How Well Can DNA Rupture DNA? Shearing and Unzipping Forces inside DNA Nanostructures

Abstract

A purely DNA nanomachine must support internal stresses across short DNA segments with finite rigidity, producing effects that can be qualitatively very different from experimental observations of isolated DNA in fixed-force ensembles. In this article, computational simulations are used to study how well the rigidity of a driving DNA duplex can rupture a double-stranded DNA target into single-stranded segments and how well this stress can discriminate between unzipping or shearing geometries. This discrimination is found to be maximized at an optimal length but deteriorates as the driving duplex is either lengthened or shortened. This differs markedly from a fixed-force ensemble and has implications for the design parameters and limitations of dynamic DNA nanomachines.

Figure 1

As a short duplex DNA target attached to a longer main duplex (a, b) undergoes either unzipping (c) or shearing (d) to release single strands (e, f), the curvature and tension in the main duplex decreases. The different parts of each configuration are color-coded as follows: the main duplex is blue and red, whereas the overhangs are composed of green sticky ends that are complementary and come together to form the target duplex and purple linkers that provide mechanical flexibility. Configurations are shown for the main duplex length of 40 bp.

Figure 2

As (a) unzipping or (b) shearing progresses, the free energy increases due to bond-breaking up until the reaction barrier, which is consistently the state with only one bond remaining. After this barrier is passed, the free energy steadily decreases to a relaxed minimum and only increases again when the distance between sticky ends is forced to be larger than the contour length of the main duplex. Free-energy curves are for main duplex lengths of (top to bottom) 20, 25, 30, 35, 40, 50, and 60 bp and are offset by 5 k_BT from each other at 0 bonds for clarity. Insets show characteristic configurations with either all 10 pair bonds intact, only one bond remaining, or completely unbound. Uncertainties are comparable to or smaller than the size of the symbols.

Figure 3

(a) For either shearing or unzipping (shown here for main duplex length 30 bp), the transition barrier ΔG^‡ and ΔG_tot can be defined by the free energy of the transition state (1 bond) and the minimum free energy of the unbound states, respectively, relative to the initial 10-bond state. Cut-outs on the right correspond to insets in graphs (b), depicting the derivation of these free energies graphically. (b) The transition barrier (top) remains largely constant for shearing and shows a minimum of around 30 bp for unzipping; the total free-energy change (bottom) mostly decreases with increasing main duplex length. These can be fitted to eqs 1 and 2 of Section 2.4, where allowing the main duplex to kink at a critical torque of 29 pN nm (solid lines) improves fitting of the transition barrier but degrades fitting of the total free-energy difference of unzipping, relative to a model in which the main duplex does not kink (dashed lines).

Figure 4

(a) (i) As either shearing or unzipping proceeds (shown for main duplex length 40 bp), the end-to-end distance across the main duplex increases as it relaxes, whereas the contour length increases slightly at either high bond number or high min distance. (Here and in Figure 5, error bars are in-run fluctuations; the standard error of mean is the size of the symbols or smaller.) The inset shows how contour length (solid) and end-to-end distance (dashed) are calculated for a typical configuration. The end-to-end distance is extracted at 10 bonds, one bond, and the unbound energy minimum for subsequent analysis, with the cutout corresponding to the inset in graph (ii). Graph (ii) shows how the end-to-end length increases as shearing and unzipping proceed. (b) (i) The melting of base pairs in the main duplex results in either kinking or fraying. Graphs (ii) and (iii) show how kinking and fraying, respectively, decrease as shearing and unzipping proceed. In graphs (a) (ii), (b) (ii), and (b) (iii), solid lines show the relaxation from the 10-bond state to the one bond state and dashed lines show the subsequent relaxation to the fully relaxed unbound state; unzipping data points are shifted 1 bp right for clarity.

Figure 5

End-to-end length and contour length of the 5 nt single-stranded linker is consistently longer for unzipping than for shearing, showing the consistently higher tension throughout the structure during unzipping until the configuration is fully unbound and even for some small distance after. The consistent contour length decrease during unzipping indicates the recovery of base stacking, which may further decrease the energy cost of unzipping (the main duplex length is 40 bp; other lengths result in similar data).

Figure 6

(a) Effective force driving shearing and unzipping in the studied structures ranges between 3.5 and 6 pN. (b) Replacing the main duplex with a polymer with higher persistence length dramatically increases the transition barrier difference between shearing and unzipping, as shown for hypothetical persistence lengths l_p = 60 and 80 nm. The activation energies from ref (28) at a constant force of 11.8 pN are also shown as a benchmark; the constant force shear–unzip gap is readily surpassed.

Figure 7

Between competitive DNA-rupturing pathways, unzipping is both kinetically and thermodynamically favored over shearing. The balance between reversed, DNA-binding processes “zipping” and “unshearing” is more subtle: zipping should proceed more quickly and be kinetically favored, but unshearing (or cyclization) is thermodynamically favored. Energy landscapes here are for a main duplex length of 30 bp.

Figure 8

Free energies calculated from individual runs in the bound (purple), transitional (green), and unbound (blue) windows agree with other runs in the same windows and match the free energies from other windows where there is overlap. Data shown here are for unzipping for a 40 bp main duplex; other data are similar.

Figure 9

Physical variables x (end-to-end distance), x_offset (width or length of the target duplex), n_bpl_c/bp, and n_ntl_c/nt (the contour lengths of the main duplex and single-stranded linkers, respectively), depicted on a typical configuration.