Atomic force microscopic and theoretical studies of poly-ubiquitin proteins

In this Letter, a theoretical model for the force-extension experiment applied to protein folding-unfolding is presented. This model explicitly takes into account the interplay between the mechanical energy and chemical energy. It can treat the effect of denaturing agents (like pH, GdnHCl, urea, etc.) and temperature on the force-extension experiment of protein folding-unfolding. We further apply the model to analyze our own force-extension experiment on ubiquitin tetramers and to the experimental data of other protein systems reported in literature. The current model can predict the quantities like the values of equilibrium constant, chemical potential and mole fraction of unfolded state involved in protein folding-unfolding and we have found that the proteins adsorbed on gold surfaces are partially unfolded in comparison with the bulk state.