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Effects of Intermediate Bound States in Dynamic Force Spectroscopy

Imre Derényi ^*, Denis Bartolo  and Armand Ajdari 

^* Department of Biological Physics, Eötvös University, H-1117 Budapest, Hungary; and Laboratoire de Physico-Chimie Théorique, UMR 7083 CNRS, Ecole Supérieure de Physique et de Chimie Industrielles, F-75231 Paris Cédex 05, France

Correspondence: Address reprint requests to Imre Derényi, Dept. of Biological Physics, Eötvös University, Pázmány P. Stny. 1A, H-1117 Budapest, Hungary. E-mail: derenyi{at}elte.hu.

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.

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