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Virtual Journal for Biomedical Optics

| EXPLORING THE INTERFACE OF LIGHT AND BIOMEDICINE

  • Editor: Gregory W. Faris
  • Vol. 4, Iss. 10 — Oct. 2, 2009
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Manipulation of single DNA molecules by using optically projected images

Yen-Heng Lin, Chen-Min Chang, and Gwo-Bin Lee  »View Author Affiliations


Optics Express, Vol. 17, Issue 17, pp. 15318-15329 (2009)
http://dx.doi.org/10.1364/OE.17.015318


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Abstract

A new platform is presented that is capable of manipulating a single DNA molecule based on optically-induced dielectrophoretic forces. The ends of a single DNA molecule are bound with a micro-bead, which is then manipulated by interactions with optical images projected from a commercially available projector. Thus a single DNA molecule is indirectly manipulated by a projected animation pre-programmed using simple computer software. Real-time observation of the manipulation process is made possible by using a fluorescent dye and an oxygen scavenging buffer. Two types of DNA manipulation modes, specifically DNA elongation and rotation, are successfully demonstrated and are characterized. The maximum stretching force can be as high as 61.3 pN for a 10.1 μm bead. Experimental data show that the force-extension curve measured using this platform fits reasonably with the worm-like chain model. The developed platform can be a promising and flexible tool for further applications requiring single molecule manipulation.

© 2009 OSA

1. Introduction

In the past two decades, investigating single DNA molecules has attracted considerable interest in the fields of biology and nanotechnology [1

1. J. Yuqiu, C.-B. Juang, D. Keller, C. Bustamante, D. Beach, T. Houseal, and E. Builes, “Mechanical, electrical, and chemical manipulation of single DNA molecules,” Nanotechnology 3(1), 16–20 (1992).

3

3. M. C. Williams, K. Pant, I. Rouzina, and R. L. Karpel, “Single molecule force spectroscopy studies of DNA denaturation by T4 gene 32 protein,” Spectroscopy 18, 203–211 (2004).

]. It has been envisioned that the ability to stretch a single DNA molecule will yield numerous scientific insights from measurements of the mechanical properties [4

4. S. B. Smith, L. Finzi, and C. Bustamante, “Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads,” Science 258(5085), 1122–1126 (1992). [PubMed]

] and the electrical properties [5

5. D. Porath, A. Bezryadin, S. de Vries, and C. Dekker, “Direct measurement of electrical transport through DNA molecules,” Nature 403(6770), 635–638 (2000). [PubMed]

] of a DNA elastic strand. Traditionally, relatively tedious procedures have been adopted to measure the properties of a DNA molecule including light scattering, sedimentation velocity, viscometry, electro-optics, and ligase-catalyzed cyclization [4

4. S. B. Smith, L. Finzi, and C. Bustamante, “Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads,” Science 258(5085), 1122–1126 (1992). [PubMed]

]. However, these traditional approaches can only estimate the DNA properties by indirect calculation based on theoretical models. In contrast, several tools capable of directly manipulating a single DNA molecule have been demonstrated including magnetic tweezers [4

4. S. B. Smith, L. Finzi, and C. Bustamante, “Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads,” Science 258(5085), 1122–1126 (1992). [PubMed]

,6

6. J. Zlatanova and S. H. Leuba, “Magnetic tweezers: a sensitive tool to study DNA and chromatin at the single-molecule level,” Biochem. Cell Biol. 81(3), 151–159 (2003). [PubMed]

8

8. C. H. Chiou, Y. Y. Huang, M. H. Chiang, H. H. Lee, and G. B. Lee, “New magnetic tweezers for investigation of the mechanical properties of single DNA molecules,” Nanotechnology 17(5), 1217–1224 (2006).

], an atomic force microscope (AFM) probe tip [9

9. A. Noy, D. V. Vezenov, J. F. Kayyem, T. J. Meade, and C. M. Lieber, “Stretching and breaking duplex DNA by chemical force microscopy,” Chem. Biol. 4(7), 519–527 (1997). [PubMed]

,10

10. T. Morii, R. Mizuno, H. Haruta, and T. Okada, “An AFM study of the elasticity of DNA molecules,” Thin Solid Films 464–465, 456–458 (2004).

], hydrodynamic forces [11

11. P. K. Wong, Y. K. Lee, and C. M. Ho, “Deformation of DNA molecules by hydrodynamic focusing,” J. Fluid Mech. 497, 55–65 (2003).

17

17. H. Y. Lin, L. C. Tsai, P. Y. Chi, and C. D. Chen, “Positioning of extended individual DNA molecules on electrodes by non-uniform AC electric fields,” Nanotechnology 16(11), 2738–2742 (2005).

], electrical driving forces [14

14. G. C. Randall, K. M. Schultz, and P. S. Doyle, “Methods to electrophoretically stretch DNA: microcontractions, gels, and hybrid gel-microcontraction devices,” Lab Chip 6(4), 516–525 (2006). [PubMed]

18

18. G. Maubach, A. Csaki, D. Born, and W. Fritzsche, “Controlled positioning of a DNA molecule in an electrode setup based on self-assembly and microstructuring,” Nanotechnology 14(5), 546–550 (2003).

], and optical tweezers [19

19. S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996). [PubMed]

23

23. C. Rusu, R. van’t Oever, M. J. de Boer, H. V. Jansen, J. W. Berenschot, M. L. Bennink, J. S. Kanger, B. G. de Grooth, M. Elwenspoek, J. Greve, J. Brugger, and A. van den Berg, “Direct integration of micromachined pipettes in a flow channel for single DNA molecule study by optical tweezers,” J. Microelectromech. Syst. 10(2), 238–246 (2001).

]. These direct approaches provide a more accurate method for investigation of the properties of a single DNA molecule.

For instance, the use of magnetic tweezers can directly measure the elasticity of a single DNA molecule [4

4. S. B. Smith, L. Finzi, and C. Bustamante, “Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads,” Science 258(5085), 1122–1126 (1992). [PubMed]

]. Different salt concentrations with forces ranging from 0.01 to 10 pN have been investigated in this platform. Also, the tension and torsion forces present in magnetic tweezers is used to study the behavior of single a DNA molecule [6

6. J. Zlatanova and S. H. Leuba, “Magnetic tweezers: a sensitive tool to study DNA and chromatin at the single-molecule level,” Biochem. Cell Biol. 81(3), 151–159 (2003). [PubMed]

]. Additionally, magnetic tweezers generated by micro-fabricated copper coils have been presented by our research group [7

7. C. H. Chiou and G. B. Lee, “A micromachined DNA manipulation platform for the stretching and rotation of a single DNA molecule,” J. Micromech. Microeng. 15(1), 109–117 (2005).

, 8

8. C. H. Chiou, Y. Y. Huang, M. H. Chiang, H. H. Lee, and G. B. Lee, “New magnetic tweezers for investigation of the mechanical properties of single DNA molecules,” Nanotechnology 17(5), 1217–1224 (2006).

]. Either two-dimensional or three-dimensional micro-coils can be integrated onto a microfluidic chip to produce a local magnetic force for stretching a single DNA molecule. However, the use of magnetic tweezers may not provide enough spatial resolution. The calibration of the applied magnetic force is also relatively difficult. Another useful tool to manipulate a DNA molecule and to measure its mechanical properties is to use an AFM probe tip [9

9. A. Noy, D. V. Vezenov, J. F. Kayyem, T. J. Meade, and C. M. Lieber, “Stretching and breaking duplex DNA by chemical force microscopy,” Chem. Biol. 4(7), 519–527 (1997). [PubMed]

]. One end of a DNA molecule is attached onto the tip of an AFM probe while the other end is covalently bonded onto the surface of a substrate. Then the DNA molecule is pulled by the AFM probe to measure the DNA extension lengths [10

10. T. Morii, R. Mizuno, H. Haruta, and T. Okada, “An AFM study of the elasticity of DNA molecules,” Thin Solid Films 464–465, 456–458 (2004).

]. This provides a straightforward method to directly investigate the elasticity of a DNA molecule. Nonetheless, the cost of an AFM and its probe are relatively high.

Hydrodynamic forces have also been widely employed to stretch a single DNA molecule. A micro-channel is used to achieve hydrodynamic focusing to elongate a single DNA molecule in the sample flow [11

11. P. K. Wong, Y. K. Lee, and C. M. Ho, “Deformation of DNA molecules by hydrodynamic focusing,” J. Fluid Mech. 497, 55–65 (2003).

]. A low-Reynolds-number flow can be setup in a micro-channel, so that a long focused stream can be used to extend a DNA molecule. Furthermore, a nano-scale channel has been reported to stretch a DNA molecule through a similar hydrodynamic approach. Either a rectangular [12

12. L. Guo, X. Cheng, and C. F. Chou, “Fabrication of size-controllable nanofluidic channels by nanoimprinting and its application for DNA stretching,” Nano Lett. 4(1), 69–73 (2004).

] or funnel-shape [13

13. J. Gu, R. Gupta, C. F. Chou, Q. Wei, and F. Zenhausern, “A simple polysilsesquioxane sealing of nanofluidic channels below 10 nm at room temperature,” Lab Chip 7(9), 1198–1201 (2007). [PubMed]

] nano-channel can be used to achieve this function. In addition, applying an electric field inside a nano-channel has also been demonstrated for DNA stretching [14

14. G. C. Randall, K. M. Schultz, and P. S. Doyle, “Methods to electrophoretically stretch DNA: microcontractions, gels, and hybrid gel-microcontraction devices,” Lab Chip 6(4), 516–525 (2006). [PubMed]

16

16. L. C. Campbell, M. J. Wilkinson, A. Manz, P. Camilleri, and C. J. Humphreys, “Electrophoretic manipulation of single DNA molecules in nanofabricated capillaries,” Lab Chip 4(3), 225–229 (2004). [PubMed]

]. Fluids in the nano-channel can be driven by an electrokinetic force and thus a single DNA molecule can be elongated. Another ingenious method which uses a combination of hydrodynamic forces and an electric field was also reported to elongate a single DNA molecule [17

17. H. Y. Lin, L. C. Tsai, P. Y. Chi, and C. D. Chen, “Positioning of extended individual DNA molecules on electrodes by non-uniform AC electric fields,” Nanotechnology 16(11), 2738–2742 (2005).

]. This method can position the DNA without modifying its terminal bonds. Moreover, a single DNA molecule can be placed at a defined position on micro-fabricated metal electrodes using electrically driven self-assembly steps [18

18. G. Maubach, A. Csaki, D. Born, and W. Fritzsche, “Controlled positioning of a DNA molecule in an electrode setup based on self-assembly and microstructuring,” Nanotechnology 14(5), 546–550 (2003).

]. With this approach, DNA molecules with lengths in the micrometer range can be immobilized in the gap between the electrodes. However, even though the hydrodynamic force and the electric field can be used to elongate the DNA molecules, it is difficult to measure the applied force in such methods. Also, the fabrication process for a nano-scale channel is relatively complex and may be costly.

Alternatively, optical tweezers have been widely used to investigate the elasticity of a single DNA molecule. The force-extension curve has been precisely measured by optical tweezers [19

19. S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996). [PubMed]

,20

20. M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997). [PubMed]

]. A DNA molecule can be stretched to about 70% under a transition force of about 65 pN [20

20. M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997). [PubMed]

]. Different lengths of single- and double-stranded DNA were also investigated using optical tweezers [21

21. M. Salomo, K. Kegler, C. Gutsche, M. Struhalla, J. Reinmuth, W. Skokow, H. Hahn, and F. Kremer, “The elastic properties of single double-stranded DNA chains of different lengths as measured with optical tweezers,” Colloid Polym. Sci. 284(11), 1325–1331 (2006).

]. Furthermore, fluorescent-stained DNA molecules were stretched and observed in real-time while manipulated by optical tweezers [22

22. M. L. Bennink, O. D. Schärer, R. Kanaar, K. Sakata-Sogawa, J. M. Schins, J. S. Kanger, B. G. de Grooth, and J. Greve, “Single-molecule manipulation of double-stranded DNA using optical tweezers: interaction studies of DNA with RecA and YOYO-1,” Cytometry 36(3), 200–208 (1999). [PubMed]

]. Recently, due to advances in micro-machining techniques, optical tweezers has also been integrated with micro-pipettes and micro-channels on a single chip [23

23. C. Rusu, R. van’t Oever, M. J. de Boer, H. V. Jansen, J. W. Berenschot, M. L. Bennink, J. S. Kanger, B. G. de Grooth, M. Elwenspoek, J. Greve, J. Brugger, and A. van den Berg, “Direct integration of micromachined pipettes in a flow channel for single DNA molecule study by optical tweezers,” J. Microelectromech. Syst. 10(2), 238–246 (2001).

]. However, although optical tweezers can precisely manipulate a single DNA molecule with controllable applied forces, the experimental setup is relatively complicated and expensive.

Recently, a new technology which is referred to as optoelectronic tweezers (OET) or optically-induced dielectrophoresis (ODEP) has been applied to manipulate micro-particles [24

24. P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005). [PubMed]

]. It is a flexible and user-friendly approach to manipulate a micro-particle to a desired position by using optical patterns, illuminated from a commercial projector. Recently, the OET has been reported to enable manipulation of nano-wires [25

25. A. Jamshidi, P. J. Pauzauskie, P. J. Schuck, A. T. Ohta, P.-Y. Chiou, J. Chou, P. Yang, and M. C. Wu, “Dynamic manipulation and separation of individual semiconducting and metallic nanowires,” Nat. Photonics 2(2), 86–89 (2008). [PubMed]

]. In this study, we demonstrate a new approach capable of stretching and revolving a single DNA molecule under real-time observation by using the ODEP platform. To the best of authors’ knowledge, this is the first time that ODEP has been used for the extension of a single DNA molecule. This developed platform can provide a simple and flexible tool to manipulate a single DNA molecule.

2. Materials and methods

2.1 Chip design

The experimental procedures are described as follows. First, two ends of a λ-phage DNA are modified with biotin in order to attach onto micro-beads or a substrate. The modified DNA and the micro-bead surface-modified with streptavidin are then incubated together to form the tethered-bead DNA. Meanwhile, the DNA is stained with fluorescent dye so that it can be observed in real-time. Then the tethered-bead DNA is placed into the ODEP platform. Finally, a high-frequency driving voltage is provided and an optical image is projected to manipulate the single DNA molecule. Before the DNA elongation process, one end of the DNA is anchored onto the substrate while the other end is bound with a micro-bead (Fig. 1(a)
Fig. 1 Schematic illustration of (a) the stretching of a single DNA molecule by using the ODEP platform. One end of the DNA is anchored onto the substrate and the other end of DNA is bound with a micro-bead. The ODEP platform can manipulate the micro-bead and thus, correspondingly, the attached DNA molecule. (b) Rotation of the tethered-DNA molecule is achieved by projecting a moving optical image.
). When an optical image is projected on a photoconductive substrate, the micro-bead can be manipulated to any position programmed by computer software and thus a single DNA molecule can be stretched indirectly. The elongation process can be then utilized to investigate the mechanic properties of single DNA molecules. Figure 1(b) also illustrates that a DNA molecule can be rotated either clockwise or counter-clockwise through the animation of optical images generated by computer software. This provides an extremely flexible and simple approach to manipulate a single DNA molecule.

Figure 2(a)
Fig. 2 (a) Conceptual illustration of the generation of the ODEP force. The ODEP chip consists of a top and a bottom layer. The top layer is an ITO glass and the bottom layer is another ITO glass deposited with amorphous silicon as a photoconductive layer. When the top and the bottom ITO layers are applied with an AC voltage, the electron-hole pairs are excited and thus the AC voltage will drop across the fluid layer when a light illuminates the photoconductive layer. Then the micro-bead experiences a dielectrophoresis force induced by this non-uniform electric field. (b) Schematic illustration of biotinylated deoxynucleoside triphosphates modified withλ-DNA sticky ends by using the Klenow fragment (3′→5′ exo-). Biotin is labeled at the ends of DNA through modified deoxynucleoside triphosphates, and dCTP-11-biotin.
is a schematic illustration of the ODEP platform. The ODEP chip consists of a top indium-tin-oxide (ITO) glass substrate and a bottom ITO glass substrate with a photoconductive layer. The top and bottom ITO glasses are supplied with an alternating-current (AC) voltage. Before the light source illuminates the photoconductive layer, it has a high electrical impedance. After the light hits the photoconductive layer, electron-hole pairs can be excited and thus the impedance of the amorphous layer can be decreased by 4-5 orders of magnitude. Hence, the applied voltage will drop across the liquid layer and change the balance in the electric field, thus inducing a non-uniform electric field distribution between the top and bottom ITO glasses. The micro-beads are then induced with a DEP force when they are exposed to this non-uniform electric field. Therefore, the micro-beads can be manipulated by the optical image illuminating the photoconductive layer.

The time-averaged DEP force representing the interaction between the electric field and the induced dipole moment can be described as follows [26

26. X. B. Wang, Y. Huang, F. F. Becker, and P. R. C. Gascoyne, “A unified theory of dielectrophoresis and travelling wave dielectrophoresis,” J. Phys. D Appl. Phys. 27(7), 1571–1574 (1994).

]:
FDEP=2πr3εmRe(fCM)E2
(1)
where r is the radius of micro-beads, εm is the permittivity of the media surrounding the micro-beads, E is the root-mean-square value of the local electric field, and Re(fCM) is the real part of the Clausius–Mossotti factor, which can be represented as follows:
fCM(ω)=εp*εm*εp*+2εm*,εp*=εpjσpω,εm*=εmjσmω
(2)
where σ is the conductivity of the micro-bead (p) or the medium (m), and ω is the angular frequency of the electric field.

2.2 Microfabrication

2.3 Sample preparation

The λ-phage DNA is purchased from New England Biolabs, USA. It is a double-stranded DNA helix comprised of 48,502 base pairs with a length of about 16-μm. Both ends are single-stranded with the 5′ ends overhanging with the following 12-base sequences, 5′ AGGTCGCCGCCC and 5′ GGGCGGCGACCT, where A, C, G, and T are the nucleotides adenine, cytosine, guanine, and thymine, respectively. The DNA molecules are stored in Tris-EDTA (TE) buffer with 10 mM Tris-HCl (pH 8.0) and 1 mM EDTA.

2.3.1 Biotin modification of the DNA extremities

In this study, a biotinylation technique based on biotinylated deoxynucleoside triphosphates is adopted [28

28. Y. Zhang, R. H. Austin, J. Kraeft, E. C. Cox, and N. P. Ong, “Insulating behavior of λ-DNA on the micron scale,” Phys. Rev. Lett. 89(19), 198102 (2002). [PubMed]

]. Figure 2(b) is a conceptual illustration for biotinylating two ends of a λ-phage DNA molecule. The biotinylated deoxynucleoside triphosphate, dCTP-11-biotin (NEL538001EA, PerkinElmer, USA), and three other deoxynucleoside triphosphates including dATP, dGTP, and dTTP (Promega, USA) are mixed together and then are incorporated in the λ-phage DNA by using a Klenow fragment of DNA polymerase (New England Biolabs, USA). The reaction is incubated at 37°C for 24 hours. Then the corresponding deoxynucleoside triphosphate has filled in the 5′ overhanging λ-phage DNA and thus the biotin is now attached on the ends of the DNA strand.

In order to remove excess deoxynucleoside triphosphates and reaction enzyme, the biotinylated λ-phage DNA is purified using a phenol/chloroform extraction and an ethanol precipitation. First, the biotinylated DNA is mixed with a phenol/chloroform/isoamyl alcohol mixture to remove any protein contaminants. Then, the DNA is precipitated with 100% ethanol and 3 M sodium acetate. Finally, the DNA is washed with 70% ethanol to remove salts and small organic molecules. It is then re-suspended in 50 mM Tris buffer without any ethylenediaminetetraacetic acid (EDTA) and hydrochloric acid. Because any ions contained in the buffer would decrease the ODEP force, all ionic species should be avoided in the working buffer.

The biotinylated λ-phage DNA is then suspended in 50 ng/μl of Tris buffer (50 mM Tris (pH 8.0)) for bead attachment. Two sizes of beads (4.5- and 10.1-μm) are used in this study. The 4.5-μm beads with a tosylactivated group (M-450 tosylactivated, Dynal, Norway) are first conjugated with a streptavidin molecule (10 μg/ml) by directly incubating for 2 hours. The 4.5-μm beads are the largest commercially-available ones conjugated with the tosylactivated group. In order to increase the induced force, the 10.1-μm polystyrene beads are surface-modified using a surface charge modification method. The 10.1-μm polystyrene (Duke Scientific, USA) beads are first modified with polyethylenimine (PEI, 10−3 M, Sigma-Aldrich, USA) to give them a positive surface charge by incubating them for 24 hours. Then the positively-charge beads are incubated with streptavidin molecules (10 μg/ml) for 2 hours. The negatively-charged streptavidin adheres to the surface of the polystyrene bead because of its affinity for positive charges. After the beads are modified with streptavidin, a concentration of 5x106 beads/ml is mixed together with the modified λ-phage DNA for at least 30 minutes. The beads will either randomly bind to either one or both ends of the DNA.

Since a DNA molecule is about 2 nm in diameter, it is difficult to directly observe it under a microscope. In order to visualize the stretching process of a single DNA molecule in real-time, YOYO-1 dyes (Molecular Probes Inc., USA) are used to stain the DNA molecule. The optimal staining condition is to keep the base pair to dye molecule ratio at 5:1. In order to extend the observation time before the fluorescent dye becomes bleached, the stained DNA solution is mixed with 4% β-mercaptoethanol, 50 g/ml glucose oxidase, and 2% glucose. Note that a catalase should be avoided because it would decrease the ODEP force dramatically [7

7. C. H. Chiou and G. B. Lee, “A micromachined DNA manipulation platform for the stretching and rotation of a single DNA molecule,” J. Micromech. Microeng. 15(1), 109–117 (2005).

]. The stained DNA in this oxygen scavenging buffer can be observed for at least 10 minutes.

2.4 Experimental setup

Figure 3
Fig. 3 The experimental setup for the manipulation of a single DNA molecule by using the ODEP platform.
is a schematic illustration of the experimental setup for the DNA manipulation platform. The ODEP chip is mounted in a commercial microscope (BX-41, Olympus, Japan) for DNA observation and manipulation, which is equipped with a xenon light source (75 W xenon lamp, UXL-S75XE, Ushio Inc., Japan) and a filter set (excitation filter: 460-490 nm, dichroic mirror: 505 nm, emission filter: 515-550 nm, U-MWIBA, Olympus, Japan). A 60x oil-immersion objective lens is used to resolve the fluorescence image of a single DNA molecule. In order to manipulate DNA by using optical images, a commercial liquid crystal display (LCD) projector (TLP-X3000, TOSHIBA, Japan) connected to a personal computer is placed under the microscope. An objective lens and a 45° mirror (RPB3-10-550, Onset Electro-optics, Taiwan) are used to collect and to guide the optical image onto the ODEP chip. A function generator (Model 195, Wavetek, U.K.) and a power amplifier (790 Series, AVC Instrumentation, USA) are used to supply an AC voltage to generate the ODEP force. Finally, the evidence of DNA manipulation is recorded by a cooled charge-coupled device (CCD, CCD-300T-RC, DAGE-MTI, USA) connected to an image integrator (Investigator, DAGE-MTI, USA).

3. Results and discussion

In this study, we presented a new platform utilizing an ODEP force to manipulate a single DNA molecule. The single DNA molecule can be stretched or rotated simply by an optical image displayed from a commercial projector that is controlled by computer software. Using this platform, a DNA molecule can be manipulated by either fine-tuning the applied voltage while fixing the optical image or by fixing the applied voltage while moving the optical image. Furthermore, the applied force generated by the ODEP platform and the corresponding elongation length of the DNA molecule are also characterized.

3.1 Stretching DNA by fine-tuning the magnitude of the ODEP force

Figure 4
Fig. 4 A single DNA molecule is stretched by gradually increasing the magnitude of the applied voltage, thus increasing the repelling ODEP force. At larger applied voltages, the DNA molecule is stretched longer (Media 1).
shows a single DNA molecule stretched by fine-tuning the magnitude of the ODEP force. The two ends of the DNA strand are first attached with micro-beads and stained with fluorescent dye. Then the bead-tethered DNA is placed into the ODEP chip. Some of the micro-beads would attach onto the surface of the chip substrate due to physical absorption. In Fig. 4, the micro-bead at the center is anchored to the substrate. A line-shaped light is projected under the anchored micro-bead to induce the required ODEP force. Due to the fact that the other end of the bead-tethered DNA bead is free floating, it is repelled by the negative ODEP force and thus the DNA molecule is elongated indirectly. The applied voltage ranges from 0 to 86.7 Vpp with a frequency of 70 kHz. Experimental data show that the higher the applied voltage, the longer the DNA is extended. The elongation length can be determined according by gradually increasing the magnitude of the ODEP force. The free micro-bead is repelled from the illuminated line when the ODEP repulsive force is in equilibrium with the DNA elastic force. At an operating condition of 86.7 Vpp, the DNA molecule is stretched to a length of 15.9-μm. This demonstrates that a single DNA molecule can be stretched to more than 90% of its length by applying a force less than 0.5 pN [4

4. S. B. Smith, L. Finzi, and C. Bustamante, “Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads,” Science 258(5085), 1122–1126 (1992). [PubMed]

]. In this study, the experimental data show that the illuminated light can provide a sufficient force to elongate the DNA molecule. The stretching force generated by the ODEP force is calculated according to the worm-like chain (WLC) model [30

30. J. F. Marko and E. D. Siggia, “Stretching DNA,” Macromolecules 28(26), 8759–8770 (1995).

]:
FelasticityPKbT=14[1RL]214+RL
(3)
where Felasticity represents the DNA stretching force and R represents the DNA extension length. DNA has a typical persistence length (P) of about 50 nm. The contour length of the λ-DNA (L) is about 20-μm for a base pair to dye molecule ratio of 5:1. The thermal energy at 25 C (KbT) is about 4.1×10−21 J. For the DNA extension length of 15.9-μm with the aforementioned operating conditions, the theoretical DNA stretching force is calculated to be 0.53 pN. Other stretching forces can be calculated using a similar approach.

3.2 Stretching and manipulating DNA using optical images

Another method to stretch a DNA molecule is to utilize an animated optical image projecting onto the chip. Figure 5
Fig. 5 A single DNA molecule is elongated by the interaction of a tethered micro-bead and optical images.
shows that a single DNA molecule can be successfully stretched by a series of optical images. The tethered-bead DNA is first placed into the ODEP chip. Some of the ends of the DNA are randomly attached onto the surface of the chip due to physical absorption. Under the fluorescent microscope, a DNA molecule is found with one end bound to a micro-bead and the other end with the substrate. A negative ODEP force is generated and a moving circular optical image is used to trap the micro-bead. Thus a single DNA molecule can be stretched to a programmed position with the aid of computer software. Also, it is also found that the concentration of the Tris buffer cannot be below 20 mM to avoid the adsorption of the DNA molecule onto the bead surface, after which the DNA molecule cannot be manipulated.

A similar method can be used to rotate a DNA molecule. Figure 6
Fig. 6 A bead-tethered single DNA molecule can be rotated either clockwise or counter-clockwise by using a moving optical image projected through a commercial projector (Media 2).
shows that a single DNA molecule can be successfully rotated either clockwise or counter-clockwise by a moving optical image. Note that, in order to visualize the manipulation of a single DNA molecule, the illumination light intensity has to be decreased by reducing the green component of the projector light source. The fluorescent dye, YOYO-1, staining the DNA molecule is excited at about a 509 nm wavelength which corresponds to a green color. The light source used to generate the required ODEP force may interfere with observations of the fluorescent DNA molecule. Reducing the green component of the light source will help improve observation of the manipulation process. However, some manipulation force will be sacrificed due to the decrease in overall illumination intensity. The operating conditions for stretching and rotating are 86.7 Vpp at 70 kHz with a reduced power intensity of 11.7 W/cm2. Note that the moving optical images are programmed by commercial software (FLASH) and projected onto the photoconductive material through a commercially available projector. In addition, the reduction in the green light is also controlled by the same software and the green intensity is set to be 200 on a full scale of 0~255. The most important contribution of this platform is its flexibility in manipulating the bead-tethered DNA through animated optical images programmed in a computer. Besides, the components of this platform are simpler than any other optical system for the manipulation of a single DNA molecule. For example, the optical tweezers system requires an extremely precise motion control system for manipulating a single DNA molecule. In contrast, by using the ODEP platform, one can easily manipulate DNA molecules with micrometer precision through computer-generated optical images.

3.3 Characterization of the ODEP forces for DNA extension

In order to characterize the applied force for DNA extension in this ODEP platform, a micro-bead is moved at a terminal velocity which is when the drag force acting on the micro-bead is in balance with the applied ODEP force. During the experimental process, the 10.1 and 4.5 μm beads were manipulated between a gap with a height of 15 μm. It is more accurate to include the wall effect in force calibration. Therefore, the DNA extension force is calculated based on the modified Stokes’ law [8

8. C. H. Chiou, Y. Y. Huang, M. H. Chiang, H. H. Lee, and G. B. Lee, “New magnetic tweezers for investigation of the mechanical properties of single DNA molecules,” Nanotechnology 17(5), 1217–1224 (2006).

]:
F=6πrηv(1+9r16h)
(4)
where r denotes the radius of the micro-bead, η denotes the viscosity of the fluid, h denotes the height of the gap, and v denotes the terminal velocity of the micro-bead. The term 9r/16h is the modified term when considering the wall effect in Stoke’s law. Figure 7
Fig. 7 Relationship between the generated ODEP force and the applied voltage for 4.5- and 10.1-μm beads. The ODEP force is calibrated by Stokes’ law using the balance of the ODEP force and the drag force at the terminal velocity of the micro-bead.
shows the relationship between the applied voltage and the ODEP force. Experimental data show that the induced force is increased when raising the applied voltage. The maximum force for DNA extension is measured to be about 61.3 pN for a 10.1-μm bead at an applied voltage of 86.7 Vpp and a frequency of 70 kHz when an illuminating power intensity of 17.2 W/cm2 is used. Obviously, the larger the bead size, the greater the ODEP force that can be generated. However, according to the experimental results, when the bead size is more than 10.1-μm, it is difficult to bind the DNA ends with such large micro-beads. It is due to the fact that beads more than 10.1-μm have a large enough surface area such that the entire single DNA molecule would easily attach along the bead surface [29

29. S. C. Huang, M. D. Stump, R. Weiss, and K. D. Caldwell, “Binding of biotinylated DNA to streptavidin-coated polystyrene latex: effects of chain length and particle size,” Anal. Biochem. 237(1), 115–122 (1996). [PubMed]

] and the DNA molecule cannot be manipulated in this situation. Another important parameter affecting the ODEP force is the illumination power of the light source. During the manipulation process, in order to visualize the extending DNA molecule, reducing the green part of the illumination light source is necessary, as mentioned previously. Nevertheless, this also decreases the ODEP force since the illumination power is decreased from 17.2 W/cm2 to 11.7 W/cm2. Therefore, for the 10.1- and 4.5-μm beads, the ODEP forces are decreased about 5.0 times and 3.7 times, respectively.

Figure 8
Fig. 8 (a) Relationship between the applied ODEP force and the extension length of a single DNA molecule. (b) Experimental data show that the trend in elongation length is consistent with the WLC model.
shows the relationship between the stretching force and the elongation length of a single DNA molecule with 4.5- and 10.1-μm beads. The stretching force is controlled by the applied voltage. Note that the ODEP platform requires a threshold driving voltage to generate the dielectrophoretic force. This is due to the fact that enough electron-hole pairs in the amorphous silicon have to be excited to induce the ODEP force. The threshold values of the driving voltages are experimentally found to both be 4.5 Vpp. For the 4.5- and 10.1-μm beads, the corresponding ODEP forces at these driving voltages are estimated to be about 0.8 and 28.9 pN at the full illuminating power, respectively. As shown in Fig. 8(a), the initial extension length for the 4.5- and 10.1-μm beads are measured to be 15.1- and 19.3-μm, respectively. When compared with the WLC model, this is suitable for estimating the extension length at an applied force of less than 5 pN [30

30. J. F. Marko and E. D. Siggia, “Stretching DNA,” Macromolecules 28(26), 8759–8770 (1995).

], the trend in the force-extension curve measured with the ODEP platform is consistent with the one predicted by the WLC model (Fig. 8(b)). For 10.1-μm beads, the ODEP forces are estimated to be from 30.7 to 61.3 pN, which is within the β-form DNA range [19

19. S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996). [PubMed]

]. This indicates that the ODEP platform can be used for further DNA investigation. The developed platform therefore provides a simple and flexible approach to manipulate and to characterize a single DNA molecule. It also could be a promising tool for the manipulation of protein molecules.

4. Conclusion

We have demonstrated a new platform for the manipulation of a single DNA molecule by using optical images projected from a commercially available projector. No complex photolithography and metal patterning processes were used to fabricate the device. Also, no complicated and expensive optical module was needed to setup this platform. A single DNA molecule was successfully stretched and rotated clockwise and counter-clockwise using this platform. A fluorescent dye and an oxygen scavenging buffer were used during the manipulation process so that the DNA molecule can be observed in real-time. The maximum force was measured to be 61.3 pN. Force-extension curves measured by this platform fit well with the WLC model. The developed platform offers a simple and flexible approach to investigate a single DNA molecule and also provides a promising tool for further macro-molecule manipulation such as protein molecules.

Acknowledgements

The authors would like to thank Chi-Mei Optoelectronics Inc. and Dr. T. C. Tseng’s Lab for technical support. We would also like to thank the Ministry of Education, Taiwan, R.O.C. for partial financial support under the NCKU Project of Promoting Academic Excellence & Developing World Class Research Centers. Partial financial support from the National Science Council is also greatly appreciated.

References and links

1.

J. Yuqiu, C.-B. Juang, D. Keller, C. Bustamante, D. Beach, T. Houseal, and E. Builes, “Mechanical, electrical, and chemical manipulation of single DNA molecules,” Nanotechnology 3(1), 16–20 (1992).

2.

J. Zlatanova and S. H. Leuba, “Stretching and imaging single DNA molecules and chromatin,” J. Muscle Res. Cell Motil. 23(5-6), 377–395 (2002).

3.

M. C. Williams, K. Pant, I. Rouzina, and R. L. Karpel, “Single molecule force spectroscopy studies of DNA denaturation by T4 gene 32 protein,” Spectroscopy 18, 203–211 (2004).

4.

S. B. Smith, L. Finzi, and C. Bustamante, “Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads,” Science 258(5085), 1122–1126 (1992). [PubMed]

5.

D. Porath, A. Bezryadin, S. de Vries, and C. Dekker, “Direct measurement of electrical transport through DNA molecules,” Nature 403(6770), 635–638 (2000). [PubMed]

6.

J. Zlatanova and S. H. Leuba, “Magnetic tweezers: a sensitive tool to study DNA and chromatin at the single-molecule level,” Biochem. Cell Biol. 81(3), 151–159 (2003). [PubMed]

7.

C. H. Chiou and G. B. Lee, “A micromachined DNA manipulation platform for the stretching and rotation of a single DNA molecule,” J. Micromech. Microeng. 15(1), 109–117 (2005).

8.

C. H. Chiou, Y. Y. Huang, M. H. Chiang, H. H. Lee, and G. B. Lee, “New magnetic tweezers for investigation of the mechanical properties of single DNA molecules,” Nanotechnology 17(5), 1217–1224 (2006).

9.

A. Noy, D. V. Vezenov, J. F. Kayyem, T. J. Meade, and C. M. Lieber, “Stretching and breaking duplex DNA by chemical force microscopy,” Chem. Biol. 4(7), 519–527 (1997). [PubMed]

10.

T. Morii, R. Mizuno, H. Haruta, and T. Okada, “An AFM study of the elasticity of DNA molecules,” Thin Solid Films 464–465, 456–458 (2004).

11.

P. K. Wong, Y. K. Lee, and C. M. Ho, “Deformation of DNA molecules by hydrodynamic focusing,” J. Fluid Mech. 497, 55–65 (2003).

12.

L. Guo, X. Cheng, and C. F. Chou, “Fabrication of size-controllable nanofluidic channels by nanoimprinting and its application for DNA stretching,” Nano Lett. 4(1), 69–73 (2004).

13.

J. Gu, R. Gupta, C. F. Chou, Q. Wei, and F. Zenhausern, “A simple polysilsesquioxane sealing of nanofluidic channels below 10 nm at room temperature,” Lab Chip 7(9), 1198–1201 (2007). [PubMed]

14.

G. C. Randall, K. M. Schultz, and P. S. Doyle, “Methods to electrophoretically stretch DNA: microcontractions, gels, and hybrid gel-microcontraction devices,” Lab Chip 6(4), 516–525 (2006). [PubMed]

15.

J. M. Kim and P. S. Doyle, “Design and numerical simulation of a DNA electrophoretic stretching device,” Lab Chip 7(2), 213–225 (2007). [PubMed]

16.

L. C. Campbell, M. J. Wilkinson, A. Manz, P. Camilleri, and C. J. Humphreys, “Electrophoretic manipulation of single DNA molecules in nanofabricated capillaries,” Lab Chip 4(3), 225–229 (2004). [PubMed]

17.

H. Y. Lin, L. C. Tsai, P. Y. Chi, and C. D. Chen, “Positioning of extended individual DNA molecules on electrodes by non-uniform AC electric fields,” Nanotechnology 16(11), 2738–2742 (2005).

18.

G. Maubach, A. Csaki, D. Born, and W. Fritzsche, “Controlled positioning of a DNA molecule in an electrode setup based on self-assembly and microstructuring,” Nanotechnology 14(5), 546–550 (2003).

19.

S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996). [PubMed]

20.

M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997). [PubMed]

21.

M. Salomo, K. Kegler, C. Gutsche, M. Struhalla, J. Reinmuth, W. Skokow, H. Hahn, and F. Kremer, “The elastic properties of single double-stranded DNA chains of different lengths as measured with optical tweezers,” Colloid Polym. Sci. 284(11), 1325–1331 (2006).

22.

M. L. Bennink, O. D. Schärer, R. Kanaar, K. Sakata-Sogawa, J. M. Schins, J. S. Kanger, B. G. de Grooth, and J. Greve, “Single-molecule manipulation of double-stranded DNA using optical tweezers: interaction studies of DNA with RecA and YOYO-1,” Cytometry 36(3), 200–208 (1999). [PubMed]

23.

C. Rusu, R. van’t Oever, M. J. de Boer, H. V. Jansen, J. W. Berenschot, M. L. Bennink, J. S. Kanger, B. G. de Grooth, M. Elwenspoek, J. Greve, J. Brugger, and A. van den Berg, “Direct integration of micromachined pipettes in a flow channel for single DNA molecule study by optical tweezers,” J. Microelectromech. Syst. 10(2), 238–246 (2001).

24.

P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005). [PubMed]

25.

A. Jamshidi, P. J. Pauzauskie, P. J. Schuck, A. T. Ohta, P.-Y. Chiou, J. Chou, P. Yang, and M. C. Wu, “Dynamic manipulation and separation of individual semiconducting and metallic nanowires,” Nat. Photonics 2(2), 86–89 (2008). [PubMed]

26.

X. B. Wang, Y. Huang, F. F. Becker, and P. R. C. Gascoyne, “A unified theory of dielectrophoresis and travelling wave dielectrophoresis,” J. Phys. D Appl. Phys. 27(7), 1571–1574 (1994).

27.

Y. H. Lin and G. B. Lee, “Optically induced flow cytometry for continuous microparticle counting and sorting,” Biosens. Bioelectron. 24(4), 572–578 (2008). [PubMed]

28.

Y. Zhang, R. H. Austin, J. Kraeft, E. C. Cox, and N. P. Ong, “Insulating behavior of λ-DNA on the micron scale,” Phys. Rev. Lett. 89(19), 198102 (2002). [PubMed]

29.

S. C. Huang, M. D. Stump, R. Weiss, and K. D. Caldwell, “Binding of biotinylated DNA to streptavidin-coated polystyrene latex: effects of chain length and particle size,” Anal. Biochem. 237(1), 115–122 (1996). [PubMed]

30.

J. F. Marko and E. D. Siggia, “Stretching DNA,” Macromolecules 28(26), 8759–8770 (1995).

OCIS Codes
(350.4855) Other areas of optics : Optical tweezers or optical manipulation

ToC Category:
Optical Trapping and Manipulation

History
Original Manuscript: May 26, 2009
Revised Manuscript: July 22, 2009
Manuscript Accepted: August 9, 2009
Published: August 14, 2009

Virtual Issues
Vol. 4, Iss. 10 Virtual Journal for Biomedical Optics

Citation
Yen-Heng Lin, Chen-Min Chang, and Gwo-Bin Lee, "Manipulation of single DNA molecules by using optically projected images," Opt. Express 17, 15318-15329 (2009)
http://www.opticsinfobase.org/vjbo/abstract.cfm?URI=oe-17-17-15318


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References

  1. J. Yuqiu, C.-B. Juang, D. Keller, C. Bustamante, D. Beach, T. Houseal, and E. Builes, “Mechanical, electrical, and chemical manipulation of single DNA molecules,” Nanotechnology 3(1), 16–20 (1992).
  2. J. Zlatanova and S. H. Leuba, “Stretching and imaging single DNA molecules and chromatin,” J. Muscle Res. Cell Motil. 23(5-6), 377–395 (2002).
  3. M. C. Williams, K. Pant, I. Rouzina, and R. L. Karpel, “Single molecule force spectroscopy studies of DNA denaturation by T4 gene 32 protein,” Spectroscopy 18, 203–211 (2004).
  4. S. B. Smith, L. Finzi, and C. Bustamante, “Direct mechanical measurements of the elasticity of single DNA molecules by using magnetic beads,” Science 258(5085), 1122–1126 (1992). [PubMed]
  5. D. Porath, A. Bezryadin, S. de Vries, and C. Dekker, “Direct measurement of electrical transport through DNA molecules,” Nature 403(6770), 635–638 (2000). [PubMed]
  6. J. Zlatanova and S. H. Leuba, “Magnetic tweezers: a sensitive tool to study DNA and chromatin at the single-molecule level,” Biochem. Cell Biol. 81(3), 151–159 (2003). [PubMed]
  7. C. H. Chiou and G. B. Lee, “A micromachined DNA manipulation platform for the stretching and rotation of a single DNA molecule,” J. Micromech. Microeng. 15(1), 109–117 (2005).
  8. C. H. Chiou, Y. Y. Huang, M. H. Chiang, H. H. Lee, and G. B. Lee, “New magnetic tweezers for investigation of the mechanical properties of single DNA molecules,” Nanotechnology 17(5), 1217–1224 (2006).
  9. A. Noy, D. V. Vezenov, J. F. Kayyem, T. J. Meade, and C. M. Lieber, “Stretching and breaking duplex DNA by chemical force microscopy,” Chem. Biol. 4(7), 519–527 (1997). [PubMed]
  10. T. Morii, R. Mizuno, H. Haruta, and T. Okada, “An AFM study of the elasticity of DNA molecules,” Thin Solid Films 464–465, 456–458 (2004).
  11. P. K. Wong, Y. K. Lee, and C. M. Ho, “Deformation of DNA molecules by hydrodynamic focusing,” J. Fluid Mech. 497, 55–65 (2003).
  12. L. Guo, X. Cheng, and C. F. Chou, “Fabrication of size-controllable nanofluidic channels by nanoimprinting and its application for DNA stretching,” Nano Lett. 4(1), 69–73 (2004).
  13. J. Gu, R. Gupta, C. F. Chou, Q. Wei, and F. Zenhausern, “A simple polysilsesquioxane sealing of nanofluidic channels below 10 nm at room temperature,” Lab Chip 7(9), 1198–1201 (2007). [PubMed]
  14. G. C. Randall, K. M. Schultz, and P. S. Doyle, “Methods to electrophoretically stretch DNA: microcontractions, gels, and hybrid gel-microcontraction devices,” Lab Chip 6(4), 516–525 (2006). [PubMed]
  15. J. M. Kim and P. S. Doyle, “Design and numerical simulation of a DNA electrophoretic stretching device,” Lab Chip 7(2), 213–225 (2007). [PubMed]
  16. L. C. Campbell, M. J. Wilkinson, A. Manz, P. Camilleri, and C. J. Humphreys, “Electrophoretic manipulation of single DNA molecules in nanofabricated capillaries,” Lab Chip 4(3), 225–229 (2004). [PubMed]
  17. H. Y. Lin, L. C. Tsai, P. Y. Chi, and C. D. Chen, “Positioning of extended individual DNA molecules on electrodes by non-uniform AC electric fields,” Nanotechnology 16(11), 2738–2742 (2005).
  18. G. Maubach, A. Csaki, D. Born, and W. Fritzsche, “Controlled positioning of a DNA molecule in an electrode setup based on self-assembly and microstructuring,” Nanotechnology 14(5), 546–550 (2003).
  19. S. B. Smith, Y. Cui, and C. Bustamante, “Overstretching B-DNA: the elastic response of individual double-stranded and single-stranded DNA molecules,” Science 271(5250), 795–799 (1996). [PubMed]
  20. M. D. Wang, H. Yin, R. Landick, J. Gelles, and S. M. Block, “Stretching DNA with optical tweezers,” Biophys. J. 72(3), 1335–1346 (1997). [PubMed]
  21. M. Salomo, K. Kegler, C. Gutsche, M. Struhalla, J. Reinmuth, W. Skokow, H. Hahn, and F. Kremer, “The elastic properties of single double-stranded DNA chains of different lengths as measured with optical tweezers,” Colloid Polym. Sci. 284(11), 1325–1331 (2006).
  22. M. L. Bennink, O. D. Schärer, R. Kanaar, K. Sakata-Sogawa, J. M. Schins, J. S. Kanger, B. G. de Grooth, and J. Greve, “Single-molecule manipulation of double-stranded DNA using optical tweezers: interaction studies of DNA with RecA and YOYO-1,” Cytometry 36(3), 200–208 (1999). [PubMed]
  23. C. Rusu, R. van’t Oever, M. J. de Boer, H. V. Jansen, J. W. Berenschot, M. L. Bennink, J. S. Kanger, B. G. de Grooth, M. Elwenspoek, J. Greve, J. Brugger, and A. van den Berg, “Direct integration of micromachined pipettes in a flow channel for single DNA molecule study by optical tweezers,” J. Microelectromech. Syst. 10(2), 238–246 (2001).
  24. P. Y. Chiou, A. T. Ohta, and M. C. Wu, “Massively parallel manipulation of single cells and microparticles using optical images,” Nature 436(7049), 370–372 (2005). [PubMed]
  25. A. Jamshidi, P. J. Pauzauskie, P. J. Schuck, A. T. Ohta, P.-Y. Chiou, J. Chou, P. Yang, and M. C. Wu, “Dynamic manipulation and separation of individual semiconducting and metallic nanowires,” Nat. Photonics 2(2), 86–89 (2008). [PubMed]
  26. X. B. Wang, Y. Huang, F. F. Becker, and P. R. C. Gascoyne, “A unified theory of dielectrophoresis and travelling wave dielectrophoresis,” J. Phys. D Appl. Phys. 27(7), 1571–1574 (1994).
  27. Y. H. Lin and G. B. Lee, “Optically induced flow cytometry for continuous microparticle counting and sorting,” Biosens. Bioelectron. 24(4), 572–578 (2008). [PubMed]
  28. Y. Zhang, R. H. Austin, J. Kraeft, E. C. Cox, and N. P. Ong, “Insulating behavior of λ-DNA on the micron scale,” Phys. Rev. Lett. 89(19), 198102 (2002). [PubMed]
  29. S. C. Huang, M. D. Stump, R. Weiss, and K. D. Caldwell, “Binding of biotinylated DNA to streptavidin-coated polystyrene latex: effects of chain length and particle size,” Anal. Biochem. 237(1), 115–122 (1996). [PubMed]
  30. J. F. Marko and E. D. Siggia, “Stretching DNA,” Macromolecules 28(26), 8759–8770 (1995).

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