Effects of intermediate bound states in dynamic force spectroscopy

TL;DR

This paper refines the theoretical understanding of dynamic force spectroscopy by deriving a more general formula that predicts up to N(N+1)/2 segments in the force vs. log(rate) curve, complicating data interpretation.

Contribution

It extends existing models with a refined approximation, providing a more general analytical formula that accounts for multiple barriers in unbinding processes.

Findings

Up to N(N+1)/2 segments can appear in force vs. log(rate) curves.

Multiple barriers can cause bimodal or multimodal force distributions.

Data interpretation can be ambiguous due to complex barrier landscapes.

Abstract

We revisit here some aspects of the interpretation of dynamic force spectroscopy experiments. The standard theory predicts a typical unbinding force $f^*$ 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 $f^*$ 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 $N(N+1)/2$ 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.