Abstract

Optical traps are commonly constructed with high-numerical-aperture objectives. Oil- immersion objectives suffer from spherical aberrations when used for imaging in aqueous solutions. The effect of spherical aberrations on trapping strength has been modeled by approximation, and only a few experimental results are available in the case of micrometer-sized particles. We present an experimental study of the dependence of lateral and axial optical-trap stiffness on focusing depth for polystyrene and silica beads of 2 μm diameter by using oil- and water-immersion objectives. We demonstrate a strong depth dependence of trap stiffness with the oil-immersion objective, whereas no depth dependence was observed with the water-immersion objective.

© 2006 Optical Society of America

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [PubMed]
  31. H. Faxen, "Die bewegung einer Starren Kugel längs der Achse eines mit zäher Flüssigkeit gefüllten Rohres," Ark. Mat. Astron. Fys. 17, 1-28 (1923).
  32. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Noordhoff, 1973).
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    [CrossRef]

2005

2004

A. Buosciolo, G. Pesce, and A. Sasso, "New calibration method for position detector for simultaneous measurements of force constants and local viscosity in optical tweezers," Opt. Commun. 230, 357-368 (2004).
[CrossRef]

2003

2002

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
[CrossRef] [PubMed]

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

2001

R. S. Rock, S. E. Rice, A. L. Wells, T. J. Purcell, J. A. Spudich, and H. L. Sweeney, "Myosin VI is a processive motor with a large step size," Proc. Natl. Acad. Sci. USA 98, 13655-13659 (2001).
[CrossRef] [PubMed]

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage phi 29 portal motor can package DNA against a large internal force," Nature (London) 413, 748-752 (2001).
[CrossRef] [PubMed]

2000

R. J. Davenport, G. J. L. Wuite, R. Landick, and C. Bustamante, "Single-molecule study of transcriptional pausing and arrest by E-coli RNA polymerase," Science 287, 2497-2500 (2000).
[CrossRef] [PubMed]

G. J. L. Wuite, S. B. Smith, M. Young, D. Keller, and C. Bustamante, "Single-molecule studies of the effect of template tension on T7 DNA polymerase activity," Nature (London) 404, 103-106 (2000).
[CrossRef] [PubMed]

M. J. deCastro, R. M. Fondecave, L. A. Clarke, C. F. Schmidt, and R. J. Stewart, "Working strokes by single molecules of the kinesin-related microtubule motor ncd," Nat. Cell Biol. 2, 724-729 (2000).
[CrossRef] [PubMed]

G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
[CrossRef] [PubMed]

1999

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

A. D. Mehta, R. S. Rock, M. Rief, J. A. Spudich, M. S. Mooseker, and R. E. Cheney, "Myosin-V is a processive actin-based motor," Nature (London) 400, 590-593 (1999).
[CrossRef] [PubMed]

1998

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, S75-S78 (1998).
[CrossRef]

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

C. Veigel, M. L. Bartoo, D. C. S. White, J. C. Sparrow, and J. E. Molloy, "The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer," Biophys. J. 75, 1424-1438 (1998).
[CrossRef] [PubMed]

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, "Two-dimensional tracking of ncd motility by back focal plane interferometry," Biophys. J. 74, 1074-1085 (1998).
[CrossRef] [PubMed]

F. Gittes and C. F. Schmidt, "Interference model for back-focal-plane displacement detection in optical tweezers," Opt. Lett. 23, 7-9 (1998).
[CrossRef]

S. H. Wiersma, T. D. Visser, and P. Torok, "Annular focusing through a dielectric interface: scanning and confining the intensity," Pure Appl. Opt. 7, 1237-1248 (1998).
[CrossRef]

1997

1995

J. E. Molloy, J. E. Burns, J. Kendrickjones, R. T. Tregear, and D. C. S. White, "Movement and force produced by a single myosin head," Nature (London) 378, 209-212 (1995).
[CrossRef] [PubMed]

H. Felgner, O. Müller, and M. Schliwa, "Calibration of light forces in optical tweezers," Appl. Opt. 34, 977-982 (1995).
[CrossRef] [PubMed]

1994

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics—piconewton forces and nanometer steps," Nature (London) 368, 113-119 (1994).
[CrossRef] [PubMed]

L. P. Ghislain, N. A. Switz, and W. W. Webb, "Measurement of small forces using an optical trap," Rev. Sci. Instrum. 65, 2762-2768 (1994).
[CrossRef]

W. H. Wright, G. J. Sonek, and M. W. Berns, "Parametric study of the forces on microspheres held by optical tweezers," Appl. Opt. 33, 1735-1748 (1994).
[CrossRef] [PubMed]

1993

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

1986

1923

H. Faxen, "Die bewegung einer Starren Kugel längs der Achse eines mit zäher Flüssigkeit gefüllten Rohres," Ark. Mat. Astron. Fys. 17, 1-28 (1923).

Abbondanzieri, E. A.

Allersma, M. W.

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, "Two-dimensional tracking of ncd motility by back focal plane interferometry," Biophys. J. 74, 1074-1085 (1998).
[CrossRef] [PubMed]

Anderson, D. L.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage phi 29 portal motor can package DNA against a large internal force," Nature (London) 413, 748-752 (2001).
[CrossRef] [PubMed]

Asbury, C. L.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

Ashkin, A.

Axner, O.

Ballerini, R.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Bartoo, M. L.

C. Veigel, M. L. Bartoo, D. C. S. White, J. C. Sparrow, and J. E. Molloy, "The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer," Biophys. J. 75, 1424-1438 (1998).
[CrossRef] [PubMed]

Berns, M. W.

Bjorkholm, J. E.

Block, S. M.

K. C. Neuman, E. A. Abbondanzieri, and S. M. Block, "Measurement of the effective focal shift in an optical trap," Opt. Lett. 30, 1318-1320 (2005).
[CrossRef] [PubMed]

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

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

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

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

Brenner, H.

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Noordhoff, 1973).

Buosciolo, A.

A. Buosciolo, G. Pesce, and A. Sasso, "New calibration method for position detector for simultaneous measurements of force constants and local viscosity in optical tweezers," Opt. Commun. 230, 357-368 (2004).
[CrossRef]

Burns, J. E.

J. E. Molloy, J. E. Burns, J. Kendrickjones, R. T. Tregear, and D. C. S. White, "Movement and force produced by a single myosin head," Nature (London) 378, 209-212 (1995).
[CrossRef] [PubMed]

Bustamante, C.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage phi 29 portal motor can package DNA against a large internal force," Nature (London) 413, 748-752 (2001).
[CrossRef] [PubMed]

R. J. Davenport, G. J. L. Wuite, R. Landick, and C. Bustamante, "Single-molecule study of transcriptional pausing and arrest by E-coli RNA polymerase," Science 287, 2497-2500 (2000).
[CrossRef] [PubMed]

G. J. L. Wuite, S. B. Smith, M. Young, D. Keller, and C. Bustamante, "Single-molecule studies of the effect of template tension on T7 DNA polymerase activity," Nature (London) 404, 103-106 (2000).
[CrossRef] [PubMed]

G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
[CrossRef] [PubMed]

Capitanio, M.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Cheney, R. E.

A. D. Mehta, R. S. Rock, M. Rief, J. A. Spudich, M. S. Mooseker, and R. E. Cheney, "Myosin-V is a processive actin-based motor," Nature (London) 400, 590-593 (1999).
[CrossRef] [PubMed]

Chu, S.

Clarke, L. A.

M. J. deCastro, R. M. Fondecave, L. A. Clarke, C. F. Schmidt, and R. J. Stewart, "Working strokes by single molecules of the kinesin-related microtubule motor ncd," Nat. Cell Biol. 2, 724-729 (2000).
[CrossRef] [PubMed]

Davenport, R. J.

R. J. Davenport, G. J. L. Wuite, R. Landick, and C. Bustamante, "Single-molecule study of transcriptional pausing and arrest by E-coli RNA polymerase," Science 287, 2497-2500 (2000).
[CrossRef] [PubMed]

G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
[CrossRef] [PubMed]

deCastro, M. J.

M. J. deCastro, R. M. Fondecave, L. A. Clarke, C. F. Schmidt, and R. J. Stewart, "Working strokes by single molecules of the kinesin-related microtubule motor ncd," Nat. Cell Biol. 2, 724-729 (2000).
[CrossRef] [PubMed]

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, "Two-dimensional tracking of ncd motility by back focal plane interferometry," Biophys. J. 74, 1074-1085 (1998).
[CrossRef] [PubMed]

Dunlap, D.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Dziedzic, J. M.

Fällman, E.

Faxen, H.

H. Faxen, "Die bewegung einer Starren Kugel längs der Achse eines mit zäher Flüssigkeit gefüllten Rohres," Ark. Mat. Astron. Fys. 17, 1-28 (1923).

Felgner, H.

Finer, J. T.

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics—piconewton forces and nanometer steps," Nature (London) 368, 113-119 (1994).
[CrossRef] [PubMed]

Finzi, L.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Florin, E. L.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, S75-S78 (1998).
[CrossRef]

Fondecave, R. M.

M. J. deCastro, R. M. Fondecave, L. A. Clarke, C. F. Schmidt, and R. J. Stewart, "Working strokes by single molecules of the kinesin-related microtubule motor ncd," Nat. Cell Biol. 2, 724-729 (2000).
[CrossRef] [PubMed]

Gelles, J.

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

Ghislain, L. P.

L. P. Ghislain, N. A. Switz, and W. W. Webb, "Measurement of small forces using an optical trap," Rev. Sci. Instrum. 65, 2762-2768 (1994).
[CrossRef]

Gittes, F.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, "Laser-induced heating in optical traps," Biophys. J. 84, 1308-1316 (2003).
[CrossRef] [PubMed]

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, "Two-dimensional tracking of ncd motility by back focal plane interferometry," Biophys. J. 74, 1074-1085 (1998).
[CrossRef] [PubMed]

F. Gittes and C. F. Schmidt, "Interference model for back-focal-plane displacement detection in optical tweezers," Opt. Lett. 23, 7-9 (1998).
[CrossRef]

F. Gittes and C. F. Schmidt, "Signals and noise in micromechanical measurements," in Methods in Cell Biology, M.Sheetz, ed. (Academic, 1998), Vol. 55, pp. 129-156.
[PubMed]

Giuntini, M.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Grimes, S.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage phi 29 portal motor can package DNA against a large internal force," Nature (London) 413, 748-752 (2001).
[CrossRef] [PubMed]

Happel, J.

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Noordhoff, 1973).

Horber, J. K. H.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, S75-S78 (1998).
[CrossRef]

Keller, M. Young

G. J. L. Wuite, S. B. Smith, M. Young, D. Keller, and C. Bustamante, "Single-molecule studies of the effect of template tension on T7 DNA polymerase activity," Nature (London) 404, 103-106 (2000).
[CrossRef] [PubMed]

Kendrickjones, J.

J. E. Molloy, J. E. Burns, J. Kendrickjones, R. T. Tregear, and D. C. S. White, "Movement and force produced by a single myosin head," Nature (London) 378, 209-212 (1995).
[CrossRef] [PubMed]

Landick, R.

R. J. Davenport, G. J. L. Wuite, R. Landick, and C. Bustamante, "Single-molecule study of transcriptional pausing and arrest by E-coli RNA polymerase," Science 287, 2497-2500 (2000).
[CrossRef] [PubMed]

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

Lang, M. J.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

Mehta, A. D.

A. D. Mehta, R. S. Rock, M. Rief, J. A. Spudich, M. S. Mooseker, and R. E. Cheney, "Myosin-V is a processive actin-based motor," Nature (London) 400, 590-593 (1999).
[CrossRef] [PubMed]

Molloy, J. E.

C. Veigel, M. L. Bartoo, D. C. S. White, J. C. Sparrow, and J. E. Molloy, "The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer," Biophys. J. 75, 1424-1438 (1998).
[CrossRef] [PubMed]

J. E. Molloy, J. E. Burns, J. Kendrickjones, R. T. Tregear, and D. C. S. White, "Movement and force produced by a single myosin head," Nature (London) 378, 209-212 (1995).
[CrossRef] [PubMed]

Mooseker, M. S.

A. D. Mehta, R. S. Rock, M. Rief, J. A. Spudich, M. S. Mooseker, and R. E. Cheney, "Myosin-V is a processive actin-based motor," Nature (London) 400, 590-593 (1999).
[CrossRef] [PubMed]

Müller, O.

Neuman, K. C.

Pavone, F. S.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Pesce, G.

A. Buosciolo, G. Pesce, and A. Sasso, "New calibration method for position detector for simultaneous measurements of force constants and local viscosity in optical tweezers," Opt. Commun. 230, 357-368 (2004).
[CrossRef]

Peterman, E. J. G.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, "Laser-induced heating in optical traps," Biophys. J. 84, 1308-1316 (2003).
[CrossRef] [PubMed]

Pralle, A.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, S75-S78 (1998).
[CrossRef]

Prummer, M.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

Purcell, T. J.

R. S. Rock, S. E. Rice, A. L. Wells, T. J. Purcell, J. A. Spudich, and H. L. Sweeney, "Myosin VI is a processive motor with a large step size," Proc. Natl. Acad. Sci. USA 98, 13655-13659 (2001).
[CrossRef] [PubMed]

Rappaport, A.

G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
[CrossRef] [PubMed]

Rice, S. E.

R. S. Rock, S. E. Rice, A. L. Wells, T. J. Purcell, J. A. Spudich, and H. L. Sweeney, "Myosin VI is a processive motor with a large step size," Proc. Natl. Acad. Sci. USA 98, 13655-13659 (2001).
[CrossRef] [PubMed]

Rief, M.

A. D. Mehta, R. S. Rock, M. Rief, J. A. Spudich, M. S. Mooseker, and R. E. Cheney, "Myosin-V is a processive actin-based motor," Nature (London) 400, 590-593 (1999).
[CrossRef] [PubMed]

Rock, R. S.

R. S. Rock, S. E. Rice, A. L. Wells, T. J. Purcell, J. A. Spudich, and H. L. Sweeney, "Myosin VI is a processive motor with a large step size," Proc. Natl. Acad. Sci. USA 98, 13655-13659 (2001).
[CrossRef] [PubMed]

A. D. Mehta, R. S. Rock, M. Rief, J. A. Spudich, M. S. Mooseker, and R. E. Cheney, "Myosin-V is a processive actin-based motor," Nature (London) 400, 590-593 (1999).
[CrossRef] [PubMed]

Rohrbach, A.

Romano, G.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

Sasso, A.

A. Buosciolo, G. Pesce, and A. Sasso, "New calibration method for position detector for simultaneous measurements of force constants and local viscosity in optical tweezers," Opt. Commun. 230, 357-368 (2004).
[CrossRef]

Schliwa, M.

Schmidt, C. F.

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, "Laser-induced heating in optical traps," Biophys. J. 84, 1308-1316 (2003).
[CrossRef] [PubMed]

M. J. deCastro, R. M. Fondecave, L. A. Clarke, C. F. Schmidt, and R. J. Stewart, "Working strokes by single molecules of the kinesin-related microtubule motor ncd," Nat. Cell Biol. 2, 724-729 (2000).
[CrossRef] [PubMed]

F. Gittes and C. F. Schmidt, "Interference model for back-focal-plane displacement detection in optical tweezers," Opt. Lett. 23, 7-9 (1998).
[CrossRef]

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, "Two-dimensional tracking of ncd motility by back focal plane interferometry," Biophys. J. 74, 1074-1085 (1998).
[CrossRef] [PubMed]

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

F. Gittes and C. F. Schmidt, "Signals and noise in micromechanical measurements," in Methods in Cell Biology, M.Sheetz, ed. (Academic, 1998), Vol. 55, pp. 129-156.
[PubMed]

Schnapp, B. J.

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

Schnitzer, M. J.

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

Shaevitz, J. W.

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

Simmons, R. M.

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics—piconewton forces and nanometer steps," Nature (London) 368, 113-119 (1994).
[CrossRef] [PubMed]

Smith, D. E.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage phi 29 portal motor can package DNA against a large internal force," Nature (London) 413, 748-752 (2001).
[CrossRef] [PubMed]

Smith, S. B.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage phi 29 portal motor can package DNA against a large internal force," Nature (London) 413, 748-752 (2001).
[CrossRef] [PubMed]

G. J. L. Wuite, S. B. Smith, M. Young, D. Keller, and C. Bustamante, "Single-molecule studies of the effect of template tension on T7 DNA polymerase activity," Nature (London) 404, 103-106 (2000).
[CrossRef] [PubMed]

Sonek, G. J.

Sparrow, J. C.

C. Veigel, M. L. Bartoo, D. C. S. White, J. C. Sparrow, and J. E. Molloy, "The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer," Biophys. J. 75, 1424-1438 (1998).
[CrossRef] [PubMed]

Spudich, J. A.

R. S. Rock, S. E. Rice, A. L. Wells, T. J. Purcell, J. A. Spudich, and H. L. Sweeney, "Myosin VI is a processive motor with a large step size," Proc. Natl. Acad. Sci. USA 98, 13655-13659 (2001).
[CrossRef] [PubMed]

A. D. Mehta, R. S. Rock, M. Rief, J. A. Spudich, M. S. Mooseker, and R. E. Cheney, "Myosin-V is a processive actin-based motor," Nature (London) 400, 590-593 (1999).
[CrossRef] [PubMed]

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics—piconewton forces and nanometer steps," Nature (London) 368, 113-119 (1994).
[CrossRef] [PubMed]

Stelzer, E. H. K.

A. Rohrbach and E. H. K. Stelzer, "Trapping forces, force constants, and potential depths for dielectric spheres in the presence of spherical aberrations," Appl. Opt. 41, 2494-2507 (2002).
[CrossRef] [PubMed]

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, S75-S78 (1998).
[CrossRef]

Stewart, R. J.

M. J. deCastro, R. M. Fondecave, L. A. Clarke, C. F. Schmidt, and R. J. Stewart, "Working strokes by single molecules of the kinesin-related microtubule motor ncd," Nat. Cell Biol. 2, 724-729 (2000).
[CrossRef] [PubMed]

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, "Two-dimensional tracking of ncd motility by back focal plane interferometry," Biophys. J. 74, 1074-1085 (1998).
[CrossRef] [PubMed]

Svoboda, K.

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

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

Sweeney, H. L.

R. S. Rock, S. E. Rice, A. L. Wells, T. J. Purcell, J. A. Spudich, and H. L. Sweeney, "Myosin VI is a processive motor with a large step size," Proc. Natl. Acad. Sci. USA 98, 13655-13659 (2001).
[CrossRef] [PubMed]

Switz, N. A.

L. P. Ghislain, N. A. Switz, and W. W. Webb, "Measurement of small forces using an optical trap," Rev. Sci. Instrum. 65, 2762-2768 (1994).
[CrossRef]

Tans, S. J.

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage phi 29 portal motor can package DNA against a large internal force," Nature (London) 413, 748-752 (2001).
[CrossRef] [PubMed]

Torok, P.

S. H. Wiersma, T. D. Visser, and P. Torok, "Annular focusing through a dielectric interface: scanning and confining the intensity," Pure Appl. Opt. 7, 1237-1248 (1998).
[CrossRef]

S. H. Wiersma, P. Torok, T. D. Visser, and P. Varga, "Comparison of different theories for focusing through a plane interface," J. Opt. Soc. Am. A 14, 1482-1490 (1997).
[CrossRef]

Tregear, R. T.

J. E. Molloy, J. E. Burns, J. Kendrickjones, R. T. Tregear, and D. C. S. White, "Movement and force produced by a single myosin head," Nature (London) 378, 209-212 (1995).
[CrossRef] [PubMed]

Varga, P.

Veigel, C.

C. Veigel, M. L. Bartoo, D. C. S. White, J. C. Sparrow, and J. E. Molloy, "The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer," Biophys. J. 75, 1424-1438 (1998).
[CrossRef] [PubMed]

Visser, T. D.

S. H. Wiersma, T. D. Visser, and P. Torok, "Annular focusing through a dielectric interface: scanning and confining the intensity," Pure Appl. Opt. 7, 1237-1248 (1998).
[CrossRef]

S. H. Wiersma, P. Torok, T. D. Visser, and P. Varga, "Comparison of different theories for focusing through a plane interface," J. Opt. Soc. Am. A 14, 1482-1490 (1997).
[CrossRef]

Wang, M. D.

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

Webb, W. W.

L. P. Ghislain, N. A. Switz, and W. W. Webb, "Measurement of small forces using an optical trap," Rev. Sci. Instrum. 65, 2762-2768 (1994).
[CrossRef]

Wells, A. L.

R. S. Rock, S. E. Rice, A. L. Wells, T. J. Purcell, J. A. Spudich, and H. L. Sweeney, "Myosin VI is a processive motor with a large step size," Proc. Natl. Acad. Sci. USA 98, 13655-13659 (2001).
[CrossRef] [PubMed]

White, D. C. S.

C. Veigel, M. L. Bartoo, D. C. S. White, J. C. Sparrow, and J. E. Molloy, "The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer," Biophys. J. 75, 1424-1438 (1998).
[CrossRef] [PubMed]

J. E. Molloy, J. E. Burns, J. Kendrickjones, R. T. Tregear, and D. C. S. White, "Movement and force produced by a single myosin head," Nature (London) 378, 209-212 (1995).
[CrossRef] [PubMed]

Wiersma, S. H.

S. H. Wiersma, T. D. Visser, and P. Torok, "Annular focusing through a dielectric interface: scanning and confining the intensity," Pure Appl. Opt. 7, 1237-1248 (1998).
[CrossRef]

S. H. Wiersma, P. Torok, T. D. Visser, and P. Varga, "Comparison of different theories for focusing through a plane interface," J. Opt. Soc. Am. A 14, 1482-1490 (1997).
[CrossRef]

Wright, W. H.

Wuite, G. J. L.

G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
[CrossRef] [PubMed]

G. J. L. Wuite, S. B. Smith, M. Young, D. Keller, and C. Bustamante, "Single-molecule studies of the effect of template tension on T7 DNA polymerase activity," Nature (London) 404, 103-106 (2000).
[CrossRef] [PubMed]

R. J. Davenport, G. J. L. Wuite, R. Landick, and C. Bustamante, "Single-molecule study of transcriptional pausing and arrest by E-coli RNA polymerase," Science 287, 2497-2500 (2000).
[CrossRef] [PubMed]

Yin, H.

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

Annu. Rev. Biophys. Biomol. Struct.

K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
[CrossRef] [PubMed]

Appl. Opt.

Appl. Phys. A

E. L. Florin, A. Pralle, E. H. K. Stelzer, and J. K. H. Horber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, S75-S78 (1998).
[CrossRef]

Ark. Mat. Astron. Fys.

H. Faxen, "Die bewegung einer Starren Kugel längs der Achse eines mit zäher Flüssigkeit gefüllten Rohres," Ark. Mat. Astron. Fys. 17, 1-28 (1923).

Biophys. J.

G. J. L. Wuite, R. J. Davenport, A. Rappaport, and C. Bustamante, "An integrated laser trap/flow control video microscope for the study of single biomolecules," Biophys. J. 79, 1155-1167 (2000).
[CrossRef] [PubMed]

E. J. G. Peterman, F. Gittes, and C. F. Schmidt, "Laser-induced heating in optical traps," Biophys. J. 84, 1308-1316 (2003).
[CrossRef] [PubMed]

M. W. Allersma, F. Gittes, M. J. deCastro, R. J. Stewart, and C. F. Schmidt, "Two-dimensional tracking of ncd motility by back focal plane interferometry," Biophys. J. 74, 1074-1085 (1998).
[CrossRef] [PubMed]

M. J. Lang, C. L. Asbury, J. W. Shaevitz, and S. M. Block, "An automated two-dimensional optical force clamp for single molecule studies," Biophys. J. 83, 491-501 (2002).
[CrossRef] [PubMed]

C. Veigel, M. L. Bartoo, D. C. S. White, J. C. Sparrow, and J. E. Molloy, "The stiffness of rabbit skeletal actomyosin cross-bridges determined with an optical tweezers transducer," Biophys. J. 75, 1424-1438 (1998).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A

Microsc. Res. Tech.

A. Pralle, M. Prummer, E. L. Florin, E. H. K. Stelzer, and J. K. H. Horber, "Three-dimensional high-resolution particle tracking for optical tweezers by forward scattered light," Microsc. Res. Tech. 44, 378-386 (1999).
[CrossRef] [PubMed]

Nat. Cell Biol.

M. J. deCastro, R. M. Fondecave, L. A. Clarke, C. F. Schmidt, and R. J. Stewart, "Working strokes by single molecules of the kinesin-related microtubule motor ncd," Nat. Cell Biol. 2, 724-729 (2000).
[CrossRef] [PubMed]

Nature

A. D. Mehta, R. S. Rock, M. Rief, J. A. Spudich, M. S. Mooseker, and R. E. Cheney, "Myosin-V is a processive actin-based motor," Nature (London) 400, 590-593 (1999).
[CrossRef] [PubMed]

D. E. Smith, S. J. Tans, S. B. Smith, S. Grimes, D. L. Anderson, and C. Bustamante, "The bacteriophage phi 29 portal motor can package DNA against a large internal force," Nature (London) 413, 748-752 (2001).
[CrossRef] [PubMed]

G. J. L. Wuite, S. B. Smith, M. Young, D. Keller, and C. Bustamante, "Single-molecule studies of the effect of template tension on T7 DNA polymerase activity," Nature (London) 404, 103-106 (2000).
[CrossRef] [PubMed]

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

J. T. Finer, R. M. Simmons, and J. A. Spudich, "Single myosin molecule mechanics—piconewton forces and nanometer steps," Nature (London) 368, 113-119 (1994).
[CrossRef] [PubMed]

J. E. Molloy, J. E. Burns, J. Kendrickjones, R. T. Tregear, and D. C. S. White, "Movement and force produced by a single myosin head," Nature (London) 378, 209-212 (1995).
[CrossRef] [PubMed]

Opt. Commun.

A. Buosciolo, G. Pesce, and A. Sasso, "New calibration method for position detector for simultaneous measurements of force constants and local viscosity in optical tweezers," Opt. Commun. 230, 357-368 (2004).
[CrossRef]

Opt. Lett.

Proc. Natl. Acad. Sci. USA

R. S. Rock, S. E. Rice, A. L. Wells, T. J. Purcell, J. A. Spudich, and H. L. Sweeney, "Myosin VI is a processive motor with a large step size," Proc. Natl. Acad. Sci. USA 98, 13655-13659 (2001).
[CrossRef] [PubMed]

Pure Appl. Opt.

S. H. Wiersma, T. D. Visser, and P. Torok, "Annular focusing through a dielectric interface: scanning and confining the intensity," Pure Appl. Opt. 7, 1237-1248 (1998).
[CrossRef]

Rev. Sci. Instrum.

M. Capitanio, G. Romano, R. Ballerini, M. Giuntini, F. S. Pavone, D. Dunlap, and L. Finzi, "Calibration of optical tweezers with differential interference contrast signals," Rev. Sci. Instrum. 73, 1687-1696 (2002).
[CrossRef]

L. P. Ghislain, N. A. Switz, and W. W. Webb, "Measurement of small forces using an optical trap," Rev. Sci. Instrum. 65, 2762-2768 (1994).
[CrossRef]

Science

R. J. Davenport, G. J. L. Wuite, R. Landick, and C. Bustamante, "Single-molecule study of transcriptional pausing and arrest by E-coli RNA polymerase," Science 287, 2497-2500 (2000).
[CrossRef] [PubMed]

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

Other

J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Noordhoff, 1973).

F. Gittes and C. F. Schmidt, "Signals and noise in micromechanical measurements," in Methods in Cell Biology, M.Sheetz, ed. (Academic, 1998), Vol. 55, pp. 129-156.
[PubMed]

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Figures (7)

Fig. 1
Fig. 1

(a) Ray-optics sketch of a beam focused into water with an oil-immersion objective through a glass–water interface. Spherical aberration occurring at the glass–water interface produces an elongated focus with rays at critical angle for total internal reflection remaining at the surface. Rays with a small angle to the optical axis are focused deeper in the sample than rays with a larger angle to the optical axis. Dotted lines indicate where the focal point would have been in the absence of spherical aberrations (matching refractive indices). (b) When a water-immersion objective is used, the beam is refracted at both the water–glass and the glass–water interfaces, resulting in an undistorted focus, even at large distances from the surface.

Fig. 2
Fig. 2

Measured power spectral density (solid curve) of the thermal position fluctuations of a 2.1 μm silica bead in water, measured with a sample rate of 20 kHz for 15 s and smoothed by logarithmic binning. A Lorentzian (dashed curve) is fitted to the data. The left-hand axis is labeled in units of volts squared per hertz, the right-hand axis in nanometers squared per hertz with a detector response factor R of 7.45 × 10−8 m∕V.

Fig. 3
Fig. 3

(a) Dependence of the corner frequency of the Lorentzian fit to the power spectral density on the distance between bead and glass surface. A data set is shown for a silica bead, 2.1 μm in diameter, trapped with the water-immersion objective. Open circles are the corner frequency fc (right-hand axis), closed circles 1∕fc (left-hand axis). We fitted Faxen's law [relation (3)] to 1∕fc with two free fitting parameters: the large-distance limit and an offset of the distance axis. (b) Residuals of the fit.

Fig. 4
Fig. 4

Lateral trap stiffness as a function of the distance to the glass surface for silica beads (2.1 μm diameter, circles) and polystyrene beads (2.17 μm diameter, squares), trapped by the water-immersion objective. Closed symbols represent the results of the corner-frequency analysis; open symbols represent the results of the variance analysis. Each point in the graph is the average of at least two separate measurements.

Fig. 5
Fig. 5

Lateral optical-trap stiffness as a function of the distance to the glass surface for silica beads (2.1 μm diameter, circles) and polystyrene beads (2.17 μm diameter, squares), trapped with the oil-immersion objective. Trap stiffness was determined with the corner-frequency method. Data points in the graph are averages over multiple data sets. Error bars are calculated from uncertainties in bead radius and distance. Error bars are larger close to the surface because of the strong dependence of Faxen's law on bead radius and distance in this region. The distance of the bead to the surface is smaller than the distance traveled by the piezo stage because of refraction. We approximately corrected for this effect by using Eq. (1).

Fig. 6
Fig. 6

Examples of the axial trap stiffness as a function of the distance between bead and glass surfaces for silica beads (2.1 μm diameter, circles) and polystyrene beads (2.17 μm diameter, squares), trapped with the oil-immersion objective. Trap stiffness was determined with the corner-frequency method. Data were taken under different conditions, and only the relative changes in trap stiffnesses are compared by normalization of the curves to 1 at a distance of 10 μm.

Fig. 7
Fig. 7

Comparison of an approximate model with measured trap stiffnesses for silica beads (2.1 μm diameter, circles) and polystyrene beads (2.17 μm diameter, squares), trapped with the oil-immersion objective (see text). In this model, light intensity on the bead is a measure for trap stiffness. The experimental data are scaled to fit to the theoretical curve at large distances. Distance to the surface was calculated from stage displacement by use of Eq. (1).

Equations (6)

Equations on this page are rendered with MathJax. Learn more.

h bead = n w n g h piezo ,
κ = 2 π γ f c ,
γ 6 π η a [ 1 9 16 ( a h ) + 1 8 ( a h ) 3 45 256 ( a h ) 4 1 16 ( a h ) 5 ] ,
x 2 ( m 2 ) = k B T κ .
lim f f c f 2 S V ( f ) = f c 2 S 0 V ,
R ( m / V ) = k B T π 2 γ f c     2 S 0     V .

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