Theory for nonlinear dynamic force spectroscopy

Dynamic force spectroscopy (DFS) is an experimental technique that is commonly used to assess information on the strength, energy landscape, and lifetime of noncovalent bio-molecular interactions. DFS traditionally requires an applied force that increases linearly with time so that the bio-complex under investigation is exposed to a constant loading rate. However, tethers or polymers can modulate the applied force in a nonlinear manner. For example, bacterial adhesion pili and polymers with worm-like chain properties are structures that show nonlinear force responses. In these situations, the theory for traditional DFS cannot be readily applied. In this work, we expand the theory for DFS to also include nonlinear external forces while still maintaining compatibility with the linear DFS theory. To validate the theory, we modeled a bio-complex expressed on a stiff, an elastic, and a worm-like chain polymer, using Monte Carlo methods, and assessed the corresponding rupture force spectra. It was found that the nonlinear DFS (NLDFS) theory correctly predicted the numerical results. We also present a protocol suggesting an experimental approach and analysis method of the data to estimate the bond length and the thermal off-rate.