Stochastic particle unbinding modulates growth dynamics and size of transcription factor condensates in living cells

Abstract

Liquid-liquid phase separation (LLPS) is emerging as a key physical principle for biological organization inside living cells, forming condensates that play important regulatory roles. Inside living nuclei, transcription factor (TF) condensates regulate transcriptional initiation and amplify the transcriptional output of expressed genes. However, the biophysical parameters controlling TF condensation are still poorly understood. Here we applied a battery of single-molecule imaging, theory, and simulations to investigate the physical properties of TF condensates of the progesterone receptor (PR) in living cells. Analysis of individual PR trajectories at different ligand concentrations showed marked signatures of a ligand-tunable LLPS process. Using a machine learning architecture, we found that receptor diffusion within condensates follows fractional Brownian motion resulting from viscoelastic interactions with chromatin. Interestingly, condensate growth dynamics at shorter times is dominated by Brownian motion coalescence (BMC), followed by a growth plateau at longer timescales that result in nanoscale condensate sizes. To rationalize these observations, we extended on the BMC model by including the stochastic unbinding of particles within condensates. Our model reproduced the BMC behavior together with finite condensate sizes at the steady state, fully recapitulating our experimental data. Overall, our results are consistent with condensate growth dynamics being regulated by the escaping probability of PR molecules from condensates. The interplay between condensation assembly and molecular escaping maintains an optimum physical condensate size. Such phenomena must have implications for the biophysical regulation of other nuclear condensates and could also operate in multiple biological scenarios.

Keywords: Brownian motion coalescence; biomolecular condensates; liquid–liquid phase separation; single particle tracking; transcription factor.

Fig. 1.

Lateral diffusion of individual PR molecules in the nucleus of living cells. (A) Representative frame of a SPT video. Individual PR molecules (bright spots) were visualized in the nucleus (green outline) of MCF7 breast cancer cells, under a highly inclined illumination at a 15 ms frame rate. Diffraction-limited single-molecule localizations were tracked in successive frames to generate individual trajectories (superimposed color lines). (B) Schematic representation of the trajectory analysis. For each trajectory, we extracted the displacement between frames to generate individual tMSD plots as a function of the time lag and extracted the diffusion coefficients (D_2 − 4) for each trajectory (Left, Bottom) (Error bars, SEM). In addition, we calculated the angles between successive steps to create polar histograms (Right, Bottom). (C) Distribution of the D_2 − 4 (μm²/s) values of individual PR trajectories exposed to increasing R5020 concentrations for 1 h. Ethanol corresponds to the control condition, i.e., in the absence of the ligand. The y axis corresponds to the frequency of events. Vertical dash lines indicate D_2 − 4 values 0.0061 (left line) and 0.5 μm²/s (right line). Data extracted from at least 1,000 trajectories belonging to at least eight cells from three independent experiments. (D) Polar histograms of the angle between successive steps of diffusing PR under increasing R5020 concentrations. (E) Anisotropy values as a function of R5020 concentration for at least eight cells analyzed. Results of a one-way ANOVA test are shown as n.s. for not significant, ***P value< 0.001.

Fig. 2.

ML analysis of individual PR trajectories in living cells. (A) Percentage of trajectories associated to ATTM (blue) or FBM (yellow) by the ML algorithm as a function of ligand concentration. The shadowed areas represent the error of the prediction, calculated by means of a confusion matrix (see Materials and Methods) (B) D_2 − 4 (μm²/s) distributions for varying ligand concentrations, with trajectories associated to ATTM (blue) and FBM (yellow), as identified by ML. (C) Corresponding histograms of the ML predicted anomalous exponents. (D) Scatter plot of the D_2 − 4 vs. anomalous exponent for every trajectory. Background color represents the prediction of an SVM trained on the data (see Materials and Methods).

Fig. 3.

Nanometer–scale spatiotemporal mapping of PR in living nuclei. (A) 2D density maps of individual PR localizations collected over 75 s on an area of 2.4 × 2.4 μm², after 1 h ligand stimulation (Top) and control (Bottom). Each map contains 1,000 localizations. (B) Snapshots of two different condensates as they merge over the indicated time windows. The 2D maps have been generated by accumulating single-molecule localizations in time windows of 4.5 s (300 frames). (C) Merging events of two different PR condensates (highlighted by orange and green arrows) visualized by confocal microscopy using GFP labeling conditions. (D) Distribution of PR condensate radius normalized to the mean radius, over a time course of 60 min after 10⁻⁸ M hormone stimulation (see color bar). Each curve corresponds to a 5-min time point. The red curve corresponds to the size distribution in the absence of the hormone. a.u. refers to arbitrary units. (E) Mean condensate radius as a function of time. At each time point, data correspond to several regions of interest analyzed from two different cells and two separate experiments.

Fig. 4.

Extended BMC model including stochastic unbinding of PR molecules from condensates. (A) Snapshots of two simulations of the theoretical model, showcasing the temporal evolution of two systems, one with P_u = 0 (Top) and one with P_u > 0 (Bottom). (B) Mean radius size evolution as a function of time, for a system of n = 80, L = √N/0.01. Each color represents the result for a different P_u. The dotted line shows the expected BMC growth (<R> ∼ t^1/3). The horizontal dashed line shows the maximum mean size possible for the simulated system (<R> =√N). The inset shows the steady-state normalized radius distribution for a system of n = 500 and L = √N/0.01 for P_u = 0.2, in arbitrary units (a.u.). (C) Percentage of particles forming condensates as a function of time for different P_u values. (D) Experimental data showing the percentage of particles forming condensates as a function of time. The data correspond to the same experiments shown in Fig. 3 D and E. (E) Diffusion coefficient distributions resulting from the simulations, for free particles (centered around Log(D) = 0) and for condensates (left distribution) for four different P_u values. Y axes for all the histograms correspond to Frequency in arbitrary units