Effects of intermediate bound states in dynamic force spectroscopy

We revisit some aspects of the interpretation of dynamic force spectroscopy experiments. The standard theory predicts that the typical unbinding force f* is linearly proportional to the logarithm of the loading rate r when a single energy barrier controls the unbinding process. For a more complex situation of N barriers, it predicts at most N linear segments for the f* vs. log(r) curve, each segment characterizing a different barrier. Here we extend this existing picture using a refined approximation, provide a more general analytical formula, and show that in principle up to N(N + 1) / 2 segments can show up experimentally. As a consequence, the determination of the positions and even the number of the energy barriers from the experimental data can be ambiguous. A further possible consequence of a multiple-barrier landscape is a bimodal or multimodal distribution of the unbinding force at certain loading rates, a feature recently observed experimentally.