Abstract

High-resolution long-time force measurements by optical tweezers are often limited by low- frequency (1/f) noise. A dual-trap technique is presented that can reduce such noise in the force signal. It incorporates a second trap (a reference trap) that probes the noise in the system and it is based upon the assumption that the low-frequency parts of the noise from the two traps are correlated. A subtraction of the low-frequency signal from the reference trap from the signal from the force measuring trap will therefore yield a net signal that is significantly less influenced by noise. It is shown that this dual-trap technique can reduce the noise in the force signal up to 60% depending on detection bandwidth.

© 2007 Optical Society of America

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  1. K. Svoboda and S. M. Block, "Biological applications of optical forces," Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994).
    [CrossRef] [PubMed]
  2. C. Bustamante, J. C. Macosko, and G. J. L. Wuite, "Grabbing the cat by the tail: manipulating molecules one by one," Nat. Rev. Mol. Cell Biol. 1, 130-136 (2000).
    [CrossRef]
  3. C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, "Single-molecule studies of DNA mechanics," Curr. Opin. Struct. Biol. 10, 279-285 (2000).
    [CrossRef] [PubMed]
  4. A. Janshoff, M. Neitzert, Y. Oberdorfer, and H. Fuchs, "Force spectroscopy of molecular systems--Single molecule spectroscopy of polymers and biomolecules," Angew. Chem., Int. Ed. 39, 3213-3237 (2000).
  5. K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
    [CrossRef]
  6. W. Denk and W. W. Watt, "Optical measurement of picometer displacements of transparent microscopic objects," Appl. Opt. 29, 2382-2391 (1990).
    [CrossRef] [PubMed]
  7. K. Visscher, S. P. Gross, and S. M. Block, "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
    [CrossRef]
  8. 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]
  9. R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans, "Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy," Nature 397, 50-53 (1999).
    [CrossRef] [PubMed]
  10. E. Evans and K. Ritchie, "Dynamic strength of molecular adhesion bonds," Biophys. J. 72, 1541-1555 (1997).
    [CrossRef] [PubMed]
  11. E. Evans, "Energy landscapes of biomolecular adhesion and receptor anchoring at interfaces explored with dynamic force spectroscopy," Faraday Discuss. 111, 1-16 (1999).
    [CrossRef]
  12. E. Evans, "Probing the relation between force lifetime and chemistry in single molecular bonds," Annu. Rev. Biophys. Biomol. Struct . 30, 105-128 (2001).
    [CrossRef] [PubMed]
  13. U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, "Unzipping DNA with optical tweezers: high sequence sensitivity and force flips," Biophys. J. 82, 1537-1553 (2002).
    [CrossRef] [PubMed]
  14. J. Jass, S. Schedin, E. Fällman, J. Ohlsson, U. Nilsson, B. E. Uhlin, and O. Axner, "Physical properties of Escherichia coli P pili measured by optical tweezers," Biophys. J. 87, 4271-4283 (2004).
    [CrossRef] [PubMed]
  15. E. Fällman, S. Schedin, J. Jass, B. E. Uhlin, and O. Axner, "The unfolding of the P pili quaternary structure by stretching is reversible, not plastic," EMBO Rep. 6, 52-56 (2005).
    [CrossRef]
  16. M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "A sticky chain model of the elongation of Escherichia coli P pili under strain," Biophys. J. 90, 1521-1534 (2006).
    [CrossRef]
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  18. L. Nugent-Glandorf and T. T. Perkins, "Measuring 0.1-nm motion in 1 ms in an optical microscope with differential back-focal-plane detection," Opt. Lett. 29, 2611-2613 (2004).
    [CrossRef] [PubMed]
  19. J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, "Backtracking by single RNA polymerase molecules observed at near-base-pair resolution," Nature 426, 684-687 (2003).
    [CrossRef] [PubMed]
  20. E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
    [CrossRef] [PubMed]
  21. J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," Proc. Natl. Acad. Sci. U.S.A. 103, 9006-9011 (2006).
    [CrossRef] [PubMed]
  22. E. Fällman, S. Schedin, J. Jass, M. Andersson, B. E. Uhlin, and O. Axner, "Optical tweezers based force measurement system for quantitating binding interactions: system design and application for the study of bacterial adhesion," Biosens. Bioelectron. 19, 1429-1437 (2004).
    [CrossRef] [PubMed]
  23. E. Fällman and O. Axner, "Design for fully steerable dual-trap optical tweezers," Appl. Opt. 36, 2107-2113 (1997).
    [CrossRef] [PubMed]
  24. K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, "Characterization of photodamage to Escherichia coli in optical traps," Biophys. J. 77, 2856-2863 (1999).
    [CrossRef] [PubMed]
  25. J. C. Meiners and S. R. Quake, "Direct measurement of hydrodynamic cross correlations between two particles in an external potential," Phys. Rev. Lett. 82, 2211-2214 (1999).
    [CrossRef]
  26. G. Leitz, E. Fällman, S. Tuck, and O. Axner, "Stress response in Caenorhabditis elegans caused by optical tweezers: wavelength, power, and time dependence," Biophys. J. 82, 2224-2231 (2002).
    [CrossRef] [PubMed]
  27. F. Gittes and C. F. Schmidt, "Thermal noise limitations on micromechanical experiments," Eur. Biophys. J. 27, 75-81 (1998).
    [CrossRef]
  28. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C--The Art of Scientific Computing (Cambridge U. Press, 1992).
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2006 (3)

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "A sticky chain model of the elongation of Escherichia coli P pili under strain," Biophys. J. 90, 1521-1534 (2006).
[CrossRef]

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "Force measuring optical tweezers system for long time measurements of Pili stability," in Proc. SPIE 6088, 286-295 (2006).

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," Proc. Natl. Acad. Sci. U.S.A. 103, 9006-9011 (2006).
[CrossRef] [PubMed]

2005 (2)

E. Fällman, S. Schedin, J. Jass, B. E. Uhlin, and O. Axner, "The unfolding of the P pili quaternary structure by stretching is reversible, not plastic," EMBO Rep. 6, 52-56 (2005).
[CrossRef]

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

2004 (4)

E. Fällman, S. Schedin, J. Jass, M. Andersson, B. E. Uhlin, and O. Axner, "Optical tweezers based force measurement system for quantitating binding interactions: system design and application for the study of bacterial adhesion," Biosens. Bioelectron. 19, 1429-1437 (2004).
[CrossRef] [PubMed]

L. Nugent-Glandorf and T. T. Perkins, "Measuring 0.1-nm motion in 1 ms in an optical microscope with differential back-focal-plane detection," Opt. Lett. 29, 2611-2613 (2004).
[CrossRef] [PubMed]

J. Jass, S. Schedin, E. Fällman, J. Ohlsson, U. Nilsson, B. E. Uhlin, and O. Axner, "Physical properties of Escherichia coli P pili measured by optical tweezers," Biophys. J. 87, 4271-4283 (2004).
[CrossRef] [PubMed]

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

2003 (1)

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, "Backtracking by single RNA polymerase molecules observed at near-base-pair resolution," Nature 426, 684-687 (2003).
[CrossRef] [PubMed]

2002 (2)

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, "Unzipping DNA with optical tweezers: high sequence sensitivity and force flips," Biophys. J. 82, 1537-1553 (2002).
[CrossRef] [PubMed]

G. Leitz, E. Fällman, S. Tuck, and O. Axner, "Stress response in Caenorhabditis elegans caused by optical tweezers: wavelength, power, and time dependence," Biophys. J. 82, 2224-2231 (2002).
[CrossRef] [PubMed]

2001 (1)

E. Evans, "Probing the relation between force lifetime and chemistry in single molecular bonds," Annu. Rev. Biophys. Biomol. Struct . 30, 105-128 (2001).
[CrossRef] [PubMed]

2000 (3)

C. Bustamante, J. C. Macosko, and G. J. L. Wuite, "Grabbing the cat by the tail: manipulating molecules one by one," Nat. Rev. Mol. Cell Biol. 1, 130-136 (2000).
[CrossRef]

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, "Single-molecule studies of DNA mechanics," Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

A. Janshoff, M. Neitzert, Y. Oberdorfer, and H. Fuchs, "Force spectroscopy of molecular systems--Single molecule spectroscopy of polymers and biomolecules," Angew. Chem., Int. Ed. 39, 3213-3237 (2000).

1999 (5)

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]

R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans, "Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy," Nature 397, 50-53 (1999).
[CrossRef] [PubMed]

E. Evans, "Energy landscapes of biomolecular adhesion and receptor anchoring at interfaces explored with dynamic force spectroscopy," Faraday Discuss. 111, 1-16 (1999).
[CrossRef]

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, "Characterization of photodamage to Escherichia coli in optical traps," Biophys. J. 77, 2856-2863 (1999).
[CrossRef] [PubMed]

J. C. Meiners and S. R. Quake, "Direct measurement of hydrodynamic cross correlations between two particles in an external potential," Phys. Rev. Lett. 82, 2211-2214 (1999).
[CrossRef]

1998 (1)

F. Gittes and C. F. Schmidt, "Thermal noise limitations on micromechanical experiments," Eur. Biophys. J. 27, 75-81 (1998).
[CrossRef]

1997 (2)

E. Fällman and O. Axner, "Design for fully steerable dual-trap optical tweezers," Appl. Opt. 36, 2107-2113 (1997).
[CrossRef] [PubMed]

E. Evans and K. Ritchie, "Dynamic strength of molecular adhesion bonds," Biophys. J. 72, 1541-1555 (1997).
[CrossRef] [PubMed]

1996 (1)

K. Visscher, S. P. Gross, and S. M. Block, "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

1994 (1)

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

1990 (1)

Abbondanzieri, E. A.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, "Backtracking by single RNA polymerase molecules observed at near-base-pair resolution," Nature 426, 684-687 (2003).
[CrossRef] [PubMed]

Andersson, M.

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "A sticky chain model of the elongation of Escherichia coli P pili under strain," Biophys. J. 90, 1521-1534 (2006).
[CrossRef]

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "Force measuring optical tweezers system for long time measurements of Pili stability," in Proc. SPIE 6088, 286-295 (2006).

E. Fällman, S. Schedin, J. Jass, M. Andersson, B. E. Uhlin, and O. Axner, "Optical tweezers based force measurement system for quantitating binding interactions: system design and application for the study of bacterial adhesion," Biosens. Bioelectron. 19, 1429-1437 (2004).
[CrossRef] [PubMed]

Axner, O.

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "A sticky chain model of the elongation of Escherichia coli P pili under strain," Biophys. J. 90, 1521-1534 (2006).
[CrossRef]

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "Force measuring optical tweezers system for long time measurements of Pili stability," in Proc. SPIE 6088, 286-295 (2006).

E. Fällman, S. Schedin, J. Jass, B. E. Uhlin, and O. Axner, "The unfolding of the P pili quaternary structure by stretching is reversible, not plastic," EMBO Rep. 6, 52-56 (2005).
[CrossRef]

J. Jass, S. Schedin, E. Fällman, J. Ohlsson, U. Nilsson, B. E. Uhlin, and O. Axner, "Physical properties of Escherichia coli P pili measured by optical tweezers," Biophys. J. 87, 4271-4283 (2004).
[CrossRef] [PubMed]

E. Fällman, S. Schedin, J. Jass, M. Andersson, B. E. Uhlin, and O. Axner, "Optical tweezers based force measurement system for quantitating binding interactions: system design and application for the study of bacterial adhesion," Biosens. Bioelectron. 19, 1429-1437 (2004).
[CrossRef] [PubMed]

G. Leitz, E. Fällman, S. Tuck, and O. Axner, "Stress response in Caenorhabditis elegans caused by optical tweezers: wavelength, power, and time dependence," Biophys. J. 82, 2224-2231 (2002).
[CrossRef] [PubMed]

E. Fällman and O. Axner, "Design for fully steerable dual-trap optical tweezers," Appl. Opt. 36, 2107-2113 (1997).
[CrossRef] [PubMed]

Bergman, K.

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, "Characterization of photodamage to Escherichia coli in optical traps," Biophys. J. 77, 2856-2863 (1999).
[CrossRef] [PubMed]

Block, S. M.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, "Backtracking by single RNA polymerase molecules observed at near-base-pair resolution," Nature 426, 684-687 (2003).
[CrossRef] [PubMed]

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, "Characterization of photodamage to Escherichia coli in optical traps," Biophys. J. 77, 2856-2863 (1999).
[CrossRef] [PubMed]

K. Visscher, S. P. Gross, and S. M. Block, "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

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

Bockelmann, U.

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, "Unzipping DNA with optical tweezers: high sequence sensitivity and force flips," Biophys. J. 82, 1537-1553 (2002).
[CrossRef] [PubMed]

Bustamante, C.

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," Proc. Natl. Acad. Sci. U.S.A. 103, 9006-9011 (2006).
[CrossRef] [PubMed]

C. Bustamante, J. C. Macosko, and G. J. L. Wuite, "Grabbing the cat by the tail: manipulating molecules one by one," Nat. Rev. Mol. Cell Biol. 1, 130-136 (2000).
[CrossRef]

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, "Single-molecule studies of DNA mechanics," Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

S. B. Smith, Y. J. Cui, and C. Bustamante, "Optical-trap force transducer that operates by direct measurement of light momentum," Meth. Enzymol. 361, 134-162 (2003).

Chadd, E. H.

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, "Characterization of photodamage to Escherichia coli in optical traps," Biophys. J. 77, 2856-2863 (1999).
[CrossRef] [PubMed]

Chemla, Y. R.

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," Proc. Natl. Acad. Sci. U.S.A. 103, 9006-9011 (2006).
[CrossRef] [PubMed]

Cui, Y. J.

S. B. Smith, Y. J. Cui, and C. Bustamante, "Optical-trap force transducer that operates by direct measurement of light momentum," Meth. Enzymol. 361, 134-162 (2003).

Denk, W.

Essevaz-Roulet, B.

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, "Unzipping DNA with optical tweezers: high sequence sensitivity and force flips," Biophys. J. 82, 1537-1553 (2002).
[CrossRef] [PubMed]

Evans, E.

E. Evans, "Probing the relation between force lifetime and chemistry in single molecular bonds," Annu. Rev. Biophys. Biomol. Struct . 30, 105-128 (2001).
[CrossRef] [PubMed]

R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans, "Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy," Nature 397, 50-53 (1999).
[CrossRef] [PubMed]

E. Evans, "Energy landscapes of biomolecular adhesion and receptor anchoring at interfaces explored with dynamic force spectroscopy," Faraday Discuss. 111, 1-16 (1999).
[CrossRef]

E. Evans and K. Ritchie, "Dynamic strength of molecular adhesion bonds," Biophys. J. 72, 1541-1555 (1997).
[CrossRef] [PubMed]

Fällman, E.

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "Force measuring optical tweezers system for long time measurements of Pili stability," in Proc. SPIE 6088, 286-295 (2006).

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "A sticky chain model of the elongation of Escherichia coli P pili under strain," Biophys. J. 90, 1521-1534 (2006).
[CrossRef]

E. Fällman, S. Schedin, J. Jass, B. E. Uhlin, and O. Axner, "The unfolding of the P pili quaternary structure by stretching is reversible, not plastic," EMBO Rep. 6, 52-56 (2005).
[CrossRef]

J. Jass, S. Schedin, E. Fällman, J. Ohlsson, U. Nilsson, B. E. Uhlin, and O. Axner, "Physical properties of Escherichia coli P pili measured by optical tweezers," Biophys. J. 87, 4271-4283 (2004).
[CrossRef] [PubMed]

E. Fällman, S. Schedin, J. Jass, M. Andersson, B. E. Uhlin, and O. Axner, "Optical tweezers based force measurement system for quantitating binding interactions: system design and application for the study of bacterial adhesion," Biosens. Bioelectron. 19, 1429-1437 (2004).
[CrossRef] [PubMed]

G. Leitz, E. Fällman, S. Tuck, and O. Axner, "Stress response in Caenorhabditis elegans caused by optical tweezers: wavelength, power, and time dependence," Biophys. J. 82, 2224-2231 (2002).
[CrossRef] [PubMed]

E. Fällman and O. Axner, "Design for fully steerable dual-trap optical tweezers," Appl. Opt. 36, 2107-2113 (1997).
[CrossRef] [PubMed]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C--The Art of Scientific Computing (Cambridge U. Press, 1992).

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]

Fuchs, H.

A. Janshoff, M. Neitzert, Y. Oberdorfer, and H. Fuchs, "Force spectroscopy of molecular systems--Single molecule spectroscopy of polymers and biomolecules," Angew. Chem., Int. Ed. 39, 3213-3237 (2000).

Gittes, F.

F. Gittes and C. F. Schmidt, "Thermal noise limitations on micromechanical experiments," Eur. Biophys. J. 27, 75-81 (1998).
[CrossRef]

Greenleaf, W. J.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

Gross, S. P.

K. Visscher, S. P. Gross, and S. M. Block, "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Heslot, F.

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, "Unzipping DNA with optical tweezers: high sequence sensitivity and force flips," Biophys. J. 82, 1537-1553 (2002).
[CrossRef] [PubMed]

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]

Izhaky, D.

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," Proc. Natl. Acad. Sci. U.S.A. 103, 9006-9011 (2006).
[CrossRef] [PubMed]

Janshoff, A.

A. Janshoff, M. Neitzert, Y. Oberdorfer, and H. Fuchs, "Force spectroscopy of molecular systems--Single molecule spectroscopy of polymers and biomolecules," Angew. Chem., Int. Ed. 39, 3213-3237 (2000).

Jass, J.

E. Fällman, S. Schedin, J. Jass, B. E. Uhlin, and O. Axner, "The unfolding of the P pili quaternary structure by stretching is reversible, not plastic," EMBO Rep. 6, 52-56 (2005).
[CrossRef]

J. Jass, S. Schedin, E. Fällman, J. Ohlsson, U. Nilsson, B. E. Uhlin, and O. Axner, "Physical properties of Escherichia coli P pili measured by optical tweezers," Biophys. J. 87, 4271-4283 (2004).
[CrossRef] [PubMed]

E. Fällman, S. Schedin, J. Jass, M. Andersson, B. E. Uhlin, and O. Axner, "Optical tweezers based force measurement system for quantitating binding interactions: system design and application for the study of bacterial adhesion," Biosens. Bioelectron. 19, 1429-1437 (2004).
[CrossRef] [PubMed]

Landick, R.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, "Backtracking by single RNA polymerase molecules observed at near-base-pair resolution," Nature 426, 684-687 (2003).
[CrossRef] [PubMed]

Leitz, G.

G. Leitz, E. Fällman, S. Tuck, and O. Axner, "Stress response in Caenorhabditis elegans caused by optical tweezers: wavelength, power, and time dependence," Biophys. J. 82, 2224-2231 (2002).
[CrossRef] [PubMed]

Leung, A.

R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans, "Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy," Nature 397, 50-53 (1999).
[CrossRef] [PubMed]

Liou, G. F.

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, "Characterization of photodamage to Escherichia coli in optical traps," Biophys. J. 77, 2856-2863 (1999).
[CrossRef] [PubMed]

Liphardt, J.

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, "Single-molecule studies of DNA mechanics," Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

Macosko, J. C.

C. Bustamante, J. C. Macosko, and G. J. L. Wuite, "Grabbing the cat by the tail: manipulating molecules one by one," Nat. Rev. Mol. Cell Biol. 1, 130-136 (2000).
[CrossRef]

Meiners, J. C.

J. C. Meiners and S. R. Quake, "Direct measurement of hydrodynamic cross correlations between two particles in an external potential," Phys. Rev. Lett. 82, 2211-2214 (1999).
[CrossRef]

Merkel, R.

R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans, "Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy," Nature 397, 50-53 (1999).
[CrossRef] [PubMed]

Moffitt, J. R.

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," Proc. Natl. Acad. Sci. U.S.A. 103, 9006-9011 (2006).
[CrossRef] [PubMed]

Nassoy, P.

R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans, "Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy," Nature 397, 50-53 (1999).
[CrossRef] [PubMed]

Neitzert, M.

A. Janshoff, M. Neitzert, Y. Oberdorfer, and H. Fuchs, "Force spectroscopy of molecular systems--Single molecule spectroscopy of polymers and biomolecules," Angew. Chem., Int. Ed. 39, 3213-3237 (2000).

Neuman, K. C.

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, "Characterization of photodamage to Escherichia coli in optical traps," Biophys. J. 77, 2856-2863 (1999).
[CrossRef] [PubMed]

Nilsson, U.

J. Jass, S. Schedin, E. Fällman, J. Ohlsson, U. Nilsson, B. E. Uhlin, and O. Axner, "Physical properties of Escherichia coli P pili measured by optical tweezers," Biophys. J. 87, 4271-4283 (2004).
[CrossRef] [PubMed]

Nugent-Glandorf, L.

Oberdorfer, Y.

A. Janshoff, M. Neitzert, Y. Oberdorfer, and H. Fuchs, "Force spectroscopy of molecular systems--Single molecule spectroscopy of polymers and biomolecules," Angew. Chem., Int. Ed. 39, 3213-3237 (2000).

Ohlsson, J.

J. Jass, S. Schedin, E. Fällman, J. Ohlsson, U. Nilsson, B. E. Uhlin, and O. Axner, "Physical properties of Escherichia coli P pili measured by optical tweezers," Biophys. J. 87, 4271-4283 (2004).
[CrossRef] [PubMed]

Perkins, T. T.

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]

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C--The Art of Scientific Computing (Cambridge U. Press, 1992).

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]

Quake, S. R.

J. C. Meiners and S. R. Quake, "Direct measurement of hydrodynamic cross correlations between two particles in an external potential," Phys. Rev. Lett. 82, 2211-2214 (1999).
[CrossRef]

Ritchie, K.

R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans, "Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy," Nature 397, 50-53 (1999).
[CrossRef] [PubMed]

E. Evans and K. Ritchie, "Dynamic strength of molecular adhesion bonds," Biophys. J. 72, 1541-1555 (1997).
[CrossRef] [PubMed]

Schedin, S.

E. Fällman, S. Schedin, J. Jass, B. E. Uhlin, and O. Axner, "The unfolding of the P pili quaternary structure by stretching is reversible, not plastic," EMBO Rep. 6, 52-56 (2005).
[CrossRef]

J. Jass, S. Schedin, E. Fällman, J. Ohlsson, U. Nilsson, B. E. Uhlin, and O. Axner, "Physical properties of Escherichia coli P pili measured by optical tweezers," Biophys. J. 87, 4271-4283 (2004).
[CrossRef] [PubMed]

E. Fällman, S. Schedin, J. Jass, M. Andersson, B. E. Uhlin, and O. Axner, "Optical tweezers based force measurement system for quantitating binding interactions: system design and application for the study of bacterial adhesion," Biosens. Bioelectron. 19, 1429-1437 (2004).
[CrossRef] [PubMed]

Schmidt, C. F.

F. Gittes and C. F. Schmidt, "Thermal noise limitations on micromechanical experiments," Eur. Biophys. J. 27, 75-81 (1998).
[CrossRef]

Shaevitz, J. W.

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, "Backtracking by single RNA polymerase molecules observed at near-base-pair resolution," Nature 426, 684-687 (2003).
[CrossRef] [PubMed]

Smith, D.

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, "Single-molecule studies of DNA mechanics," Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

Smith, S. B.

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, "Single-molecule studies of DNA mechanics," Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

S. B. Smith, Y. J. Cui, and C. Bustamante, "Optical-trap force transducer that operates by direct measurement of light momentum," Meth. Enzymol. 361, 134-162 (2003).

Stelzer, E. H. K.

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]

Svoboda, K.

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

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C--The Art of Scientific Computing (Cambridge U. Press, 1992).

Thomen, P.

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, "Unzipping DNA with optical tweezers: high sequence sensitivity and force flips," Biophys. J. 82, 1537-1553 (2002).
[CrossRef] [PubMed]

Tuck, S.

G. Leitz, E. Fällman, S. Tuck, and O. Axner, "Stress response in Caenorhabditis elegans caused by optical tweezers: wavelength, power, and time dependence," Biophys. J. 82, 2224-2231 (2002).
[CrossRef] [PubMed]

Uhlin, B. E.

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "A sticky chain model of the elongation of Escherichia coli P pili under strain," Biophys. J. 90, 1521-1534 (2006).
[CrossRef]

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "Force measuring optical tweezers system for long time measurements of Pili stability," in Proc. SPIE 6088, 286-295 (2006).

E. Fällman, S. Schedin, J. Jass, B. E. Uhlin, and O. Axner, "The unfolding of the P pili quaternary structure by stretching is reversible, not plastic," EMBO Rep. 6, 52-56 (2005).
[CrossRef]

J. Jass, S. Schedin, E. Fällman, J. Ohlsson, U. Nilsson, B. E. Uhlin, and O. Axner, "Physical properties of Escherichia coli P pili measured by optical tweezers," Biophys. J. 87, 4271-4283 (2004).
[CrossRef] [PubMed]

E. Fällman, S. Schedin, J. Jass, M. Andersson, B. E. Uhlin, and O. Axner, "Optical tweezers based force measurement system for quantitating binding interactions: system design and application for the study of bacterial adhesion," Biosens. Bioelectron. 19, 1429-1437 (2004).
[CrossRef] [PubMed]

Vetterling, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C--The Art of Scientific Computing (Cambridge U. Press, 1992).

Viasnoff, V.

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, "Unzipping DNA with optical tweezers: high sequence sensitivity and force flips," Biophys. J. 82, 1537-1553 (2002).
[CrossRef] [PubMed]

Visscher, K.

K. Visscher, S. P. Gross, and S. M. Block, "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Watt, W. W.

Wuite, G. J. L.

C. Bustamante, J. C. Macosko, and G. J. L. Wuite, "Grabbing the cat by the tail: manipulating molecules one by one," Nat. Rev. Mol. Cell Biol. 1, 130-136 (2000).
[CrossRef]

Angew. Chem., Int. Ed. (1)

A. Janshoff, M. Neitzert, Y. Oberdorfer, and H. Fuchs, "Force spectroscopy of molecular systems--Single molecule spectroscopy of polymers and biomolecules," Angew. Chem., Int. Ed. 39, 3213-3237 (2000).

Annu. Rev. Biophys. Biomol. Struct (1)

E. Evans, "Probing the relation between force lifetime and chemistry in single molecular bonds," Annu. Rev. Biophys. Biomol. Struct . 30, 105-128 (2001).
[CrossRef] [PubMed]

Annu. Rev. Biophys. Biomol. Struct. (1)

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

Appl. Opt. (2)

Biophys. J. (6)

K. C. Neuman, E. H. Chadd, G. F. Liou, K. Bergman, and S. M. Block, "Characterization of photodamage to Escherichia coli in optical traps," Biophys. J. 77, 2856-2863 (1999).
[CrossRef] [PubMed]

G. Leitz, E. Fällman, S. Tuck, and O. Axner, "Stress response in Caenorhabditis elegans caused by optical tweezers: wavelength, power, and time dependence," Biophys. J. 82, 2224-2231 (2002).
[CrossRef] [PubMed]

U. Bockelmann, P. Thomen, B. Essevaz-Roulet, V. Viasnoff, and F. Heslot, "Unzipping DNA with optical tweezers: high sequence sensitivity and force flips," Biophys. J. 82, 1537-1553 (2002).
[CrossRef] [PubMed]

J. Jass, S. Schedin, E. Fällman, J. Ohlsson, U. Nilsson, B. E. Uhlin, and O. Axner, "Physical properties of Escherichia coli P pili measured by optical tweezers," Biophys. J. 87, 4271-4283 (2004).
[CrossRef] [PubMed]

E. Evans and K. Ritchie, "Dynamic strength of molecular adhesion bonds," Biophys. J. 72, 1541-1555 (1997).
[CrossRef] [PubMed]

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "A sticky chain model of the elongation of Escherichia coli P pili under strain," Biophys. J. 90, 1521-1534 (2006).
[CrossRef]

Biosens. Bioelectron. (1)

E. Fällman, S. Schedin, J. Jass, M. Andersson, B. E. Uhlin, and O. Axner, "Optical tweezers based force measurement system for quantitating binding interactions: system design and application for the study of bacterial adhesion," Biosens. Bioelectron. 19, 1429-1437 (2004).
[CrossRef] [PubMed]

Curr. Opin. Struct. Biol. (1)

C. Bustamante, S. B. Smith, J. Liphardt, and D. Smith, "Single-molecule studies of DNA mechanics," Curr. Opin. Struct. Biol. 10, 279-285 (2000).
[CrossRef] [PubMed]

EMBO Rep. (1)

E. Fällman, S. Schedin, J. Jass, B. E. Uhlin, and O. Axner, "The unfolding of the P pili quaternary structure by stretching is reversible, not plastic," EMBO Rep. 6, 52-56 (2005).
[CrossRef]

Eur. Biophys. J. (1)

F. Gittes and C. F. Schmidt, "Thermal noise limitations on micromechanical experiments," Eur. Biophys. J. 27, 75-81 (1998).
[CrossRef]

Faraday Discuss. (1)

E. Evans, "Energy landscapes of biomolecular adhesion and receptor anchoring at interfaces explored with dynamic force spectroscopy," Faraday Discuss. 111, 1-16 (1999).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

K. Visscher, S. P. Gross, and S. M. Block, "Construction of multiple-beam optical traps with nanometer-resolution position sensing," IEEE J. Sel. Top. Quantum Electron. 2, 1066-1076 (1996).
[CrossRef]

Microsc. Res. Tech. (1)

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. Rev. Mol. Cell Biol. (1)

C. Bustamante, J. C. Macosko, and G. J. L. Wuite, "Grabbing the cat by the tail: manipulating molecules one by one," Nat. Rev. Mol. Cell Biol. 1, 130-136 (2000).
[CrossRef]

Nature (3)

R. Merkel, P. Nassoy, A. Leung, K. Ritchie, and E. Evans, "Energy landscapes of receptor-ligand bonds explored with dynamic force spectroscopy," Nature 397, 50-53 (1999).
[CrossRef] [PubMed]

J. W. Shaevitz, E. A. Abbondanzieri, R. Landick, and S. M. Block, "Backtracking by single RNA polymerase molecules observed at near-base-pair resolution," Nature 426, 684-687 (2003).
[CrossRef] [PubMed]

E. A. Abbondanzieri, W. J. Greenleaf, J. W. Shaevitz, R. Landick, and S. M. Block, "Direct observation of base-pair stepping by RNA polymerase," Nature 438, 460-465 (2005).
[CrossRef] [PubMed]

Opt. Lett. (1)

Phys. Rev. Lett. (1)

J. C. Meiners and S. R. Quake, "Direct measurement of hydrodynamic cross correlations between two particles in an external potential," Phys. Rev. Lett. 82, 2211-2214 (1999).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A. (1)

J. R. Moffitt, Y. R. Chemla, D. Izhaky, and C. Bustamante, "Differential detection of dual traps improves the spatial resolution of optical tweezers," Proc. Natl. Acad. Sci. U.S.A. 103, 9006-9011 (2006).
[CrossRef] [PubMed]

Proc. SPIE (1)

M. Andersson, E. Fällman, B. E. Uhlin, and O. Axner, "Force measuring optical tweezers system for long time measurements of Pili stability," in Proc. SPIE 6088, 286-295 (2006).

Rev. Sci. Instrum. (1)

K. C. Neuman and S. M. Block, "Optical trapping," Rev. Sci. Instrum. 75, 2787-2809 (2004).
[CrossRef]

Other (2)

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C--The Art of Scientific Computing (Cambridge U. Press, 1992).

S. B. Smith, Y. J. Cui, and C. Bustamante, "Optical-trap force transducer that operates by direct measurement of light momentum," Meth. Enzymol. 361, 134-162 (2003).

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Figures (5)

Fig. 1
Fig. 1

(Color online) Schematic of the experimental setup. PBSC, polarizing beam-splitting cube; C, chopper; FR, Fresnel rhomb; PSD, position sensitive detector.

Fig. 2
Fig. 2

(Color online) (a) Power spectrum of a bead trapped in the reference trap for a period of 260   s . Solid curve represents the best fit to the data of the expression for the Brownian motion of a bead in a trap, slightly corrected for the finite detection bandwidth, of the form S x ( f ) = a f c b / ( f c b + f b ) , where a, b, and f c took values of 0.35 nm 2 / Hz , 2.44, and 191   Hz , respectively. (b)–(d) Solid curves, standard deviation of the force signal corresponding to the position data used for the power spectrum displayed in (a) for measurement sequences with time periods τ of 1, 10, and 100   s , respectively, as a function of detection bandwidth f c det . Dotted curves, standard deviation of the force signal corresponding to the Brownian motion of the trapped bead [i.e., the fit in (a)]. Dashed curve, standard deviation of the 1 / f noise.

Fig. 3
Fig. 3

(Color online) Correlation coefficient R for the correlation between the two raw data sets, B 1 and B 2 * , as a function of cutoff frequency of the low-pass filtering of the reference bead data f c ref .

Fig. 4
Fig. 4

(Color online) Typical set of force data in the time domain. Curve b, raw data from the force transducer bead, B 1 . Curve c, raw data from the reference bead, B 2 . Both detected with a detection bandwidth of 100   Hz . Solid curve inside curve d, low-pass filtered data from the reference bead, B 2 * , filtered with a cutoff frequency of 2   Hz . Curve a, corrected force transducer bead data, B 1 * , created by a subtraction of B 2 * from B 1 . Data sets have been arbitrarily shifted in the plot for illustrative purposes.

Fig. 5
Fig. 5

(Color online) Demonstration of the applicability of the dual-beam noise reduction technique for a case when the force measuring bead was exposed to an external force of about 17   pN . Curves correspond to the same measurement conditions as those in Fig. 4.

Equations (5)

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

σ x 2 = 1 / τ f c det S x ( f ) d f ,
σ F = κ σ x 2 ,
S x B = k B T γ π 2 1 ( f c 2 + f 2 ) ,
σ F = 2 κ k B T π [ arctan ( f c det f c ) arctan ( 1 f c τ ) ] .
R = ( B 1 B 1 ¯ ) ( B 2 * B 2 * ¯ ) ( B 1 B 1 ¯ ) 2 ( B 2 * B 2 * ¯ ) 2 ,

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