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

Abstract

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.

E-cadherin binds to desmoglein to facilitate desmosome assembly

“…The most probable unbinding force at the different loading rates were fit to the Bell-Evans model ( Bell, 1978 ; Evans and Ritchie, 1997 ) to measure the intrinsic off-rate under zero force, k 0 off and the width of energy barrier that inhibit protein dissociation, x β ( Figure 2A,B,C ). We used cluster analysis to group the single molecule unbinding events for fitting ( Yen and Sivasankar, 2018 ). We have previously shown that a K-means clustering algorithm greatly improves the estimation of kinetic parameters in DFS ( Yen and Sivasankar, 2018 ).…”

“…We used cluster analysis to group the single molecule unbinding events for fitting ( Yen and Sivasankar, 2018 ). We have previously shown that a K-means clustering algorithm greatly improves the estimation of kinetic parameters in DFS ( Yen and Sivasankar, 2018 ). This analysis showed that the off-rate of Dsc2/Dsc2 dimers ( Figure 2A ) and Dsg2/Ecad dimers ( Figure 2C ) were comparable with a k 0 off of 1.26 s −1 and 1.24 s −1 respectively.…”

“…Loading rates were calculated as described elsewhere ( Ray et al, 2007 ). K-means clustering method was used to group loading rates ( Yen and Sivasankar, 2018 ). Mean force and mean loading rate were calculated for each group and plots of * vs. were fit using nonlinear least-squares fitting with bisquare weights to the Bell-Evans model ( Bell, 1978 ; Evans and Ritchie, 1997 ) Confidence intervals (CIs) for and were determined using bootstrap-with-replacement, as described previously ( Yen et al, 2016 ).…”

Inside-out regulation of E-cadherin conformation and adhesion

“…4 C-E) were calculated by multiplying the slope of the jump by the pulling velocity. k-means clustering was used to group the loading rates as described previously (70). Mean unbinding force and mean loading rate for the groups were fit using a weighted nonlinear least square fit to the Bell-Evans model (37).…”

Inside-out regulation of E-cadherin conformation and adhesion

“…Loading rates for the jump events used for dynamic force spectroscopy analysis ( Figure 4C-E) were calculated by multiplying the slope of the jump by the pulling velocity. K-means clustering was used to group the loading rates as described previously 64 . Mean unbinding force and mean loading rate for the groups were fit using a weighted non-linear least square fit to the Bell-Evans model 37 .…”