An Intrusive Entropic Barrier Induced by Force

Abstract

Single-molecule force spectroscopy has opened up new approaches to the study of protein dynamics. For example, an extended protein folding after an abrupt quench in the pulling force was shown to follow variable collapse trajectories marked by well-defined stages that departed from the expected two-state folding behavior that is commonly observed in bulk. Here, we explain these observations by developing a simple approach that models the free energy of a mechanically extended protein as a combination of an entropic elasticity term and a short-range potential representing enthalpic hydrophobic interactions. The resulting free energy of the molecule shows a force-dependent energy barrier of magnitude, ΔE = e(F - Fc)3/2, separating the collapsed state of the molecule from a force-driven extended conformation, that vanishes at a critical force Fc. By solving the Langevin equation under force quench conditions, we generate folding trajectories corresponding to the diffusional collapse of an extended polypeptide that mimics those observed experimentally. Further we apply this model to force extension conditions in order to investigate the role played by the force-induced energy barrier on the two-state hopping phenomena that has been observed in single protein molecules placed under a stretching force. Langevin dynamics across such force induced barrier readily demonstrates the hopping behavior observed for a variety of single molecules placed under force. Our model interprets AFM force-clamp data and accounts as well for force-extension and hopping observed in optical tweezers, thus unifying the field of protein force spectroscopy. Moreover, given that this barrier does not exist at zero force, extrapolating hopping trajectories to zero force could not be compared to bulk measurements.