Stretching of a Single Tethered Polymer in a Uniform Flow

TLDR

Fluorescence microscopy was used to directly visualize single, tethered DNA molecules (22–84 μm) held stationary by optical trapping of a latex microsphere while a uniform flow stretched them. The fractional extension of tethered DNA follows a universal scaling law x/L ∝ (ηvL)^0.54, indicating significant hydrodynamic coupling even near full extension, with small deformations scaling as v^0.70, reduced relative fluctuations, and a cone‑shaped envelope observed in fluorescence images.

Abstract

The stretching of single, tethered DNA molecules by a flow was directly visualized with fluorescence microscopy. Molecules ranging in length ( L ) from 22 to 84 micrometers were held stationary against the flow by the optical trapping of a latex microsphere attached to one end. The fractional extension x / L is a universal function of η v L 0.54 ± 0.05 , where η and v are the viscosity and velocity of the flow, respectively. This relation shows that the DNA is not "free-draining" (that is, hydrodynamic coupling within the chain is not negligible) even near full extension (∼80 percent). This function has the same form over a long range as the fractional extension versus force applied at the ends of a worm-like chain. For small deformations (< 30 percent of full extension), the extension increases with velocity as x ∼ v 0.70 ± 0.08 . The relative size of fluctuations in extension decreases as σ x / x ≅ 0.42 exp(-4.9 x / L ). Video images of the fluctuating chain have a cone-like envelope and show a sharp increase in intensity at the free end.