Theory and Simulations of condensin mediated loop extrusion in DNA

Condensation of hundreds of mega-base-pair-long human chromosomes in a small nuclear volume is a spectacular phenomenon. This process is driven by the formation of chromosome loops. ATP consuming motor, condensin, interacts with chromatin segments to actively extrude loops. Motivated by real-time imaging of loop extrusion (LE) and measurements using magnetic tweezer experiments, we created an analytically solvable model, predicting the LE velocity and step size distribution as a function of external load. The theory fits the experimental data quantitatively, and suggests that condensin must undergo a large conformational change, induced by ATP binding, bringing distant parts of the motor to proximity. Simulations using a simple model confirm that the motor transitions between an open to closed state in order to extrude loops by a scrunching mechanism, similar to that proposed in DNA bubble formation during bacterial transcription. Changes in the orientation of the motor domains are transmitted over $\sim$ 50 nm, connecting the motor head and the hinge, thus providing an allosteric basis for LE.