Theory

The model behind LoopSage: loop extrusion, the energy function, Monte Carlo sampling and the 3D polymer.

• Scope: what the model should explain, and how a few rules produce the patterns of a contact map.
• Loop extrusion: the molecular players (cohesin, CTCF, condensin), the loop extrusion model with its assumptions, TADs and contact maps, stripes and why dynamics is needed.
• Mechanics: Hamiltonian, phase space, ensembles, the Boltzmann law, and why an energy-based model is a good approximation for a cell that is not in equilibrium.
• MCMC: Markov chains, detailed balance, ergodicity, ergodic means, burn-in and autocorrelation.
• Molecular dynamics: the polymer, the force field, Newton's second law and the Langevin equation.
• Topology: knots, links and the linking number, how it is computed in 3D, and how loops are checked for linking (optional, advanced).