^{1}, Jiamin Wu

^{2}, Di Gao

^{2}and Jianzhong Wu

^{1,a)}

### Abstract

In a recent work [Gao *et al.*, Appl. Phys. Lett.134, 113902 (2007)], we reported a novel DNA separation method by tethering DNA chains to a solid surface and then stretching the DNA chains with an electric field. The anchor is such designed that the critical force to detach a DNA chain is independent of its length. Because the stretching force is proportional to the DNA net charge, a gradual increase of the electric field leads to size-based removal of the DNA strands from the surface and thus DNA separation. Originally proposed for separation of long double-stranded DNA chains (>10 000 bps), this method has been proven useful also for short single-stranded DNA fragments (<100 bases) for which the fluctuation force induced by the solvent becomes significant. Here we show that the fluctuation force can be approximately represented by a Gaussian model for tethered DNA chains. Analytical expressions have been derived to account for the dependence of the fluctuation force on the surface confinement, the polymer chain length, and the DNA tethering potential. The theoretical predictions are found to coincide with experiment.

The authors are grateful to the National Institute of Health for the financial support of this research (5R21HG004769-02).

I. INTRODUCTION

II. STATISTICS OF A TETHERED GAUSSIAN CHAIN

A. Grafted Gaussian chain

B. Semigrafted Gaussian chain

C. Fluctuation force in a tethered DNA

III. CONCLUSION AND DISCUSSION

### Key Topics

- DNA
- 65.0
- Polymers
- 22.0
- Bioelectrochemistry
- 19.0
- Electric fields
- 19.0
- Free energy
- 17.0

## Figures

Differential fluorescence intensity −*d*α(*E*)/*dE* vs electric field *E* for three short ssDNAs. From left to right the lines are corresponding to ssDNA chains with 90, 80, and 60 nucleotides.

Differential fluorescence intensity −*d*α(*E*)/*dE* vs electric field *E* for three short ssDNAs. From left to right the lines are corresponding to ssDNA chains with 90, 80, and 60 nucleotides.

Schematic representation of (a) grafted Gaussian chain and (b) semigrafted Gaussian chain. In both cases, the Gaussian chain is constrained in *z* > 0 half space with one end fixed at (0, 0, *z* _{0}) (for grafted chain) or anchored through a harmonic spring (for semigrafted chain). The planar wall is located at *z* = 0.

Schematic representation of (a) grafted Gaussian chain and (b) semigrafted Gaussian chain. In both cases, the Gaussian chain is constrained in *z* > 0 half space with one end fixed at (0, 0, *z* _{0}) (for grafted chain) or anchored through a harmonic spring (for semigrafted chain). The planar wall is located at *z* = 0.

Confinement free energy per segment for a grafted Gaussian chain in terms of chain length *N*. The solid line, the dashed-dotted line, and the dotted line correspond to *z* _{0}/*a* = 1, 2, and 3, respectively.

Confinement free energy per segment for a grafted Gaussian chain in terms of chain length *N*. The solid line, the dashed-dotted line, and the dotted line correspond to *z* _{0}/*a* = 1, 2, and 3, respectively.

Surface force for a grafted Gaussian chain in terms of chain length *N*. The solid line, the dashed-dotted line, and the dotted line correspond to *z* _{0}/*a* = 1, 2 and 3, respectively.

Surface force for a grafted Gaussian chain in terms of chain length *N*. The solid line, the dashed-dotted line, and the dotted line correspond to *z* _{0}/*a* = 1, 2 and 3, respectively.

Confinement free energy per segment for a semigrafted Gaussian chain as a function of chain length *N*. (a) spring constant *k*β*a* ^{2} = 1 and natural length *l* _{0}/*a* = 1 (solid line), 2 (dashed-dotted line), and 3 (dotted line); (b) *l* _{0}/*a* = 1 and *k*β*a* ^{2} = 1 (solid line), 2 (dashed-dotted line), and 3 (dotted line).

Confinement free energy per segment for a semigrafted Gaussian chain as a function of chain length *N*. (a) spring constant *k*β*a* ^{2} = 1 and natural length *l* _{0}/*a* = 1 (solid line), 2 (dashed-dotted line), and 3 (dotted line); (b) *l* _{0}/*a* = 1 and *k*β*a* ^{2} = 1 (solid line), 2 (dashed-dotted line), and 3 (dotted line).

The mean fluctuation force for a semigrafted Gaussian chain as a function of the chain length *N*. (a) spring constant *k*β*a* ^{2} = 1 and natural length *l* _{0}/*a* = 1 (solid line), 2 (dashed-dotted line), and 3 (dotted line); (b) *l* _{0}/*a* = 1 and *k*β*a* ^{2} = 1 (solid line), 2 (dashed-dotted line), and 3 (dotted line).

The mean fluctuation force for a semigrafted Gaussian chain as a function of the chain length *N*. (a) spring constant *k*β*a* ^{2} = 1 and natural length *l* _{0}/*a* = 1 (solid line), 2 (dashed-dotted line), and 3 (dotted line); (b) *l* _{0}/*a* = 1 and *k*β*a* ^{2} = 1 (solid line), 2 (dashed-dotted line), and 3 (dotted line).

The probability density of the fluctuation force for *N* = 90 predicted with three sets of spring parameters.

The probability density of the fluctuation force for *N* = 90 predicted with three sets of spring parameters.

Distribution of *Nq*ρ(*f* _{ t } − *NqE*) in terms of electric filed *E*: (a) Here the spring parameters are *k*β*a* ^{2} = 2, *l* _{0}/*a* = 1, and *f* _{ t } = 9/β*a*; the chain lengths are *N* = 60 (dotted blue line), 80 (dashed-dotted red line), and 90 (solid black line). (b) The chain length is fixed at *N* = 80, while the reduced rigidity and the natural spring length (*k*β*a* ^{2}, *l* _{0}/*a*) are (1, 1), (2, 1), and (2, 2) for the solid line, the dashed-dotted line, and dotted line, respectively. The parameter *f* _{ t } remains the same as in (a).

Distribution of *Nq*ρ(*f* _{ t } − *NqE*) in terms of electric filed *E*: (a) Here the spring parameters are *k*β*a* ^{2} = 2, *l* _{0}/*a* = 1, and *f* _{ t } = 9/β*a*; the chain lengths are *N* = 60 (dotted blue line), 80 (dashed-dotted red line), and 90 (solid black line). (b) The chain length is fixed at *N* = 80, while the reduced rigidity and the natural spring length (*k*β*a* ^{2}, *l* _{0}/*a*) are (1, 1), (2, 1), and (2, 2) for the solid line, the dashed-dotted line, and dotted line, respectively. The parameter *f* _{ t } remains the same as in (a).

Dependence of on the chain length for four ssDNA chains studied in experiment. Solid triangle is the data from Fig. 1, while the squared solid triangle is from supplementary experiment data in Ref. 3. The dotted line connects the first point (*N* = 60) and the last point (*N* = 90).

Dependence of on the chain length for four ssDNA chains studied in experiment. Solid triangle is the data from Fig. 1, while the squared solid triangle is from supplementary experiment data in Ref. 3. The dotted line connects the first point (*N* = 60) and the last point (*N* = 90).

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