Improving estimation of kinetic parameters in dynamic force spectroscopy using cluster analysis.

Dynamic Force Spectroscopy (DFS) is a widely used technique to characterize the dissociation kinetics and interaction energy landscape of receptor-ligand complexes with single-molecule resolution. In an Atomic Force Microscope (AFM)-based DFS experiment, receptor-ligand complexes, sandwiched between an AFM tip and substrate, are ruptured at different stress rates by varying the speed at which the AFM-tip and substrate are pulled away from each other. The rupture events are grouped according to their pulling speeds, and the mean force and loading rate of each group are calculated. These data are subsequently fit to established models, and energy landscape parameters such as the intrinsic off-rate (k) and the width of the potential energy barrier (x) are extracted. However, due to large uncertainties in determining mean forces and loading rates of the groups, errors in the estimated k and x can be substantial. Here, we demonstrate that the accuracy of fitted parameters in a DFS experiment can be dramatically improved by sorting rupture events into groups using cluster analysis instead of sorting them according to their pulling speeds. We test different clustering algorithms including Gaussian mixture, logistic regression, and K-means clustering, under conditions that closely mimic DFS experiments. Using Monte Carlo simulations, we benchmark the performance of these clustering algorithms over a wide range of k and x, under different levels of thermal noise, and as a function of both the number of unbinding events and the number of pulling speeds. Our results demonstrate that cluster analysis, particularly K-means clustering, is very effective in improving the accuracy of parameter estimation, particularly when the number of unbinding events are limited and not well separated into distinct groups. Cluster analysis is easy to implement, and our performance benchmarks serve as a guide in choosing an appropriate method for DFS data analysis.