Chromosome positioning from activity-based segregation

Abstract

Chromosomes within eukaryotic cell nuclei at interphase are not positioned at random, since gene-rich chromosomes are predominantly found towards the interior of the cell nucleus across a number of cell types. The physical mechanisms that could drive and maintain the spatial segregation of chromosomes based on gene density are unknown. Here, we identify a mechanism for such segregation, showing that the territorial organization of chromosomes, another central feature of nuclear organization, emerges naturally from our model. Our computer simulations indicate that gene density-dependent radial segregation of chromosomes arises as a robust consequence of differences in non-equilibrium activity across chromosomes. Arguing that such differences originate in the inhomogeneous distribution of ATP-dependent chromatin remodeling and transcription machinery on each chromosome, we show that a variety of non-random positional distributions emerge through the interplay of such activity, nuclear shape and specific interactions of chromosomes with the nuclear envelope. Results from our model are in reasonable agreement with experimental data and we make a number of predictions that can be tested in experiments.

Figure 1.

Schematic of model illustrating individual monomers, each providing a coarse-grained description of a 1 Mb section along the chromosome, subdivided into active and inactive, depending on their gene density. The schematic expands out two monomers, one active and one inactive, illustrating how chromatin remodeling and transcription-coupled enzymatic activity translate into differing levels of stochastic forces acting on each monomer. In the expanded figures, colored polygons and spheres represent chromatin remodeling enzymes exerting such stochastic forces on chromatin through their activity. The strength of these forces is captured in our model through an effective temperature—a higher effective temperature means a larger activity.

Figure 2.

Configurational snapshot showing positions of simulated human chromosome 18 (red) and chromosome 19 (blue) for our model in the background of other chromosomes (gray), for (A) and (C), spherical nuclei and (B), a prolate ellipsoidal nucleus. The surface configuration of monomers, color coded by chromosome, are shown in (D) and (E). Chromosomes contain no permanent loops in (A), (B) and (D), whereas the configurations in (C) and (E) represent a snapshot of the more compact configurations obtained by allowing for a fixed, small density of loops of random sizes. The nuclear envelope is represented by a repulsive, short-ranged potential, confining chromosomes to a given geometry in all these cases. These simulations in (A) and (B) represent thermal equilibrium, with chromosomes displaying substantial intermingling. In contrast, the configurations in (C), for a model of compact chromosomes, represent the non-equilibrium case discussed in this article, reflecting the ‘activity-based segregation’ of chromosomes, concomitant with the formation of chromosome territories. The more gene-dense chromosome 19 occupies a more interior position than does the gene-poor chromosome 18 in (C). (D) is the non-equilibrium case with no loops. The contrast between (D) and (E) illustrates how activity-based segregation, a feature of both these snapshots, is insufficient to generate chromosome territories on its own. In (E), for a model of compact chromosomes constructed using the random loop model, the combination of such compactness and activity-based segregation yields configurational snapshots which clearly show evidence for a territorial organization.

Figure 3.

Activity distributions and S(R) for specified chromosome pairs in a spherical nucleus. (A) (i)–(iii) show a cut-away section illustrating the time-averaged local activity measured in units of the time-averaged local monomer active temperature, color coded with activity strength and normalized to the range (0:1). The color code correspond to the interval between the thermodynamic temperature T_eq and the active temperature assigned to monomers with a high density of active genes, . The darkest shades represent T_eq, whereas the lightest shades represent T_a. (A) (i) represents the thermal equilibrium case, whereas (A) (ii) represents the case where all monomers are assigned a uniform high activity. (A) (iii) shows the case for non-uniform activity. Note that the distribution of activity is unstructured in cases (i) and (ii), being uniformly low in the first case and uniformly high in the second, while it is structured in case (iii), with activity enhanced towards the center. While the data in (i)–(iii) are averaged over all chromosomes, data for the chromosome pairs 18 (red-filled squares) and 19 [blue-filled circles; (B) (i)–(iii)] as well as for 12 (red-filled symbols) and 20 (blue-filled symbols) [B (iv)–(vi)], are shown corresponding to the activity distributions above them. Note that for the uniform activity case, these chromosome pairs are distributed uniformly, with S(R) quadratically increasing toward the nuclear periphery. (B) (iii) and (vi) show these distributions in the case where activity is non-uniform, illustrating that these distributions are non-trivially structured, being enhanced toward the nuclear interior in the case of the more active chromosome. Along with the simulation data in (B) (iii) and (vi) (filled symbols), we also show open symbols in the same chromosome-specific color representing the experimental data displayed in another study (45) for these chromosomes. Error bars indicated refer to standard deviations.

Figure 4.

Activity distributions and S(R) for specified chromosome pairs in an ellipsoidal nucleus. (A) (i) and (ii) show a cut-away section representing the time-averaged local activity, as discussed in the caption of Figure 2 and in the main text, for the case of a prolate ellipsoid in A (i) and an oblate ellipsoid in A (ii). These are shown for the case of non-uniform activity, but where chromosomes uniformly experience a passive interaction with the nuclear envelope, acting through a confining short-ranged potential. Data for the chromosome pairs 18 (red-filled squares) and 19 (blue-filled circles) [(B) (i) and (ii)] as well as for 12 (red-filled symbols) and 20 (blue-filled symbols) [(B) (iii) and (iv)] are shown. The distributions are to be compared with the distributions in Figure 2B (iii) and (vi) and indicate that geometrical confinement does not qualitatively alter the positioning of our model chromosomes. We also show the experimental data displayed inanother study (45) as open symbols in the corresponding chromosome-specific colors.

Figure 5.

Activity distributions, total densities and gene densities in an ellipsoidal nucleus allowing for specific interactions with the NE. (A) (i)–(iii) show a cut-away sphere, prolate ellipsoid and oblate ellipsoid displaying the time-averaged local activity measured in units of the thermodynamic temperature, color coded with activity strength as indicated, following the conventions of Figures 2 and 3. The confinement exerted by the nuclear envelope is now taken to be active, acting specifically on those monomers at a higher effective temperature interacting with them through a short-ranged attractive potential whose minimum is at the boundaries of the nuclear envelope. Note that the earlier described segregation of activity is now substantially modified, with the distribution of more active monomers peaking towards the periphery as opposed to its more central location in Figures 2 and 3. (B) (i) shows the total density [: open circles] and the gene density [: filled circles] for the case of inhomogeneous activity but with a passive interaction with the nuclear envelope, whereas (ii) shows these quantities in the presence of a selective interaction of active monomers with the inner surface of the simulated nucleus, both for a spherical nucleus. Note that only a small fraction (5%) of monomers are active and therefore feel the attraction due to the boundary. Such a marginal effect has strong consequences for positioning, inverting the conventional (active/euchromatin inside, inactive/heterochromatin outside) arrangement of chromosomes.

Figure 6.

Evolution of the positional distribution of chromosomes 18 (red squares) and 19 (blue circles), shown as a function of time in sequence as indicated, following the switching on of the active interaction with the nuclear envelope in a simulated spherical nucleus. Initial configurations are drawn from a steady-state ensemble prepared by taking the nuclear confinement to be passive. Time is measured in units of millions of simulation timesteps as shown in each subgraph and denotes the steady state. This sequence illustrates how sequences intermediate between steady state ones can be attained and possibly stabilized by other processes, not included in the present description, yielding a broad variety of distributions in S(R).

Figure 7.

Emergence of chromosome territories and S(R) for specified chromosome pairs in a spherical nucleus assuming a random loop model. In (A), we show instantaneous configurations of chromosomes 18, 19, 12 and 20 for the random loop model with inhomogeneous activity, providing evidence for spatial separation and considerably reduced intermingling. In (B), the probability distribution of chromosomes 18 (red-filled squares) and 19 (blue-filled circles) in the compact case is shown, indicating that the activity-based segregation studied earlier continues to be seen in this case. The looping probability chosen is , yielding ∼1400 loops for the 6098 monomers we consider. As before, probability distributions for chromosomes with similar gene densities, chromosomes 12 (red-filled squares) and 20 (blue-filled circles) in (C) show no segregation. Again, as before, the corresponding experimental data of another study (45) is shown as open symbols of the same color.

Figure 8.

Robustness of chromosome territories and their quantification. (A) Four steady-state surface configurations of monomers belonging to different chromosomes, color coded by chromosome, with each configuration obtained using a different initialization. These illustrate, pictorially, the observation that chromosome territory formation is not a property of a specially chosen initial condition, but arises naturally and in an emergent way from the twin requirements of activity-based segregation and compact chromosome configurations, in this case enforced through the random loop model for chromosomes. In (B), we show , a quantity constructed by situating around each monomer a sphere of radius R_sphere, counting the number of monomers belonging to the same chromosome weighted by the quantity +1 and the number of monomers belonging to different chromosomes, weighted by –1. This quantity provides an indication of whether chromosomes are organized territorially and in a non-overlapping manner. We show results for three values of the looping probability: 0, and . As the number of random loops is increased, leading to more compact chromosome configurations, the tendency for overlap is reduced, further enhancing the tendency to separate which is a consequence of activity-induced segregation.