Force-fluctuation relation of a single DNA molecule

We observed transverse fluctuations of single DNA molecules by fluorescence microscopy. The end-to-end distance of DNA molecules was varied by using dual trap optical tweezers, and the force-fluctuation relation was experimentally obtained in wide ranges of the force regime. In strong force regime, the theory of a stretched worm-like chain with fixed both ends explains the experimental results. On the other hand, in the low force regime, the fluctuations approach the value for an ideal ring polymer. We introduce an interpolate formula for the force-fluctuation relation by considering strong and low force limits, which captures the overall trend of experimental results. The proposed force-fluctuation relation will be useful for quantitative discussions in various sectors of polymer physics and biological processes which involve the conformation change of DNA and other biopolymers, where the loading and the fluctuation are relevant factors.