Learning Lab

Every model of a chromosome starts from a polymer, and the choice of polymer decides what the model can and cannot explain. These pages work through that choice one ingredient at a time, and then show what happens when you use the result to build an actual model of chromatin.

They are built to be used rather than read. None of them is an animation of a stored result. Every number on screen is measured from the model running in front of you, and changing a parameter changes the physics rather than the picture. Two of them run the same algorithms as the simulation code behind my papers; those are marked.

Polymer theory

These pages build up one polymer model at a time: an ideal chain first, then stiffness, then self-avoidance, then attraction. Each addition changes the scaling exponents in ways you can derive directly, and each derivation is checked against a live simulation on the same page. By the end, the four candidate models for chromatin sit on one set of axes with their measured values overlaid.

• The ideal chain

  Why a chain's size grows as the square root of its length: the scaling every coarse-grained chromatin model inherits.

• The worm-like chain and persistence length

  Persistence length as the decay constant of a correlation you can watch, not an abstract parameter.

• The self-avoiding walk

  A chain cannot pass through itself. That swells it, and it also suppresses contacts by more than the swelling alone accounts for.

• From size scaling to chain dynamics

  Fix how a chain's size grows and the relaxation times and diffusion exponents follow by algebra. The shortcut used on every page after this one.

• The equilibrium globule

  Turn on attraction and the chain collapses to constant density. What a subchain looks like from inside that drop is the interesting part.

• The fractal globule

  Squeeze a self-avoiding chain with a shrinking spherical wall. It cannot thread through itself, so it ends up crumpled, unknotted, and close to P(s) ~ 1/s.

• Comparing polymer models against chromatin data

  Four candidate polymers, four observables, and the measured chromatin ranges shaded behind them. No model fits everything.

Building a model

A different question from the theory pages: not which scaling law chromatin obeys, but how a three-dimensional model of a real locus actually gets built, and what each construction method can and cannot be trusted to show. Two physical mechanisms, one inverse (contact-to-structure) method, and the measurement that supplies the parameters.

• Reconstructing a structure from contacts

  Turn a contact map into 3D coordinates by fitting distances. Then do it again from a different random start and see how much the answer moves.

• Loop extrusion

  Cohesin reels chromatin through itself until CTCF stops it. The one-dimensional kinetics from our simulations, on the real 1 Mb locus from the paper.

  From my research

• 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.

• Coarse-graining a polymer

  Group monomers into effective beads and measure what the new bonds and angles actually look like: the reference calculation behind the paper, running live.

  From my research

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