Extending Bell's Model: How Force Transducer Stiffness Alters Measured Unbinding Forces and Kinetics of Molecular Complexes

Abstract

Forced unbinding of complementary macromolecules such as ligand-receptor complexes can reveal energetic and kinetic details governing physiological processes ranging from cellular adhesion to drug metabolism. Although molecular-level experiments have enabled sampling of individual ligand-receptor complex dissociation events, disparities in measured unbinding force F(R) among these methods lead to marked variation in inferred binding energetics and kinetics at equilibrium. These discrepancies are documented for even the ubiquitous ligand-receptor pair, biotin-streptavidin. We investigated these disparities and examined atomic-level unbinding trajectories via steered molecular dynamics simulations, as well as via molecular force spectroscopy experiments on biotin-streptavidin. In addition to the well-known loading rate dependence of F(R) predicted by Bell's model, we find that experimentally accessible parameters such as the effective stiffness of the force transducer k can significantly perturb the energy landscape and the apparent unbinding force of the complex for sufficiently stiff force transducers. Additionally, at least 20% variation in unbinding force can be attributed to minute differences in initial atomic positions among energetically and structurally comparable complexes. For force transducers typical of molecular force spectroscopy experiments and atomistic simulations, this energy barrier perturbation results in extrapolated energetic and kinetic parameters of the complex that depend strongly on k. We present a model that explicitly includes the effect of k on apparent unbinding force of the ligand-receptor complex, and demonstrate that this correction enables prediction of unbinding distances and dissociation rates that are decoupled from the stiffness of actual or simulated molecular linkers.

A nanomechanical interface to rapid single-molecule interactions

“…Recent theoretical and experimental works showed that the stiffness of the force transducer can influence the measured rupture forces 28,29 . Using analytical models generalized to include stiff transducers, Maitra and Arya 29 have found that the comparison of rupture force spectra obtained with different devices is permissible if spring constants K and barrier positions x β satisfy the relationship Kx 2 β /(2k B T)1.…”

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“…1, A and B; see also "Experimental Procedures"). These results excluded differences in the molecular constructs, their immobilization protocols, the experimental techniques, and the force probe stiffness as possible causes for the observed effect (41,42). Also, the single exponential distributions of bond lifetimes suggest that a single population of bonds with the same dissociation characteristics were tested (Fig.…”

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