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 andin estimating intramolecular forces of molecular motors, especiallythose involving both stretched and compressed polymer components.
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