Effects of intermediate bound states in dynamic force spectroscopy

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