Tether-Length Dependence of Bias in Equilibrium Free-Energy Estimates for Surface-to-Molecule Unbinding Experiments

The capabilities of atomic force microscopes and optical tweezers to probe unfolding or surface-to-molecule bond rupture at a single-molecular level are widely appreciated. These measurements are typically carried out unidirectionally under nonequilibrium conditions. Jarzynski's equality has proven useful to relate the work obtained along these nonequilibrium trajectories to the underlying free energy of the unfolding or unbinding process. Here, we quantify biases that arise from the molecular design of the bond rupture experiment for probing surface-to-molecule bonds. In particular, we probe the well-studied amine/gold bond as a function of the linker's length which is used to anchor the specific amine functionality during a single molecule unbinding experiment. With increasing linker length, we observe a significant increase in the average work spent on polymer stretching and a strongly biased estimated interaction free energy. Our data demonstrate that free energy estimates converge well for linker lengths below 20 nm, where the bias is <10-15%. With longer linkers severe methodical limits of the method are reached, and convergence within a reasonable number of realizations of the bond rupture is not feasible. Our results also provide new insights into stability and work dissipation mechanisms at adhesive interfaces at the single-molecular level, and offer important design and analysis aspects for single-molecular surface-to-molecule experiments.