Optimizing the calculation of energy landscape parameters from single-molecule protein unfolding experiments

Single-molecule force spectroscopy using an atomic force microscope (AFM) can be used to measure the average unfolding force of proteins in a constant velocity experiment. In combination with Monte Carlo simulations and through the application of the Zhurkov-Bell model, information about the parameters describing the underlying unfolding energy landscape of the protein can be obtained. Using this approach, we have completed protein unfolding experiments on the polyprotein (I27)(5) over a range of pulling velocities. In agreement with previous work, we find that the observed number of protein unfolding events observed in each approach-retract cycle varies between one and five, due to the nature of the interactions between the polyprotein, the AFM tip, and the substrate, and there is an unequal unfolding probability distribution. We have developed a Monte Carlo simulation that incorporates the impact of this unequal unfolding probability distribution on the median unfolding force and the calculation of the protein unfolding energy landscape parameters. These results show that while there is a significant, unequal unfolding probability distribution, the unfolding energy landscape parameters obtained from use of the Zhurkov-Bell model are not greatly affected. This result is important because it demonstrates that the minimum acceptance criteria typically used in force extension experiments are justified and do not skew the calculation of the unfolding energy landscape parameters. We further validate this approach by determining the error in the energy landscape parameters for two extreme cases, and we provide suggestions for methods that can be employed to increase the level of accuracy in single-molecule experiments using polyproteins.