Loop Extrusion Model

The cohesin complex, a ring-shaped protein assembly, loads onto chromatin and uses ATP hydrolysis to actively reel DNA bidirectionally through its lumen. This motor activity creates a progressively enlarging loop that brings linearly distant loci into spatial proximity. The extrusion rate is approximately 0.5–2 kb per second in mammalian cells, with processivity limited by boundary encounters and cohesin release factors like WAPL. The directionality of extrusion is determined by the orientation of CTCF binding sites encountered during translocation.

CCCTC-binding factor (CTCF) acts as a directional barrier to loop extrusion by binding to specific DNA sequence motifs. When cohesin encounters a CTCF protein bound in the correct orientation, translocation is stalled but not permanently arrested, creating a transient anchor point. Convergent CTCF sites—where two binding motifs face each other—form stable loop anchors by trapping cohesin between them. This explains why ~90% of chromatin loops identified in Hi-C data are anchored at convergent CTCF motifs. Divergent or tandem orientations fail to block extrusion effectively.

Topologically Associating Domains (TADs) emerge as a direct consequence of loop extrusion dynamics. As multiple cohesin complexes extrude simultaneously along a chromatin fiber, the region between convergent CTCF boundaries becomes insulated from outside interactions while internal contacts are enriched. The insulation score at TAD boundaries correlates with CTCF occupancy and motif orientation. TADs are not static structures—they are dynamic and probabilistic, with extrusion occurring in bursts and boundaries showing variable permeability depending on CTCF binding stability and cohesin residence time.

Cohesin loading is mediated by the NIPBL-MAU2 complex, which facilitates topological entrapment of DNA within the cohesin ring. Loading occurs preferentially at active promoters and enhancers, explaining the enrichment of loop anchors at regulatory elements. Unloading is primarily driven by WAPL, which opens the cohesin ring to release DNA. The balance between loading and unloading rates determines the residence time of cohesin on chromatin—typically 10–25 minutes in mammalian cells—which directly constrains maximum loop size. PDS5 proteins stabilize cohesin on DNA, counteracting WAPL-mediated release.

While CTCF is the primary boundary element, additional factors modulate extrusion dynamics:

• Transcription machinery: Actively transcribing RNA Polymerase II can push cohesin along DNA or displace it entirely, creating transcription-dependent boundaries
• Nucleosome density: Tightly packed heterochromatin reduces cohesin loading and slows translocation
• DNA supercoiling: Torsional stress ahead of the extruding cohesin can stall translocation
• Cohesin-cohesin collisions: Two converging cohesin complexes can mutually block each other, forming boundaries independent of CTCF These secondary mechanisms explain why TAD boundaries are not perfectly predicted by CTCF occupancy alone.

Loop extrusion is modeled computationally using polymer physics simulations that treat chromatin as a semi-flexible polymer chain. Key implementations include:

• OpenMM-based simulations: Molecular dynamics frameworks that simulate extrusion with explicit cohesin motors and CTCF barriers
• LEM (Loop Extrusion Model): A minimal model parameterizing extrusion rate, processivity, and boundary permeability
• MiChroM: Integrates loop extrusion with compartmentalization forces to reproduce Hi-C maps
• Chrom3D: Combines extrusion with nuclear lamina interactions for whole-nucleus simulations These frameworks validate that extrusion alone can recapitulate ~70–80% of observed Hi-C contact patterns.

Computational modeling of the ring-shaped cohesin protein complex that acts as the molecular motor of loop extrusion. Simulations predict its loading at chromatin, ATP-dependent translocation along the DNA fiber, and unloading at boundary elements. Key parameters include processivity (how far it travels), velocity, and the probability of stalling or dissociating upon encountering a CTCF protein. These models bridge molecular biophysics with genome-scale folding predictions.

The computational identification of DNA sequence motifs bound by the CCCTC-binding factor (CTCF). CTCF acts as the primary barrier to loop extrusion; its asymmetric binding orientation determines whether a cohesin complex is blocked or permitted to pass. Deep learning models predict CTCF occupancy from sequence context and chromatin accessibility data, defining the boundary elements that partition the genome into topologically associating domains (TADs).

A self-interacting genomic region where DNA sequences contact each other more frequently than with sequences outside the domain. TADs are the direct structural consequence of loop extrusion constrained by CTCF boundaries. They function as regulatory microenvironments, restricting enhancer-promoter interactions to genes within the same domain. Disruption of TAD boundaries by structural variants can cause gene misexpression and disease.

A quantitative metric calculated from Hi-C contact maps that measures the degree to which a genomic locus is insulated from interactions with neighboring regions. Low insulation scores correspond to TAD boundaries where loop extrusion is blocked. The score is computed by summing contacts across a sliding window and normalizing against local background. It is the primary computational method for identifying domain boundaries genome-wide.

A metric quantifying the upstream or downstream bias of chromatin interactions at a given genomic bin. It reveals the directionality of loop extrusion by measuring whether a locus interacts preferentially with regions to its left or right. Convergent CTCF sites produce a characteristic directional flip, marking the boundaries of TADs. The index is essential for inferring extrusion dynamics from static Hi-C data.

A deep learning model that integrates principles of polymer physics to generate physically plausible 3D genome structures. Constraints include:

• Contact probability decay as a function of genomic distance
• Excluded volume preventing chromatin fiber self-intersection
• Loop extrusion dynamics enforcing TAD formation These physics-informed architectures ensure that predicted structures obey both data-driven patterns and fundamental biophysical laws.