Graphic summary. Transcription factories-mediated attachments between transcriptionally active chromosomal territories are sufficient to explain experimentally observed features of nuclear architecture: (i) Territories formed by transcriptionally active chromosomes (marked in red) are on average located closer to the centre of the nucleus than the territories formed by transcriptionally non-active chromosomes (marked in blue). (ii) Actively transcribed genes interacting with a transcription factory (black circle) are located at the periphery of their chromosomal territories. (iii) Transcriptionally active and also transcriptionally non-active chromatin domains have a tendency for self-association.

Contact probabilities ratios between two random points located on two free polygons P_free,free and between two random points where one is located on a free and another on an attached polygon P_{free,attached}. The P_free,free/P_{free,attached} ratio is plotted as a function of the distance d, where d is the threshold distance below which a pair of points is considered in contact. In case of infinitely thin polygons (A) the topological restriction was needed to favour contacts between random points located on different free polygons. In the case of beaded chains (B) the contacts between random points located on different free polygons was favoured irrespectively of whether the topological restriction was imposed or not.

Radial positions of circular beaded chains confined within a small sphere depend on whether these chains are attached to each other or not. (A and B) Representative snapshots from simulations involving topologically unrestricted and restricted beaded chains, respectively. Individual beaded chains are coloured differently and in addition these that were attached to each other to simulate binding to the same transcription factory are coloured using a stripped pattern. (C and D) Radial distributions of points on the underlying polygons of beaded chains that were free (green), or were attached with other chains (red). Blue profiles show radial distribution of centres of beads representing points of attachment to the transcription factory. C and D correspond to simulations without and with topological restriction, respectively. For red and green profiles the error bars are smaller than the width of the lines.

Radial positions of infinitely thin polygons confined within a small sphere depend on whether these polygons are attached to each other or not. (A and B) Representative snapshots from simulations involving topologically unrestricted and restricted polygons, respectively. Individual polygons are coloured differently and in addition these that were attached to each other to simulate binding to the same transcription factory are coloured using a stripped pattern. To help visualize individual polygons that were modelled as infinitely thin, they are presented as having a significant thickness. (C and D) Radial distributions of points on free polygons (green), points on the polygons attached together (red) and the vertices that were representing points of attachment to a transcription factory (blue). Panels C and D correspond to simulations without and with topological restriction, respectively. For red and green profiles the error bars are smaller than the width of the lines.

Localization of beads representing points of attachment to the transcription factory with respect to the territories formed by topologically unrestricted (A and C) and topologically restricted beaded chains (B and D). A and B, cross sections of the configurations shown in Figure 2A and B, respectively. Points of intersection of lines connecting centres of beads of individual chains with the cross-sectional plane define convex envelopes that approximate the extent of territories formed by these chains in the cross section. Territories formed by beaded chains attached to a transcription factory (indicated with a circle) are demarcated with striped lines. (C, D) Relative radial distributions with respect to centres of mass of beaded chains for points on the underlying polygons of beaded chains that were unattached to other chains (green) or were attached to other chains (red) and for centres of beads that were representing points of attachment to the transcription factory (blue). For red and green profiles the error bars are smaller than the width of the lines.

Localization of vertices representing points of attachment to the transcription factory with respect to the territories formed by topologically unrestricted (A and D) and topologically restricted infinitely thin polygons (B and E). (A and B) Cross sections of the configurations are shown in Figure 1A and B, respectively. Points of intersection of individual polygons with the plane of the cross section define convex envelopes that are analogous to cross sections through chromosomal territories (7,14). Territories formed by polygons modelled as attached to a transcription factory (indicated with a circle) are demarcated with striped lines. (C) The principle of determining whether a given point on a polygon has a peripheral or central position within a territory formed by this polygon. For a given point X, the relative distance to the centre of mass CM of the polygon was defined as the ratio between the distance X-CM and P-CM, where P is the intersection between the ray X-CM and the characteristic ellipsoid of inertia defined by a given polygon (47). (D, E) Relative radial distributions with respect to centres of mass of polygons for: points on free polygons (green), points on the polygons attached together (red) and for the vertices that were representing points of attachment to a transcription factory (blue) are shown. For red and green profiles the error bars are smaller than the width of the lines.