in the same cell. In PMEF, on the other hand, such decays are largely monotonic (inset to Fig. 5 C), indicating relatively homogenous dynamics in this case.

Fig. 5 B shows two interesting features: the autocorrelation function does not asymptote to zero over a timescale of observation of 600s and appears oscillatory with a characteristic timescale of ∼350 s. The first feature indicates the presence of slow temporal fluctuations of a period exceeding 600 s consistent with the observed slow decay of the area fluctuation power spectrum. The characteristic period of the oscillatory feature in the autocorrelation function appears consistent with the period of oscillation of the nuclear area (Fig. 4 B), although these may vary from cell to cell.

To examine this relationship further, we computed the correlation of nuclear area fluctuations for the same cell in which the anisotropy time series was obtained (Fig. 5, D and E). The correlation of pixel-wise anisotropy (averaged) and nuclear area shows similar oscillations in ES cells. Our observation of an intrinsic oscillatory component to nuclear area fluctuations mirrored in a corresponding component in chromatin dynamics argues that these phenomena must be coupled in the stem cell state. However, such coupling is largely suppressed or absent altogether in PMEF.

Physical model for observed chromatin and nuclear dynamics

Our results include the observation of a slow (100–350 s) oscillation of the nuclear area in ES cells, the suppression of these oscillations in differentiated cells, slow dynamics in nuclear area fluctuations in both cell types, and a considerable variety in spatial correlations of chromatin compaction inferred through anisotropy measurements. We first address the question of how nuclear area oscillations might originate. ES cells are believed to maintain a state of highly active or hyperdynamic chromatin through constant exchange of a bound fraction of histones as well as other chromatin-associated proteins, with an unbound or loosely bound pool of such proteins. We now assume: i), that there is positive feedback, associated with bistability, in binding and unbinding, such that recruitment (or detachment) of these proteins and protein complexes to DNA promotes further recruitment or detachment. This is constrained by the accessibility of binding sites in highly compact configurations and by the limited number of such sites in more loosely bound structures. A related positive feedback effect in the dynamic modification of histones has been suggested as a mechanism to maintain epigenetic states (31). We couple such feedback effects to mechanics, by assuming ii), that the binding of histones acts to compress DNA locally leading at larger scales to an overall compaction of chromatin structure vis-a-vis states in which fewer histones are bound. Thus, this couples histone binding fractions to the state of chromatin compaction and thence to nuclear size. Finally, iii), although histone addition and removal is a fast process, the subsequent compaction/relaxation of DNA is a slow process, reflecting the dynamics of a long, compact, chain-like molecule.

With these assumptions we may derive a set of simplified equations (see the Supporting Material) representing the dynamics of fluctuations in the fraction of bound histones and the nuclear radius. These equations, formulated in terms of the dimensionless fluctuations in the number of bound histones (Ø) and the nuclear radius (R) are

$$\dot{\mathrm{Ø}}=\mathrm{Ø}-{\mathrm{Ø}}^3+\mathit{R},$$ (1a)

$$\dot{\mathit{R}}=-\mathit{cR}-\mathit{d}\mathrm{Ø}.$$ (1b)

These model equations possess both oscillatory and nonperiodic solutions, and an appropriate choice of parameters (c and d, see the Supporting Material) and the addition of weak stochastic noise modeling histone binding/unbinding events yields oscillatory behavior similar to that seen in the experiments (see the Supporting Material). Physically, the oscillatory states may be understood as follows. A fluctuation in the bound histone population, say one that increases the fraction of bound histones from its average value, recruits more histones, thereby compacts the DNA in its vicinity. Over a longer timescale, the histone-induced compaction of the DNA competes against elastic stresses (arising from both nuclear and cytoskeletal elements) attempting to restore the nuclear radius to its resting state, leading to a slow relaxation of the nuclear size. Such structural relaxation allows histones to leave the complex, a process accelerated by cooperativity, and the fraction of histones is depleted below its time averaged value, thus allowing the cycle to start again. The separation of time scales of τ_Ø (∼0.01–1s) for histone dynamics and the longer scale of relaxation of nuclear area fluctuations τ_R (∼10–100s) plays a crucial role in enabling this mechanism.

In Fig. 6 A we show results for nuclear area fluctuations in our model with a ratio of timescales ($c={\tau }_{\mathrm{Ø}}/{\tau }_R$ = 0.01, 0.3, and 1, d = 0.01). The data for the case ${\tau }_{\mathrm{Ø}}/{\tau }_R$ = 0.01 yield a time series with the characteristic peak in the power spectrum (inset to Fig. 6 A) qualitatively matching the experimental data. As the ratio of timescales become larger the oscillations are suppressed in amplitude. Note that the ratio of timescales can be increased either through a reduction in the histone on/off rate, as be the case when the hyperdynamic character of histone binding is suppressed during cellular differentiation (20). Alternatively, this could happen through a decrease in the nuclear structural relaxation time, as might for example occur through the incorporation of lamins in the nuclear envelope as can be seen in Fig. 4, G and H, or through stiffening of cytoskeletal networks (Fig. 1 B and Fig. 4, C and D).

Figure 6.

Physical model for observed chromatin and nuclear dynamics. (A) Nuclear area fluctuations from the model with parameter values i), c = d = 0.01 (black); ii), c = 0.3, d = 0.01 (red); iii), c = 1, d = 0.01 (blue) with weak additive noise. Inset: Corresponding power spectrum of area fluctuations. (B) Autocorrelation functions for parameter c = d = 0.01, showing relative nuclear area fluctuation (black) and anisotropy (red).

In relating the observation of hyperdynamic chromatin in ES cells to nuclear area fluctuations, our model suggests a microscopic mechanism for these fluctuations. Active fluctuations, for example from the cytoskeleton enter via parameters in our model such as those involved in specifying the stochastic noise terms. We have computed the autocorrelation functions both of the area and of the compaction variable Ø in the previous equations verifying that both exhibit oscillatory decays for the parameter choice $c={\tau }_{\mathrm{Ø}}/{\tau }_R$ = 0.01, d = 0.01 as seen in Fig. 6 B. An experimentally testable prediction of our model is that oscillations similar to those seen in the nuclear area should exist in the local compaction in ES cells, as verified through our measurements of the anisotropy correlations (Fig. 5 E). Generalizations of this simple model to include spatial correlations arising out of cooperative binding suggest a generic mechanism for large correlation lengths. A detailed self-contained description of the model is available in the Supporting Material.

Discussion

We have shown that stem cells exhibit distinct nuclear and cytoskeletal organization in comparison to differentiated cells, specifically addressing their differences at the level of spatio-temporal fluctuations in chromatin compaction and nuclear size. Individual stem cells display largely homogenous chromatin compaction, although there is substantial variability when such cells are taken as a population (Fig. 2, A–E). In addition, chromatin compaction in ES cells exhibits strong and correlated fluctuations both in space and time. On the other hand, individual differentiated cells exhibit a broad, largely frozen-in spatial heterogeneity in chromatin compaction. Fig. 2 H, showing the decay of spatial correlations of anisotropy fluctuations across different ES cells, displays a wide spectrum of variation ranging from fairly short range decays to longer ranged ones. This spectrum is significantly narrowed in PMEF and the correlation peak indicative of structured chromatin begins to manifest.

The absence of stress fibers (Fig. 1, A and B), and the plasticity of actin cytoskeleton (Fig. 1, F and G), and histone-DNA (16,20) association suggests that the nucleus may not be strongly coupled to the cytoskeleton in ES cells, giving rise to its higher nuclear pliability. The appearance of stress fibers (Fig. 1 B) during differentiation coincides with the freezing-in of chromatin compaction (Fig. 1 C).

The inset to Fig. 3 F shows the heterogeneity in the length scales (computed as the length where spatial correlations are reduced by a factor of one-fourth) across the two cell types and with ATP depletion in ES cells. This spatial heterogeneity is around a factor of four larger in ES cells compared to PMEF. ATP depletion in ES cells has a strong effect on anisotropy correlation (Fig. 3 E, inset to Fig. 3 F), indicative of the importance of active fluctuations in maintaining this heterogeneity. Interestingly, similar ATP depletion conditions in PMEFs appear to yield a weaker effect on anisotropy correlation (Fig. 3, H and I, inset to Fig. 3 F).

In the temporal domain for ES cells, Fig. 4 B shows nuclear area fluctuations relaxing over a broad range of timescales. The peak corresponding to the characteristic oscillation frequency appears against a nontrivial but smooth background. In contrast, for PMEFs, no characteristic peak frequency is seen and the scale of such fluctuations is reduced by about an order of magnitude while still decaying as a power law (Fig. 4 B).

Biological factors regulating nuclear area fluctuations include both the cytoskeleton and nuclear structural proteins. In differentiated cells, depolymerizing actin resulted in enhanced nuclear area fluctuations (Fig. 4, C and D), similar to those observed in ES cells that lack a well-defined actin network (Fig. 1 A). In such cells, the contractility of the actin cytoskeleton exerts a tensile force on the nucleus, balanced by compressive loading by microtubules (26). In the absence of actin contractility, the forces exerted by the microtubule network are sufficient to drive nuclear fluctuations as also seen during early Drosophila embryogenesis (32). However, in ES cells, the active stresses controlling nuclear area fluctuations appear to be generated by both nuclear (16) and cytoskeletal activity (Fig. 1, F and G). As these ES cells differentiate, the expression of Lamin A/C (24) results in a stiffened nucleus (22,33). Consistent with this, exogenous incorporation of Lamin A/C by transient transfection in ES cells resulted in reduced nuclear area fluctuations (Fig. 4, G and H).

In Fig. 5 B the pixel-wise autocorrelation of anisotropy values for ES cells shows a weak peak at a timescale consistent with the period of nuclear area oscillations. This indicates that relatively macroscopic fluctuations at the scale of nuclear size are felt even at far smaller scales of local chromatin compaction, as corroborated in Fig. 5 E. In contrast, PMEFs show relatively less structured autocorrelations. The physical model we have outlined captures both the chromatin and nuclear dynamics qualitatively (Fig. 6, A and B).

These observations suggest the following analogy: the extended spatial and temporal correlations seen in ES cells are reminiscent of physical systems near critical points where no single length scale or relaxation time dominates. Such behavior naturally combines two useful and yet contradictory requirements for differentiation: excessive fluidity of chromatin compaction states allows a system to find its local preferred state, without regard to global requirements, yet too little fluidity militates against this. Thus, a compromise permitting communication across significant length scales while still retaining fluidity could well resemble the states discussed previously.

Because such systems exhibit fluctuations at all scales, they can explore the full variety of available states and are very sensitive to even small perturbations. The differentiated cell on the other hand exhibits a far more static organization. Reduced fluctuations in chromatin compaction in differentiated cells should allow for differential access to regulatory sites resulting in lineage-specific gene expression and specific networks of genetic programs (34). The fluidic chromatin assembly in ES cells may assist in maintaining a highly active transcriptome through enhanced interchromatin interactions. Supporting this, our chromosome painting studies reveal that chromosomes are more diffuse, occupying a larger fractional volume of the nucleus in ES cells as opposed to PMEFs (Fig. S10, A and B).

Our results also support recent work (31), which describes stem cells as dynamical systems that combine both robustness and sensitivity to stochastic fluctuations. The simple and novel, to our knowledge, dynamical system we construct suggests a physical mechanism for coupled nuclear size and chromatin compaction oscillations, which is robust to noise. Such a mechanism may be an equally important physical contributor to maintaining the stem cell state. Thus, we conclude that the freezing-in of the heterogeneous yet strongly correlated spatio-temporal dynamics in chromatin compaction states may be the fundamental physical hallmark of cellular differentiation (Fig. 7).

Figure 7.

Schematic illustration summarizing our observations of the coupling between chromatin compaction and nuclear area fluctuations in undifferentiated and differentiated cells.