Effects of kink and flexible hinge defects on mechanical responses of short double-stranded DNA molecules

We predict various detectable mechanical responses to the presence of local DNA defects which are defined as short DNA segments exhibiting mechanical properties obviously different from the 50 nm persistence length based semiflexible polymer model. The defects discussed are kinks and flexible hinges either permanently fixed on DNA or thermally excited. Their effects on extension shift, the effective persistence length, the end-to-end distance distribution, and the cyclization probability are computed using a transfer-matrix method. Our predictions will be useful in future experimental designs to study DNA nicks or mismatch base pairs, mechanics of specific DNA sequences, and specific DNA-protein interaction using magnetic tweezer, fluorescence resonance energy transfer, plasmon resonance techniques, and the traditional biochemistry cyclization probability measurements.

Figure 1

The effects of fixed defects on force-extension curve measurements. (a) The force-extension curve of 100 nm DNA that does not contain defects (solid curve), contains a single flexible hinge defect at center (dashed curve), and contains a single 90° kink defect at center (dotted curve). Inset shows the magnitude of the shift of the defect-containing DNA curves from the defect-free DNA curve. (b) The slopes are used to compute effective persistence lengths, which are found to be $\sim 36\text{nm}$ for the defect-free DNA, $\sim 30\text{nm}$ for the fixed flexible hinge containing DNA, and $\sim 22\text{nm}$ for the fixed kink containing DNA.

Figure 2

$⟨r^2⟩$ as functions of stretching force for defect-free and defect-containing DNA. The symbols are the same as in Fig. 1.

Figure 3

Effects of defects on scalar end-to-end distance distribution of 40 nm long DNA plotted in linear scale (a) and logarithm scale (b). In (a), curves for excited defects are nearly overlapped with defect-free DNA. The fixed defects are located in the middle of the DNA. For excited defects, excitation energy for the kink is $10k_{B}T$, and that for the flexible hinge is $11k_{B}T$.

Figure 4

The effects of the positions of fixed defects on the scalar distribution of end-to-end distance of 100 nm long DNA. (a) The positional effect of a fixed 90° kink. (b) The positional effect of a flexible hinge. In (a) and (b) the reference distributions of the defect-free DNA are displayed in gray. The dark curves, from top to bottom, are results computed for defect locations at 5, 10, 20, 30, and 50 nm from one end of the DNA, respectively.

Figure 5

$\mathit{J}$-factors as functions of DNA length. The fixed defects are located in the middle of the DNA. For excited defects, the excitation energy for the kink is $10k_{B}T$, and that for the flexible hinge is $11k_{B}T$.

Figure 6

The effect of separation of two fixed flexible hinge defects on the $\mathit{J}$-factor of 50 nm DNA.

Figure 7

Effects of defects on DNA looping under a free boundary condition. The fixed defects are in the middle of the DNA. For excitation of defects, the excitation energy for the kink is $10k_{B}T$ and that for the flexible hinge is $11k_{B}T$.

Figure 8

The dependence of looping probability on the meeting angle $\theta$ between the first and last tangent vector for 40 nm DNA. $\text{cos}\theta =1$ for a parallel boundary condition, while $\text{cos}\theta =-1$ for an antiparallel boundary condition. The symbols are the same as in Fig. 7.

Figure 9

Dependence of looping probability of 100 nm DNA on the positions of single fixed defects.