Force-driven separation of short double-stranded DNA

Abstract

Short double-stranded DNA is used in a variety of nanotechnological applications, and for many of them, it is important to know for which forces and which force loading rates the DNA duplex remains stable. In this work, we develop a theoretical model that describes the force-dependent dissociation rate for DNA duplexes tens of basepairs long under tension along their axes ("shear geometry"). Explicitly, we set up a three-state equilibrium model and apply the canonical transition state theory to calculate the kinetic rates for strand unpairing and the rupture-force distribution as a function of the separation velocity of the end-to-end distance. Theory is in excellent agreement with actual single-molecule force spectroscopy results and even allows for the prediction of the rupture-force distribution for a given DNA duplex sequence and separation velocity. We further show that for describing double-stranded DNA separation kinetics, our model is a significant refinement of the conventionally used Bell-Evans model.

Figure 1

(a) Schematic of a single-molecule DNA stretching experiment. The 5′ ends of a short, double-stranded DNA duplex are attached to a surface and an atomic force microscope cantilever via elastic poly(ethylene glycol) (PEG) polymers. Separation of the substrate and the cantilever at constant velocity leads to an increasing end-to-end distance and thus to an increasing force. (b) Superposition of 20 experimentally obtained force-extension traces obtained from the same 30-basepair 1 × 2 DNA duplex with a separation velocity of 1 μm/s. The duplex dissociates at ∼60–65 pN. (c) Schematic of the three-state model. Every basepair of the DNA duplex appears in one of three states: B-DNA, S-DNA, or single-stranded DNA. Every state s of an N-basepair-long DNA may thus be represented by a list of length N with entries 0 (B-DNA), 1 (S-DNA), and 2 (ssDNA) for every basepair.

Figure 2

(a) Force-extension traces obtained from phenomenological models for the three different states of double-stranded DNA. (b) Corresponding free-energy difference/basepair between B-DNA and ssDNA as well as between S-DNA and ssDNA. A free-energy penalty of 2.4 k_BT, the average basepair free energy of the 1 × 2 and 1 × 3 DNA duplexes, is introduced to the free energy of ssDNA due to the loss of basepairing interactions. Highlighted in black is the state that is thermodynamically most favorable. The most favorable state is B-DNA for forces <60 pN, S-DNA for forces between 60 pN and 130 pN, and ssDNA for forces >130 pN.

Figure 3

Force-extension data of short, double-stranded DNA attached to a surface and an atomic force microscope cantilever via a 5-kDa poly(ethylene glycol) linker for each strand. Data for 20 pulling experiments at a separation velocity of 1 μm/s was binned into 1-pN intervals and averaged (circles). The solid line is the corresponding fit of the model presented here. The dashed line represents the fit in the case where the DNA duplex remains in its canonical B-form. At <30 pN, the fit underestimates forces, an observation that we attribute to nonspecific interactions and entanglements with neighboring constructs on the surface. (Inset) For forces >30 pN, theory and experimental data agree within the experimental error.

Figure 4

(a) Calculated rupture-force distribution for the 1 × 2 and the 1 × 3 duplex for 50, 500, and 5000 nm/s pulling velocity. (b) Comparison of the experimental (gray bars) and calculated (lines) rupture-force distribution for the 1 × 2 and 1 × 3 duplex at 895 nm/s and 1007 nm/s, respectively. The calculated rupture-force distributions were convolved with a Gaussian cantilever detection noise of 4.7 pN. (c) Comparison of the experimental and calculated most probable rupture forces for different most probable loading rates. The gray data points refer to the experimental data and the black data points to the theory data. Squares refer to the 30-basepair DNA 1 × 2 duplex and triangles to the 20-basepair 1 × 3 duplex.

Figure 5

(a) Calculated effective barrier height, according to the standard Bell-Evans model. At forces between 10 and 50 pN, the free energy decreases proportionally to the applied force f. At forces >65 pN, when B-DNA is converted into S-DNA, the energy again decreases linearly, yet with a significantly smaller slope. (b) The negative derivative of the force versus free energy profile yields x_tst, the effective distance between the equilibrium state and the transition state. The dashed line represents the difference in end-to-end distance for B-DNA and ssDNA for the 1 × 2 DNA duplex as a function of force. (c) For forces <60 pN, x_tst reflects the increase in end-to-end distance from B-DNA to ssDNA. (d) For forces >65 pN, x_tst reflects the increase in end-to-end distance from S-DNA to ssDNA.