Learning Lab · Building a model
A/B compartments from a single rule
Give every bead a type and let like types attract. A checkerboard appears in the contact map, and nothing in the model was told to make one.
The loop extrusion page showed one way to fold a specific region: a motor runs along the fibre and stalls at particular sites. This page shows the other main mechanism, and it works quite differently. Nothing here moves along the chain, and no position is special.
Each bead carries a type. In chromatin the type stands for epigenetic state: broadly, A for open, transcriptionally active regions carrying marks like H3K27ac, and B for compact, repressed regions carrying H3K9me3 or H3K27me3. The single rule is that beads of the same type attract each other weakly when they touch, and beads of different types do not.
That is the entire model. It is a block copolymer, one of the oldest and best understood objects in polymer physics, and its behaviour is well known: blocks of like type gather together, and because the blocks are tied into one chain they cannot separate completely. The result is microphase separation.
What appears in the contact map
Watch the map accumulate. The bright band along the diagonal is trivial: neighbours along the sequence are always close in space. The feature to look for is off-diagonal enrichment, forming a checkerboard.
That checkerboard is the signature. Two stretches of chain far apart along the sequence show elevated contact whenever they share a type, and depressed contact whenever they do not. The type track along the top edge of the map lets you check this directly: bright off-diagonal squares line up with same-coloured stretches.
The readout compresses the same information into one number: how much more often two beads in contact share a type than they would by chance. Only pairs more than one block apart along the chain are counted, and the comparison is against the type sequence’s own statistics at the same separations, so the number is 1 when type has no physical effect, regardless of how the blocks are laid out. Set \(\varepsilon = 0\) and it settles near \(1.05\); at the default \(\varepsilon = 0.9\,k_BT\) it reaches about \(1.4\) after a few thousand sweeps and is still climbing. Full microphase separation takes far longer than a browser tab will sit still for, so read the trend rather than the final value.
The comparison worth making
Open this page and the loop extrusion page side by side. They are the two mechanisms that between them account for most of what is seen in Hi-C, and their signatures are distinct.
Loop extrusion gives squares on the diagonal, bounded by CTCF sites, with a corner dot where two anchors are held together and stripes running from an anchor across its domain. The pattern is local: a domain has a definite start and end along the sequence, and contacts do not jump across the genome.
Compartments give a checkerboard. The pattern is non-local: regions megabases apart interact if they share a state, and there is no boundary element anywhere in the model. The scale is set by the block lengths and the strength of attraction, not by any site.
This is why the two are usually described as acting at different scales, with extrusion producing TADs and compartmentalisation producing the A/B pattern seen at longer range. They are not alternatives. Both run at once in a real nucleus, and a real contact map shows both patterns superposed.
Where this connects to the X chromosome
The X-inactivation work uses exactly this kind of attraction, with one important difference: the types are not made up. They are read from measured H3K27me3 and H3K27ac profiles, so the pattern of A and B along the chain comes from data rather than from a block length slider.
That is the step from a physics demonstration to a model of a particular locus. The mechanism is the one on this page. What changes is that the one-dimensional input is real, and so the three-dimensional prediction can be compared against a measured contact map for the same region.
Caveats
The chain here is a few hundred beads relaxed by local Monte Carlo moves, so it explores conformations slowly. The contact map is accumulated over the whole run rather than measured from an equilibrated ensemble, which means early frames contribute the poorly mixed conformations you can see on screen at the start. Give it time before reading the map closely, and press restart after changing the attraction so the map is not an average over two different models.
Why it matters · Two mechanisms, two signatures. Domains and stripes come from a motor running along the fibre; checkerboards come from segments recognising each other by state. A contact map showing both is telling you both are running.