On the free energy of protein folding in optical tweezers experiments

Abstract

Free energy is a critical parameter in understanding the equilibrium in chemical reactions. It enables us to determine the equilibrium proportion between the different species in the reaction and to predict in which direction the reaction will proceed if a change is performed in the system. Historically, to calculate this value, bulk experiments were performed where a parameter was altered at a gradual rate to change the population until a new equilibrium was established. In protein folding studies, it is common to vary the temperature or chaotropic agents in order to change the population and then to extrapolate to physiological conditions. Such experiments were time-consuming due to the necessity of ensuring equilibrium and reversibility. Techniques of single-molecule manipulation, such as optical/magnetic tweezers and atomic force microscopy, permit the direct measurement of the work performed by a protein undergoing unfolding/refolding at particular forces. Also, with the development of non-equilibrium free energy theorems (Jarzynski equality, Crooks fluctuation theorem, Bennett acceptance ratio, and overlapping method), it is possible to obtain free energy values in experiments far from equilibrium. This review compares different methodologies and their application in optical tweezers. Interestingly, in many proteins, discrepancies in free energy values obtained through different methods suggest additional complexities in the folding pathway, possibly involving intermediate states such as the molten globule. Further studies are needed to confirm their presence and significance.

Supplementary information: The online version contains supplementary material available at 10.1007/s12551-025-01310-0.

Keywords: Free energy; Non-equilibrium free energy theorems; Optical tweezers experiments; Protein folding.