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]
  4. 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]
  5. I. Vladescu, M. McCauley, M. Nünez, I. Rouzina, and M. Williams, “Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching,” Nature Methods 4, 517–522 (2007).
    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  7. 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]
  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]
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    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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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. Nünez, I. Rouzina, and M. Williams, “Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching,” Nature 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. Knöner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, “Optical tweezers computational toolbox,” J. Optic. Pure. Appl. Optic. 9,, S196–S203 (2007).
[Crossref]

2006 (3)

2005 (1)

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

2004 (1)

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

2003 (1)

2001 (1)

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

2000 (1)

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

1998 (2)

F. Gittes and C. Schmidt, “Signals and noise in micromechanical measurements,” Methods in cell Biology 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. Fällman 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.

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]

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]

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 microscopy 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. Knöner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, “Optical tweezers computational toolbox,” J. Optic. Pure. Appl. Optic. 9,, S196–S203 (2007).
[Crossref]

Cesar, C.L.

Chillce, E.

Chu, S.

Delacrétaz, G.

Dziedzic, J. M.

Fällman, 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 in cell Biology 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 microscopy 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. Knöner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, “Optical tweezers computational toolbox,” J. Optic. Pure. Appl. Optic. 9,, S196–S203 (2007).
[Crossref]

Howard, J.

Jannash, A.

Jonáš, A.

King, T.A.

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

Knöner, G.

T.A. Nieminen, V.L.Y. Loke, A.B. Stilgoe, G. Knöner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, “Optical tweezers computational toolbox,” J. Optic. Pure. Appl. Optic. 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. Knöner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, “Optical tweezers computational toolbox,” J. Optic. Pure. Appl. Optic. 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. Nünez, I. Rouzina, and M. Williams, “Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching,” Nature 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. Knöner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, “Optical tweezers computational toolbox,” J. Optic. Pure. Appl. Optic. 9,, S196–S203 (2007).
[Crossref]

Nørrelykke, S.

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

Nünez, M.

I. Vladescu, M. McCauley, M. Nünez, I. Rouzina, and M. Williams, “Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching,” Nature 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 microscopy 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. Nünez, I. Rouzina, and M. Williams, “Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching,” Nature Methods 4, 517–522 (2007).
[Crossref] [PubMed]

Rubinsztein- Dunlop, H.

T.A. Nieminen, V.L.Y. Loke, A.B. Stilgoe, G. Knöner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, “Optical tweezers computational toolbox,” J. Optic. Pure. Appl. Optic. 9,, S196–S203 (2007).
[Crossref]

Salathé, R.

Schäffer, E.

Schmidt, C.

F. Gittes and C. Schmidt, “Signals and noise in micromechanical measurements,” Methods in cell Biology 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]

Smith, F.G.

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

Speidel, M.

Stilgoe, A.B.

T.A. Nieminen, V.L.Y. Loke, A.B. Stilgoe, G. Knöner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, “Optical tweezers computational toolbox,” J. Optic. Pure. Appl. Optic. 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]

Uhlenbeck, G.

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

van Blaadern, A.

van Kats, C.M.

Vladescu, I.

I. Vladescu, M. McCauley, M. Nünez, I. Rouzina, and M. Williams, “Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching,” Nature Methods 4, 517–522 (2007).
[Crossref] [PubMed]

Wang, C.

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

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. Nünez, I. Rouzina, and M. Williams, “Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching,” Nature 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. Optic. Pure. Appl. Optic. (1)

T.A. Nieminen, V.L.Y. Loke, A.B. Stilgoe, G. Knöner, A.M. Branczyk, N.R. Heckenberg, and H. Rubinsztein- Dunlop, “Optical tweezers computational toolbox,” J. Optic. Pure. Appl. Optic. 9,, S196–S203 (2007).
[Crossref]

Methods in cell Biology (1)

F. Gittes and C. Schmidt, “Signals and noise in micromechanical measurements,” Methods in cell Biology 55, 129–156 (1998).
[Crossref]

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]

Nature Methods (1)

I. Vladescu, M. McCauley, M. Nünez, I. Rouzina, and M. Williams, “Quantifying force-dependent and zero-force DNA intercalation by single-molecule stretching,” Nature Methods 4, 517–522 (2007).
[Crossref] [PubMed]

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)

Phys. Rev. Lett. (1)

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

Probe microscopy (1)

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

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 (2)

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

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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