Protein unfolding and refolding as transitions through virtual states

Single-molecule atomic force spectroscopy probes elastic properties of titin, ubiquitin and other relevant proteins. We explain bioprotein folding dynamics under both length- and force-clamp by modeling polyprotein modules as particles in a bistable potential, weakly connected by harmonic spring linkers. Multistability of equilibrium extensions provides the characteristic sawtooth force-extension curve. We show that abrupt or stepwise unfolding and refolding under force-clamp conditions involve transitions through virtual states (which are quasi-stationary domain configurations) modified by thermal noise. These predictions agree with experimental observations.