Polymer-Based Accurate Positioning: An Exact Worm-like-Chain Study

Precise positioning of molecular objects from one location to another is important for nanomanipulation and is also involved in molecular motors. Here, we study single-polymer-based positioning on the basis of the exact solution to the realistic three-dimensional worm-like-chain (WLC) model. The results suggest the possibility of a surprisingly accurate flyfishing-like positioning in which tilting one end of a flexible short polymer enables positioning of the other diffusing end to a distant location within an error of ∼1 nm. This offers a new mechanism for designing molecular positioning devices. The flyfishing effect (and reverse process) likely plays a role in biological molecular motors and may be used to improve speed of artificial counterparts. To facilitate these applications, a new force-extension formula is obtained from the exact WLC solution. This formula has an improved accuracy over the widely used Marko-Siggia formula for stretched polymers and is valid for compressed polymers too. The new formula is useful in analysis of single-molecule stretching experiments and in estimating intramolecular forces of molecular motors, especially those involving both stretched and compressed polymer components.