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Chromatin mechanics dictates subdiffusion and coarsening dynamics of embedded condensates

Abstract

DNA is organized into chromatin, a complex polymeric material that stores information and controls gene expression. An emerging mechanism for biological organization, particularly within the crowded nucleus, is biomolecular phase separation into condensed droplets of protein and nucleic acids. However, the way in which chromatin impacts the dynamics of phase separation and condensate formation is poorly understood. Here we utilize a powerful optogenetic strategy to examine the interplay of droplet coarsening with the surrounding viscoelastic chromatin network. We demonstrate that droplet growth dynamics are directly inhibited by the chromatin-dense environment, which gives rise to an anomalously slow coarsening exponent, β ≈ 0.12, contrasting with the classical prediction of β = 1/3. Using scaling arguments and simulations, we show how this arrested growth can arise due to subdiffusion of individual condensates, predicting β ≈ α/3, where α is the diffusive exponent. Tracking the fluctuating motion of condensates within chromatin reveals a subdiffusive exponent, α ≈ 0.5, which explains the anomalous coarsening behaviour and is also consistent with Rouse-like dynamics arising from the entangled chromatin. Our findings have implications for the biophysical regulation of the size and shape of biomolecular condensates and suggest that condensate emulsions can be used to probe the viscoelastic mechanical environment within living cells.

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Fig. 1: Coarsening dynamics of light-activated protein condensates in living cells.
Fig. 2: Droplet growth is dominated by coalescence.
Fig. 3: Simulations quantitatively demonstrate the scaling relation between the diffusive exponent and the coarsening exponent.
Fig. 4: Droplets within the nucleus exhibit strongly subdiffusive motion.
Fig. 5: Droplets are constrained by chromatin.
Fig. 6: Condensates as microrheological probes of the intracellular environment.

Data availability

All data within this paper are available from C.P.B. upon reasonable request.

Code availability

All code utilized in this paper is available from C.P.B. upon reasonable request.

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Acknowledgements

This work was supported by the NIH 4D Nucleome Program (U01 DA040601, C.P.B.), the Howard Hughes Medical Institute (C.P.B.) and the National Science Foundation, through the Center for the Physics of Biological Function (PHY-1734030) and the Graduate Research Fellowship Program (DCE-1656466, D.S.W.L.). We thank J. Riback, P. Ronceray, S. Shimobayashi, A. Strom, Y. Zhang, and the rest of the Brangwynne and Wingreen groups for constructive comments on this work. We also thank S. Keller (University of Washington, Department of Chemistry) for useful discussions at the Marine Biological Laboratory. We acknowledge E. Gatzogiannis for microscopy assistance and K. Rittenbach and the Princeton Molecular Biology Flow Cytometry Resource Facility, which is partially supported by the Cancer Institute of New Jersey Cancer Center Support Grant (P30CA072720), for assistance with cell-sorting experiments.

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D.S.W.L., N.S.W. and C.P.B. conceptualized the project and wrote the manuscript. D.S.W.L. performed the experiments, formal data analysis, theory and simulations.

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Correspondence to Ned S. Wingreen or Clifford P. Brangwynne.

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C.P.B. is a founder and consultant for Nereid Therapeutics. All other authors declare no competing interests.

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Peer review information Nature Physics thanks David Zwicker and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data

Extended Data Fig. 1 We characterized our system at early times immediately following a blue-light quench by taking high-speed images for the first 5 minutes of activation.

a, First, the degree of supersaturation was calculated by estimating the intensity in the nucleus but outside droplets and dividing by the average nuclear intensity in the first frame (that is, before any visible condensation). This ratio of intensities was averaged over cells for each timepoint; shading represents standard error of the mean. Supersaturation initially decreased very quickly following activation and continues to decrease much more slowly after 100 seconds (t0 was set to 180 s), which we attribute to photobleaching. b, To quantify nucleation dynamics, the number of droplets was calculated at each frame following activation: a quick increase is followed by saturation and then a slow decrease as droplets begin to coalesce. For each cell, the number of droplets was taken at each frame, divided by the time average for that cell, and then averaged over cells. Error bars reflect standard error of the mean across cells. c, To characterize the heterogeneity of coarsening behavior across cells, we individually fit the average droplet radius versus time for each cell to obtain a coarsening exponent. We also computed the volume fraction of droplets in each cell by dividing the number of pixels containing droplets at the final frame of activation (105 minutes) by the total number of pixels in the nucleus in the first frame of activation. The best-fit coarsening exponent for individual cells (error bar is 95% CI) was plotted against this volume fraction. The cell-to-cell variation in the coarsening exponent decreases with volume fraction, approaching an average value of ~0.12. d, Finally, for our estimate of the average rate of droplet growth due to subdiffusive merger, we compared minimum inter-droplet distance per droplet (lmin) versus average radius of droplets at t0 per cell and found that because volume fraction and nuclear size are similar over the cell population, the two quantities are strongly correlated. Error bars reflect SEM.

Extended Data Fig. 2 Analysis from Figs. 1c,d and 2d were repeated using an integrated intensity metric to estimate the size of droplets.

a, Average integrated droplet intensity grows as a power law in time. b, Nondimensionalizing with t0 = 3 min, averaging, and fitting gives a coarsening exponent of β = 0.13 ± 0.01 (95% CI of fit). c, Integrated intensity is conserved among collisions. d, Mean squared error (MSE).was calculated by assuming that volume must be conserved among collisions and then determining the deviation of the final volume post collision from the prediction, that is, as \({\mathrm{MSE}} = \left\langle {\left( {1 - \frac{{V_1 + V_2}}{{V_3}}} \right)^2} \right\rangle\), where \(V_i = R_i^3\) or \({\mathrm{{\Sigma}}}I_i\) for radius and integrated intensity methods, respectively. The root mean square error (RMSE) is similar but slightly greater for the integrated intensity method.

Extended Data Fig. 3 Average droplet size and geometry is robust to thresholding of images.

a, To test the robustness of the image segmentation to thresholding, we first calculated the threshold as described in the main text methods (two standard deviations above mean nuclear intensity at time 0). We then multiplied the threshold by a factor ranging from 0 to 5 (‘Factor change’) and calculated what percentage of each image was above the threshold and would be identified as a droplet (‘Fraction of image’). Each colored curve corresponds to a single image containing one nucleus (N=18 images total) after 105 minutes of activation; black dashed line reports the average over all images. Trivially, the entire image is above the threshold at a factor value of 0 and decreases quickly. However, as the factor approaches 1 and higher values (that is, the chosen threshold) the fraction of the image segmented decreases only slowly (see inset), suggesting that segmentation is robust with respect to the threshold above these values. b, The identical procedure was applied to the same images to evaluate the dependence of the average droplet radius on threshold, as demonstrated in inset example images. Similar to the fraction of image metric, the average droplet radius was robust above a factor of approximately 0.75, suggesting that our results are not sensitive to the precise threshold.

Extended Data Fig. 4 Equilibration of dilute-phase concentration in Fig. 2e, f is fast.

Nuclei from Fig. 2e were segmented and pixel intensity in the dilute phase was binned by location with respect to the gradient of activation, normalized, averaged over cells, and plotted. Cells were activated using a blue light intensity gradient for 30 seconds; at the end of that time, a gradient was observed in the dilute-phase concentration, favoring the side of the nucleus experiencing higher intensity stimulation (black curve). Within one frame (3 seconds) following the switch to global activation, the concentration of protein in the dilute phase became uniform (blue curve). By 6 seconds (dark red curve), small sub-diffraction-size droplets began to nucleate in the previously unactivated half of the nucleus, accounting for the slight increase in intensity which persists in the 9 second profile (red curve).

Extended Data Fig. 5 Example images of nuclei undergoing local activation.

a, Nuclei exhibit typical chromatin structure before local activation, whereupon chromatin becomes depleted in regions where droplets form. b. Outside of regions containing droplets (lower row), chromatin structure is unperturbed with respect to typical U2OS cells. Multiple droplets can be formed in a single nucleus given a sufficient concentration of material.

Extended Data Fig. 6 Cell size and morphology is minimally affected by blue light activation.

a, Nuclear structure and morphology in both FUS Corelet cells expressing H2B-miRFP and in a control line expressing only H2B-miRFP is qualitatively unaffected by typical imaging protocols. b, Nuclear size is identical before and after 20 minutes of activation, based on segmentation on pre-activated ferritin “core” (GFP) image and post-activation H2B-miRFP image, suggesting no major change in osmotic environment of the nucleus. c. Diffusive exponent α is unaffected by volume fraction, remaining at approximately 0.5 for volume fractions ranging from 5% to 20%, suggesting that the same material properties of chromatin are measured by droplet MSDs regardless of volume fraction. d, Effective diffusion coefficient decreases with droplet volume fraction, consistent with data in Fig. 6 suggesting that droplet size is inversely correlated with diffusion coefficient, since cells with higher volume fractions have larger average droplet sizes.

Extended Data Fig. 7 Scaling behavior of coarsening simulated with \(D_R = \frac{1}{{\sqrt R }}\) and \(D_R = \frac{1}{{2R}}\).

a, To test how the relation between α and β changes depending on the scaling of DR with R, step size was scaled with R−0.5. As in Fig. 3, values of α were chosen ranging from 0.1 to 1 with 20 replicates per condition, and droplets were merged over 104 timesteps. Average radius of droplets in each replicate was averaged for each condition over 20 replicates and plotted. Shaded error bar reflects standard error of the mean. Power laws were fit between 102 and 5 × 103 timesteps. b, The best-fit coarsening exponent β was plotted against the input α for each condition and fit with a line passing through the origin (0,0), yielding a slope of 0.40. c. To test whether a non-trivial number of mergers were missed in the simulation conditions in Fig. 3, simulations were repeated with halved step size (that is, \(D_R = \frac{1}{{2R}}\) instead of \(D_R = \frac{1}{R}\)). The dynamics are quite similar, demonstrating increasing coarsening exponent with increasing subdiffusive exponent, suggesting that mergers are rarely missed in the original simulation. d, With halved step size, relation between coarsening and diffusive exponent is similar (0.28, blue reference line) to simulations in Fig. 3 (0.3), as well as to theoretical prediction (0.33).

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Lee, D.S.W., Wingreen, N.S. & Brangwynne, C.P. Chromatin mechanics dictates subdiffusion and coarsening dynamics of embedded condensates. Nat. Phys. 17, 531–538 (2021). https://doi.org/10.1038/s41567-020-01125-8

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