Transcription-driven genome organization: a model for chromosome structure and the regulation of gene expression tested through simulations

Chromatin mobility

Time-lapse imaging of a GFP-tagged gene in a living mammalian cell is consistent with it diffusing for ∼1 min through a ‘corral’ in chromatin, ‘jumping’ to a nearby corral the next and bouncing back to the original one (17). Consequently, a gene explores a volume with a diameter of ∼250 nm in a min, ∼750 nm in 1 h and ∼1.4 μm in 24 h (18); therefore, it inspects only part of one territory in ∼24 h, as a yeast gene—which diffuses as fast—ranges throughout its smaller nucleus.

Entropic forces

Monte Carlo simulations of polymers confined in a sphere uncovered several entropic effects depending solely on excluded volume (19,20). Flexible thin polymers (‘euchromatin’) spontaneously move to the interior, and stiff thick ones (‘heterochromatin’) to the periphery—as seen in human nuclei (Supplementary Figure S1Ai); ‘euchromatin’ loses more configurations (and so entropy) than ‘heterochromatin’ when squashed against the lamina, and so ends up internally. Stiff polymers also contact each other more than flexible ones; this favors phase separation and formation of distinct A and B compartments. Additionally, linear polymers intermingle, but looped ones segregate into discrete territories (Supplementary Figure S1Aii).

Ellipsoidal territories and trans contacts

Whether a typical human gene diffuses within its own territory and makes cis contacts (i.e. involving contacts with the same chromosome), or visits others to make trans ones depends significantly on territory shape. Children who buy MMs and Smarties sense ellipsoids pack more tightly than spheres of similar volume; packed ellipsoids also touch more neighbours than spheres (Supplementary Figure S1B). As territories found in cells and simulations are ellipsoidal, and as much of the volume of ellipsoids is near the surface, genes should make many cis contacts plus some trans ones (Supplementary Figure S1).

Some processes driving looping

If human chromosomes were a polymer melt in a sphere, two loci 40 Mb distant on the genetic map would be ∼4 μm apart in 3D space and interact as infrequently as loci on different chromosomes. If the two were 10, 1 or 0.1 Mb apart, they would interact with probabilities of ∼2 × 10⁻⁵, ∼5 × 10⁻⁴ and ∼1.5 × 10⁻², respectively (calculated using a 20 nm fiber, 50 bp/nm and a threshold of 50 nm for contact detection; see also (1)). Hi-C shows some contacts occur more frequently; this begs the question—what drives looping?

One process is the classical one involving promoter-enhancer contacts (21). We discuss later that contacting partners are often transcriptionally active. We also use the term ‘promoter’ to describe the 5′ end of both genic and non-genic units, and ‘factor’ to include both activators and repressors. Many factors (often bound to polymerases) can bind to DNA and each other (e.g. YY1 (22)). Binding to two cognate sites spaced 10 kb apart creates a high local concentration, and—when two bound factors collide—dimerization stabilizes a loop if entropic looping costs are not prohibitive (Figure 1A). Such loops persist as long as factors remain bound (typically ∼10 s).

Another mechanism—the ‘depletion attraction’—is non-specific. It originates from the increase in entropy of macromolecules in a crowded cell when large complexes come together (Figure 1Bi (23)). Modeling indicates this attraction can cluster bound polymerases and stabilize loops (Figure 1Bii) that persist for as long as polymerases remain bound (i.e. seconds to hours; below).

A third mechanism involves cohesin—a ring-like complex that clips on to a fiber like a carabiner on a climber’s rope. In Hi-C maps, many human domains are contained in loops apparently delimited by CTCF bound to cognate sites in convergent orientations (6). Such ‘contact loops’—many with contour lengths of >1 Mb—are thought to arise as follows. A cohesin ring binds at a ‘loading site’ to form a tiny loop, this loop enlarges as an in-built motor translocates the ring down the fiber, and enlargement ceases when CTCF bound to convergent sites blocks further extrusion (Figure 1C (24,25)). This is known as the ‘loop-extrusion model’. We note that other mechanisms could enlarge such loops (including one not involving a motor; Supplementary Note 2), and that loop extrusion (by whatever mechanism) and its blocking by convergent CTCF sites can be readily incorporated into the model that follows.

A transcription-factor model

We now review results of simulations involving what we will call the ‘transcription-factor model’. This incorporates the few assumptions implicit in the classical model illustrated in Figure 1A: spheres (‘factors’) bind to selected beads in a string (‘cognate sites’ on ‘chromatin fibers’) to form molecular bridges stabilizing loops (26–30). This superficially simple model yields several unexpected results.

First, and extraordinarily, bound factors cluster spontaneously in the absence of any specified DNA–DNA or protein–protein interactions (Figure 2A (27)). This clustering requires bi- or multi-valency (so factors can bridge different regions and make loops) plus reversible binding (otherwise the system does not evolve), and it occurs robustly with respect to changes in DNA–protein affinity and factor number. The process driving it was dubbed the ‘bridging-induced attraction’ (27). We stress this attraction occurs spontaneously without the need to specify any additional forces between one bead and another, or between one protein and another.

The basic mechanism yielding clustering is a simple positive feedback loop which works as sketched in Figure 2A and B. First, proteins bind to chromatin (Figure 2A). Then, once a bridge forms, the local density of binding sites (e.g. pink spheres in Figure 2A) inevitably increases. This attracts further factors from the soluble pool (like 2 in Figure 2B): their binding further increases the local chromatin concentration (through bridging) creating a virtuous cycle which repeats. This triggers the self-assembly of stable protein clusters, where growth is eventually limited by entropic crowding costs (28). Several factors cluster in nuclei (e.g. Sox2 in living mouse cells (31)) and the bridging-induced attraction provides a simple and general explanation for this phenomenon.

This process drives local phase separation of polymerases and factors, and so naturally explains how super-enhancer (SE) clusters form (Supplementary Figure S2Ai (32)). This generic tendency to cluster will be augmented by specific protein–protein and DNA–protein interactions, with their balance determining whether protein or DNA lies at the core. Similarly, the same process—this time augmented by HP1, a multivalent protein that staples together histones carrying certain modifications—could drive phase separation and compaction of inactive heterochromatin (Supplementary Figure S2Aii (33,34)).

Creating stable clusters of different types, TADs and compartments

This transcription-factor model yields a second remarkable result: red and green factors binding to distinct sites on the string self-assemble into distinct clusters containing only red factors or only green ones (Figure 2A (28)). This has a simple basis: the model specifies that red and green binding sites are separate in 1D sequence space (as they are in vivo), so they are inevitably in different places in 3D space (Figure 2B).

A third result is that clusters and loops self-assemble into ‘TADs’ and ‘A/B compartments’ (26–28). Thus, if chromosome 19 in human GM12878 cells is modeled as a string of beads colored according to whether corresponding regions are active or inactive, binding of just red and black spheres (‘activators’ and ‘repressors’) yields contact maps much like Hi-C ones (Figure 2C). As neither TADs, compartments, nor experimental Hi-C data are used as inputs, this points to polymerases and their factors driving the organization without the need to invoke roles for higher-order features (see also (7)). We suggest TADs arise solely by aggregation of pre-existing loops/clusters (note that degradation of cohesin or its loader induces TAD disappearance and the emergence of complex sub-structures, as A/B compartments persist and become more prominent (16,35)).

The simple transcription-factor model has been extended to explain how pre-existing red clusters can evolve into green clusters, or persist for hours as individual factors exchange with the soluble pool in seconds—as in photo-bleaching experiments (Supplementary Figure S3A,B (28,36)). Additionally, introducing ‘bookmarking’ factors that bind selected beads (genomic sequences), as well as ‘writers’ that ‘mark’ chromatin beads and ‘readers’ which bind beads with specific marks, can create local ‘epigenetic states’ and epigenetic domains (e.g. domains of red and green marks, representing for instance active or inactive histone modifications). Such domains spontaneously establish around bookmarks, and are stably inherited through ‘semi-conservative replication’, when half of the marks are erased (and/or some of the bookmarks are lost due to dilution (37,38); Supplementary Figure S3C).

Most contacts are between active transcription units

Contacts seen by 3C-based approaches often involve active promoters and enhancers; for example, FIRES (frequently-interacting regions) in 14 different human tissues and 7 human cell lines are usually active enhancers (48). Similarly, contacts detected by an independent method—genome architecture mapping—again involve enhancers and/or genic transcription start/end sites (49). Why should active sequences lie together? As factories nucleate local concentrations of active units, we expect promoters and enhancers to dominate contact lists.

While 3C focuses on contacts between two DNA sequences, the ligation involved can join >2 together (24 is the current record), and these again generally encode active sequences (50,51). Why do so many active sequences contact each other? We expect to see co-ligations involving some/all of the many anchors in a typical factory.

Early studies also point to a correlation between transcription and structure. For example, switching on/off many mammalian genes correlates with their attachment/detachment (40). What underlies this? Our model requires that units must attach before they can be transcribed.

Frequencies of cis and trans contacts

Cis Hi-C contacts fall off rapidly with increasing genetic distance, whereas trans ones are so rare they are often treated as background. However, ChIA-PET yields more trans than cis contacts when active sequences are selected by pulling down ERα or polymerase II (45,47). Our model again predicts this—active genes on different chromosomes are often co-transcribed in the same specialized factory (as genes diffuse out of one ellipsoidal territory into another).

In addition, cis:trans ratios can change rapidly, and we explain this by reference to ‘NFκB’ factories (47) (see also Supplementary Figure S5A). TNFα induces phosphorylation of NFκB, nuclear import of phospho-NFκB, and transcriptional initiation of many inflammatory genes including SAMD4A. Before induction, the SAMD4A promoter makes only a few local cis contacts (shown by 4C and ChIA-PET applied with a ‘pull-down’ of polymerase II); it spends most time roaming ‘outer space’ making a few chance contacts with nearby segments of its own loop, and—if it visits a factory—it cannot initiate in the absence of phospho-NFκB. But once phospho-NFκB appears (10 min after adding TNFα), it initiates. Then, NFκB binding sites in SAMD4A become tethered to the factory, these bind phospho-NFκB, exchange of the factor increases the local concentration, and this increases the chances that other inflammatory genes initiate when they pass by. And once they do, this creates a virtuous cycle; as more inflammatory genes initiate, more NFκB binding sites become tethered to the factory, the local NFκB concentration rises, this further increases the chances that passing responsive genes initiate, and the factory evolves into one specializing in transcribing inflammatory genes. As a result, the rapid concentration of inflammatory genes around the resulting ‘NFκB’ factory yields the rapid increase in cis and trans contacts between them seen by 3C-based methods and RNA-FISH (47).

TADs exist at all scales

Intra- and inter-TAD contact frequencies differ only ∼2-fold; therefore, it is unsurprising that TAD calling depends on which algorithm is used, and the resolution achieved (52–55). However, it is surprising that TADs become more elusive as algorithms and resolution improve. For example, CaTCH (Caller of Topological Chromosomal Hierarchies) identifies a continuous spectrum of domains covering all scales; TADs do not stand out as distinct structures at any level in the hierarchy (55). Moreover, TADs are sometimes invisible in single-cell data (56,57), and—if detected—their borders weaken as cells progress through G1 into S phase (58). In our model, TADs do not exist as distinct entities representing anything other than one or more loops around one or more factories. [TADs are said to be major architectural features because they are invariant between cell types (4,5) and highly conserved (59). However, there are always slight differences between cell types that could reflect slight differences in expression profile, and the conservation could just reflect the conserved transcriptional pattern encoded by the underlying DNA sequence.]

The relationship between TADs and transcription

Various studies address this issue, and give conflicting results. For example, in mouse neural progenitor cells, one of the two X chromosomes is moderately compacted and largely inactive. Inactive regions do not assemble into A/B compartments or TADs, unlike active ones. Moreover, in different clones, different regions in the inactive X escape inactivation, and these form TADs (60). Here, structure and activity are tightly correlated (in accord with our model). Similarly, inhibiting transcription in the fly leads to a general reorganization of TAD structure, and a weakening of border strength (61).

Another study points to some TADs appearing even though transcription is inhibited (62). After fertilization, the zygotic nucleus in the fly egg is transcriptionally inactive. As the embryo divides, zygotic genome activation occurs so that by nuclear cycle 8 (nc8), ∼180 genes are active, and these seem to nucleate a few TADs detected at nc12 (so transcriptional onset and the appearance of loops/TADs correlate—again in accord with our model). As more genes become active at nc13, 3-fold more TADs develop by nc14, and polymerase II plus Zelda (a zinc-finger transcription factor) are at boundaries (again a positive correlation). If transcriptional inhibitors are injected into embryos before nc8, boundaries and TADs seen at nc14 are less prominent, but some TADs still develop (implying loops/TADs appear independently of transcription, which is inconsistent with our model). However, interpretation is complicated. Although inhibitors reduce levels of five mRNAs already being expressed, they only slightly affect levels of polymerase II bound at the 5′ end of genes expressed at nc14; this indicates that inhibition is inefficient, so it remains possible that the remaining transcription stabilizes the loops/TADs seen.

Studies on mouse eggs and embryos also provide conflicting data. Thus, activity is lost as oocytes mature, and TADs plus A/B compartments disappear (56,63,64); therefore, loss of structure and activity again correlate (consistent with our model). After fertilization, the zygote contains two nuclei with different conformations; both contain TADs, but the maternal one lacks A/B compartments. Then, as transcription begins, TADs appear (again a positive correlation), but α-amanitin (a transcriptional inhibitor) does not prevent this (63,64)—which is inconsistent with our model. However, interpretation is again complicated: α-amanitin acts notoriously slowly (65), and inhibition was demonstrated indirectly (levels of steady-state poly(A)⁺ RNA fall, but reduction of intronic RNA would be a more direct indicator of inhibition).

Data from zebrafish make unified interpretation even more difficult. In contrast to some cases cited earlier, TADs and compartments exist before zygotic gene activation, and many of each are lost when transcription begins (66). Clearly, TAD-centric models will find it difficult to explain such conflicting data. In ours, TADs are not major architectural features determining function; they just reflect the underlying network of loops, and—even if all polymerases are inactive—bound factors can still stabilize some loops (and so TADs).

Enhancers and super-enhancers

Enhancers are important regulatory motifs, but there remains little agreement on how they work (67). They were originally defined as motifs stimulating firing of genic promoters when inserted in either orientation upstream or downstream. However, their molecular marks are so like those of their targets (68) that FANTOM5 now defines them solely as promoters firing to yield eRNAs (enhancer RNAs) rather than mRNAs (69). Then, is it eRNA production or some role of the eRNA product that underlies function? Studies of the Sfmbt2 enhancer in mouse ES cells indicates it is the former (70). Thus, deleting the eRNA promoter (but not downstream sequences) impairs enhancer activity; this points to the promoter being required. Moreover, inserting a poly(A) site just 40 bp down-stream of the eRNA promoter abolishes enhancer activity, and amounts of polymerase on the enhancer (and enhancer activity) increase as the insert is moved progressively 3′; this points to a reduction in transcription correlating with reduced enhancer activity.

Our model suggests a simple mechanism for enhancer function: transcription of e in Figure 4Ai ensures p is tethered close to an appropriate factory. In other words, e is an enhancer of p because close tethering increases the probability that p collides with a polymerase in the factory (and so often initiates). The model also explains how enhancers can act over such great distances (Supplementary Figure S5B,C). Thus, a typical factory in a human cell is associated with ∼10 loops each with an average contour length of ∼86 kbp (Supplementary Note 1), so an enhancer anchored to it can (indirectly) tether a target promoter in any one of these other loops to the same factory. As we will see, enhancers can act over even greater distances to tether targets in a nuclear region containing an appropriate factory.

This model provides solutions to many conundrums associated with enhancers, including the following. (i) Enhancer activity depends on contact with its target promoter (71,72). We suggest the two often share a factory, and so are often in contact. (ii) Enhancers can act on two targets simultaneously, and coordinate their firing (73,74)—impossible according to classical models. In Figure 4Ai, e acts on both d and p, and it is easy to imagine that d and p initiate coordinately because the two polymerases involved sit side-by-side in the same factory. (iii) Promoters of protein-coding genes are often enhancers of other protein-coding genes (70,75,76). In our model, e is an enhancer irrespective of whether it encodes an mRNA or eRNA. (iv) Enhancers act both promiscuously and selectively. They interact with many other enhancers and targets (77–79), with ≥4 controlling a typical gene expressed during fly embryogenesis (80). At the same time, they are selective; thousands have the potential to activate a fly gene encoding an ubiquitously-expressed ribosomal-protein, whilst a different set can act on a developmentally-regulated factor (81). In our model, ‘red’ enhancers tether ‘red’ genic promoters close to ‘red’ factories, as ‘green’ ones do the same with a different set. (v) Enhancer-target contacts apparently track with the polymerase down the target (82). Thus, when mouse Kit becomes active, the enhancer first touches the Kit promoter before contacts move progressively 3′ at the speed of the pioneering polymerase. This is impossible with conventional models, but simply explained if polymerases transcribing enhancer and target are attached to one factory (Figure 4Aii,iii). (vi) Single-molecule RNA FISH shows forced looping of the β-globin enhancer to its target increases transcriptional burst frequency but not burst size (83), and this general effect is confirmed by live-cell imaging of Drosophila embryos (73,74). Such bursting arises because many ‘active’ genes are silent much of the time, and when active they are associated with only one elongating polymerase (Supplementary Note 8). Periods of activity do not occur randomly; rather, short bursts are interspersed by long silent periods. Bursting is usually explained by an equilibrium between ill-defined permissive and restrictive states; we explain it as follows. In Figure 4A, p often fires when tethered near the factory (giving a burst). Then, once e terminates, close tethering is lost—and p remains silent for as long as it remains far from an appropriate factory. RNA FISH experiments on human SAMD4A support this explanation; the promoter is usually silent, but adding TNFα induces successive attachments/detachments to/from a factory (44).

A related conundrum concerns how SEs work. SEs are groups of enhancers that are closely-spaced on the genetic map and often target genes determining cell identity (32,84). In Figure 4Bi, increasing the number of closely-spaced promoters (e, e’, e’’) in the SE increases the time p spends near a factory (to increase its firing probability).

Boundaries

TAD boundaries in higher eukaryotes are often marked by CTCF; however, they are also rich in active units marked by polymerase II, nascent RNA, and factors like YY1 (4,6,22). Similarly, fly boundaries are rich in constitutively-active genes but de-enriched for insulators dCTCF and Su(Hw) (7,85). Additionally, in yeast (which lacks CTCF), boundaries are often active promoters (11). Then, does the act of transcription create a boundary? Studies in Caulobacter crescentus—which lacks CTCF but possesses TADs—shows it does (14). For example, in a rich medium, a rDNA gene is a strong boundary; however, this boundary disappears in a poor medium when rRNA synthesis subsides. Inserting active rsaA in the middle of a TAD also creates a new boundary, and boundary strength progressively falls when the length of the transcribed insert is reduced. We imagine ongoing transcription underlies boundary activity (Figure 4C).

eQTLs

Quantitative trait loci (QTLs) are sequence variants (usually single-nucleotide changes) occurring naturally in populations that influence phenotypes. Most QTLs affecting disease do not encode transcription factors or global regulators; instead, they map to non-coding regions, especially enhancers (77,88). eQTLs are QTLs affecting transcript levels, and were also expected to encode transcription factors; but again, many do not (88,89). They also map to enhancers (88) and regulate distant genes both cis and trans (90–92). Additionally, eQTLs and their targets are often in contact (77), and one trans-eQTL can act on hundreds of genes around the genome—which often encode functionally-related proteins regulated by similar factors (88,90,92,93). In summary, eukaryotic gene regulation involves distant and distributed eQTLs that look like enhancers. Moreover, copy number of a transcript is a polygenic trait much like susceptibility to type II diabetes or human height—traits where hundreds of regulatory loci have been identified and where many more await discovery (91). This complexity is captured by the ‘omnigenic’ model, where eQTLs affect levels of target mRNAs indirectly; they modulate levels, locations, and post-translational modifications of unrelated proteins, and these changes percolate throughout the cellular network before feeding back into nuclei to affect transcription of targets (88). We suggest another—very direct—mechanism.

A model for direct eQTL action

In Figure 5A, all units in the volume determine network structure, and how often each unit visits an appropriate factory; consequently, all units directly affect production of all other transcripts. In other words, gene regulation is widely distributed. A single nucleotide change in enhancer b (perhaps an eQTL) might reduce binding of a ‘yellow’ factor and b’s firing frequency, and this has consequential effects on how often d and a are tethered close to the yellow factory—and so can initiate. But this change influences the whole network. By altering positions relative to appropriate factories, an eQTL ‘communicates’ directly with functionally-related targets, and indirectly (but still at the level of transcription) with all other genes around it in nuclear space. This neatly reconciles how eQTLs target functionally-related genes whilst having omnigenic effects (because targets often share the same specialized factory and nuclear volume, respectively).

The idea that altering one loop in a network has global effects was tested using simulations of five factors binding to cognate sites in a 5000-bead string (Figure 5Bi; Supplementary Note 6 gives details); as expected, bound factors spontaneously cluster (Figure 5Bii). We next create an ‘eQTL’ in the middle of the (‘wild-type’) string by abolishing binding to one yellow bead. This ‘mutant’ bead is now rarely in a cluster (Figure 5Biii, arrow), and it increases or decreases clustering probabilities of many other genes on the string (Figure 5Biv). As clustering determines activity, these simulations provide a physical basis for direct omnigenic effects, and open up the possibility of modeling their action. Results are robust, as, for instance, simulations with different binding affinity, or with factors and binding sites of only a single color, lead to qualitatively similar conclusions.