Refolding upon force quench and pathways of mechanical and thermal unfolding of ubiquitin.

The refolding from stretched initial conformations of ubiquitin (PDB ID: 1ubq) under the quenched force is studied using the C(alpha)-Gō model and the Langevin dynamics. It is shown that the refolding decouples the collapse and folding kinetics. The force-quench refolding-times scale as tau(F) approximately exp(f(q)Deltax(F)/k(B)T), where f(q) is the quench force and Deltax(F) approximately 0.96 nm is the location of the average transition state along the reaction coordinate given by the end-to-end distance. This value is close to Deltax(F) approximately 0.8 nm obtained from the force-clamp experiments. The mechanical and thermal unfolding pathways are studied and compared with the experimental and all-atom simulation results in detail. The sequencing of thermal unfolding was found to be markedly different from the mechanical one. It is found that fixing the N-terminus of ubiquitin changes its mechanical unfolding pathways much more drastically compared to the case when the C-end is anchored. We obtained the distance between the native state and the transition state Deltax(UF) approximately 0.24 nm, which is in reasonable agreement with the experimental data.