Reconciling Intermediates in Mechanical Unfolding Experiments with Two-State Protein Folding in Bulk

Most experimentally well-characterized single domain proteins of less than 100 residues have been found to be two-state folders. That is, only two distinct populations can explain both equilibrium and kinetic measurements. Results from single molecule force spectroscopy, where a protein is unfolded by applying a mechanical pulling force to its ends, have largely confirmed this description for proteins found to be two-state in ensemble experiments. Recently, however, stable intermediates have been reported in mechanical unfolding experiments on a cold-shock protein previously found to be a prototypical two-state folder. Here, we tackle this discrepancy using free energy landscapes and Markov state models derived from coarse-grained molecular simulations. We show that protein folding intermediates can be selectively stabilized by the pulling force and that the populations of these intermediates vary in a force-dependent manner. Our model qualitatively captures the experimental results and suggests a possible origin of the apparent discrepancy.