The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur

doi:10.1364/OE.14.012517

The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur

Wesley P. Wong and Ken Halvorsen »View Author Affiliations

Optics Express, Vol. 14, Issue 25, pp. 12517-12531 (2006)
http://dx.doi.org/10.1364/OE.14.012517

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Abstract

Dynamical instrument limitations, such as finite detection bandwidth, do not simply add statistical errors to fluctuation measurements, but can create significant systematic biases that affect the measurement of steady-state properties. Such effects must be considered when calibrating ultra-sensitive force probes by analyzing the observed Brownian fluctuations. In this article, we present a novel method for extracting the true spring constant and diffusion coefficient of a harmonically confined Brownian particle that extends the standard equipartition and power spectrum techniques to account for video-image motion blur. These results are confirmed both numerically with a Brownian dynamics simulation, and experimentally with laser optical tweezers.

OCIS Codes
(110.4280) Imaging systems : Noise in imaging systems
(140.7010) Lasers and laser optics : Laser trapping
(170.4520) Medical optics and biotechnology : Optical confinement and manipulation

ToC Category:
Trapping

History
Original Manuscript: July 21, 2006
Revised Manuscript: October 24, 2006
Manuscript Accepted: November 24, 2006
Published: December 11, 2006

Virtual Issues
Vol. 2, Iss. 1 Virtual Journal for Biomedical Optics

Citation
Wesley P. Wong and Ken Halvorsen, "The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur," Opt. Express 14, 12517-12531 (2006)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-14-25-12517

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References

K. Svoboda, P.P. Mitra, and S.M. Block, "Fluctuation analysis of Motor Protein Movement and Single Enzyme Kinetics," Proc. Natl. Acad. Sci. USA 91, 11782-11786 (1994). [CrossRef] [PubMed]
T.G. Mason and D.A. Weitz, "Optical Measurements of Frequency-Dependent Linear Viscoelastic Moduli of Complex Fluids," Phys. Rev. Lett. 74, 1250-1253 (1995). [CrossRef] [PubMed]
E. Evans and K. Ritchie, "Dynamic strength of molecular adhesion bonds," Biophys. J. 72, 1541-1555 (1997). [CrossRef] [PubMed]
D. Collin, F. Ritort, C. Jarzynski, S.B. Smith, I. Tinoco, Jr., and C. Bustamante, "Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies," Nature (London) 437, 231-234 (2005). [CrossRef] [PubMed]
T.R. Strick, J.F. Allemand, D. Bensimon, A. Bensimon, and V. Croquette, "The elasticity of a single supercoiled DNA molecule." Science 271, 1835-1837 (1996). [CrossRef] [PubMed]
D.T. Chen, E.R. Weeks, J.C. Crocker, M.F. Islam, R. Verma, J. Gruber, A.J. Levine, T.C. Lubensky, and A.G. Yodh, "Rheological Microscopy: Local Mechanical Properties from Microrheology," Phys. Rev. Lett. 90, 108301 (2003). [CrossRef] [PubMed]
R. Yasuda, H. Miyata, and K. Kinosita, Jr., "Direct measurement of the torsional rigidity of single actin filaments," J. Mol. Biol. 263, 227-236 (1996). [CrossRef] [PubMed]
T. Savin and P.S. Doyle, "Static and Dynamic Errors in Particle Tracking Microrheology," Biophys. J. 88, 623-638 (2005). [CrossRef]
T. Savin and P.S. Doyle, "Role of a finite exposure time on measuring an elastic modulus using microrheology," Phys. Rev. E 71, 41106 (2005). [CrossRef]
L.P. Ghislain and W.W. Webb, "Scanning-force microscope based on an optical trap," Opt. Lett. 18, 1678-1680 (1993). [CrossRef] [PubMed]
K. Svoboda and S.M. Block, "Biological applications of optical forces." Annu. Rev. Biophys. Biomol. Struct. 23, 247-285 (1994). [CrossRef] [PubMed]
F. Gittes and C.F. Schmidt, "Signals and noise in micromechanical measurements." Methods Cell Biol. 55, 129-156 (1998). [CrossRef]
E.-L. Florin, A. Pralle, E.H.K. Stelzer, and J.K.H. Hörber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, 75-78 (1998). [CrossRef]
K. Berg-Sørensen and H. Flyvbjerg, "Power spectrum analysis for optical tweezers," Rev. Sci. Instrum. 75, 594-612 (2004). [CrossRef]
A.V. Oppenheim, A.S. Willsky, and S.H. Nawab, Signals & systems (Prentice-Hall, Inc., Upper Saddle River, NJ, 1996).
M.C. Wang and G.E. Uhlenbeck, "On the Theory of the Brownian Motion II," Rev. Mod. Phys. 17, 323-342 (1945). [CrossRef]
D.L. Ermak and J.A. McCammon. "Brownian dynamics with hydrodynamic interactions," J. Chem. Phys. 69, 1352-1360 (1978). [CrossRef]
M. Doi and S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).
J.F. Kenney and E.S. Keeping, Mathematics of Statistics, Pt. 2, 2nd ed. (Van Nostrand, Princeton, NJ, 1951).
Data aquisition software was written by Volkmar Heinrich.
E.J.G. Peterman, F. Gittes, and C.F. Schmidt, "Laser-Induced Heating in Optical Traps," Biophys. J. 84, 1308-1316 (2003). [CrossRef] [PubMed]
P.M. Celliers and J. Conia, "Measurement of localized heating in the focus of an optical trap," Appl. Opt. 39, 3396-3407 (2000). [CrossRef]

Allemand, J.F.
Bensimon, A.
Bensimon, D.
Berg-Sørensen, K.
Block, S.M.
Bustamante, C.
Celliers, P.M.
Chen, D.T.
Collin, D.
Conia, J.
Crocker, J.C.
Croquette, V.
Doyle, P.S.
Ermak, D.L.
Evans, E.
Florin, E.-L.
Flyvbjerg, H.
Ghislain, L.P.
Gittes, F.
Gruber, J.
Hörber, J.K.H.
Islam, M.F.
Jarzynski, C.
Kinosita, K.
Levine, A.J.
Lubensky, T.C.
Mason, T.G.
McCammon, J.A.
Mitra, P.P.
Miyata, H.
Peterman, E.J.G.
Pralle, A.
Ritchie, K.
Ritort, F.
Savin, T.
Schmidt, C.F.
Smith, S.B.
Stelzer, E.H.K.
Strick, T.R.
Svoboda, K.
Tinoco, I.
Uhlenbeck, G.E.
Verma, R.
Wang, M.C.
Webb, W.W.
Weeks, E.R.
Weitz, D.A.
Yasuda, R.
Yodh, A.G.

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.

P.M. Celliers and J. Conia, "Measurement of localized heating in the focus of an optical trap," Appl. Opt. 39, 3396-3407 (2000). [CrossRef]

Appl. Phys. A

E.-L. Florin, A. Pralle, E.H.K. Stelzer, and J.K.H. Hörber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, 75-78 (1998). [CrossRef]

Biophys. J.

E. Evans and K. Ritchie, "Dynamic strength of molecular adhesion bonds," Biophys. J. 72, 1541-1555 (1997). [CrossRef] [PubMed]
T. Savin and P.S. Doyle, "Static and Dynamic Errors in Particle Tracking Microrheology," Biophys. J. 88, 623-638 (2005). [CrossRef]
E.J.G. Peterman, F. Gittes, and C.F. Schmidt, "Laser-Induced Heating in Optical Traps," Biophys. J. 84, 1308-1316 (2003). [CrossRef] [PubMed]

J. Chem. Phys.

D.L. Ermak and J.A. McCammon. "Brownian dynamics with hydrodynamic interactions," J. Chem. Phys. 69, 1352-1360 (1978). [CrossRef]

J. Mol. Biol.

R. Yasuda, H. Miyata, and K. Kinosita, Jr., "Direct measurement of the torsional rigidity of single actin filaments," J. Mol. Biol. 263, 227-236 (1996). [CrossRef] [PubMed]

Methods Cell Biol.

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

Nature (London)

D. Collin, F. Ritort, C. Jarzynski, S.B. Smith, I. Tinoco, Jr., and C. Bustamante, "Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies," Nature (London) 437, 231-234 (2005). [CrossRef] [PubMed]

Opt. Lett.

L.P. Ghislain and W.W. Webb, "Scanning-force microscope based on an optical trap," Opt. Lett. 18, 1678-1680 (1993). [CrossRef] [PubMed]

Phys. Rev. E

T. Savin and P.S. Doyle, "Role of a finite exposure time on measuring an elastic modulus using microrheology," Phys. Rev. E 71, 41106 (2005). [CrossRef]

Phys. Rev. Lett.

D.T. Chen, E.R. Weeks, J.C. Crocker, M.F. Islam, R. Verma, J. Gruber, A.J. Levine, T.C. Lubensky, and A.G. Yodh, "Rheological Microscopy: Local Mechanical Properties from Microrheology," Phys. Rev. Lett. 90, 108301 (2003). [CrossRef] [PubMed]
T.G. Mason and D.A. Weitz, "Optical Measurements of Frequency-Dependent Linear Viscoelastic Moduli of Complex Fluids," Phys. Rev. Lett. 74, 1250-1253 (1995). [CrossRef] [PubMed]

Proc. Natl. Acad. Sci. USA

K. Svoboda, P.P. Mitra, and S.M. Block, "Fluctuation analysis of Motor Protein Movement and Single Enzyme Kinetics," Proc. Natl. Acad. Sci. USA 91, 11782-11786 (1994). [CrossRef] [PubMed]

Rev. Mod. Phys.

M.C. Wang and G.E. Uhlenbeck, "On the Theory of the Brownian Motion II," Rev. Mod. Phys. 17, 323-342 (1945). [CrossRef]

Rev. Sci. Instrum.

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

Science

T.R. Strick, J.F. Allemand, D. Bensimon, A. Bensimon, and V. Croquette, "The elasticity of a single supercoiled DNA molecule." Science 271, 1835-1837 (1996). [CrossRef] [PubMed]

Other

A.V. Oppenheim, A.S. Willsky, and S.H. Nawab, Signals & systems (Prentice-Hall, Inc., Upper Saddle River, NJ, 1996).
M. Doi and S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).
J.F. Kenney and E.S. Keeping, Mathematics of Statistics, Pt. 2, 2nd ed. (Van Nostrand, Princeton, NJ, 1951).
Data aquisition software was written by Volkmar Heinrich.

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[1] K. Svoboda, P.P. Mitra, and S.M. Block, "Fluctuation analysis of Motor Protein Movement and Single Enzyme Kinetics," Proc. Natl. Acad. Sci. USA 91, 11782-11786 (1994). [CrossRef] [PubMed]

[2] T.G. Mason and D.A. Weitz, "Optical Measurements of Frequency-Dependent Linear Viscoelastic Moduli of Complex Fluids," Phys. Rev. Lett. 74, 1250-1253 (1995). [CrossRef] [PubMed]

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

[4] D. Collin, F. Ritort, C. Jarzynski, S.B. Smith, I. Tinoco, Jr., and C. Bustamante, "Verification of the Crooks fluctuation theorem and recovery of RNA folding free energies," Nature (London) 437, 231-234 (2005). [CrossRef] [PubMed]

[5] T.R. Strick, J.F. Allemand, D. Bensimon, A. Bensimon, and V. Croquette, "The elasticity of a single supercoiled DNA molecule." Science 271, 1835-1837 (1996). [CrossRef] [PubMed]

[6] D.T. Chen, E.R. Weeks, J.C. Crocker, M.F. Islam, R. Verma, J. Gruber, A.J. Levine, T.C. Lubensky, and A.G. Yodh, "Rheological Microscopy: Local Mechanical Properties from Microrheology," Phys. Rev. Lett. 90, 108301 (2003). [CrossRef] [PubMed]

[7] R. Yasuda, H. Miyata, and K. Kinosita, Jr., "Direct measurement of the torsional rigidity of single actin filaments," J. Mol. Biol. 263, 227-236 (1996). [CrossRef] [PubMed]

[8] T. Savin and P.S. Doyle, "Static and Dynamic Errors in Particle Tracking Microrheology," Biophys. J. 88, 623-638 (2005). [CrossRef]

[9] T. Savin and P.S. Doyle, "Role of a finite exposure time on measuring an elastic modulus using microrheology," Phys. Rev. E 71, 41106 (2005). [CrossRef]

[10] L.P. Ghislain and W.W. Webb, "Scanning-force microscope based on an optical trap," Opt. Lett. 18, 1678-1680 (1993). [CrossRef] [PubMed]

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

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

[13] E.-L. Florin, A. Pralle, E.H.K. Stelzer, and J.K.H. Hörber, "Photonic force microscope calibration by thermal noise analysis," Appl. Phys. A 66, 75-78 (1998). [CrossRef]

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

[15] A.V. Oppenheim, A.S. Willsky, and S.H. Nawab, Signals & systems (Prentice-Hall, Inc., Upper Saddle River, NJ, 1996).

[16] M.C. Wang and G.E. Uhlenbeck, "On the Theory of the Brownian Motion II," Rev. Mod. Phys. 17, 323-342 (1945). [CrossRef]

[17] D.L. Ermak and J.A. McCammon. "Brownian dynamics with hydrodynamic interactions," J. Chem. Phys. 69, 1352-1360 (1978). [CrossRef]

[18] M. Doi and S.F. Edwards, The Theory of Polymer Dynamics (Clarendon Press, Oxford, 1986).

[19] J.F. Kenney and E.S. Keeping, Mathematics of Statistics, Pt. 2, 2nd ed. (Van Nostrand, Princeton, NJ, 1951).

[20] Data aquisition software was written by Volkmar Heinrich.

[21] E.J.G. Peterman, F. Gittes, and C.F. Schmidt, "Laser-Induced Heating in Optical Traps," Biophys. J. 84, 1308-1316 (2003). [CrossRef] [PubMed]

[22] P.M. Celliers and J. Conia, "Measurement of localized heating in the focus of an optical trap," Appl. Opt. 39, 3396-3407 (2000). [CrossRef]

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The effect of integration time on fluctuation measurements: calibrating an optical trap in the presence of motion blur

Article Tools

Abstract

References

Annu. Rev. Biophys. Biomol. Struct.

Appl. Opt.

Appl. Phys. A

Biophys. J.

J. Chem. Phys.

J. Mol. Biol.

Methods Cell Biol.

Nature (London)

Opt. Lett.

Phys. Rev. E

Phys. Rev. Lett.

Proc. Natl. Acad. Sci. USA

Rev. Mod. Phys.

Rev. Sci. Instrum.

Science

Other

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