Force-clamp experiments reveal the free-energy profile and diffusion coefficient of the collapse of protein molecules

We present force-clamp data on the collapse of ubiquitin polyproteins from a highly extended state to the folded length, in response to a quench in the force from 110 pN to 5 or 10 pN. Using a recent method for free-energy reconstruction from the observed nonequilibrium trajectories, we find that their statistics is captured by simple diffusion along the end-to-end length. The estimated diffusion coefficient of ∼100 nm2 s^-1 is significantly slower than expected from viscous effects alone, possibly because of the internal degrees of freedom of the protein. The free-energy profiles give validity to a physical model in which the multiple protein domains collapse all at once and the role of the force is approximately captured by the Bell model.