Transcription-dependent mobility of single genes and genome-wide motions in live human cells

Visualization of active and inactive genes in vivo

To simultaneously visualize and interrogate dynamics of a single gene and its surrounding chromatin in vivo (Fig. 1a), we created a transgenic HeLa cell line stably expressing both the cleavage-deficient Cas9 (dCas9) and histone H2B-GFP (see Methods for detailed protocols). These cells were then simultaneously transfected with sequence-specific single-guide RNAs (sgRNAs), which contain two PP7 RNAs stem loops, and PCP-mCherry, a fluorescently labeled PP7 coat protein, which binds to PP7 RNA loops, following procedures in⁴² (Fig. 1b-c). To validate this approach, we first imaged telomeres, known for their repetitive sequence, using previously published sgRNA design containing 22 nucleotide target sequence with PP7 loops¹⁴. Employing this approach we successfully obtained the characteristic punctate signal for telomeres, whose correct localization we confirmed by telomere-specific peptide nucleic acid (PNA) fluorescence in situ hybridization (FISH) (Supplementary Fig. 1).

To investigate the dynamics of a single gene undergoing transcription, we chose to study genes MUC4 (65 kb) and IL6 (5 kb), which are part of the immune response in HeLa cells^43,44. MUC4 encodes for a glycoprotein, which constitutes mucus on the epithelial cell layers, and IL6 encodes for an interleukin, which acts as a pro-inflammatory cytokine^43,45. While MUC4 has a repetitive sequence requiring a single sgRNA for its visualization in vivo using the CRISPR-dCas9-PCP-mCherry approach, IL6 has a non-repetitive sequence, which necessitated a design of 67 unique sgRNAs (see Methods). Figure 1d shows nuclei with fluorescently labeled chromatin (H2B-GFP, cyan) and the positions of MUC4 and IL6, respectively, determined by the CRISPR-dCas9-PCP-mCherry signal (PCP-mCherry, magenta). Signal-to-noise ratio of detected gene loci is shown in Supplementary Fig. 2a. We verified the specificity of the CRISPR-dCas9-PCP-mCherry signal (Fig. 1d, magenta) by showing its co-localization with the respective gene sequence visualized by FISH using human BAC clones for MUC4 and IL6, respectively (Fig. 1d, green).

MUC4 and IL6 are initially transcriptionally inactive in HeLa cells, but can be activated by inflammatory stimuli such as IFNγ and TNFα for MUC4⁴⁶, and lipopolysaccharide (LPS) for IL6^47,48. We activated transcription of MUC4 and IL6 using these respective stimuli. To verify the transcription activation of MUC4/IL6, we visualized nascent RNA at MUC4/IL6 using RNA FISH (see Methods). We find foci of nascent RNA at MUC4/IL6 in transcriptionally stimulated (active) nuclei, but never in unstimulated (inactive) nuclei (Fig. 1e). Specifically, we found 102 RNA foci across 72 IL6-stimulated nuclei and 48 RNA foci across 37 MUC4-stimulated nuclei, while we detected no RNA foci across 30 IL6-unstimulated nuclei and 30 MUC4-unstimulated nuclei. Signal-to-noise ratio of the detected RNA FISH foci was consistent with earlier studies⁴⁹(Supplementary Fig. 2b). Considering that transcriptional bursts have a duration of  ~10–100 min, with time of inactivity between bursts of ~100 min^50,51, we could be randomly sampling active genes bursting or in between bursts. Given our observed RNA foci counts and the HeLa cell ploidy⁵² (we expect 3 copies of both genes per nucleus), we can estimate that at least 47% of IL6 and 43% of MUC4 genes are actively transcribing at the time of observation. With the mRNA splicing times  ~15 s–5 min⁵³ and the degradation half-life of spliced introns  ~5 min⁵⁴, the detected RNA FISH foci point to an ongoing transcriptional activity. Our estimates present a lower bound, as some mRNA targets may be lost (e.g. washed away) during the fixation procedure. In addition, stimulated genes are subject to forms of activity beyond the transcription itself, e.g. remodeling pre/post transcription⁵⁵.

To monitor production of nascent RNA at active MUC4/IL6 as a function of time, we performed RNA FISH at different time points up to 3 hrs after the transcriptional stimulation and observed no significant changes in the encounter frequency of RNA FISH foci (Supplementary Fig. 3). In addition, we visualized transcriptionally active RNA polymerase II (RNA pol II with phosphorylated S5 CTD) in control cells and transcriptionally stimulated cells using immunofluorescence. We observe a co-localization of MUC4/IL6 genes with active RNA pol II only upon their transcriptional activation (Supplementary Fig. 4). However, the colocalization of the two signals in the active case is not a definitive evidence of the gene activation, since active genes in close proximity (below optical resolution) would also yield RNA pol II signal. Hence, the definitive evidence is provided in Fig. 1e, where we show the sequence-specific RNA FISH imaging for both MUC4 and IL6.

Transcriptional stimulation of MUC4/IL6 could also lead to activation of other genes. To assess any potential changes in the overall gene activity upon the two studied stimuli, we measure the density of active genes in the nucleus before and after LSP/IFNγ + TNFα stimulation (Supplementary Fig. 5a). Specifically, we count the number of active RNA pol II foci in a focal plane, which we normalize by the nuclear area in the given plane, and find the average active RNA pol II density of 0.92  ± 0.09 foci/μm² over 94 unstimulated nuclei, 0.94 ± 0.09 foci/μm² over 67 IL6 stimulated nuclei, and 0.97 ± 0.07 foci/μm²over 67 MUC4 stimulated nuclei (mean  ± standard deviation, Supplementary Fig. 5b). Our data show, there are no significant changes in the overall gene activity upon the two studied stimuli. It is important to note that we apply LPS only for 30 min. Our observations are consistent with an earlier study showing minimal changes in overall transcriptional activity after 1 h LPS stimulation⁵⁶. Thus, our approach allows for visualization of MUC4/IL6 genes in vivo, while controlling for their respective transcriptional activity at a local level.

Single gene vs. large scale chromatin dynamics

To monitor the transcription-dependent motion of MUC4 and IL6 (CRISPR-dCas9-PCP-mCherry), while observing dynamics of their surrounding chromatin (H2B-GFP), we used simultaneous two-color spinning disc confocal microscopy allowing us to record both signals, CRISPR-dCas9-PCP-mCherry and H2B-GFP at the same time (see Methods and Supplementary Movies 1–2). Specifically, we recorded high-resolution streams (~65 nm pixel size in x and y, 250 ms per frame) for both signals for 20 s before and after the transcription activation of MUC4 and IL6 (Fig. 2a). Using single particle tracking (SPT), we follow the MUC4/IL6 motion in their respective CRISPR-dCas9-PCP-mCherry signals and obtain trajectories for all tracked genes (Fig. 2b, see Methods and Supplementary Movie 3). In addition, we analyze the H2B-GFP signal by Displacement Correlation Spectroscopy (DCS)⁹, which maps chromatin motion across the entire nucleus in real time (see Methods). DCS measures chromatin motion over time intervals Δt, sampling over all time intervals, i.e., timescales, accessible by the experiment. We obtain the DCS maps for Δt = 0.25 – 15 s: Fig. 2c and d show examples of DCS maps at Δt = 0.25 s and Δt = 10 s, respectively (Supplementary Movies 4–5). The displacement vectors are color-coded by their direction, i.e., vectors of the same color point into the same direction.

Consistent with earlier studies⁹, at short time intervals chromatin displacements are uncorrelated (Fig. 2c and Supplementary Fig. 6b), while at longer time intervals chromatin displacements become correlated over few microns (Fig. 2d and Supplementary Fig. 6c). To quantify the extent of displacement correlation at different Δt, we compute the spatial autocorrelation function \({C}_{\!{d}_{x}}(\Delta {{\bf{r}}},\Delta t)=\langle {d}_{x}({{\bf{r}}},\Delta t),{d}_{x}({{\bf{r}}}+\Delta {{\bf{r}}},\Delta t)\rangle\) for the x-component d_x of the measured chromatin displacements d_ch(r, Δt), where r is the displacement vector’s position. Figure 2e shows the radially averaged \(\langle {C}_{\!{d}_{x}}(\Delta {r},\Delta t)\rangle\) for different Δt, with 〈〉 being the ensemble average over all \({C}_{\!{d}_{x}}(\Delta {r},\Delta t)\) at a given Δt. We confirm that the spatial autocorrelation monotonously grows with an increasing Δt for Δt = 0.25 – 15 s (Fig. 2e and Supplementary Fig. 6d). Further, we assess changes in nucleus-wide chromatin dynamics before/after transcription activation by measuring the chromatin velocity amplitude \({\langle | {{{\bf{v}}}}_{{{\rm{DCS}}}}(\Delta t)| \rangle }_{r}={\langle | {{{\bf{d}}}}_{{{\rm{DCS}}}}({{\bf{r}}},\Delta t)| \rangle }_{r}/\Delta t\) averaged over the entire nucleus at each Δt (Supplementary Fig. 7). Our data show that the average nucleus-wide chromatin dynamics is unperturbed by the MUC4 and IL6 transcription activation stimuli, (TNFα + IFNγ) and LPS, respectively, but we do not rule out changes in the spatial distribution of chromatin velocities across the nucleus. In contrast, the average chromatin velocity in the immediate vicinity of both MUC4 and IL6 exhibits noticeable changes, in particular at longer timescales. Taken together, our data show no significant changes in the density of actively transcribing genes (Supplementary Fig. 5) and average nucleus-wide chromatin dynamics (Supplementary Fig. 7) upon MUC4/IL6 transcriptional stimulation. This suggests that the baseline level of transcription activity in the nucleus has not changed upon these stimuli, which is in agreement with an earlier QPCR study⁵⁶.

To examine the contribution of a single gene motion (Fig. 2b) to the movement of the surrounding chromatin, and thus to the larger scale chromatin dynamics (Fig. 2c–d), we survey the concurrent movements of MUC4 and IL6 and their surrounding chromatin (Fig. 2f). We review these two types of motion in the gene frame, by keeping the direction of the gene displacement vector (pink and green arrows) constant and plotting the corresponding DCS field (grey arrows) of the surrounding chromatin (raw data shown in Supplementary Fig. 8a). Figure 2f presents such visualization for both inactive (pink arrow) and active (green arrow) MUC4/IL6 within the context of the flows of the surrounding chromatin (grey arrows) for Δt = 0.25 and 10 s at three consecutive time steps. We find that at short timescales (Δt = 0.25 s), the motions of MUC4 and IL6 appear independent of the surrounding chromatin in both transcriptionally active and inactive state. Conversely, at long timescales (Δt = 10 s) active MUC4 and IL6 (green arrows) move in concert with the surrounding chromatin (grey arrows), but there is no visible correlation when MUC4 and IL6 are inactive. This suggests that the local motion of an active gene might indeed contribute to the large-scale chromatin dynamics at longer timescales.

We assess the correlation between the local gene movement and surrounding chromatin flows by computing a correlation score S_c = 〈d_g(t)/d_g(t) ⋅ d_ch(r, Δt)/d_ch(r, Δt)〉, given by the scalar product between the displacement vectors of the gene d_g and of the surrounding chromatin d_ch at Δt = 0.25 s and Δt = 10 s, with 〈〉 denoting an average over all time frames. Figure 2g–h show a plot of 〈S_c〉, a radially integrated S_c averaged over a gene population, where N(MUC4)_i = 22, N(IL6)_i = 17, N(MUC4)_a = 21 and N(IL6)_a = 18 (Supplementary Table 1), as a function of the distance Δr from the gene position. Indices i and a denote inactive and active state, respectively. For 〈S_c〉 at Δt = 0.25 s, we find no correlation between motion of the genes and their surrounding chromatin, regardless of the gene’s activity level (Fig. 2g). In contrast, for 〈S_c〉 at Δt = 10 s, the difference is striking: When inactive, the motion of both MUC4 and IL6 is not correlated with the surrounding chromatin (Fig. 2h, pink). Upon activation, however, both MUC4 and IL6 show about  ~50% increase in their correlation with the surrounding chromatin (Δr ≤ 0.13 μm) at the gene center (Fig. 2h, green). The distances over which we observe high correlation are large in comparison to the diameter of chromatin fiber is ~10 nm. Remarkably, this correlation decreases 2–3 fold for active genes, but only  ~20% for inactive genes over  ~1.25 μm at Δt = 10 s. The decrease of correlation with the distance is expected for motion correlation caused by activity in a viscous fluid. Note, p-values of all observed changes are ≤ 10⁻³ (Supplementary Table 2). Thus, our results suggest that active genes might contribute to local chromatin flows.

Real-time dynamics of active and inactive genes

Next, we examine the amplitude of local displacements exhibited by a transcriptionally active versus inactive single gene and its surrounding chromatin. Figure 3a shows nuclei with CRISPR-dCas9-PCP-mCherry signal indicating the position of MUC4/IL6 in the two respective states (highlighted by an orange box) and the corresponding H2B-GFP signal visualizing the surrounding chromatin. As described earlier, we track the motion of the labeled genes as well as the neighboring chromatin at temporal resolution of 250 ms over 20 s. The obtained trajectories are displayed in Fig. 3b, with time progression color-coded from blue to red. We also measure the trajectory area A_L given by the area of a convex hull (pink) enveloping the trajectory.

Further, we compute the mean square displacement for the tracked genes MSD (Δt) = 〈∣d_g(t + Δt)  −  d_g(t)∣²〉, with d_g(t) being the gene displacement at time t and average over the respective gene populations, where N(MUC4)_i = 44, N(IL6)_i = 43, N(MUC4)_a = 42 and N(IL6)_a = 37 (Fig. 3c). Surprisingly, although the MSD visibly changes upon activation for both genes (Fig. 3c), these changes are not statistically significant (p-values listed in Supplementary Table 2). However, IL6 explores on average larger area A_s = MSD(250 ms) for a short timescale when active than inactive (p-value = 0.01), while MUC4 shows no appreciable change. On the other hand, the area A_L explored over a longer time (20 s) remains similar for both genes after the activation (Supplementary Tables 3 and 4).

For the surrounding chromatin, we evaluate dynamics of chromatin in a 1.3 μm × 1.3 μm region, with the gene located in its center (Fig. 2f). We calculate the mean square network displacement⁹: MSND (Δt) = 〈∣d_ch(r, Δt)∣²〉, where d_ch(r, Δt) denotes the chromatin displacements at position r. As shown in Fig. 3c, the local MSND reveals that for MUC4 the surrounding chromatin is less mobile upon activation (p-value −3), while there is no appreciable change for IL6 (p-value = 0.22). As a negative control, we measure MSD (Δt) and MSND (Δt) for MUC4 in formaldehyde-fixed cells, demonstrating that both MSD (Δt) and MSND (Δt) measurements are well above the noise floor (Fig. 3c).

To evaluate the type of motion a gene undergoes at the time scale of our measurement, we fit the average MSD to a power law, MSD (Δt) = A + BΔt^α. As previously shown^9,57, the constant A accounts for a possibility of an additional fast motion at time scales below our time resolution. Our data shows that for both genes A increases upon activation: for MUC4 from 0.5 ± 0.5 ⋅ 10⁻³ μm² to 1.9 ± 0.5 ⋅ 10⁻³μm² and for IL6 from 1.7 ± 0.3 ⋅ 10⁻³μm² to 4.1 ± 0.3 ⋅ 10⁻³μm². We report B = 8.0 ± 0.5 ⋅ 10⁻³μm²s^−α for inactive MUC4 and 5.6 ± 0.4 ⋅ 10⁻³μm²s^−α for active MUC4, whereas B = 6.3 ± 0.2 ⋅ 10⁻³μm²s^−α for inactive IL6 and 5.6 ± 0.3 ⋅ 10⁻³μm²s^−α for active IL6. We find that both MUC4 and IL6 move subdiffusively (α 14,58,59. However, our data reveals that for both MUC4 and IL6, α increases upon activation from 0.47 ± 0.02 to 0.60 ± 0.02 and from 0.67 ± 0.01 to 0.7 ± 0.02, respectively (Fig. 3c & Supplementary Table 5). It is important to note that any fluorescent label may affect dynamics of its labeled structure. However, assuming similar label binding statistics for both active and inactive genes, such an effect would be comparable for genes in both states. Therefore, we interpret our results as informing on relative changes between active and inactive states, but not directly informing on the unlabeled state.

Similarly, to assess the type of motion exhibited by the chromatin surrounding the gene, we fit the average MSND to a power law, MSND (Δt) = A + BΔt^α. We find that the surrounding chromatin of both genes undergoes a reduction upon activation from α ~0.6 ± 0.02 to 0.5 ± 0.02. (Supplementary Table 5). Our data suggest, that transcription activity of a gene is manifested by a dynamical signature of an increase in α for the gene motion, while the amplitude of the motion does not change appreciably. We hypothesize that genes residing in distinct local environments may be subject to different physical resistance to their motions, and hence possess a different displacement amplitude – yet, this information is lost upon averaging over all genes. Hence, to reveal the differences in displacement amplitudes between the active and inactive genes, we need to investigate motions of genes residing in a similar physical environment. In what follows, we investigate the hypothesis that the compaction of the chromatin surrounding different active genes provides varying resistance to their motion.

Chromatin compaction at active and inactive genes

To test the impact of local chromatin compaction on the mobility of a gene, we analyze the H2B-GFP signal around the gene of interest. H2B-GFP is a reliable marker of chromatin position and its relative compaction^9,57,60. Figure 4a shows micrographs of MUC4 and IL6 (CRISPR-dCas9-PCP-mCherry, orange circle) in inactive/active state and the surrounding chromatin (H2B-GFP). The orange cross in the H2B-GFP signal marks the position of the gene center and the grey solid and dashed circles denote the 0.5 μm and 1 μm distances from the gene center, respectively. The difference in the compaction of chromatin surrounding different genes is clearly visible as variations in the H2B-GFP intensity.

To quantify differences in the chromatin compaction, we evaluate I_ch, the H2B-GFP intensity I measured at the gene center at t = 0 s and normalized by the average H2B-GFP intensity in the entire nucleus 〈I〉. I_ch = I(0) is representative of the chromatin compaction over the 20 s observation time in our experiments (Supplementary Fig. 9). Figure 4b shows distributions of I_ch obtained for populations of inactive and active MUC4 and IL6 genes. While the mean I_ch value does not change significantly upon activation of MUC4 or IL6, a closer inspection of the distributions reveals a presence of two distinct modes in all 4 populations: one at I_ch I_ch > 1. Since I_ch = 1 corresponds to the average H2B-GFP intensity in the nucleus (Fig. 4b, grey line), I_ch I_ch > 1 to higher chromatin compaction. This suggests that for both inactive and active MUC4/IL6 we find genes that are located in less as well as more compact chromatin, indicating that each gene might have a rather unique local environment. The schematics in Fig. 4c illustrates these different chromatin compaction states by depicting the local H2B-GFP intensity (green). In addition to I_ch, it introduces S_rel, which assesses the H2B-GFP intensity change over 0.75 μm from gene by measuring its linear slope⁵⁷. The means and standard errors for measured I_ch and S_rel are listed in Supplementary Table 3.

Next, we measure I_r(Δr), the chromatin compaction as a function of the distance Δr from the gene, by radially averaging H2B-GFP intensity over 0.13 μm increments and normalizing by 〈I〉 (see Methods). Note, the first point of I_r(Δr) corresponds to I_ch. We sort both inactive and active genes by their local chromatin compaction I_ch, specifically, low compaction (I_ch I_ch > 1) chromatin, and obtain average I_r(Δr) for both genes in each chromatin compaction state (Fig. 4d). Strikingly, our data reveal that both active genes can be found in both less and more compact chromatin, similarly, both inactive genes do not show a strict preference for a specific compaction state. We further confirm this finding by measuring I_ch at IL6 and MUC4 nascent RNA sites visualized by RNA FISH (Supplementary Fig. 3) and finding that active loci can indeed exist with similar probability in both low and high chromatin compaction states.

To further explore a possible correlation between the local chromatin compaction and the activity of genes, we have performed the same analysis for all active transcription sites in a cell, providing us with much larger statistics. Specifically, we used IF labeling of active RNA pol II (N = 1661 over 50 cells) and evaluated the chromatin compaction in their vicinity (Supplementary Fig. 10e). We find that  ~80% of active transcription sites are located in less compact chromatin (I_ch I_ch > 1) (Supplementary Fig. 10f). This observation is consistent with previous studies, which found transcription to occur predominantly (but not exclusively) in less compact chromatin^{32,36,37,38,61}. Moreover, our data show that average chromatin compaction at active RNA poll II sites is intermediate with 〈I_ch〉 ~ 0.9, which is in agreement with an earlier study⁶¹. When we evaluate S_rel for all the states introduced in Fig. 4d, we find that independently of their activity, genes located in I_ch S_rel values, while genes located in I_ch > 1, have lower S_rel values (Fig. 4e, Supplementary Table 3). Therefore, while many active genes tend to locate in less compact chromatin, it is critical to survey the unique properties of the local environment of each active gene in order to elucidate the physical mechanism underlying their dynamics.

Contribution of active genes to coherent chromatin motions

To further examine the impact of local chromatin compaction on the mobility of inactive and active genes, we sort genes by their local chromatin compaction I_ch and compute the corresponding MSD and MSND. We then evaluate the time dependence of MSD and MSND by fitting it to f(Δt) = A + BΔt^α. As shown in Fig. 5a, we find that MSD of single genes strongly depends on both their chromatin compaction I_ch and their transcriptional state. Specifically, inactive MUC4 and IL6 have surprisingly similar behavior, with their MSD showing significantly larger displacements and α (and thus higher mobility), for genes located in less compact chromatin (I_ch 5a, pink curves) than in more compact chromatin (I_ch > 1, Fig. 5a, magenta curves), with p-values  −3 (Supplementary Table 2). Upon activation, MUC4 and IL6 located in more compact chromatin show no significant changes in their mobility (I_ch > 1, Fig. 5a, dark green curves) compared to their inactive state. However, active MUC4 and IL6 located in less compact chromatin exhibit remarkably different behavior (I_ch 5a, light green curves) from their inactive counterparts. While α increases for both MUC4 and IL6 genes located in less compact chromatin upon activation (I_ch 5a, light green curves), the absolute values of their displacements do not appreciably change for IL6, but decrease significantly for MUC4 (p-value = 0.01), when compared to their MSD in inactive state. This suggests that the genes located in more compact chromatin are more constrained by the surrounding chromatin and thus the effect of their activity on their mobility is weak. Conversely, genes whose surrounding chromatin has a lower compaction can move easily, allowing us to investigate their contribution to the local chromatin dynamics.

In contrast, Fig. 5b displays the MSND of the chromatin surrounding the genes: For MUC4 upon transcriptional activation, its MSND decreases significantly in both compaction states (p-values ≤ 0.04). Whereas, for IL6 upon transcriptional activation, we observe significant decrease in MSND only at higher chromatin compaction (I_ch > 1, p-value = 0.03). Moreover, when we assess the amplitude of the average velocity 〈∣v_DCS(Δt)∣〉 of the chromatin surrounding the gene, we find a decrease for chromatin surrounding the active genes (Supplementary Fig. 7), which is consistent with the above observations. The fitting parameters and their errors from both MSD and MSND are shown in Supplementary Table 5 and the p-values in Supplementary Table 2.

Our observations suggest that the dynamic behavior of genes upon their transcriptional activation largely depends on the compaction of their surrounding chromatin (Fig. 5a). We confirm this by computing the average correlation score 〈S_c〉 at Δt = 10 s for groups of genes located in chromatin of the same compaction I_ch (Fig. 5c–d). Indeed, we find that genes residing in lower compaction chromatin exhibit dramatic difference in 〈S_c〉 upon activation, especially IL6 showing an increase from  ~0.1 to  ~0.5 at Δr ≤ 0.13 μm (Fig. 5c). For both MUC4 and IL6 in low compaction chromatin, the 〈S_c〉 significantly increases upon activation (p-values −3). Interestingly, 〈S_c〉 decreases with increasing distance from the gene until reaching the values comparable to inactive genes at  ~1.4 μm, thus leading to regions of coherent motion of  ~2.8 μm. This is in excellent agreement with the size of coherent regions (~3–5 μm) measured by DCS⁹. Inactive genes do not show any changes in 〈S_c〉 with increasing distance from the gene. In contrary, genes residing in more compact chromatin show a slight correlation (~0.3) in both active and inactive states (Fig. 5d, Supplementary Table 1). This suggests an orientational order of local chromatin motions, which likely arises due to tight physical coupling within regions of high chromatin compaction. Hence, larger regions of chromatin move together, when they are in more condensed state (e.g., heterochromatin).

To validate our observation of gene mobility depending on both its local chromatin compaction and transcriptional state, we assess the mobility and chromatin compaction of random genomic sites as a control measurement. Naturally, random sites will vary in their physical properties (size/compaction/intensity distribution). To enable comparison of motions of random sites and MUC4/IL6 gene loci, we choose only a subset of random sites that have physical properties identical to those of MUC4/IL6 active (or inactive) sites. We identify such random sites as mock active (or inactive) sites and track their motions. Specifically, using a previously published machine-learning algorithm⁵⁷, we first generate a population of random sites across the entire nucleus in the H2B-GFP signal, for which we measure I_ch and S_rel. Hence, we next identify subpopulations of these random sites whose I_ch and S_rel match those of the H2B-GFP signal at MUC4/IL6 genes in inactive/active states (Fig. 5e). This yields eight distinct random sites groups that match I_ch and S_rel of MUC4/IL6 in the different studied states: inactive/active MUC4/IL6 in low/high compaction chromatin. Once these groups of random sites are established, we track the motion of each random site over the same time interval (20 s) as we did for MUC4/IL6 and calculate their average correlation score 〈S_c〉 at Δt = 10 s with the surrounding DCS fields (Fig. 5f, Supplementary Table 1). Our data reveal that the motion of random sites in more compact chromatin shows indeed an inherent correlation with the surrounding chromatin, whereas random sites in less compact chromatin show on average no correlation (Fig. 5f). This suggests that local chromatin compaction affects the mobility of gene loci. Moreover, it is consistent with a picture of active genes driving the coherent motions in low compaction chromatin.

Gene activity and chromatin compaction affect chromatin flow alignment

To assess the effect of transcriptional activity of a single gene on the surrounding chromatin flow, we analyze these flows before/after the gene’s activation. To this end, we measure the divergence and vorticity (curl) of chromatin velocity fields directly around the gene site. Roughly speaking, the divergence of a velocity field measures the tendency of the surrounding chromatin fluid to collect or disperse at the gene site, whereas the curl of a velocity field measures the tendency of the chromatin fluid to circulate around the gene. We obtain the velocity fields from the DCS-measured displacement fields as v_DCS(r, Δt) = d(r, Δt)/Δt.

We specifically choose to measure the divergence and curl over the timescale Δt = 10 s, where the large-scale coherent chromatin motions occur, while at shorter timescales (9. Both, the fast uncorrelated motion and slow coherent motion happen concurrently. However, the large-scale coherency was shown to be eliminated upon ATP depletion as well as RNA pol II inhibition^9,23,24, suggesting that active processes drive large-scale coherency. Importantly, the chromatin coherency in vivo has a lifetime of 5–10 s, after which the coherent regions break-up, new ones form and move into new directions⁹. Thus, to examine the effect of active transcriptional events on the coherent motions, it is informative to analyze the vector field characteristics over 10 s.

Figure 6 a illustrates four canonical cases, where a 2D velocity field would exhibit some circulation (∣∇ × v_DCS∣ > 0) or no circulation (∣ ∇ × v_DCS∣ = 0), while also exhibiting net flow inward (∇ ⋅ v_DCS ∇ ⋅ v_DCS > 0), or equal inward and outward flow (∇ ⋅ v_DCS  = 0). Unlike the direction of flow in or out of a region, the direction of the circulation is not relevant. In order to read out vorticity and divergence at a gene site, the nearest four displacement vectors of DCS calculated at Δt = 10 s are evaluated. We find that upon transcriptional activation, the magnitude of the vorticity is significantly reduced (p-values ≤ 0.01) for both genes when located in low compaction chromatin (Fig. 6b, top, and Supplementary Table 6), while remaining the same for both genes when located in high compaction chromatin (Fig. 6d, top, and Supplementary Table 6). Notably, upon activation we observe for both genes a significant increase in the divergence values from negative (inwards flows) to positive (outward flows), with the divergence distributions showing a strong shift upward (p-values −3), when located in low compaction chromatin (Fig. 6b, bottom, and Supplementary Table 6). Interestingly, IL6 divergence exhibits a bimodal distribution, while MUC4 divergence exhibits a trimodal distribution with a dominant peak at ∇ ⋅ v_DCS ~ 0. In contrast, upon activation of genes in high compaction chromatin, we observe opposite trends for divergence distributions of the two genes: While for MUC4 the distribution shifts to higher values, for IL6 it moves to lower values (Fig. 6d, bottom, and Supplementary Table 6). A non-zero divergence indicates chromatin acts as a compressible material, which is consistent with the fact that chromatin can condense and decondense within its solvent. Given the 5–10 s lifetime of chromatin coherency, it is unlikely that any given active site exhibits single-signed divergence over long times. This is consistent with wide distributions in Fig. 6b and d, spanning both negative and positive values.

Close inspection of individual chromatin displacement fields reveals that upon transcriptional activation chromatin flows align with the motion of the active genes in low compaction chromatin (Fig. 6c, gray arrows). This is in contrast to inactive genes in low compaction chromatin, whose surrounding chromatin flows are not aligned. We find that for active genes local chromatin flows display higher alignment, when ∣∇ × v_DCS∣ −1, as higher vorticity introduces visible misalignment of the flows. This suggests that at low compaction chromatin, active genes may be involved in the alignment of the surrounding chromatin flows.

In contrast, we find for both genes when they are located in high chromatin compaction, that the surrounding chromatin flow is aligned before and misaligned after activation (Fig. 6e, gray arrows). This corroborates our findings in Fig. 5f suggesting that high compaction chromatin induces an inherent correlation due to a tight physical coupling of the chromatin polymeric network (e.g., heterochromatin). Polymer entanglements can serve as topological crosslinks and thus effectively cause an elastic coupling of the neighboring chromatin fibers. Taken together, these results suggest that active transcription sites may be contributing to the coherent chromatin motions.