DNA Nunchucks: Nanoinstrumentation for Single-Molecule Measurement of Stiffness and Bending

Abstract

Bending of double-stranded DNA (dsDNA) has important applications in biology and engineering, but measurement of DNA bend angles is notoriously difficult and rarely dynamic. Here we introduce a nanoscale instrument that makes dynamic measurement of the bend in short dsDNAs easy enough to be routine. The instrument works by embedding the ends of a dsDNA in stiff, fluorescently labeled DNA nanotubes, thereby mechanically magnifying their orientations. The DNA nanotubes are readily confined to a plane and imaged while freely diffusing. Single-molecule bend angles are rapidly and reliably extracted from the images by a neural network. We find that angular variance across a population increases with dsDNA length, as predicted by the worm-like chain model, although individual distributions can differ significantly from one another. For dsDNAs with phased A6-tracts, we measure an intrinsic bend of 17 ± 1° per A6-tract, consistent with other methods, and a length-dependent angular variance that indicates A6-tracts are (80 ± 30)% stiffer than generic dsDNA.

Orientational Fluctuations and Bimodality in Semiflexible Nunchucks

“…This propagator is particularly useful in the analysis of the bending fluctuations of DNA nunchucks. Fygenson et al [ 7 ] attached both ends of short double-stranded DNA (dsDNA) chains to fluorescently labeled DNA nanotubes confined to fluctuate in two dimensions. They extracted the distribution of the bending angle of the dsDNA through direct imaging of the nanotubes.…”

“…To connect Equation ( 10 ) with Reference [ 7 ], the middle segment of contour length corresponds to the dsDNA chain. In the experiment, its elasticity is probed by measuring the bending angle .…”

“…As we see from Equation ( 25 ), we treat the hinge as an angular spring. This may represent an F-actin cross-linking protein, which prescribes a finite angle (e.g., filamin), or it may be a coarse-grained version of a short dsDNA link of the two DNA nanotubes in the nunchuck complex of Reference [ 7 ]. In the latter case, and comparing Equation ( 25 ) with Equation ( 9 ) we have , where s is the length of the link.…”

“…We now focus on a hinge with and calculate numerically the integrals that give in order to see the dependence of its form on the bending stiffness of the hinge and that of the two arms. In Figure 4 , we use parameters appropriate for the DNA nanotube nunchuck experiments of Reference [ 7 ]. We assume that the two arms are identical, with contour length 3 m and persistence length of 27 m. We see that for a hinge strength of , which corresponds to a WLC link of , the distribution of transverse fluctuations exhibits a plateau.…”

“…In the case of double-stranded (ds) DNA, various techniques have been used in order to measure the bending angle, ranging from gel shift electrophoresis [ 5 ] to atomic force microscopy [ 6 ]. Recently, Fygenson et al introduced a novel physical method to measure the bending angle with minimal sample preparation, direct visualization, and straightforward analysis procedures [ 7 , 8 ]. It involves the assembly of semiflexible “nunchucks”, composed of two long DNA nanotubes of large bending stiffness end-linked by a short segment of dsDNA, which acts as a hinge.…”