DNA Nanotweezers Studied with a Coarse-Grained Model of DNA

We introduce a coarse-grained rigid nucleotide model of DNA that reproduces the basic thermodynamics of short strands, duplex hybridization, single-stranded stacking, and hairpin formation, and also captures the essential structural properties of DNA: the helical pitch, persistence length, and torsional stiffness of double-stranded molecules, as well as the comparative flexibility of unstacked single strands. We apply the model to calculate the detailed free-energy landscape of one full cycle of DNA “tweezers,” a simple machine driven by hybridization and strand displacement.

Figure 1

A duplex as represented by the model and a detailed view of a nucleotide.

Figure 2

(a) Comparison of melting temperatures as computed for our model (crosses connected by a solid line) and predicted by the nearest-neighbor model [24] (squares connected by a dashed line) for duplexes as a function of the single-stranded length, and hairpins as a function of loop length for a stem of six bases. (b) Melting profile for an eight base duplex as predicted by our model (solid line) and the nearest-neighbor model (dashed line).

Figure 3

Simulation snapshots showing stages of operation of DNA tweezers. (a) Tweezers initially open. (b) Fuel ($f$) is added and binds to one arm ($\beta$). (c) Fuel binds to the second arm ($\alpha$) and closes the tweezers. (d) Antifuel ($\overline{f}$) is added and binds to the toehold of the fuel. (e) Antifuel begins to displace first arm of the tweezers. (f) Tweezers open as first arm is displaced, and antifuel starts to displace the second arm. (g) Antifuel fully hybridizes to fuel and the waste duplex is formed.

Figure 4

Free energy $F$ plotted as a function the number of $f/\overline{f}$ and $f/\mathrm{\text{tweezer}}$ base pairs for DNA tweezers at 300 K. White areas indicate regions of high free-energy relative to their environment that were unsampled.

Figure 5

(a) Free-energy profile along the one-dimensional pathway indicated in Fig. 4. Coordinates indicate the number of $f/\overline{f}$ and $f/\mathrm{\text{tweezer}}$ base pairs. (b) The displacement process “$e$” in more detail. Squares represent the original system, circles a system with the tail of $\overline{f}$ unable to form a hairpin, and crosses a system with the last eight bases of $\overline{f}$ and most of the $f/\beta$ arm removed (see text).