Abstract

Since the invention of optical traps based on a single laser beam, the potential experienced by a trapped specimen has been assumed harmonic, in the central part of the trap. It has remained unknown to what extent the harmonic region persists and what occurs beyond. By employing a new method, we have forced the trapped object to extreme positions, significantly further than previously achieved in a single laser beam, and thus experimentally explore an extended trapping potential. The potential stiffens considerably as the bead moves to extreme positions and therein is not well described by simple Uhlenbeck theories.

© 2008 Optical Society of America

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References

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  1. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, "Observation of a single-beam gradient force optical trap for dielectric particles," Opt. Lett. 11, 288-290 (1986).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  8. A. Rohrbach, "Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory," Phys. Rev. Lett. 95, 168102-1-168102-4 (2005).
    [CrossRef]
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    [CrossRef] [PubMed]
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  17. P. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MatLab package for precise calibration of optical tweezers," Comput. Phys. Commun. 174, 572-573 (2006).
    [CrossRef]
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    [CrossRef]
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2008 (1)

2007 (4)

S. Reihani and L. Oddershede, "Optimizing immersion media refractive index improves optical trapping by compensating spherical aberrations," Opt. Lett. 32, 1998-2000 (2007).
[CrossRef] [PubMed]

I. Vladescu, M. McCauley, M. Nunez, I. Rouzina, and M. Williams, "Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching," Nat. Methods 4, 517-522 (2007).
[CrossRef] [PubMed]

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, "Axial deviation of an optically trapped particle in trapping force calibration using the drag force method," Opt. Commun. 273, 37-42 (2007).
[CrossRef]

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

2006 (3)

2004 (1)

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594- 612 (2004).
[CrossRef]

2003 (1)

1998 (2)

F. Gittes and C. Schmidt, "Signals and noise in micromechanical measurements," Methods Cell Biol. 55, 129-156 (1998).
[CrossRef]

M. Wang, M. Schnitzer, H. Yin, and R. Landick, "Force and velocity measured for single molecules of RNA polymerase," Science 282, 902-907 (1998).
[CrossRef] [PubMed]

1993 (3)

S. Kuo and M. Sheetz, "Force of single kinesin molecules measured with optical tweezers," Science 260, 232-234 (1993).
[CrossRef] [PubMed]

K. Svoboda, C. Schmidt, B. Schnapp, and S. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature (London) 365, 721-727 (1993).
[CrossRef]

E. Fallman and O. Axner, "Influence of a glass-water interface on the on-axis trapping of micrometer-sized spherical objects by optical tweezers," Appl. Opt. 42, 3915-3926 (1993).
[CrossRef]

1992 (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

1986 (1)

Ander, M.

Ashkin, A.

Axner, O.

Barbosa, L. C.

Berg-Sørensen, K.

P. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MatLab package for precise calibration of optical tweezers," Comput. Phys. Commun. 174, 572-573 (2006).
[CrossRef]

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594- 612 (2004).
[CrossRef]

L. Oddershede, S. Grego, S. Nørrelykke, and K. Berg-Sørensen, "Optical tweezers: probing biological surfaces," Probe Microsc. 2, 129-137 (2001).

Bjorkholm, J. E.

Block, S.

K. Svoboda, C. Schmidt, B. Schnapp, and S. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature (London) 365, 721-727 (1993).
[CrossRef]

Boer, G.

Bormuth, V.

Branczyk, A. M.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

Cesar, C. L.

Chillce, E.

Chu, S.

Delacretaz, G.

Dziedzic, J. M.

Fallman, E.

Florin, E. L.

Flyvbjerg, H.

P. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MatLab package for precise calibration of optical tweezers," Comput. Phys. Commun. 174, 572-573 (2006).
[CrossRef]

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594- 612 (2004).
[CrossRef]

Fontes, A.

Gittes, F.

F. Gittes and C. Schmidt, "Signals and noise in micromechanical measurements," Methods Cell Biol. 55, 129-156 (1998).
[CrossRef]

Gong, Z.

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, "Axial deviation of an optically trapped particle in trapping force calibration using the drag force method," Opt. Commun. 273, 37-42 (2007).
[CrossRef]

Grego, S.

L. Oddershede, S. Grego, S. Nørrelykke, and K. Berg-Sørensen, "Optical tweezers: probing biological surfaces," Probe Microsc. 2, 129-137 (2001).

Hansen, P.

P. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MatLab package for precise calibration of optical tweezers," Comput. Phys. Commun. 174, 572-573 (2006).
[CrossRef]

Heckenberg, N. R.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

Howard, J.

Jannash, A.

Jonas, A.

Knoner, G.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

Kuo, S.

S. Kuo and M. Sheetz, "Force of single kinesin molecules measured with optical tweezers," Science 260, 232-234 (1993).
[CrossRef] [PubMed]

Landick, R.

M. Wang, M. Schnitzer, H. Yin, and R. Landick, "Force and velocity measured for single molecules of RNA polymerase," Science 282, 902-907 (1998).
[CrossRef] [PubMed]

Li, Y.

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, "Axial deviation of an optically trapped particle in trapping force calibration using the drag force method," Opt. Commun. 273, 37-42 (2007).
[CrossRef]

Loke, V. L. Y.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

Lou, L.

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, "Axial deviation of an optically trapped particle in trapping force calibration using the drag force method," Opt. Commun. 273, 37-42 (2007).
[CrossRef]

McCauley, M.

I. Vladescu, M. McCauley, M. Nunez, I. Rouzina, and M. Williams, "Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching," Nat. Methods 4, 517-522 (2007).
[CrossRef] [PubMed]

Merenda, F.

Neves, A. A. R.

Nieminen, T. A.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

Nørrelykke, S.

L. Oddershede, S. Grego, S. Nørrelykke, and K. Berg-Sørensen, "Optical tweezers: probing biological surfaces," Probe Microsc. 2, 129-137 (2001).

Nunez, M.

I. Vladescu, M. McCauley, M. Nunez, I. Rouzina, and M. Williams, "Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching," Nat. Methods 4, 517-522 (2007).
[CrossRef] [PubMed]

Oddershede, L.

S. Reihani and L. Oddershede, "Optimizing immersion media refractive index improves optical trapping by compensating spherical aberrations," Opt. Lett. 32, 1998-2000 (2007).
[CrossRef] [PubMed]

L. Oddershede, S. Grego, S. Nørrelykke, and K. Berg-Sørensen, "Optical tweezers: probing biological surfaces," Probe Microsc. 2, 129-137 (2001).

Pozzo, L. Y.

Reihani, S.

Rodriguez, E.

Rohner, J.

Rohrbach, A.

A. Rohrbach, "Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory," Phys. Rev. Lett. 95, 168102-1-168102-4 (2005).
[CrossRef]

Rouzina, I.

I. Vladescu, M. McCauley, M. Nunez, I. Rouzina, and M. Williams, "Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching," Nat. Methods 4, 517-522 (2007).
[CrossRef] [PubMed]

Schaffer, E.

Schmidt, C.

F. Gittes and C. Schmidt, "Signals and noise in micromechanical measurements," Methods Cell Biol. 55, 129-156 (1998).
[CrossRef]

K. Svoboda, C. Schmidt, B. Schnapp, and S. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature (London) 365, 721-727 (1993).
[CrossRef]

Schnapp, B.

K. Svoboda, C. Schmidt, B. Schnapp, and S. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature (London) 365, 721-727 (1993).
[CrossRef]

Schnitzer, M.

M. Wang, M. Schnitzer, H. Yin, and R. Landick, "Force and velocity measured for single molecules of RNA polymerase," Science 282, 902-907 (1998).
[CrossRef] [PubMed]

Sheetz, M.

S. Kuo and M. Sheetz, "Force of single kinesin molecules measured with optical tweezers," Science 260, 232-234 (1993).
[CrossRef] [PubMed]

Speidel, M.

Stilgoe, A. B.

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

Svoboda, K.

K. Svoboda, C. Schmidt, B. Schnapp, and S. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature (London) 365, 721-727 (1993).
[CrossRef]

Thomaz, A.

Tolic-Nørrelykke, I.

P. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MatLab package for precise calibration of optical tweezers," Comput. Phys. Commun. 174, 572-573 (2006).
[CrossRef]

van Blaadern, A.

van Kats, C. M.

Vladescu, I.

I. Vladescu, M. McCauley, M. Nunez, I. Rouzina, and M. Williams, "Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching," Nat. Methods 4, 517-522 (2007).
[CrossRef] [PubMed]

Wang, M.

M. Wang, M. Schnitzer, H. Yin, and R. Landick, "Force and velocity measured for single molecules of RNA polymerase," Science 282, 902-907 (1998).
[CrossRef] [PubMed]

Wang, Z.

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, "Axial deviation of an optically trapped particle in trapping force calibration using the drag force method," Opt. Commun. 273, 37-42 (2007).
[CrossRef]

Williams, M.

I. Vladescu, M. McCauley, M. Nunez, I. Rouzina, and M. Williams, "Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching," Nat. Methods 4, 517-522 (2007).
[CrossRef] [PubMed]

Xu, S.

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, "Axial deviation of an optically trapped particle in trapping force calibration using the drag force method," Opt. Commun. 273, 37-42 (2007).
[CrossRef]

Yin, H.

M. Wang, M. Schnitzer, H. Yin, and R. Landick, "Force and velocity measured for single molecules of RNA polymerase," Science 282, 902-907 (1998).
[CrossRef] [PubMed]

Appl. Opt. (1)

Biophys. J. (1)

A. Ashkin, "Forces of a single-beam gradient laser trap on a dielectric sphere in the ray optics regime," Biophys. J. 61, 569-582 (1992).
[CrossRef] [PubMed]

Comput. Phys. Commun. (1)

P. Hansen, I. Tolic-Nørrelykke, H. Flyvbjerg, and K. Berg-Sørensen, "tweezercalib 2.1: Faster version of MatLab package for precise calibration of optical tweezers," Comput. Phys. Commun. 174, 572-573 (2006).
[CrossRef]

J. Opt. Pure Appl. Opt. (1)

T. A. Nieminen, V. L. Y. Loke, A. B. Stilgoe, G. Knoner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, "Optical tweezers computational toolbox," J. Opt. Pure Appl. Opt. 9, S196-S203 (2007).
[CrossRef]

Methods Cell Biol. (1)

F. Gittes and C. Schmidt, "Signals and noise in micromechanical measurements," Methods Cell Biol. 55, 129-156 (1998).
[CrossRef]

Nat. Methods (1)

I. Vladescu, M. McCauley, M. Nunez, I. Rouzina, and M. Williams, "Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching," Nat. Methods 4, 517-522 (2007).
[CrossRef] [PubMed]

Nature (London) (1)

K. Svoboda, C. Schmidt, B. Schnapp, and S. Block, "Direct observation of kinesin stepping by optical trapping interferometry," Nature (London) 365, 721-727 (1993).
[CrossRef]

Opt. Commun. (1)

Z. Gong, Z. Wang, Y. Li, L. Lou, and S. Xu, "Axial deviation of an optically trapped particle in trapping force calibration using the drag force method," Opt. Commun. 273, 37-42 (2007).
[CrossRef]

Opt. Express (3)

Opt. Lett. (3)

Rev. Sci. Instrum. (1)

K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594- 612 (2004).
[CrossRef]

Science (2)

S. Kuo and M. Sheetz, "Force of single kinesin molecules measured with optical tweezers," Science 260, 232-234 (1993).
[CrossRef] [PubMed]

M. Wang, M. Schnitzer, H. Yin, and R. Landick, "Force and velocity measured for single molecules of RNA polymerase," Science 282, 902-907 (1998).
[CrossRef] [PubMed]

Other (4)

A. Rohrbach, "Stiffness of optical traps: quantitative agreement between experiment and electromagnetic theory," Phys. Rev. Lett. 95, 168102-1-168102-4 (2005).
[CrossRef]

C. Wang and G. Uhlenbeck, "Selected papers on noise and stochastic processes," (Dover, New York, 1952).

L. Oddershede, S. Grego, S. Nørrelykke, and K. Berg-Sørensen, "Optical tweezers: probing biological surfaces," Probe Microsc. 2, 129-137 (2001).

F. G. Smith and T. A. King. "Optics and Photonics an Introduction," (Wiley & Sons, Ltd., 2000).

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Figures (5)

Fig. 1.
Fig. 1.

Sketch of the experimental settings for performing the drag force measurements. As the stage is moved with a constant velocity (middle drawing) the bead is displaced a distance, both laterally and axially, with respect to the center of the trap.

Fig. 2.
Fig. 2.

CCD camera images of equilibrium bead positions as the drag force, F, is increased; vstage and F are given in units if µm/second and pN, respectively. Panel A: normal setup, image diameter decreases with lateral distance. Panel B: improved setup, diameter remains constant. Both panels show the images of a 2.1µm bead in the trap

Fig. 3.
Fig. 3.

Diameter of outer white ring from the image of the bead as a function of axial height, serves as a calibration curve. Curve shown is for a bead of diameter 2.1 µm.

Fig. 4.
Fig. 4.

The axial displacement of an optically trapped 2.01 µm bead is shown as a function of the lateral displacement. The upper axis gives the approxmiate corresponding trapping force (within 10 pct). Black squares: NM with significant spherical aberrations at the focus. Red dots: IM where spherical aberrations are eliminated. Each point on the graph represents an average of 10 data points.

Fig. 5.
Fig. 5.

Lateral trapping force as a function of lateral displacement for a 2.01 µm bead (black squares) and a 2.1 µm bead (black dots), in an optical trap. Two independent data sets are shown that were taken using the IM, minimizing spherical aberrations. Most of the error bars are smaller than the symbols. The full lines are fits to equations 1.

Equations (1)

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F trap = { F trap 1 = k 1 x if | x | < 0 . 55 a F trap 2 = k 2 x + constant , otherwise

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