Abstract

The frequency-dependent viscous and elastic properties of fluids can be determined from measurements of the thermal fluctuations of a micron-sized particle trapped by optical tweezers. Finite bandwidth and other instrument limitations lead to systematic errors in measurement of the fluctuations. In this work, we numerically represented power spectra of bead position measurements as if collected by two different measurement devices: a quadrant photodiode, which measures the deflection of the trapping laser; and a high-speed camera, which images the trapped bead directly. We explored the effects of aliasing, camera blur, sampling frequency, and measurement time. By comparing the power spectrum, complex response function, and the complex shear modulus with the ideal values, we found that the viscous and elastic properties inferred from the data are affected by the instrument limitations of each device. We discuss how these systematic effects might affect experimental results from microrheology measurements and suggest approaches to reduce discrepancies.

© 2017 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  5. I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, “Anomalous diffusion probes microstructure dynamics of entangled F-actin networks,” Phys. Rev. Lett. 92, 178101–111 (2004).
    [Crossref]
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    [Crossref]
  7. T. G. Mason, H. Gang, and D. A. Weitz, “Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids,” J. Opt. Soc. Am. 14, 139 (1997).
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  8. R. E. Mahaffy, C. K. Shih, F. C. MacKintosh, and J. Käs, “Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells,” Phys. Rev. Lett. 85, 880–883 (2000).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]

2016 (2)

T. A. Waigh, “Advances in the microrheology of complex fluids,” Rep. Prog. Phys. 79, 074601 (2016).
[Crossref]

M. Shayegan, T. Altindal, E. Kiefl, and N. R. Forde, “Intact Telopeptides Enhance Interactions between Collagens,” Biophys. J. 111, 2404–2416 (2016).
[Crossref] [PubMed]

2015 (1)

A. D. Wessel, M. Gumalla, J. Grosshans, and C. F. Schmidt, “The mechanical properties of early drosophila embryos measured by high-speed video microrheology,” Biophys. J. 108, 1899–1907 (2015).
[Crossref] [PubMed]

2013 (1)

M. Shayegan and N. R. Forde, “Microrheological characterization of collagen systems: from molecular solutions to fibrillar gels,” PLoS ONE 8, 23–28 (2013).
[Crossref]

2012 (1)

H. Lee, Y. Shin, S. T. Kim, E. L. Reinherz, and M. J. Lang, “Stochastic optical active rheology,” Appl. Phys. Lett. 101, 1–4 (2012).

2011 (1)

S. F. Nørrelykke and H. Flyvbjerg, “Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data and exact analytical benchmark statistics,” Phys. Rev. E 83, 1–10 (2011).
[Crossref]

2010 (1)

2009 (2)

B. D. Hoffman and J. C. Crocker, “Cell mechanics: dissecting the physical responses of cells to force,” Annu. Rev. Biomed. Eng. 11, 259–288 (2009).
[Crossref] [PubMed]

D. Wirtz, “Particle-tracking microrheology of living cells: principles and applications,” Annu. Rev. Biophys. 38, 301–326 (2009).
[Crossref] [PubMed]

2008 (2)

A. van der Horst and N. R. Forde, “Calibration of dynamic holographic optical tweezers for force measurements on biomaterials,” Opt. Express 16, 20987 (2008).
[Crossref]

D. Mizuno, D. A. Head, F. C. MacKintosh, and C. F. Schmidt, “Active and Passive Microrheology in Equilibrium and Nonequilibrium Systems,” Macromolecules 41, 7194–7202 (2008).
[Crossref]

2007 (1)

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

2006 (2)

2005 (3)

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, 6–11 (2005).
[Crossref]

T. A. Waigh, “Microrheology of complex fluids,” Rep. Prog. Phys. 68, 685–742 (2005).
[Crossref]

2004 (3)

I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, “Anomalous diffusion probes microstructure dynamics of entangled F-actin networks,” Phys. Rev. Lett. 92, 178101–111 (2004).
[Crossref]

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

K. M. Addas, C. F. Schmidt, and J. X. Tang, “Microrheology of solutions of semiflexible biopolymer filaments using laser tweezers interferometry,” Phys. Rev. E 70, 1–16 (2004).
[Crossref]

2002 (1)

D. S. Martin, M. B. Forstner, and J. A. Käs, “Apparent Subdiffusion Inherent to Single Particle Tracking,” Biophys. J. 83, 2109–2117 (2002).
[Crossref] [PubMed]

2000 (1)

R. E. Mahaffy, C. K. Shih, F. C. MacKintosh, and J. Käs, “Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells,” Phys. Rev. Lett. 85, 880–883 (2000).
[Crossref] [PubMed]

1999 (1)

A. R. Bausch, W. Möller, and E. Sackmann, “Measurement of local viscoelasticity and forces in living cells by magnetic tweezers,” Biophys. J. 76, 573–579 (1999).
[Crossref] [PubMed]

1997 (3)

B. Schnurr, F. Gittes, F. C. Mackintosh, and C. F. Schmidt, “Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations,” Macromolecules 9297, 7781–7792 (1997).
[Crossref]

T. G. Mason, K. Ganesan, J. van Zanten, D. Wirtz, and S. Kuo, “Particle Tracking Microrheology of Complex Fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[Crossref]

T. G. Mason, H. Gang, and D. A. Weitz, “Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids,” J. Opt. Soc. Am. 14, 139 (1997).
[Crossref]

1988 (1)

Addas, K. M.

K. M. Addas, C. F. Schmidt, and J. X. Tang, “Microrheology of solutions of semiflexible biopolymer filaments using laser tweezers interferometry,” Phys. Rev. E 70, 1–16 (2004).
[Crossref]

Altindal, T.

M. Shayegan, T. Altindal, E. Kiefl, and N. R. Forde, “Intact Telopeptides Enhance Interactions between Collagens,” Biophys. J. 111, 2404–2416 (2016).
[Crossref] [PubMed]

Bausch, A. R.

I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, “Anomalous diffusion probes microstructure dynamics of entangled F-actin networks,” Phys. Rev. Lett. 92, 178101–111 (2004).
[Crossref]

A. R. Bausch, W. Möller, and E. Sackmann, “Measurement of local viscoelasticity and forces in living cells by magnetic tweezers,” Biophys. J. 76, 573–579 (1999).
[Crossref] [PubMed]

Berg-Sørensen, K.

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

Boyce, M. C.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

Brau, R. R.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

Castro, C. E.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

Crocker, J. C.

B. D. Hoffman and J. C. Crocker, “Cell mechanics: dissecting the physical responses of cells to force,” Annu. Rev. Biomed. Eng. 11, 259–288 (2009).
[Crossref] [PubMed]

Doyle, P. S.

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, 6–11 (2005).
[Crossref]

Ferrer, J. M.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

Flyvbjerg, H.

S. F. Nørrelykke and H. Flyvbjerg, “Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data and exact analytical benchmark statistics,” Phys. Rev. E 83, 1–10 (2011).
[Crossref]

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

Forde, N. R.

M. Shayegan, T. Altindal, E. Kiefl, and N. R. Forde, “Intact Telopeptides Enhance Interactions between Collagens,” Biophys. J. 111, 2404–2416 (2016).
[Crossref] [PubMed]

M. Shayegan and N. R. Forde, “Microrheological characterization of collagen systems: from molecular solutions to fibrillar gels,” PLoS ONE 8, 23–28 (2013).
[Crossref]

A. van der Horst and N. R. Forde, “Power spectral analysis for optical trap stiffness calibration from high-speed camera position detection with limited bandwidth,” Opt. Express 18, 7670–7677 (2010).
[Crossref] [PubMed]

A. van der Horst and N. R. Forde, “Calibration of dynamic holographic optical tweezers for force measurements on biomaterials,” Opt. Express 16, 20987 (2008).
[Crossref]

Forstner, M. B.

D. S. Martin, M. B. Forstner, and J. A. Käs, “Apparent Subdiffusion Inherent to Single Particle Tracking,” Biophys. J. 83, 2109–2117 (2002).
[Crossref] [PubMed]

Furst, E. M.

J. Y. Huh and E. M. Furst, “Colloid dynamics in semiflexible polymer solutions,” Phys. Rev. E 74031802 (2006).
[Crossref]

Ganesan, K.

T. G. Mason, K. Ganesan, J. van Zanten, D. Wirtz, and S. Kuo, “Particle Tracking Microrheology of Complex Fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[Crossref]

Gang, H.

T. G. Mason, H. Gang, and D. A. Weitz, “Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids,” J. Opt. Soc. Am. 14, 139 (1997).
[Crossref]

Gardel, M. L.

I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, “Anomalous diffusion probes microstructure dynamics of entangled F-actin networks,” Phys. Rev. Lett. 92, 178101–111 (2004).
[Crossref]

Gittes, F.

B. Schnurr, F. Gittes, F. C. Mackintosh, and C. F. Schmidt, “Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations,” Macromolecules 9297, 7781–7792 (1997).
[Crossref]

Graessley, W. W.

W. W. Graessley, Polymeric Liquids and Networks: Dynamics and Rheology (Taylor & Francis Group, LLC, 2008).

Grosshans, J.

A. D. Wessel, M. Gumalla, J. Grosshans, and C. F. Schmidt, “The mechanical properties of early drosophila embryos measured by high-speed video microrheology,” Biophys. J. 108, 1899–1907 (2015).
[Crossref] [PubMed]

Gumalla, M.

A. D. Wessel, M. Gumalla, J. Grosshans, and C. F. Schmidt, “The mechanical properties of early drosophila embryos measured by high-speed video microrheology,” Biophys. J. 108, 1899–1907 (2015).
[Crossref] [PubMed]

Halvorsen, K.

Head, D. A.

D. Mizuno, D. A. Head, F. C. MacKintosh, and C. F. Schmidt, “Active and Passive Microrheology in Equilibrium and Nonequilibrium Systems,” Macromolecules 41, 7194–7202 (2008).
[Crossref]

Hoffman, B. D.

B. D. Hoffman and J. C. Crocker, “Cell mechanics: dissecting the physical responses of cells to force,” Annu. Rev. Biomed. Eng. 11, 259–288 (2009).
[Crossref] [PubMed]

Huh, J. Y.

J. Y. Huh and E. M. Furst, “Colloid dynamics in semiflexible polymer solutions,” Phys. Rev. E 74031802 (2006).
[Crossref]

Ishida, H.

Kamm, R. D.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

Käs, J.

R. E. Mahaffy, C. K. Shih, F. C. MacKintosh, and J. Käs, “Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells,” Phys. Rev. Lett. 85, 880–883 (2000).
[Crossref] [PubMed]

Käs, J. A.

D. S. Martin, M. B. Forstner, and J. A. Käs, “Apparent Subdiffusion Inherent to Single Particle Tracking,” Biophys. J. 83, 2109–2117 (2002).
[Crossref] [PubMed]

Kiefl, E.

M. Shayegan, T. Altindal, E. Kiefl, and N. R. Forde, “Intact Telopeptides Enhance Interactions between Collagens,” Biophys. J. 111, 2404–2416 (2016).
[Crossref] [PubMed]

Kim, S. T.

H. Lee, Y. Shin, S. T. Kim, E. L. Reinherz, and M. J. Lang, “Stochastic optical active rheology,” Appl. Phys. Lett. 101, 1–4 (2012).

Kuo, S.

T. G. Mason, K. Ganesan, J. van Zanten, D. Wirtz, and S. Kuo, “Particle Tracking Microrheology of Complex Fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[Crossref]

Lang, M. J.

H. Lee, Y. Shin, S. T. Kim, E. L. Reinherz, and M. J. Lang, “Stochastic optical active rheology,” Appl. Phys. Lett. 101, 1–4 (2012).

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

Lee, H.

H. Lee, Y. Shin, S. T. Kim, E. L. Reinherz, and M. J. Lang, “Stochastic optical active rheology,” Appl. Phys. Lett. 101, 1–4 (2012).

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

MacKintosh, F. C.

D. Mizuno, D. A. Head, F. C. MacKintosh, and C. F. Schmidt, “Active and Passive Microrheology in Equilibrium and Nonequilibrium Systems,” Macromolecules 41, 7194–7202 (2008).
[Crossref]

R. E. Mahaffy, C. K. Shih, F. C. MacKintosh, and J. Käs, “Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells,” Phys. Rev. Lett. 85, 880–883 (2000).
[Crossref] [PubMed]

B. Schnurr, F. Gittes, F. C. Mackintosh, and C. F. Schmidt, “Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations,” Macromolecules 9297, 7781–7792 (1997).
[Crossref]

Mahaffy, R. E.

R. E. Mahaffy, C. K. Shih, F. C. MacKintosh, and J. Käs, “Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells,” Phys. Rev. Lett. 85, 880–883 (2000).
[Crossref] [PubMed]

Martin, D. S.

D. S. Martin, M. B. Forstner, and J. A. Käs, “Apparent Subdiffusion Inherent to Single Particle Tracking,” Biophys. J. 83, 2109–2117 (2002).
[Crossref] [PubMed]

Mason, T. G.

T. G. Mason, H. Gang, and D. A. Weitz, “Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids,” J. Opt. Soc. Am. 14, 139 (1997).
[Crossref]

T. G. Mason, K. Ganesan, J. van Zanten, D. Wirtz, and S. Kuo, “Particle Tracking Microrheology of Complex Fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[Crossref]

Matsudaira, P.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

Mizuno, D.

D. Mizuno, D. A. Head, F. C. MacKintosh, and C. F. Schmidt, “Active and Passive Microrheology in Equilibrium and Nonequilibrium Systems,” Macromolecules 41, 7194–7202 (2008).
[Crossref]

Möller, W.

A. R. Bausch, W. Möller, and E. Sackmann, “Measurement of local viscoelasticity and forces in living cells by magnetic tweezers,” Biophys. J. 76, 573–579 (1999).
[Crossref] [PubMed]

Nørrelykke, S. F.

S. F. Nørrelykke and H. Flyvbjerg, “Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data and exact analytical benchmark statistics,” Phys. Rev. E 83, 1–10 (2011).
[Crossref]

Ohta, K.

Reichman, D. R.

I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, “Anomalous diffusion probes microstructure dynamics of entangled F-actin networks,” Phys. Rev. Lett. 92, 178101–111 (2004).
[Crossref]

Reinherz, E. L.

H. Lee, Y. Shin, S. T. Kim, E. L. Reinherz, and M. J. Lang, “Stochastic optical active rheology,” Appl. Phys. Lett. 101, 1–4 (2012).

Sackmann, E.

A. R. Bausch, W. Möller, and E. Sackmann, “Measurement of local viscoelasticity and forces in living cells by magnetic tweezers,” Biophys. J. 76, 573–579 (1999).
[Crossref] [PubMed]

Savin, T.

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, 6–11 (2005).
[Crossref]

Schmidt, C. F.

A. D. Wessel, M. Gumalla, J. Grosshans, and C. F. Schmidt, “The mechanical properties of early drosophila embryos measured by high-speed video microrheology,” Biophys. J. 108, 1899–1907 (2015).
[Crossref] [PubMed]

D. Mizuno, D. A. Head, F. C. MacKintosh, and C. F. Schmidt, “Active and Passive Microrheology in Equilibrium and Nonequilibrium Systems,” Macromolecules 41, 7194–7202 (2008).
[Crossref]

K. M. Addas, C. F. Schmidt, and J. X. Tang, “Microrheology of solutions of semiflexible biopolymer filaments using laser tweezers interferometry,” Phys. Rev. E 70, 1–16 (2004).
[Crossref]

B. Schnurr, F. Gittes, F. C. Mackintosh, and C. F. Schmidt, “Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations,” Macromolecules 9297, 7781–7792 (1997).
[Crossref]

Schnurr, B.

B. Schnurr, F. Gittes, F. C. Mackintosh, and C. F. Schmidt, “Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations,” Macromolecules 9297, 7781–7792 (1997).
[Crossref]

Shayegan, M.

M. Shayegan, T. Altindal, E. Kiefl, and N. R. Forde, “Intact Telopeptides Enhance Interactions between Collagens,” Biophys. J. 111, 2404–2416 (2016).
[Crossref] [PubMed]

M. Shayegan and N. R. Forde, “Microrheological characterization of collagen systems: from molecular solutions to fibrillar gels,” PLoS ONE 8, 23–28 (2013).
[Crossref]

Shih, C. K.

R. E. Mahaffy, C. K. Shih, F. C. MacKintosh, and J. Käs, “Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells,” Phys. Rev. Lett. 85, 880–883 (2000).
[Crossref] [PubMed]

Shin, Y.

H. Lee, Y. Shin, S. T. Kim, E. L. Reinherz, and M. J. Lang, “Stochastic optical active rheology,” Appl. Phys. Lett. 101, 1–4 (2012).

Tam, B. K.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

Tang, J. X.

K. M. Addas, C. F. Schmidt, and J. X. Tang, “Microrheology of solutions of semiflexible biopolymer filaments using laser tweezers interferometry,” Phys. Rev. E 70, 1–16 (2004).
[Crossref]

Tarsa, P. B.

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

Valentine, M. T.

I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, “Anomalous diffusion probes microstructure dynamics of entangled F-actin networks,” Phys. Rev. Lett. 92, 178101–111 (2004).
[Crossref]

van der Horst, A.

A. van der Horst and N. R. Forde, “Power spectral analysis for optical trap stiffness calibration from high-speed camera position detection with limited bandwidth,” Opt. Express 18, 7670–7677 (2010).
[Crossref] [PubMed]

A. van der Horst and N. R. Forde, “Calibration of dynamic holographic optical tweezers for force measurements on biomaterials,” Opt. Express 16, 20987 (2008).
[Crossref]

van Zanten, J.

T. G. Mason, K. Ganesan, J. van Zanten, D. Wirtz, and S. Kuo, “Particle Tracking Microrheology of Complex Fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[Crossref]

Waigh, T. A.

T. A. Waigh, “Advances in the microrheology of complex fluids,” Rep. Prog. Phys. 79, 074601 (2016).
[Crossref]

T. A. Waigh, “Microrheology of complex fluids,” Rep. Prog. Phys. 68, 685–742 (2005).
[Crossref]

Weeks, E. R.

I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, “Anomalous diffusion probes microstructure dynamics of entangled F-actin networks,” Phys. Rev. Lett. 92, 178101–111 (2004).
[Crossref]

Weitz, D. A.

I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, “Anomalous diffusion probes microstructure dynamics of entangled F-actin networks,” Phys. Rev. Lett. 92, 178101–111 (2004).
[Crossref]

T. G. Mason, H. Gang, and D. A. Weitz, “Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids,” J. Opt. Soc. Am. 14, 139 (1997).
[Crossref]

Wessel, A. D.

A. D. Wessel, M. Gumalla, J. Grosshans, and C. F. Schmidt, “The mechanical properties of early drosophila embryos measured by high-speed video microrheology,” Biophys. J. 108, 1899–1907 (2015).
[Crossref] [PubMed]

Wirtz, D.

D. Wirtz, “Particle-tracking microrheology of living cells: principles and applications,” Annu. Rev. Biophys. 38, 301–326 (2009).
[Crossref] [PubMed]

T. G. Mason, K. Ganesan, J. van Zanten, D. Wirtz, and S. Kuo, “Particle Tracking Microrheology of Complex Fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[Crossref]

Wong, I. Y.

I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, “Anomalous diffusion probes microstructure dynamics of entangled F-actin networks,” Phys. Rev. Lett. 92, 178101–111 (2004).
[Crossref]

Wong, W. P.

Annu. Rev. Biomed. Eng. (1)

B. D. Hoffman and J. C. Crocker, “Cell mechanics: dissecting the physical responses of cells to force,” Annu. Rev. Biomed. Eng. 11, 259–288 (2009).
[Crossref] [PubMed]

Annu. Rev. Biophys. (1)

D. Wirtz, “Particle-tracking microrheology of living cells: principles and applications,” Annu. Rev. Biophys. 38, 301–326 (2009).
[Crossref] [PubMed]

Appl. Phys. Lett. (1)

H. Lee, Y. Shin, S. T. Kim, E. L. Reinherz, and M. J. Lang, “Stochastic optical active rheology,” Appl. Phys. Lett. 101, 1–4 (2012).

Appl. Spectrosc. (1)

Biophys. J. (5)

D. S. Martin, M. B. Forstner, and J. A. Käs, “Apparent Subdiffusion Inherent to Single Particle Tracking,” Biophys. J. 83, 2109–2117 (2002).
[Crossref] [PubMed]

M. Shayegan, T. Altindal, E. Kiefl, and N. R. Forde, “Intact Telopeptides Enhance Interactions between Collagens,” Biophys. J. 111, 2404–2416 (2016).
[Crossref] [PubMed]

A. D. Wessel, M. Gumalla, J. Grosshans, and C. F. Schmidt, “The mechanical properties of early drosophila embryos measured by high-speed video microrheology,” Biophys. J. 108, 1899–1907 (2015).
[Crossref] [PubMed]

T. Savin and P. S. Doyle, “Static and Dynamic Errors in Particle Tracking Microrheology,” Biophys. J. 88, 623–638 (2005).
[Crossref]

A. R. Bausch, W. Möller, and E. Sackmann, “Measurement of local viscoelasticity and forces in living cells by magnetic tweezers,” Biophys. J. 76, 573–579 (1999).
[Crossref] [PubMed]

J. Opt. (1)

R. R. Brau, J. M. Ferrer, H. Lee, C. E. Castro, B. K. Tam, P. B. Tarsa, P. Matsudaira, M. C. Boyce, R. D. Kamm, and M. J. Lang, “Passive and active microrheology with optical tweezers,” J. Opt. 9, S103–S112 (2007).

J. Opt. Soc. Am. (1)

T. G. Mason, H. Gang, and D. A. Weitz, “Diffusing-wave-spectroscopy measurements of viscoelasticity of complex fluids,” J. Opt. Soc. Am. 14, 139 (1997).
[Crossref]

Macromolecules (2)

D. Mizuno, D. A. Head, F. C. MacKintosh, and C. F. Schmidt, “Active and Passive Microrheology in Equilibrium and Nonequilibrium Systems,” Macromolecules 41, 7194–7202 (2008).
[Crossref]

B. Schnurr, F. Gittes, F. C. Mackintosh, and C. F. Schmidt, “Determining Microscopic Viscoelasticity in Flexible and Semiflexible Polymer Networks from Thermal Fluctuations,” Macromolecules 9297, 7781–7792 (1997).
[Crossref]

Opt. Express (3)

Phys. Rev. E (4)

S. F. Nørrelykke and H. Flyvbjerg, “Harmonic oscillator in heat bath: Exact simulation of time-lapse-recorded data and exact analytical benchmark statistics,” Phys. Rev. E 83, 1–10 (2011).
[Crossref]

J. Y. Huh and E. M. Furst, “Colloid dynamics in semiflexible polymer solutions,” Phys. Rev. E 74031802 (2006).
[Crossref]

T. Savin and P. S. Doyle, “Role of a finite exposure time on measuring an elastic modulus using microrheology,” Phys. Rev. E 71, 6–11 (2005).
[Crossref]

K. M. Addas, C. F. Schmidt, and J. X. Tang, “Microrheology of solutions of semiflexible biopolymer filaments using laser tweezers interferometry,” Phys. Rev. E 70, 1–16 (2004).
[Crossref]

Phys. Rev. Lett. (3)

R. E. Mahaffy, C. K. Shih, F. C. MacKintosh, and J. Käs, “Scanning probe-based frequency-dependent microrheology of polymer gels and biological cells,” Phys. Rev. Lett. 85, 880–883 (2000).
[Crossref] [PubMed]

I. Y. Wong, M. L. Gardel, D. R. Reichman, E. R. Weeks, M. T. Valentine, A. R. Bausch, and D. A. Weitz, “Anomalous diffusion probes microstructure dynamics of entangled F-actin networks,” Phys. Rev. Lett. 92, 178101–111 (2004).
[Crossref]

T. G. Mason, K. Ganesan, J. van Zanten, D. Wirtz, and S. Kuo, “Particle Tracking Microrheology of Complex Fluids,” Phys. Rev. Lett. 79, 3282–3285 (1997).
[Crossref]

PLoS ONE (1)

M. Shayegan and N. R. Forde, “Microrheological characterization of collagen systems: from molecular solutions to fibrillar gels,” PLoS ONE 8, 23–28 (2013).
[Crossref]

Rep. Prog. Phys. (2)

T. A. Waigh, “Microrheology of complex fluids,” Rep. Prog. Phys. 68, 685–742 (2005).
[Crossref]

T. A. Waigh, “Advances in the microrheology of complex fluids,” Rep. Prog. Phys. 79, 074601 (2016).
[Crossref]

Rev. Sci. Instrum. (1)

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

Other (1)

W. W. Graessley, Polymeric Liquids and Networks: Dynamics and Rheology (Taylor & Francis Group, LLC, 2008).

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Figures (9)

Fig. 1
Fig. 1 The calculated power spectral densities (PSD) of the constrained motion of a trapped bead in water (inset) with radius R = 1 µm, temperature T = 295 K, and corner frequency fc = 100 Hz. The PSDs for QPD-like measurements (red circles) and for camera-like measurements (blue x’s) are compared with the continuous Lorentzian result (black, dashed).
Fig. 2
Fig. 2 Lower: (a) A′(f) and (b) A″(f) for the ideal, infinite-bandwidth treatment (black, dashed), QPD-like data (red circles), and high-speed camera-like data (blue x’s). Upper: Ratios of device-like values to the ideal values. At low frequencies, there is a discrepancy only in A′(f), while both A″(f) and A″(f) differ from the ideal predictions at high frequencies. Vertical dashed lines correspond to cut-off frequencies determined from G*(f) data; see text for details.
Fig. 3
Fig. 3 Lower: Calculated (a) elastic and (b) viscous modulus for the ideal, infinite bandwidth case (black, dashed), QPD-like data (red circles) and camera-like data (blue x’s) for values corresponding to experimental data in Figs. 1 and 2. Upper: Ratios of device-like data to ideal (a) G′(f) and (b) G″(f), displayed up to the relevant cut-off frequencies. At high frequencies, there is a drop-off in device-like values, related to the finite sampling. At low frequencies, device-like values overestimate the moduli. Red and blue dashed lines show the cut-off frequencies for the QPD-like and camera-like data, as described in the text.
Fig. 4
Fig. 4 The (a) elastic and (b) viscous moduli for the ideal, infinite-bandwidth case (black, dashed), QPD-like data sampled at fs = 2500 Hz (red circles), and camera-like data (blue x’s), with ratio plots. The blur associated with the camera-like data worsens the estimate of the G′(f) plateau (trap stiffness) and the G″(f) intercept (viscosity). Red and blue dashed lines show the cut-off frequencies for the QPD-like and camera-like data, respectively, which are altered by the effect of blur.
Fig. 5
Fig. 5 The QPD-like (a) elastic and (b) viscous shear moduli for Δf = 0.1 Hz (burgundy stars) and Δf = 1 Hz (red circles), and ideal infinite-bandwidth moduli (black, dashed) with ratio plots. The cut-off frequencies are shown by red dashed lines (for both Δf = 0.1 Hz and Δf = 1 Hz).
Fig. 6
Fig. 6 The camera-like (a) elastic and (b) viscous shear moduli for Δf = 0.1 Hz (cyan +’s) and Δf = 1 Hz (blue x’s), and ideal infinite-bandwidth moduli (black, dashed) with ratio plots. The cut-off frequencies are shown by blue dashed lines (for both Δf = 0.1 Hz and Δf = 1 Hz).
Fig. 7
Fig. 7 Bottom: The calculated QPD-like power spectral densities using the summation method (Eq. (13); red circles), the definite method (Eq. (14); burgundy squares), perfectly anti-aliased data (discretely sampled Eq. (8); pink diamonds) and the infinite-bandwidth data (black dashed line). Top: Ratios of PSDs to the ideal infinite-bandwidth PSD.
Fig. 8
Fig. 8 Bottom: The QPD-like (a) elastic and (b) viscous shear moduli using the summation method (red circles), the definite method (burgundy squares), the anti-aliased data (pink diamonds) and the ideal infinite-bandwidth data (black, dashed). Top: Ratios of moduli to ideal infinite-bandwidth results.
Fig. 9
Fig. 9 Bottom: The viscous modulus for a bead in water in the absence of a trap. (a) Starting from f = 1 Hz and (b) starting from f = 10 Hz, for camera-like (blue) and infinite bandwidth (black) data. Top: Ratios of moduli to ideal infinite-bandwidth results. Insets: The elastic modulus, which is expected to be zero.

Equations (17)

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G * ( f ) = G ( f ) + i G ( f ) .
S ( f ) = 2 | x ˜ ( f ) | 2 T msr ,
A ( f ) = π f 2 k B T × S ( f ) ,
A ( f ) = 2 π P 0 ξ A ( ξ ) ( ξ 2 f 2 ) d ξ ,
G * ( f ) = 1 6 π R A * ( f ) .
G ( f ) = 1 6 π R ( A A 2 + A 2 )
G ( f ) = 1 6 π R ( A A 2 + A 2 ) .
S ( f ) = D π 2 × 1 ( f 2 + f c 2 ) ,
A ( f ) = D f 2 π k B T ( f 2 + f c 2 ) ,
A ( f ) = D f c 2 π k B T ( f 2 + f c 2 ) .
G ( f ) = κ 6 π R ,
G ( f ) = 2 π η f .
S ( f ) = n = D π 2 ( ( 2 n f Nyq + f ) 2 + f c 2 ) ,
S ( f ) = D ( 1 c 2 ) Δ t π f c ( 1 + c 2 2 c cos ( 2 π f / N ) ) ,
S ( f ) = n = D π 2 ( ( 2 n f Nyq + f ) 2 + f c 2 ) ( sin ( W π | 2 n f Nyq + f | ) W π | 2 n f Nyq + f | ) 2 ,
A 2 π P Δ f f Nyq ξ A ( ξ ) ( ξ 2 f 2 ) d ξ
a b f ( x ) d x b a 2 N n = 1 N ( f ( x n ) + f ( x n + 1 ) ) .

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