Calculating the force-dependent unbinding rate of biological macromolecular bonds from force-ramp optical trapping assays

Abstract

The non-covalent biological bonds that constitute protein–protein or protein–ligand interactions play crucial roles in many cellular functions, including mitosis, motility, and cell–cell adhesion. The effect of external force ($$F$$ F ) on the unbinding rate ($${k}_{\text{off}}\left(F\right)$$ k off F ) of macromolecular interactions is a crucial parameter to understanding the mechanisms behind these functions. Optical tweezer-based single-molecule force spectroscopy is frequently used to obtain quantitative force-dependent dissociation data on slip, catch, and ideal bonds. However, analyses of this data using dissociation time or dissociation force histograms often quantitatively compare bonds without fully characterizing their underlying biophysical properties. Additionally, the results of histogram-based analyses can depend on the rate at which force was applied during the experiment and the experiment’s sensitivity. Here, we present an analytically derived cumulative distribution function-like approach to analyzing force-dependent dissociation force spectroscopy data. We demonstrate the benefits and limitations of the technique using stochastic simulations of various bond types. We show that it can be used to obtain the detachment rate and force sensitivity of biological macromolecular bonds from force spectroscopy experiments by explicitly accounting for loading rate and noisy data. We also discuss the implications of our results on using optical tweezers to collect force-dependent dissociation data.

Long-range electrostatic interactions significantly modulate the affinity of dynein for microtubules

“…We plotted the cumulative distribution function (CDF) of the bound times for the MTBDs in the force-dependent dissociation assays and fit the CDFs with an exponential function ( 55 ): where t is the bound time for each unbind event, t 0 is the minimum resolvable binding time ( 56 ), and τ is the characteristic force-dependent unbinding time. We performed Kolmogorov-Smirnov (K-S) tests on the underlying bound time distributions to evaluate whether the collected samples could have been drawn from the same (but unknown) probability distribution (in this case, the distribution of unbinding time).…”