Liquid-liquid phase separation driven compartmentalization of reactive nucleoplasm

Abstract

The nucleus of eukaryotic cells harbors active and out of equilibrium environments conducive to diverse gene regulatory processes. On a molecular scale, gene regulatory processes take place within hierarchically compartmentalized sub-nuclear bodies. While the impact of nuclear structure on gene regulation is widely appreciated, it has remained much less clear whether and how gene regulation is impacting nuclear order itself. Recently, the liquid-liquid phase separation emerged as a fundamental mechanism driving the formation of biomolecular condensates, including membrane-less organelles, chromatin territories, and transcriptional domains. The transience and environmental sensitivity of biomolecular condensation are strongly suggestive of kinetic gene-regulatory control of phase separation. To better understand kinetic aspects controlling biomolecular phase-separation, we have constructed a minimalist model of the reactive nucleoplasm. The model is based on the Cahn-Hilliard formulation of ternary protein-RNA-nucleoplasm components coupled to non-equilibrium and spatially dependent gene expression. We find a broad range of kinetic regimes through an extensive set of simulations where the interplay of phase separation and reactive timescales can generate heterogeneous multi-modal gene expression patterns. Furthermore, the significance of this finding is that heterogeneity of gene expression is linked directly with the heterogeneity of length-scales in phase-separated condensates.

Figure 1.

(A) Phase diagram of the symmetric ternary protein–RNA–nucleoplasm mixture and the bulk free energy governing the solution thermodynamics f_bulk(φ₁, φ₂, φ₃) for χ = 3. The solid-line and dash-line correspond to the spinodal and binodal curves, respectively. (B) The schematic of the minimal reactive nucleoplasm model. Shown are the main reactive components (protein, RNA, DNA-seed, nucleoplasm reservoir), the corresponding reactive processes involving each components as well as their spatial generation profiles.

Figure 2.

Evolution of phase-field variables φ_i for three phase mixture undergoing the chemical reaction with a degradation time-scale fixed at the same of diffusion (τ_d = τ ). From up to bottom: snapshots corresponding to simulation results with (A) τ_R = τ _P = τ; (B) τ_R = 100τ_P = 100τ; (C) τ_P = 100τ_R = 100τ ; and (D) τ _R = τ _P = 100τ . The color code in blue, green, and red indicates the RNA, protein, and nucleoplasm regions, respectively.

Figure 3.

Evolution of phase-field variables φ_i for three phase mixture undergoing the chemical reaction with a degradation time-scale fixed at the same of diffusion (τ_d = 10τ). From up to bottom: snapshots corresponding to simulation results with (A) τ _R = τ_P = τ ; (B) τ _R = 50τ_P = 50τ; (C) τ _P = 100τ_R = 100τ ; and (D) τ _R = τ _P = 50τ . The color code in blue, green, and red indicates the RNA, protein, and nucleoplasm regions, respectively.

Figure 4.

Evolution of phase-field variables φ_i for three phase mixture undergoing the chemical reaction with a degradation time-scale fixed at the same of diffusion (τ_d = 100τ ). From up to bottom: snapshots corresponding to simulation results with (A) τ_P = 10τ_R = 10τ; (B) τ _R = 10τ_P = 50τ; (C) τ_R = 50τ_P = 10τ; and (D) τ_R = τ _P = 100τ. The color code in blue, green, and red indicates the RNA, protein, and nucleoplasm regions, respectively.

Figure 5.

Phase diagram: phase diagram showing the dominant steady-state phase and summarizing various patterns that arise at three kinetic regimes (A) τ _d = τ; (B) τ _d = 10τ; (C) τ _d = 100τ). The blue star indicates that the RNA domain becomes the dominant phase in the long timescale limit. The green star means that the proteins-droplets become the dominant phase in the long timescale limit. The pink star indicates three coexisting phases of the ternary mixture. In contrast, the red star indicates that RNA–proteins turn totally into the nucleoplasm.

Figure 6.

The dynamic structure factors for the three representative kinetic regimes with significant time-scale disparity between transcription and translation τ _P = 100τ _R (see supporting information for all the results). The inset shows the scaling and power law exponent. The three panels stand for three dynamical regimes: (A) τ _d = τ (B) τ _d = 10τ (C) τ _d = 100τ.

Figure 7.

The dominant length-scale patterns for the three representative kinetic regimes. Each panel shows a combination of transcription and translation time-scales sorted with an increasing time-scale disparity from blue to green to orange. (A) τ _d = τ (B) τ _d = 10τ (C) τ_d = 100τ.