Mechanistic Genome Folding at Scale through the Differentiable Loop Extrusion Model

The spatial folding of the genome shapes gene regulation by controlling which loci interact, yet inferring the mechanisms behind these 3D structures from contact maps remains difficult. Cohesin-mediated loop extrusion is a key organizer of domains and loops, but existing methods either predict contacts without mechanistic insight or simulate extrusion with limited scalability. We present the differentiable loop extrusion model (dLEM), a scalable framework that reformulates extrusion as a smooth, trainable process. dLEM represents extrusion through position-specific velocity profiles for leftward and rightward cohesin movement. Fitting dLEM to chromosome conformation capture data yields a one-dimensional, interpretable description of extrusion dynamics that aligns with genomic and epigenomic features. dLEM parameters also capture architectural changes under CTCF and WAPL perturbations, enabling genome-wide prediction of extrusion disruptions. Extending our observations, we demonstrate that dLEM can be seamlessly incorporated into deep learning models to infer extrusion parameters directly from sequence and chromatin features, reducing model complexity by nearly three orders of magnitude while preserving predictive accuracy. Indeed, when incorporated into deep dLEM, dLEM acts as a biophysically-motivated layer for long range genomic communication, and together they provide a predictive, interpretable framework linking 1D genomic features to 3D chromatin folding and its response to sequence and chromatin state, with dLEMs mechanistic modeling enabling prediction of trans factor perturbation effects.