Phase Separation and Correlated Motions in Motorized Genome

Abstract

The human genome is arranged in the cell nucleus nonrandomly, and phase separation has been proposed as an important driving force for genome organization. However, the cell nucleus is an active system, and the contribution of nonequilibrium activities to phase separation and genome structure and dynamics remains to be explored. We simulated the genome using an energy function parametrized with chromosome conformation capture (Hi-C) data with the presence of active, nondirectional forces that break the detailed balance. We found that active forces that may arise from transcription and chromatin remodeling can dramatically impact the spatial localization of heterochromatin. When applied to euchromatin, active forces can drive heterochromatin to the nuclear envelope and compete with passive interactions among heterochromatin that tend to pull them in opposite directions. Furthermore, active forces induce long-range spatial correlations among genomic loci beyond single chromosome territories. We further showed that the impact of active forces could be understood from the effective temperature defined as the fluctuation-dissipation ratio. Our study suggests that nonequilibrium activities can significantly impact genome structure and dynamics, producing unexpected collective phenomena.

Figure 1:

Illustration of the genome model parameterized with Hi-C data. The human genome consisting of 46 chromosomes was modeled in a spherical confinement of 10 μm in diameter. Each chromosome was represented as a string of coarse-grained particles that are one MB in size. We used Hi-C data to identify each bead as compartment A (orange), compartment B (blue), or centromeric region C (yellow) and to parameterize the interaction energy among them.

Figure 2:

Radial distribution profiles of A/B compartments at different interaction strengths between B compartments without (a, c, and e) and with (b, d, and f) the presence of active forces. The interaction strength between B compartments was increased by two and three folds from a to c, and e, and from b to d, and f. The insets provide two different views of a representative configuration for each system. The left image corresponds to the front view of a cross-section of the genome sliced through the nuclear center, while the right image corresponds to the view from the nuclear envelope. In these images, A/B compartments are colored orange and blue, respectively.

Figure 3:

Illustrative phase diagram of genome organization. We identified three phases corresponding to the conventional (blue), intermediate (yellow), and inverted (red) nuclei using the average density ratio of the outer shell over the inner sphere. Representative configurations of the three phases are shown in Figure 2b (conventional), 2a (intermediate), and 2e (inverted). The x and y axes indicate the strength of active and passive forces. The number in each bin measures the average density ratio of the outer shell over the inner sphere (a), the average volume assigned to each heterochromatin region (b), and the radius of gyration for the largest cluster formed by B compartments (c). The solid lines in parts b and c correspond to the phase boundaries shown in part a. See also Figure S9 for the corresponding results for A compartments.

Figure 4:

Active forces enhance long-range correlations among genomic loci. (a,b) Displacement correlation functions at various time separations computed without (a) and with (b) the presence of active forces. The correlation functions at different time intervals were normalized such that the maximum values are unity. See Figure S10 for results at different strengths of active forces. (c) Correlation lengths as a function of the time separation for different active forces. (d) Dependence of the spatial correlation length determined at T_a = 10T and Δt = 15s as a function of the correlation time of the active forces.

Figure 5:

The effective temperature of active systems computed using the fluctuation-dissipation ratio. (a,c) Susceptibility as a function of correlation for the system with T_a = 10T, τ = 0 s (a) and τ = 1.25 s (c). The dashed lines correspond to the thermal temperature −1/T and the theoretical value −1/(T_a + T) for non-correlated active forces. (b) Effective temperatures of A/B compartments computed using the fluctuation-dissipation ratio for T_a = 5, 10, and 20T at τ = 0 s are shown as dots. The red line corresponds to T_a + T, while the blue line represents the constant T. (d) Correlation lengths as functions of time interval Δt for different correlation time τ of the colored noise.