Abstract

In optical trapping, accurate determination of forces requires calibration of the position sensitivity relating displacements to the detector readout via the V-nm conversion factor (β). Inaccuracies in measured trap stiffness (k) and dependent calculations of forces and material properties occur if β is assumed to be constant in optically heterogeneous materials such as tissue, necessitating calibration at each probe. For solid-like samples in which probes are securely positioned, calibration can be achieved by moving the sample with a nanopositioning stage and stepping the probe through the detection beam. However, this method may be applied to samples only under select circumstances. Here, we introduce a simple method to find β in any material by steering the detection laser beam while the probe is trapped. We demonstrate the approach in the yolk of living Danio rerio (zebrafish) embryos and measure the viscoelastic properties over an order of magnitude of stress-strain amplitude.

© 2017 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Real-time in situ calibration of an optically trapped probing system

Jingfang Wan, Yanan Huang, Sissy Jhiang, and Chia-Hsiang Menq
Appl. Opt. 48(25) 4832-4841 (2009)

Simultaneous calibration of optical tweezers spring constant and position detector response

Antoine Le Gall, Karen Perronet, David Dulin, André Villing, Philippe Bouyer, Koen Visscher, and Nathalie Westbrook
Opt. Express 18(25) 26469-26474 (2010)

Optical tweezers based active microrheology of sodium polystyrene sulfonate (NaPSS)

Chia-Chun Chiang, Ming-Tzo Wei, Yin-Quan Chen, Pei-Wen Yen, Yi-Chiao Huang, Jun-Yeh Chen, Olivier Lavastre, Husson Guillaume, Darsy Guillaume, and Arthur Chiou
Opt. Express 19(9) 8847-8854 (2011)

References

  • View by:
  • |
  • |
  • |

  1. K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
    [Crossref] [PubMed]
  2. K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
    [Crossref] [PubMed]
  3. A. Ashkin, J. M. Dziedzic, J. E. Bjorkholm, and S. Chu, “Observation of a single-beam gradient force optical trap for dielectric particles,” Opt. Lett. 11(5), 288 (1986).
    [Crossref] [PubMed]
  4. S. M. Block, “Making light work with optical tweezers,” Nature 360(6403), 493–495 (1992).
    [Crossref] [PubMed]
  5. M. S. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276(5315), 1112–1116 (1997).
    [Crossref] [PubMed]
  6. W. Denk and W. W. Webb, “Optical measurement of picometer displacements of transparent microscopic objects,” Appl. Opt. 29(16), 2382–2391 (1990).
    [Crossref] [PubMed]
  7. 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(2), 1074–1085 (1998).
    [Crossref] [PubMed]
  8. 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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
    [Crossref]
  9. A. Yao, M. Tassieri, M. Padgett, and J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
    [Crossref] [PubMed]
  10. D. Preece, R. Warren, M. Tassieri, R. M. L. Evans, G. M. Gibson, M. J. Padgett, and J. M. Cooper, “Optical tweezers: wideband microrheology,” J. Opt. 13(4), 13 (2010).
  11. M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
    [Crossref] [PubMed]
  12. S. G. Shreim, E. Steward, and E. L. Botvinick, “Extending vaterite microviscometry to ex vivo blood vessels by serial calibration,” Biomed. Opt. Express 3(1), 37–47 (2012).
    [Crossref] [PubMed]
  13. E. Kniazeva, J. W. Weidling, R. Singh, E. L. Botvinick, M. A. Digman, E. Gratton, and A. J. Putnam, “Quantification of local matrix deformations and mechanical properties during capillary morphogenesis in 3D,” Integr. Biol. 4(4), 431–439 (2012).
    [Crossref]
  14. M. Tassieri, G. M. Gibson, R. M. L. Evans, A. M. Yao, R. Warren, M. J. Padgett, and J. M. Cooper, “Measuring storage and loss moduli using optical tweezers: broadband microrheology,” Phys. Rev. E 81(2), 026308 (2010).
  15. B. H. Blehm, A. Devine, J. R. Staunton, and K. Tanner, “In vivo tissue has non-linear rheological behavior distinct from 3D biomimetic hydrogels, as determined by AMOTIV microscopy,” Biomaterials 83, 66–78 (2016).
    [Crossref] [PubMed]
  16. J. R. Staunton, W. Vieira, K. L. Fung, R. Lake, A. Devine, and K. Tanner, “Mechanical properties of the tumor stromal microenvironment probed in vitro and ex vivo by in situ-calibrated optical trap-based active microrheology,” Cell. Mol. Bioeng. 9(3), 398–417 (2016).
    [Crossref] [PubMed]
  17. M. Fischer and K. Berg-sørensen, “Calibration of trapping force and response function of optical tweezers in viscoelastic media,” J. Opt. A, Pure Appl. Opt. 9(8), S239–S250 (2007).
    [Crossref]
  18. M. Fischer, A. C. Richardson, S. N. S. Reihani, L. B. Oddershede, and K. Berg-Sørensen, “Active-passive calibration of optical tweezers in viscoelastic media,” Rev. Sci. Instrum. 81(1), 015103 (2010).
    [Crossref] [PubMed]
  19. B. Blehm, Y. R. Chemla, and P. R. Selvin, “In vivo organelle tracking, calibration, and force measurement with an optical trap,” Biophys. J. 98(3), 722a (2010).
    [Crossref]
  20. B. H. Blehm, T. A. Schroer, K. M. Trybus, Y. R. Chemla, and P. R. Selvin, “In vivo optical trapping indicates kinesin’s stall force is reduced by dynein during intracellular transport,” Proc. Natl. Acad. Sci. U.S.A. 110(9), 3381–3386 (2013).
    [Crossref] [PubMed]
  21. F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23(1), 7–9 (1998).
    [Crossref] [PubMed]
  22. A. Farré, F. Marsà, and M. Montes-Usategui, “Optimized back-focal-plane interferometry directly measures forces of optically trapped particles,” Opt. Express 20(11), 12270–12291 (2012).
    [Crossref] [PubMed]
  23. K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
    [Crossref]
  24. P. Sollich, F. Lequeux, P. Hébraud, and M. Cates, “Rheology of soft glassy materials,” Phys. Rev. Lett. 78(10), 2020–2023 (1997).
    [Crossref]
  25. A. Le Gall, K. Perronet, D. Dulin, A. Villing, P. Bouyer, K. Visscher, and N. Westbrook, “Simultaneous calibration of optical tweezers spring constant and position detector response,” Opt. Express 18(25), 26469–26474 (2010).
    [Crossref] [PubMed]
  26. S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77(10), 103101 (2006).
    [Crossref]
  27. P. Dutov and J. Schieber, “Calibration of optical traps by dual trapping of one bead,” Opt. Lett. 38(22), 4923–4926 (2013).
    [Crossref] [PubMed]
  28. K. C. Vermeulen, J. Van Mameren, G. J. M. Stienen, E. J. G. Peterman, G. J. L. Wuite, and C. F. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77(1), 013704 (2006).
    [Crossref]
  29. V. V. Artym and K. Matsumoto, “Imaging cells in three-dimensional collagen matrix,” Curr. Protoc. Cell Biol. 10, 1–20 (2010).
    [PubMed]
  30. J. R. Staunton, B. L. Doss, S. Lindsay, and R. Ros, “Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices,” Sci. Rep. 6, 19686 (2016).
    [Crossref] [PubMed]
  31. M. Westerfield, The Zebrafish Book. A Guide for the Laboratory Use of Zebrafish, 5th ed. (University of Oregon Press, 2007).
  32. S. Kumar and V. M. Weaver, “Mechanics, malignancy, and metastasis: the force journey of a tumor cell,” Cancer Metastasis Rev. 28(1-2), 113–127 (2009).
    [Crossref] [PubMed]
  33. K. Tanner and M. M. Gottesman, “Beyond 3D culture models of cancer,” Sci. Transl. Med. 7(283), 283ps9 (2015).
    [Crossref] [PubMed]
  34. J. Kim and K. Tanner, “Three-dimensional patterning of the ECM microenvironment using magnetic nanoparticle self assembly,” Curr. Protoc. Cell Biol. 70, 1–14 (2016).
    [PubMed]
  35. C. A. R. Jones, M. Cibula, J. Feng, E. A. Krnacik, D. H. McIntyre, H. Levine, and B. Sun, “Micromechanics of cellularized biopolymer networks,” Proc. Natl. Acad. Sci. U.S.A. 112(37), E5117–E5122 (2015).
    [Crossref] [PubMed]
  36. G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
    [Crossref]
  37. N. El Kissi, J. M. Piau, P. Attané, and G. Turrel, “Shear rheometry of polydimethylsiloxanes: master curves and testing of Gleissle and Yamamoto relations,” Rheol. Acta 310(3), 293–310 (1993).
    [Crossref]
  38. Y. Song and L. L. Dai, “Two-particle interfacial microrheology at polymer-polymer interfaces,” Langmuir 26(16), 13044–13047 (2010).
    [Crossref] [PubMed]
  39. A. J. Barlow, G. Harrison, and J. Lamb, “Viscoelastic relaxation of polydimethylsiloxane liquids,” Proc. R. Soc. A Math. Phys. Eng. Sci. 282(1389), (1964).
    [Crossref]
  40. V. Raimbault, D. Rebière, C. Dejous, M. Guirardel, J. Pistré, and J. L. Lachaud, “High frequency microrheological measurements of PDMS fluids using saw microfluidic system,” Sens. Actuators B Chem. 144(2), 467–471 (2010).
    [Crossref]
  41. G. Foffano, J. S. Lintuvuori, A. N. Morozov, K. Stratford, M. E. Cates, and D. Marenduzzo, “Bulk rheology and microrheology of active fluids,” Eur. Phys. J. 35(10), 98 (2012).
    [Crossref] [PubMed]
  42. T. M. Squires, “Nonlinear microrheology: bulk stresses versus direct interactions,” Langmuir 24(4), 1147–1159 (2008).
    [Crossref] [PubMed]
  43. J. P. Rich, G. H. McKinley, and P. S. Doyle, “Size dependence of microprobe dynamics during gelation of a discotic colloidal clay,” J. Rheol. (N.Y.N.Y.) 55(2), 273–299 (2011).
    [Crossref]
  44. A. Tuteja, M. E. Mackay, S. Narayanan, S. Asokan, and M. S. Wong, “Breakdown of the continuum stokes-einstein relation for nanoparticle diffusion,” Nano Lett. 7(5), 1276–1281 (2007).
    [Crossref] [PubMed]
  45. E. Paluch and C. P. Heisenberg, “Biology and physics of cell shape changes in development,” Curr. Biol. 19(17), R790–R799 (2009).
    [Crossref] [PubMed]
  46. R. Cardinaels, J. Van De Velde, W. Mathues, P. Van Liedekerke, and P. Moldenaers, “A rheological characterisation of liquid egg albumen,” Insid. Food Symp.9–12 (2013).
  47. Y. Fujimura, M. Inoue, H. Kondoh, and S. Kinoshita, “Measurement of micro-elasticity within a fertilized egg by using Brillouin scattering spectroscopy,” J. Korean Phys. Soc. 51(2), 854–857 (2007).
    [Crossref]
  48. H. Berthoumieux, J. Maître, C. Heisenberg, E. K. Paluch, F. Jülicher, and G. Salbreux, “Active elastic thin shell theory for cellular deformations,” New J. Phys. 16(6), 065005 (2014).
    [Crossref]
  49. L. M. Browning, T. Huang, X. H. Xu, and X. N. Xu, “Real-time in vivo imaging of size-dependent transport and toxicity of gold nanoparticles in zebrafish embryos using single nanoparticle plasmonic spectroscopy,” Interface Focus 3(3), 20120098 (2013).
    [Crossref] [PubMed]
  50. D. Kang, W. Wang, J. Lee, Y. C. Tai, and T. K. Hsiai, “Measurement of viscosity of adult zebrafish blood using a capillary pressure-driven viscometer,” in 18th International Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2015), pp. 1661–1664.
    [Crossref]
  51. O. Campas, Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA 90314 (personal communication, 2016).
  52. P. Fratzl, K. Misof, I. Zizak, G. Rapp, H. Amenitsch, and S. Bernstorff, “Fibrillar structure and mechanical properties of collagen,” J. Struct. Biol. 122(1-2), 119–122 (1998).
    [Crossref] [PubMed]
  53. T. Gutsmann, G. E. Fantner, J. H. Kindt, M. Venturoni, S. Danielsen, and P. K. Hansma, “Force spectroscopy of collagen fibers to investigate their mechanical properties and structural organization,” Biophys. J. 86(5), 3186–3193 (2004).
    [Crossref] [PubMed]
  54. C. Storm, J. J. Pastore, F. C. MacKintosh, T. C. Lubensky, and P. A. Janmey, “Nonlinear elasticity in biological gels,” Nature 435(7039), 191–194 (2005).
    [Crossref] [PubMed]

2016 (4)

B. H. Blehm, A. Devine, J. R. Staunton, and K. Tanner, “In vivo tissue has non-linear rheological behavior distinct from 3D biomimetic hydrogels, as determined by AMOTIV microscopy,” Biomaterials 83, 66–78 (2016).
[Crossref] [PubMed]

J. R. Staunton, W. Vieira, K. L. Fung, R. Lake, A. Devine, and K. Tanner, “Mechanical properties of the tumor stromal microenvironment probed in vitro and ex vivo by in situ-calibrated optical trap-based active microrheology,” Cell. Mol. Bioeng. 9(3), 398–417 (2016).
[Crossref] [PubMed]

J. R. Staunton, B. L. Doss, S. Lindsay, and R. Ros, “Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices,” Sci. Rep. 6, 19686 (2016).
[Crossref] [PubMed]

J. Kim and K. Tanner, “Three-dimensional patterning of the ECM microenvironment using magnetic nanoparticle self assembly,” Curr. Protoc. Cell Biol. 70, 1–14 (2016).
[PubMed]

2015 (2)

C. A. R. Jones, M. Cibula, J. Feng, E. A. Krnacik, D. H. McIntyre, H. Levine, and B. Sun, “Micromechanics of cellularized biopolymer networks,” Proc. Natl. Acad. Sci. U.S.A. 112(37), E5117–E5122 (2015).
[Crossref] [PubMed]

K. Tanner and M. M. Gottesman, “Beyond 3D culture models of cancer,” Sci. Transl. Med. 7(283), 283ps9 (2015).
[Crossref] [PubMed]

2014 (1)

H. Berthoumieux, J. Maître, C. Heisenberg, E. K. Paluch, F. Jülicher, and G. Salbreux, “Active elastic thin shell theory for cellular deformations,” New J. Phys. 16(6), 065005 (2014).
[Crossref]

2013 (3)

L. M. Browning, T. Huang, X. H. Xu, and X. N. Xu, “Real-time in vivo imaging of size-dependent transport and toxicity of gold nanoparticles in zebrafish embryos using single nanoparticle plasmonic spectroscopy,” Interface Focus 3(3), 20120098 (2013).
[Crossref] [PubMed]

B. H. Blehm, T. A. Schroer, K. M. Trybus, Y. R. Chemla, and P. R. Selvin, “In vivo optical trapping indicates kinesin’s stall force is reduced by dynein during intracellular transport,” Proc. Natl. Acad. Sci. U.S.A. 110(9), 3381–3386 (2013).
[Crossref] [PubMed]

P. Dutov and J. Schieber, “Calibration of optical traps by dual trapping of one bead,” Opt. Lett. 38(22), 4923–4926 (2013).
[Crossref] [PubMed]

2012 (4)

A. Farré, F. Marsà, and M. Montes-Usategui, “Optimized back-focal-plane interferometry directly measures forces of optically trapped particles,” Opt. Express 20(11), 12270–12291 (2012).
[Crossref] [PubMed]

S. G. Shreim, E. Steward, and E. L. Botvinick, “Extending vaterite microviscometry to ex vivo blood vessels by serial calibration,” Biomed. Opt. Express 3(1), 37–47 (2012).
[Crossref] [PubMed]

E. Kniazeva, J. W. Weidling, R. Singh, E. L. Botvinick, M. A. Digman, E. Gratton, and A. J. Putnam, “Quantification of local matrix deformations and mechanical properties during capillary morphogenesis in 3D,” Integr. Biol. 4(4), 431–439 (2012).
[Crossref]

G. Foffano, J. S. Lintuvuori, A. N. Morozov, K. Stratford, M. E. Cates, and D. Marenduzzo, “Bulk rheology and microrheology of active fluids,” Eur. Phys. J. 35(10), 98 (2012).
[Crossref] [PubMed]

2011 (2)

J. P. Rich, G. H. McKinley, and P. S. Doyle, “Size dependence of microprobe dynamics during gelation of a discotic colloidal clay,” J. Rheol. (N.Y.N.Y.) 55(2), 273–299 (2011).
[Crossref]

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

2010 (8)

V. V. Artym and K. Matsumoto, “Imaging cells in three-dimensional collagen matrix,” Curr. Protoc. Cell Biol. 10, 1–20 (2010).
[PubMed]

A. Le Gall, K. Perronet, D. Dulin, A. Villing, P. Bouyer, K. Visscher, and N. Westbrook, “Simultaneous calibration of optical tweezers spring constant and position detector response,” Opt. Express 18(25), 26469–26474 (2010).
[Crossref] [PubMed]

M. Tassieri, G. M. Gibson, R. M. L. Evans, A. M. Yao, R. Warren, M. J. Padgett, and J. M. Cooper, “Measuring storage and loss moduli using optical tweezers: broadband microrheology,” Phys. Rev. E 81(2), 026308 (2010).

D. Preece, R. Warren, M. Tassieri, R. M. L. Evans, G. M. Gibson, M. J. Padgett, and J. M. Cooper, “Optical tweezers: wideband microrheology,” J. Opt. 13(4), 13 (2010).

M. Fischer, A. C. Richardson, S. N. S. Reihani, L. B. Oddershede, and K. Berg-Sørensen, “Active-passive calibration of optical tweezers in viscoelastic media,” Rev. Sci. Instrum. 81(1), 015103 (2010).
[Crossref] [PubMed]

B. Blehm, Y. R. Chemla, and P. R. Selvin, “In vivo organelle tracking, calibration, and force measurement with an optical trap,” Biophys. J. 98(3), 722a (2010).
[Crossref]

Y. Song and L. L. Dai, “Two-particle interfacial microrheology at polymer-polymer interfaces,” Langmuir 26(16), 13044–13047 (2010).
[Crossref] [PubMed]

V. Raimbault, D. Rebière, C. Dejous, M. Guirardel, J. Pistré, and J. L. Lachaud, “High frequency microrheological measurements of PDMS fluids using saw microfluidic system,” Sens. Actuators B Chem. 144(2), 467–471 (2010).
[Crossref]

2009 (4)

E. Paluch and C. P. Heisenberg, “Biology and physics of cell shape changes in development,” Curr. Biol. 19(17), R790–R799 (2009).
[Crossref] [PubMed]

A. Yao, M. Tassieri, M. Padgett, and J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[Crossref] [PubMed]

S. Kumar and V. M. Weaver, “Mechanics, malignancy, and metastasis: the force journey of a tumor cell,” Cancer Metastasis Rev. 28(1-2), 113–127 (2009).
[Crossref] [PubMed]

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[Crossref]

2008 (1)

T. M. Squires, “Nonlinear microrheology: bulk stresses versus direct interactions,” Langmuir 24(4), 1147–1159 (2008).
[Crossref] [PubMed]

2007 (4)

Y. Fujimura, M. Inoue, H. Kondoh, and S. Kinoshita, “Measurement of micro-elasticity within a fertilized egg by using Brillouin scattering spectroscopy,” J. Korean Phys. Soc. 51(2), 854–857 (2007).
[Crossref]

A. Tuteja, M. E. Mackay, S. Narayanan, S. Asokan, and M. S. Wong, “Breakdown of the continuum stokes-einstein relation for nanoparticle diffusion,” Nano Lett. 7(5), 1276–1281 (2007).
[Crossref] [PubMed]

M. Fischer and K. Berg-sørensen, “Calibration of trapping force and response function of optical tweezers in viscoelastic media,” J. Opt. A, Pure Appl. Opt. 9(8), S239–S250 (2007).
[Crossref]

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

2006 (2)

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77(10), 103101 (2006).
[Crossref]

K. C. Vermeulen, J. Van Mameren, G. J. M. Stienen, E. J. G. Peterman, G. J. L. Wuite, and C. F. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77(1), 013704 (2006).
[Crossref]

2005 (1)

C. Storm, J. J. Pastore, F. C. MacKintosh, T. C. Lubensky, and P. A. Janmey, “Nonlinear elasticity in biological gels,” Nature 435(7039), 191–194 (2005).
[Crossref] [PubMed]

2004 (3)

T. Gutsmann, G. E. Fantner, J. H. Kindt, M. Venturoni, S. Danielsen, and P. K. Hansma, “Force spectroscopy of collagen fibers to investigate their mechanical properties and structural organization,” Biophys. J. 86(5), 3186–3193 (2004).
[Crossref] [PubMed]

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[Crossref]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

1998 (3)

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(2), 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(1), 7–9 (1998).
[Crossref] [PubMed]

P. Fratzl, K. Misof, I. Zizak, G. Rapp, H. Amenitsch, and S. Bernstorff, “Fibrillar structure and mechanical properties of collagen,” J. Struct. Biol. 122(1-2), 119–122 (1998).
[Crossref] [PubMed]

1997 (2)

P. Sollich, F. Lequeux, P. Hébraud, and M. Cates, “Rheology of soft glassy materials,” Phys. Rev. Lett. 78(10), 2020–2023 (1997).
[Crossref]

M. S. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276(5315), 1112–1116 (1997).
[Crossref] [PubMed]

1994 (1)

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

1993 (1)

N. El Kissi, J. M. Piau, P. Attané, and G. Turrel, “Shear rheometry of polydimethylsiloxanes: master curves and testing of Gleissle and Yamamoto relations,” Rheol. Acta 310(3), 293–310 (1993).
[Crossref]

1992 (1)

S. M. Block, “Making light work with optical tweezers,” Nature 360(6403), 493–495 (1992).
[Crossref] [PubMed]

1990 (1)

1986 (1)

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(2), 1074–1085 (1998).
[Crossref] [PubMed]

Alvarez-Elizondo, M. B.

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Amenitsch, H.

P. Fratzl, K. Misof, I. Zizak, G. Rapp, H. Amenitsch, and S. Bernstorff, “Fibrillar structure and mechanical properties of collagen,” J. Struct. Biol. 122(1-2), 119–122 (1998).
[Crossref] [PubMed]

Artym, V. V.

V. V. Artym and K. Matsumoto, “Imaging cells in three-dimensional collagen matrix,” Curr. Protoc. Cell Biol. 10, 1–20 (2010).
[PubMed]

Ashkin, A.

Asokan, S.

A. Tuteja, M. E. Mackay, S. Narayanan, S. Asokan, and M. S. Wong, “Breakdown of the continuum stokes-einstein relation for nanoparticle diffusion,” Nano Lett. 7(5), 1276–1281 (2007).
[Crossref] [PubMed]

Attané, P.

N. El Kissi, J. M. Piau, P. Attané, and G. Turrel, “Shear rheometry of polydimethylsiloxanes: master curves and testing of Gleissle and Yamamoto relations,” Rheol. Acta 310(3), 293–310 (1993).
[Crossref]

Berg-Sørensen, K.

M. Fischer, A. C. Richardson, S. N. S. Reihani, L. B. Oddershede, and K. Berg-Sørensen, “Active-passive calibration of optical tweezers in viscoelastic media,” Rev. Sci. Instrum. 81(1), 015103 (2010).
[Crossref] [PubMed]

M. Fischer and K. Berg-sørensen, “Calibration of trapping force and response function of optical tweezers in viscoelastic media,” J. Opt. A, Pure Appl. Opt. 9(8), S239–S250 (2007).
[Crossref]

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[Crossref]

Bernstorff, S.

P. Fratzl, K. Misof, I. Zizak, G. Rapp, H. Amenitsch, and S. Bernstorff, “Fibrillar structure and mechanical properties of collagen,” J. Struct. Biol. 122(1-2), 119–122 (1998).
[Crossref] [PubMed]

Berthoumieux, H.

H. Berthoumieux, J. Maître, C. Heisenberg, E. K. Paluch, F. Jülicher, and G. Salbreux, “Active elastic thin shell theory for cellular deformations,” New J. Phys. 16(6), 065005 (2014).
[Crossref]

Bjorkholm, J. E.

Blehm, B.

B. Blehm, Y. R. Chemla, and P. R. Selvin, “In vivo organelle tracking, calibration, and force measurement with an optical trap,” Biophys. J. 98(3), 722a (2010).
[Crossref]

Blehm, B. H.

B. H. Blehm, A. Devine, J. R. Staunton, and K. Tanner, “In vivo tissue has non-linear rheological behavior distinct from 3D biomimetic hydrogels, as determined by AMOTIV microscopy,” Biomaterials 83, 66–78 (2016).
[Crossref] [PubMed]

B. H. Blehm, T. A. Schroer, K. M. Trybus, Y. R. Chemla, and P. R. Selvin, “In vivo optical trapping indicates kinesin’s stall force is reduced by dynein during intracellular transport,” Proc. Natl. Acad. Sci. U.S.A. 110(9), 3381–3386 (2013).
[Crossref] [PubMed]

Block, S. M.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

S. M. Block, “Making light work with optical tweezers,” Nature 360(6403), 493–495 (1992).
[Crossref] [PubMed]

Botvinick, E. L.

E. Kniazeva, J. W. Weidling, R. Singh, E. L. Botvinick, M. A. Digman, E. Gratton, and A. J. Putnam, “Quantification of local matrix deformations and mechanical properties during capillary morphogenesis in 3D,” Integr. Biol. 4(4), 431–439 (2012).
[Crossref]

S. G. Shreim, E. Steward, and E. L. Botvinick, “Extending vaterite microviscometry to ex vivo blood vessels by serial calibration,” Biomed. Opt. Express 3(1), 37–47 (2012).
[Crossref] [PubMed]

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Bouyer, P.

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

Browning, L. M.

L. M. Browning, T. Huang, X. H. Xu, and X. N. Xu, “Real-time in vivo imaging of size-dependent transport and toxicity of gold nanoparticles in zebrafish embryos using single nanoparticle plasmonic spectroscopy,” Interface Focus 3(3), 20120098 (2013).
[Crossref] [PubMed]

Bustamante, C.

M. S. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276(5315), 1112–1116 (1997).
[Crossref] [PubMed]

Cardinaels, R.

R. Cardinaels, J. Van De Velde, W. Mathues, P. Van Liedekerke, and P. Moldenaers, “A rheological characterisation of liquid egg albumen,” Insid. Food Symp.9–12 (2013).

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

Cates, M.

P. Sollich, F. Lequeux, P. Hébraud, and M. Cates, “Rheology of soft glassy materials,” Phys. Rev. Lett. 78(10), 2020–2023 (1997).
[Crossref]

Cates, M. E.

G. Foffano, J. S. Lintuvuori, A. N. Morozov, K. Stratford, M. E. Cates, and D. Marenduzzo, “Bulk rheology and microrheology of active fluids,” Eur. Phys. J. 35(10), 98 (2012).
[Crossref] [PubMed]

Chemla, Y. R.

B. H. Blehm, T. A. Schroer, K. M. Trybus, Y. R. Chemla, and P. R. Selvin, “In vivo optical trapping indicates kinesin’s stall force is reduced by dynein during intracellular transport,” Proc. Natl. Acad. Sci. U.S.A. 110(9), 3381–3386 (2013).
[Crossref] [PubMed]

B. Blehm, Y. R. Chemla, and P. R. Selvin, “In vivo organelle tracking, calibration, and force measurement with an optical trap,” Biophys. J. 98(3), 722a (2010).
[Crossref]

Chu, S.

Cibula, M.

C. A. R. Jones, M. Cibula, J. Feng, E. A. Krnacik, D. H. McIntyre, H. Levine, and B. Sun, “Micromechanics of cellularized biopolymer networks,” Proc. Natl. Acad. Sci. U.S.A. 112(37), E5117–E5122 (2015).
[Crossref] [PubMed]

Cooper, J.

A. Yao, M. Tassieri, M. Padgett, and J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[Crossref] [PubMed]

Cooper, J. M.

D. Preece, R. Warren, M. Tassieri, R. M. L. Evans, G. M. Gibson, M. J. Padgett, and J. M. Cooper, “Optical tweezers: wideband microrheology,” J. Opt. 13(4), 13 (2010).

M. Tassieri, G. M. Gibson, R. M. L. Evans, A. M. Yao, R. Warren, M. J. Padgett, and J. M. Cooper, “Measuring storage and loss moduli using optical tweezers: broadband microrheology,” Phys. Rev. E 81(2), 026308 (2010).

Dai, L. L.

Y. Song and L. L. Dai, “Two-particle interfacial microrheology at polymer-polymer interfaces,” Langmuir 26(16), 13044–13047 (2010).
[Crossref] [PubMed]

Danielsen, S.

T. Gutsmann, G. E. Fantner, J. H. Kindt, M. Venturoni, S. Danielsen, and P. K. Hansma, “Force spectroscopy of collagen fibers to investigate their mechanical properties and structural organization,” Biophys. J. 86(5), 3186–3193 (2004).
[Crossref] [PubMed]

De Luca, A. C.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[Crossref]

deCastro, M. J.

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(2), 1074–1085 (1998).
[Crossref] [PubMed]

Dejous, C.

V. Raimbault, D. Rebière, C. Dejous, M. Guirardel, J. Pistré, and J. L. Lachaud, “High frequency microrheological measurements of PDMS fluids using saw microfluidic system,” Sens. Actuators B Chem. 144(2), 467–471 (2010).
[Crossref]

Denk, W.

Devine, A.

B. H. Blehm, A. Devine, J. R. Staunton, and K. Tanner, “In vivo tissue has non-linear rheological behavior distinct from 3D biomimetic hydrogels, as determined by AMOTIV microscopy,” Biomaterials 83, 66–78 (2016).
[Crossref] [PubMed]

J. R. Staunton, W. Vieira, K. L. Fung, R. Lake, A. Devine, and K. Tanner, “Mechanical properties of the tumor stromal microenvironment probed in vitro and ex vivo by in situ-calibrated optical trap-based active microrheology,” Cell. Mol. Bioeng. 9(3), 398–417 (2016).
[Crossref] [PubMed]

Digman, M. A.

E. Kniazeva, J. W. Weidling, R. Singh, E. L. Botvinick, M. A. Digman, E. Gratton, and A. J. Putnam, “Quantification of local matrix deformations and mechanical properties during capillary morphogenesis in 3D,” Integr. Biol. 4(4), 431–439 (2012).
[Crossref]

Doss, B. L.

J. R. Staunton, B. L. Doss, S. Lindsay, and R. Ros, “Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices,” Sci. Rep. 6, 19686 (2016).
[Crossref] [PubMed]

Doyle, P. S.

J. P. Rich, G. H. McKinley, and P. S. Doyle, “Size dependence of microprobe dynamics during gelation of a discotic colloidal clay,” J. Rheol. (N.Y.N.Y.) 55(2), 273–299 (2011).
[Crossref]

Dulin, D.

Dutov, P.

Dziedzic, J. M.

El Kissi, N.

N. El Kissi, J. M. Piau, P. Attané, and G. Turrel, “Shear rheometry of polydimethylsiloxanes: master curves and testing of Gleissle and Yamamoto relations,” Rheol. Acta 310(3), 293–310 (1993).
[Crossref]

Estrada, L. C.

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Evans, R. M. L.

D. Preece, R. Warren, M. Tassieri, R. M. L. Evans, G. M. Gibson, M. J. Padgett, and J. M. Cooper, “Optical tweezers: wideband microrheology,” J. Opt. 13(4), 13 (2010).

M. Tassieri, G. M. Gibson, R. M. L. Evans, A. M. Yao, R. Warren, M. J. Padgett, and J. M. Cooper, “Measuring storage and loss moduli using optical tweezers: broadband microrheology,” Phys. Rev. E 81(2), 026308 (2010).

Fantner, G. E.

T. Gutsmann, G. E. Fantner, J. H. Kindt, M. Venturoni, S. Danielsen, and P. K. Hansma, “Force spectroscopy of collagen fibers to investigate their mechanical properties and structural organization,” Biophys. J. 86(5), 3186–3193 (2004).
[Crossref] [PubMed]

Farré, A.

Feng, J.

C. A. R. Jones, M. Cibula, J. Feng, E. A. Krnacik, D. H. McIntyre, H. Levine, and B. Sun, “Micromechanics of cellularized biopolymer networks,” Proc. Natl. Acad. Sci. U.S.A. 112(37), E5117–E5122 (2015).
[Crossref] [PubMed]

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

Fischer, M.

M. Fischer, A. C. Richardson, S. N. S. Reihani, L. B. Oddershede, and K. Berg-Sørensen, “Active-passive calibration of optical tweezers in viscoelastic media,” Rev. Sci. Instrum. 81(1), 015103 (2010).
[Crossref] [PubMed]

M. Fischer and K. Berg-sørensen, “Calibration of trapping force and response function of optical tweezers in viscoelastic media,” J. Opt. A, Pure Appl. Opt. 9(8), S239–S250 (2007).
[Crossref]

Flyvbjerg, H.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77(10), 103101 (2006).
[Crossref]

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[Crossref]

Foffano, G.

G. Foffano, J. S. Lintuvuori, A. N. Morozov, K. Stratford, M. E. Cates, and D. Marenduzzo, “Bulk rheology and microrheology of active fluids,” Eur. Phys. J. 35(10), 98 (2012).
[Crossref] [PubMed]

Fratzl, P.

P. Fratzl, K. Misof, I. Zizak, G. Rapp, H. Amenitsch, and S. Bernstorff, “Fibrillar structure and mechanical properties of collagen,” J. Struct. Biol. 122(1-2), 119–122 (1998).
[Crossref] [PubMed]

Fujimura, Y.

Y. Fujimura, M. Inoue, H. Kondoh, and S. Kinoshita, “Measurement of micro-elasticity within a fertilized egg by using Brillouin scattering spectroscopy,” J. Korean Phys. Soc. 51(2), 854–857 (2007).
[Crossref]

Fung, K. L.

J. R. Staunton, W. Vieira, K. L. Fung, R. Lake, A. Devine, and K. Tanner, “Mechanical properties of the tumor stromal microenvironment probed in vitro and ex vivo by in situ-calibrated optical trap-based active microrheology,” Cell. Mol. Bioeng. 9(3), 398–417 (2016).
[Crossref] [PubMed]

Fusco, S.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[Crossref]

Gibson, G. M.

M. Tassieri, G. M. Gibson, R. M. L. Evans, A. M. Yao, R. Warren, M. J. Padgett, and J. M. Cooper, “Measuring storage and loss moduli using optical tweezers: broadband microrheology,” Phys. Rev. E 81(2), 026308 (2010).

D. Preece, R. Warren, M. Tassieri, R. M. L. Evans, G. M. Gibson, M. J. Padgett, and J. M. Cooper, “Optical tweezers: wideband microrheology,” J. Opt. 13(4), 13 (2010).

Gittes, F.

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(2), 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(1), 7–9 (1998).
[Crossref] [PubMed]

Gottesman, M. M.

K. Tanner and M. M. Gottesman, “Beyond 3D culture models of cancer,” Sci. Transl. Med. 7(283), 283ps9 (2015).
[Crossref] [PubMed]

Granzier, H. L.

M. S. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276(5315), 1112–1116 (1997).
[Crossref] [PubMed]

Gratton, E.

E. Kniazeva, J. W. Weidling, R. Singh, E. L. Botvinick, M. A. Digman, E. Gratton, and A. J. Putnam, “Quantification of local matrix deformations and mechanical properties during capillary morphogenesis in 3D,” Integr. Biol. 4(4), 431–439 (2012).
[Crossref]

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Guirardel, M.

V. Raimbault, D. Rebière, C. Dejous, M. Guirardel, J. Pistré, and J. L. Lachaud, “High frequency microrheological measurements of PDMS fluids using saw microfluidic system,” Sens. Actuators B Chem. 144(2), 467–471 (2010).
[Crossref]

Gutsmann, T.

T. Gutsmann, G. E. Fantner, J. H. Kindt, M. Venturoni, S. Danielsen, and P. K. Hansma, “Force spectroscopy of collagen fibers to investigate their mechanical properties and structural organization,” Biophys. J. 86(5), 3186–3193 (2004).
[Crossref] [PubMed]

Hansma, P. K.

T. Gutsmann, G. E. Fantner, J. H. Kindt, M. Venturoni, S. Danielsen, and P. K. Hansma, “Force spectroscopy of collagen fibers to investigate their mechanical properties and structural organization,” Biophys. J. 86(5), 3186–3193 (2004).
[Crossref] [PubMed]

Hébraud, P.

P. Sollich, F. Lequeux, P. Hébraud, and M. Cates, “Rheology of soft glassy materials,” Phys. Rev. Lett. 78(10), 2020–2023 (1997).
[Crossref]

Heisenberg, C.

H. Berthoumieux, J. Maître, C. Heisenberg, E. K. Paluch, F. Jülicher, and G. Salbreux, “Active elastic thin shell theory for cellular deformations,” New J. Phys. 16(6), 065005 (2014).
[Crossref]

Heisenberg, C. P.

E. Paluch and C. P. Heisenberg, “Biology and physics of cell shape changes in development,” Curr. Biol. 19(17), R790–R799 (2009).
[Crossref] [PubMed]

Howard, J.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77(10), 103101 (2006).
[Crossref]

Hsiai, T. K.

D. Kang, W. Wang, J. Lee, Y. C. Tai, and T. K. Hsiai, “Measurement of viscosity of adult zebrafish blood using a capillary pressure-driven viscometer,” in 18th International Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2015), pp. 1661–1664.
[Crossref]

Huang, T.

L. M. Browning, T. Huang, X. H. Xu, and X. N. Xu, “Real-time in vivo imaging of size-dependent transport and toxicity of gold nanoparticles in zebrafish embryos using single nanoparticle plasmonic spectroscopy,” Interface Focus 3(3), 20120098 (2013).
[Crossref] [PubMed]

Inoue, M.

Y. Fujimura, M. Inoue, H. Kondoh, and S. Kinoshita, “Measurement of micro-elasticity within a fertilized egg by using Brillouin scattering spectroscopy,” J. Korean Phys. Soc. 51(2), 854–857 (2007).
[Crossref]

Janmey, P. A.

C. Storm, J. J. Pastore, F. C. MacKintosh, T. C. Lubensky, and P. A. Janmey, “Nonlinear elasticity in biological gels,” Nature 435(7039), 191–194 (2005).
[Crossref] [PubMed]

Jones, C. A. R.

C. A. R. Jones, M. Cibula, J. Feng, E. A. Krnacik, D. H. McIntyre, H. Levine, and B. Sun, “Micromechanics of cellularized biopolymer networks,” Proc. Natl. Acad. Sci. U.S.A. 112(37), E5117–E5122 (2015).
[Crossref] [PubMed]

Jülicher, F.

H. Berthoumieux, J. Maître, C. Heisenberg, E. K. Paluch, F. Jülicher, and G. Salbreux, “Active elastic thin shell theory for cellular deformations,” New J. Phys. 16(6), 065005 (2014).
[Crossref]

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77(10), 103101 (2006).
[Crossref]

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

Kang, D.

D. Kang, W. Wang, J. Lee, Y. C. Tai, and T. K. Hsiai, “Measurement of viscosity of adult zebrafish blood using a capillary pressure-driven viscometer,” in 18th International Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2015), pp. 1661–1664.
[Crossref]

Kellermayer, M. S.

M. S. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276(5315), 1112–1116 (1997).
[Crossref] [PubMed]

Kim, J.

J. Kim and K. Tanner, “Three-dimensional patterning of the ECM microenvironment using magnetic nanoparticle self assembly,” Curr. Protoc. Cell Biol. 70, 1–14 (2016).
[PubMed]

Kindt, J. H.

T. Gutsmann, G. E. Fantner, J. H. Kindt, M. Venturoni, S. Danielsen, and P. K. Hansma, “Force spectroscopy of collagen fibers to investigate their mechanical properties and structural organization,” Biophys. J. 86(5), 3186–3193 (2004).
[Crossref] [PubMed]

Kinoshita, S.

Y. Fujimura, M. Inoue, H. Kondoh, and S. Kinoshita, “Measurement of micro-elasticity within a fertilized egg by using Brillouin scattering spectroscopy,” J. Korean Phys. Soc. 51(2), 854–857 (2007).
[Crossref]

Kniazeva, E.

E. Kniazeva, J. W. Weidling, R. Singh, E. L. Botvinick, M. A. Digman, E. Gratton, and A. J. Putnam, “Quantification of local matrix deformations and mechanical properties during capillary morphogenesis in 3D,” Integr. Biol. 4(4), 431–439 (2012).
[Crossref]

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Kondoh, H.

Y. Fujimura, M. Inoue, H. Kondoh, and S. Kinoshita, “Measurement of micro-elasticity within a fertilized egg by using Brillouin scattering spectroscopy,” J. Korean Phys. Soc. 51(2), 854–857 (2007).
[Crossref]

Kotlarchyk, M. A.

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Krnacik, E. A.

C. A. R. Jones, M. Cibula, J. Feng, E. A. Krnacik, D. H. McIntyre, H. Levine, and B. Sun, “Micromechanics of cellularized biopolymer networks,” Proc. Natl. Acad. Sci. U.S.A. 112(37), E5117–E5122 (2015).
[Crossref] [PubMed]

Kumar, S.

S. Kumar and V. M. Weaver, “Mechanics, malignancy, and metastasis: the force journey of a tumor cell,” Cancer Metastasis Rev. 28(1-2), 113–127 (2009).
[Crossref] [PubMed]

Lachaud, J. L.

V. Raimbault, D. Rebière, C. Dejous, M. Guirardel, J. Pistré, and J. L. Lachaud, “High frequency microrheological measurements of PDMS fluids using saw microfluidic system,” Sens. Actuators B Chem. 144(2), 467–471 (2010).
[Crossref]

Lake, R.

J. R. Staunton, W. Vieira, K. L. Fung, R. Lake, A. Devine, and K. Tanner, “Mechanical properties of the tumor stromal microenvironment probed in vitro and ex vivo by in situ-calibrated optical trap-based active microrheology,” Cell. Mol. Bioeng. 9(3), 398–417 (2016).
[Crossref] [PubMed]

Lang, M. J.

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

Le Gall, A.

Lee, H.

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

Lee, J.

D. Kang, W. Wang, J. Lee, Y. C. Tai, and T. K. Hsiai, “Measurement of viscosity of adult zebrafish blood using a capillary pressure-driven viscometer,” in 18th International Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2015), pp. 1661–1664.
[Crossref]

Lequeux, F.

P. Sollich, F. Lequeux, P. Hébraud, and M. Cates, “Rheology of soft glassy materials,” Phys. Rev. Lett. 78(10), 2020–2023 (1997).
[Crossref]

Levine, H.

C. A. R. Jones, M. Cibula, J. Feng, E. A. Krnacik, D. H. McIntyre, H. Levine, and B. Sun, “Micromechanics of cellularized biopolymer networks,” Proc. Natl. Acad. Sci. U.S.A. 112(37), E5117–E5122 (2015).
[Crossref] [PubMed]

Lindsay, S.

J. R. Staunton, B. L. Doss, S. Lindsay, and R. Ros, “Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices,” Sci. Rep. 6, 19686 (2016).
[Crossref] [PubMed]

Lintuvuori, J. S.

G. Foffano, J. S. Lintuvuori, A. N. Morozov, K. Stratford, M. E. Cates, and D. Marenduzzo, “Bulk rheology and microrheology of active fluids,” Eur. Phys. J. 35(10), 98 (2012).
[Crossref] [PubMed]

Lubensky, T. C.

C. Storm, J. J. Pastore, F. C. MacKintosh, T. C. Lubensky, and P. A. Janmey, “Nonlinear elasticity in biological gels,” Nature 435(7039), 191–194 (2005).
[Crossref] [PubMed]

Mackay, M. E.

A. Tuteja, M. E. Mackay, S. Narayanan, S. Asokan, and M. S. Wong, “Breakdown of the continuum stokes-einstein relation for nanoparticle diffusion,” Nano Lett. 7(5), 1276–1281 (2007).
[Crossref] [PubMed]

MacKintosh, F. C.

C. Storm, J. J. Pastore, F. C. MacKintosh, T. C. Lubensky, and P. A. Janmey, “Nonlinear elasticity in biological gels,” Nature 435(7039), 191–194 (2005).
[Crossref] [PubMed]

Maître, J.

H. Berthoumieux, J. Maître, C. Heisenberg, E. K. Paluch, F. Jülicher, and G. Salbreux, “Active elastic thin shell theory for cellular deformations,” New J. Phys. 16(6), 065005 (2014).
[Crossref]

Marenduzzo, D.

G. Foffano, J. S. Lintuvuori, A. N. Morozov, K. Stratford, M. E. Cates, and D. Marenduzzo, “Bulk rheology and microrheology of active fluids,” Eur. Phys. J. 35(10), 98 (2012).
[Crossref] [PubMed]

Marsà, F.

Mathues, W.

R. Cardinaels, J. Van De Velde, W. Mathues, P. Van Liedekerke, and P. Moldenaers, “A rheological characterisation of liquid egg albumen,” Insid. Food Symp.9–12 (2013).

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

Matsumoto, K.

V. V. Artym and K. Matsumoto, “Imaging cells in three-dimensional collagen matrix,” Curr. Protoc. Cell Biol. 10, 1–20 (2010).
[PubMed]

McIntyre, D. H.

C. A. R. Jones, M. Cibula, J. Feng, E. A. Krnacik, D. H. McIntyre, H. Levine, and B. Sun, “Micromechanics of cellularized biopolymer networks,” Proc. Natl. Acad. Sci. U.S.A. 112(37), E5117–E5122 (2015).
[Crossref] [PubMed]

McKinley, G. H.

J. P. Rich, G. H. McKinley, and P. S. Doyle, “Size dependence of microprobe dynamics during gelation of a discotic colloidal clay,” J. Rheol. (N.Y.N.Y.) 55(2), 273–299 (2011).
[Crossref]

Misof, K.

P. Fratzl, K. Misof, I. Zizak, G. Rapp, H. Amenitsch, and S. Bernstorff, “Fibrillar structure and mechanical properties of collagen,” J. Struct. Biol. 122(1-2), 119–122 (1998).
[Crossref] [PubMed]

Moldenaers, P.

R. Cardinaels, J. Van De Velde, W. Mathues, P. Van Liedekerke, and P. Moldenaers, “A rheological characterisation of liquid egg albumen,” Insid. Food Symp.9–12 (2013).

Montes-Usategui, M.

Morozov, A. N.

G. Foffano, J. S. Lintuvuori, A. N. Morozov, K. Stratford, M. E. Cates, and D. Marenduzzo, “Bulk rheology and microrheology of active fluids,” Eur. Phys. J. 35(10), 98 (2012).
[Crossref] [PubMed]

Narayanan, S.

A. Tuteja, M. E. Mackay, S. Narayanan, S. Asokan, and M. S. Wong, “Breakdown of the continuum stokes-einstein relation for nanoparticle diffusion,” Nano Lett. 7(5), 1276–1281 (2007).
[Crossref] [PubMed]

Netti, P. A.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[Crossref]

Neuman, K. C.

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

Oddershede, L. B.

M. Fischer, A. C. Richardson, S. N. S. Reihani, L. B. Oddershede, and K. Berg-Sørensen, “Active-passive calibration of optical tweezers in viscoelastic media,” Rev. Sci. Instrum. 81(1), 015103 (2010).
[Crossref] [PubMed]

Padgett, M.

A. Yao, M. Tassieri, M. Padgett, and J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[Crossref] [PubMed]

Padgett, M. J.

D. Preece, R. Warren, M. Tassieri, R. M. L. Evans, G. M. Gibson, M. J. Padgett, and J. M. Cooper, “Optical tweezers: wideband microrheology,” J. Opt. 13(4), 13 (2010).

M. Tassieri, G. M. Gibson, R. M. L. Evans, A. M. Yao, R. Warren, M. J. Padgett, and J. M. Cooper, “Measuring storage and loss moduli using optical tweezers: broadband microrheology,” Phys. Rev. E 81(2), 026308 (2010).

Paluch, E.

E. Paluch and C. P. Heisenberg, “Biology and physics of cell shape changes in development,” Curr. Biol. 19(17), R790–R799 (2009).
[Crossref] [PubMed]

Paluch, E. K.

H. Berthoumieux, J. Maître, C. Heisenberg, E. K. Paluch, F. Jülicher, and G. Salbreux, “Active elastic thin shell theory for cellular deformations,” New J. Phys. 16(6), 065005 (2014).
[Crossref]

Pastore, J. J.

C. Storm, J. J. Pastore, F. C. MacKintosh, T. C. Lubensky, and P. A. Janmey, “Nonlinear elasticity in biological gels,” Nature 435(7039), 191–194 (2005).
[Crossref] [PubMed]

Pavone, F. S.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77(10), 103101 (2006).
[Crossref]

Perronet, K.

Pesce, G.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[Crossref]

Peterman, E. J. G.

K. C. Vermeulen, J. Van Mameren, G. J. M. Stienen, E. J. G. Peterman, G. J. L. Wuite, and C. F. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77(1), 013704 (2006).
[Crossref]

Piau, J. M.

N. El Kissi, J. M. Piau, P. Attané, and G. Turrel, “Shear rheometry of polydimethylsiloxanes: master curves and testing of Gleissle and Yamamoto relations,” Rheol. Acta 310(3), 293–310 (1993).
[Crossref]

Pistré, J.

V. Raimbault, D. Rebière, C. Dejous, M. Guirardel, J. Pistré, and J. L. Lachaud, “High frequency microrheological measurements of PDMS fluids using saw microfluidic system,” Sens. Actuators B Chem. 144(2), 467–471 (2010).
[Crossref]

Preece, D.

D. Preece, R. Warren, M. Tassieri, R. M. L. Evans, G. M. Gibson, M. J. Padgett, and J. M. Cooper, “Optical tweezers: wideband microrheology,” J. Opt. 13(4), 13 (2010).

Putnam, A. J.

E. Kniazeva, J. W. Weidling, R. Singh, E. L. Botvinick, M. A. Digman, E. Gratton, and A. J. Putnam, “Quantification of local matrix deformations and mechanical properties during capillary morphogenesis in 3D,” Integr. Biol. 4(4), 431–439 (2012).
[Crossref]

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Raimbault, V.

V. Raimbault, D. Rebière, C. Dejous, M. Guirardel, J. Pistré, and J. L. Lachaud, “High frequency microrheological measurements of PDMS fluids using saw microfluidic system,” Sens. Actuators B Chem. 144(2), 467–471 (2010).
[Crossref]

Rapp, G.

P. Fratzl, K. Misof, I. Zizak, G. Rapp, H. Amenitsch, and S. Bernstorff, “Fibrillar structure and mechanical properties of collagen,” J. Struct. Biol. 122(1-2), 119–122 (1998).
[Crossref] [PubMed]

Rebière, D.

V. Raimbault, D. Rebière, C. Dejous, M. Guirardel, J. Pistré, and J. L. Lachaud, “High frequency microrheological measurements of PDMS fluids using saw microfluidic system,” Sens. Actuators B Chem. 144(2), 467–471 (2010).
[Crossref]

Reihani, S. N. S.

M. Fischer, A. C. Richardson, S. N. S. Reihani, L. B. Oddershede, and K. Berg-Sørensen, “Active-passive calibration of optical tweezers in viscoelastic media,” Rev. Sci. Instrum. 81(1), 015103 (2010).
[Crossref] [PubMed]

Rich, J. P.

J. P. Rich, G. H. McKinley, and P. S. Doyle, “Size dependence of microprobe dynamics during gelation of a discotic colloidal clay,” J. Rheol. (N.Y.N.Y.) 55(2), 273–299 (2011).
[Crossref]

Richardson, A. C.

M. Fischer, A. C. Richardson, S. N. S. Reihani, L. B. Oddershede, and K. Berg-Sørensen, “Active-passive calibration of optical tweezers in viscoelastic media,” Rev. Sci. Instrum. 81(1), 015103 (2010).
[Crossref] [PubMed]

Ros, R.

J. R. Staunton, B. L. Doss, S. Lindsay, and R. Ros, “Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices,” Sci. Rep. 6, 19686 (2016).
[Crossref] [PubMed]

Rusciano, G.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[Crossref]

Salbreux, G.

H. Berthoumieux, J. Maître, C. Heisenberg, E. K. Paluch, F. Jülicher, and G. Salbreux, “Active elastic thin shell theory for cellular deformations,” New J. Phys. 16(6), 065005 (2014).
[Crossref]

Sasso, A.

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[Crossref]

Schäffer, E.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77(10), 103101 (2006).
[Crossref]

Schieber, J.

Schmidt, C. F.

K. C. Vermeulen, J. Van Mameren, G. J. M. Stienen, E. J. G. Peterman, G. J. L. Wuite, and C. F. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77(1), 013704 (2006).
[Crossref]

F. Gittes and C. F. Schmidt, “Interference model for back-focal-plane displacement detection in optical tweezers,” Opt. Lett. 23(1), 7–9 (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(2), 1074–1085 (1998).
[Crossref] [PubMed]

Schroer, T. A.

B. H. Blehm, T. A. Schroer, K. M. Trybus, Y. R. Chemla, and P. R. Selvin, “In vivo optical trapping indicates kinesin’s stall force is reduced by dynein during intracellular transport,” Proc. Natl. Acad. Sci. U.S.A. 110(9), 3381–3386 (2013).
[Crossref] [PubMed]

Selvin, P. R.

B. H. Blehm, T. A. Schroer, K. M. Trybus, Y. R. Chemla, and P. R. Selvin, “In vivo optical trapping indicates kinesin’s stall force is reduced by dynein during intracellular transport,” Proc. Natl. Acad. Sci. U.S.A. 110(9), 3381–3386 (2013).
[Crossref] [PubMed]

B. Blehm, Y. R. Chemla, and P. R. Selvin, “In vivo organelle tracking, calibration, and force measurement with an optical trap,” Biophys. J. 98(3), 722a (2010).
[Crossref]

Shreim, S. G.

S. G. Shreim, E. Steward, and E. L. Botvinick, “Extending vaterite microviscometry to ex vivo blood vessels by serial calibration,” Biomed. Opt. Express 3(1), 37–47 (2012).
[Crossref] [PubMed]

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Singh, R.

E. Kniazeva, J. W. Weidling, R. Singh, E. L. Botvinick, M. A. Digman, E. Gratton, and A. J. Putnam, “Quantification of local matrix deformations and mechanical properties during capillary morphogenesis in 3D,” Integr. Biol. 4(4), 431–439 (2012).
[Crossref]

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Smith, S. B.

M. S. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276(5315), 1112–1116 (1997).
[Crossref] [PubMed]

Sollich, P.

P. Sollich, F. Lequeux, P. Hébraud, and M. Cates, “Rheology of soft glassy materials,” Phys. Rev. Lett. 78(10), 2020–2023 (1997).
[Crossref]

Song, Y.

Y. Song and L. L. Dai, “Two-particle interfacial microrheology at polymer-polymer interfaces,” Langmuir 26(16), 13044–13047 (2010).
[Crossref] [PubMed]

Squires, T. M.

T. M. Squires, “Nonlinear microrheology: bulk stresses versus direct interactions,” Langmuir 24(4), 1147–1159 (2008).
[Crossref] [PubMed]

Staunton, J. R.

J. R. Staunton, B. L. Doss, S. Lindsay, and R. Ros, “Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices,” Sci. Rep. 6, 19686 (2016).
[Crossref] [PubMed]

J. R. Staunton, W. Vieira, K. L. Fung, R. Lake, A. Devine, and K. Tanner, “Mechanical properties of the tumor stromal microenvironment probed in vitro and ex vivo by in situ-calibrated optical trap-based active microrheology,” Cell. Mol. Bioeng. 9(3), 398–417 (2016).
[Crossref] [PubMed]

B. H. Blehm, A. Devine, J. R. Staunton, and K. Tanner, “In vivo tissue has non-linear rheological behavior distinct from 3D biomimetic hydrogels, as determined by AMOTIV microscopy,” Biomaterials 83, 66–78 (2016).
[Crossref] [PubMed]

Steward, E.

Stewart, R. J.

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(2), 1074–1085 (1998).
[Crossref] [PubMed]

Stienen, G. J. M.

K. C. Vermeulen, J. Van Mameren, G. J. M. Stienen, E. J. G. Peterman, G. J. L. Wuite, and C. F. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77(1), 013704 (2006).
[Crossref]

Storm, C.

C. Storm, J. J. Pastore, F. C. MacKintosh, T. C. Lubensky, and P. A. Janmey, “Nonlinear elasticity in biological gels,” Nature 435(7039), 191–194 (2005).
[Crossref] [PubMed]

Stratford, K.

G. Foffano, J. S. Lintuvuori, A. N. Morozov, K. Stratford, M. E. Cates, and D. Marenduzzo, “Bulk rheology and microrheology of active fluids,” Eur. Phys. J. 35(10), 98 (2012).
[Crossref] [PubMed]

Sun, B.

C. A. R. Jones, M. Cibula, J. Feng, E. A. Krnacik, D. H. McIntyre, H. Levine, and B. Sun, “Micromechanics of cellularized biopolymer networks,” Proc. Natl. Acad. Sci. U.S.A. 112(37), E5117–E5122 (2015).
[Crossref] [PubMed]

Svoboda, K.

K. Svoboda and S. M. Block, “Biological applications of optical forces,” Annu. Rev. Biophys. Biomol. Struct. 23(1), 247–285 (1994).
[Crossref] [PubMed]

Tai, Y. C.

D. Kang, W. Wang, J. Lee, Y. C. Tai, and T. K. Hsiai, “Measurement of viscosity of adult zebrafish blood using a capillary pressure-driven viscometer,” in 18th International Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2015), pp. 1661–1664.
[Crossref]

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

Tanner, K.

B. H. Blehm, A. Devine, J. R. Staunton, and K. Tanner, “In vivo tissue has non-linear rheological behavior distinct from 3D biomimetic hydrogels, as determined by AMOTIV microscopy,” Biomaterials 83, 66–78 (2016).
[Crossref] [PubMed]

J. Kim and K. Tanner, “Three-dimensional patterning of the ECM microenvironment using magnetic nanoparticle self assembly,” Curr. Protoc. Cell Biol. 70, 1–14 (2016).
[PubMed]

J. R. Staunton, W. Vieira, K. L. Fung, R. Lake, A. Devine, and K. Tanner, “Mechanical properties of the tumor stromal microenvironment probed in vitro and ex vivo by in situ-calibrated optical trap-based active microrheology,” Cell. Mol. Bioeng. 9(3), 398–417 (2016).
[Crossref] [PubMed]

K. Tanner and M. M. Gottesman, “Beyond 3D culture models of cancer,” Sci. Transl. Med. 7(283), 283ps9 (2015).
[Crossref] [PubMed]

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

Tassieri, M.

D. Preece, R. Warren, M. Tassieri, R. M. L. Evans, G. M. Gibson, M. J. Padgett, and J. M. Cooper, “Optical tweezers: wideband microrheology,” J. Opt. 13(4), 13 (2010).

M. Tassieri, G. M. Gibson, R. M. L. Evans, A. M. Yao, R. Warren, M. J. Padgett, and J. M. Cooper, “Measuring storage and loss moduli using optical tweezers: broadband microrheology,” Phys. Rev. E 81(2), 026308 (2010).

A. Yao, M. Tassieri, M. Padgett, and J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[Crossref] [PubMed]

Tolic-Nørrelykke, S. F.

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77(10), 103101 (2006).
[Crossref]

Trybus, K. M.

B. H. Blehm, T. A. Schroer, K. M. Trybus, Y. R. Chemla, and P. R. Selvin, “In vivo optical trapping indicates kinesin’s stall force is reduced by dynein during intracellular transport,” Proc. Natl. Acad. Sci. U.S.A. 110(9), 3381–3386 (2013).
[Crossref] [PubMed]

Turrel, G.

N. El Kissi, J. M. Piau, P. Attané, and G. Turrel, “Shear rheometry of polydimethylsiloxanes: master curves and testing of Gleissle and Yamamoto relations,” Rheol. Acta 310(3), 293–310 (1993).
[Crossref]

Tuteja, A.

A. Tuteja, M. E. Mackay, S. Narayanan, S. Asokan, and M. S. Wong, “Breakdown of the continuum stokes-einstein relation for nanoparticle diffusion,” Nano Lett. 7(5), 1276–1281 (2007).
[Crossref] [PubMed]

Valdevit, L.

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Van De Velde, J.

R. Cardinaels, J. Van De Velde, W. Mathues, P. Van Liedekerke, and P. Moldenaers, “A rheological characterisation of liquid egg albumen,” Insid. Food Symp.9–12 (2013).

Van Liedekerke, P.

R. Cardinaels, J. Van De Velde, W. Mathues, P. Van Liedekerke, and P. Moldenaers, “A rheological characterisation of liquid egg albumen,” Insid. Food Symp.9–12 (2013).

Van Mameren, J.

K. C. Vermeulen, J. Van Mameren, G. J. M. Stienen, E. J. G. Peterman, G. J. L. Wuite, and C. F. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77(1), 013704 (2006).
[Crossref]

Venturoni, M.

T. Gutsmann, G. E. Fantner, J. H. Kindt, M. Venturoni, S. Danielsen, and P. K. Hansma, “Force spectroscopy of collagen fibers to investigate their mechanical properties and structural organization,” Biophys. J. 86(5), 3186–3193 (2004).
[Crossref] [PubMed]

Vermeulen, K. C.

K. C. Vermeulen, J. Van Mameren, G. J. M. Stienen, E. J. G. Peterman, G. J. L. Wuite, and C. F. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77(1), 013704 (2006).
[Crossref]

Vieira, W.

J. R. Staunton, W. Vieira, K. L. Fung, R. Lake, A. Devine, and K. Tanner, “Mechanical properties of the tumor stromal microenvironment probed in vitro and ex vivo by in situ-calibrated optical trap-based active microrheology,” Cell. Mol. Bioeng. 9(3), 398–417 (2016).
[Crossref] [PubMed]

Villing, A.

Visscher, K.

Wang, W.

D. Kang, W. Wang, J. Lee, Y. C. Tai, and T. K. Hsiai, “Measurement of viscosity of adult zebrafish blood using a capillary pressure-driven viscometer,” in 18th International Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2015), pp. 1661–1664.
[Crossref]

Warren, R.

M. Tassieri, G. M. Gibson, R. M. L. Evans, A. M. Yao, R. Warren, M. J. Padgett, and J. M. Cooper, “Measuring storage and loss moduli using optical tweezers: broadband microrheology,” Phys. Rev. E 81(2), 026308 (2010).

D. Preece, R. Warren, M. Tassieri, R. M. L. Evans, G. M. Gibson, M. J. Padgett, and J. M. Cooper, “Optical tweezers: wideband microrheology,” J. Opt. 13(4), 13 (2010).

Weaver, V. M.

S. Kumar and V. M. Weaver, “Mechanics, malignancy, and metastasis: the force journey of a tumor cell,” Cancer Metastasis Rev. 28(1-2), 113–127 (2009).
[Crossref] [PubMed]

Webb, W. W.

Weidling, J. W.

E. Kniazeva, J. W. Weidling, R. Singh, E. L. Botvinick, M. A. Digman, E. Gratton, and A. J. Putnam, “Quantification of local matrix deformations and mechanical properties during capillary morphogenesis in 3D,” Integr. Biol. 4(4), 431–439 (2012).
[Crossref]

Westbrook, N.

Wong, M. S.

A. Tuteja, M. E. Mackay, S. Narayanan, S. Asokan, and M. S. Wong, “Breakdown of the continuum stokes-einstein relation for nanoparticle diffusion,” Nano Lett. 7(5), 1276–1281 (2007).
[Crossref] [PubMed]

Wuite, G. J. L.

K. C. Vermeulen, J. Van Mameren, G. J. M. Stienen, E. J. G. Peterman, G. J. L. Wuite, and C. F. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77(1), 013704 (2006).
[Crossref]

Xu, X. H.

L. M. Browning, T. Huang, X. H. Xu, and X. N. Xu, “Real-time in vivo imaging of size-dependent transport and toxicity of gold nanoparticles in zebrafish embryos using single nanoparticle plasmonic spectroscopy,” Interface Focus 3(3), 20120098 (2013).
[Crossref] [PubMed]

Xu, X. N.

L. M. Browning, T. Huang, X. H. Xu, and X. N. Xu, “Real-time in vivo imaging of size-dependent transport and toxicity of gold nanoparticles in zebrafish embryos using single nanoparticle plasmonic spectroscopy,” Interface Focus 3(3), 20120098 (2013).
[Crossref] [PubMed]

Yao, A.

A. Yao, M. Tassieri, M. Padgett, and J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[Crossref] [PubMed]

Yao, A. M.

M. Tassieri, G. M. Gibson, R. M. L. Evans, A. M. Yao, R. Warren, M. J. Padgett, and J. M. Cooper, “Measuring storage and loss moduli using optical tweezers: broadband microrheology,” Phys. Rev. E 81(2), 026308 (2010).

Zizak, I.

P. Fratzl, K. Misof, I. Zizak, G. Rapp, H. Amenitsch, and S. Bernstorff, “Fibrillar structure and mechanical properties of collagen,” J. Struct. Biol. 122(1-2), 119–122 (1998).
[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(1), 247–285 (1994).
[Crossref] [PubMed]

Appl. Opt. (1)

Biomaterials (1)

B. H. Blehm, A. Devine, J. R. Staunton, and K. Tanner, “In vivo tissue has non-linear rheological behavior distinct from 3D biomimetic hydrogels, as determined by AMOTIV microscopy,” Biomaterials 83, 66–78 (2016).
[Crossref] [PubMed]

Biomed. Opt. Express (1)

Biophys. J. (3)

T. Gutsmann, G. E. Fantner, J. H. Kindt, M. Venturoni, S. Danielsen, and P. K. Hansma, “Force spectroscopy of collagen fibers to investigate their mechanical properties and structural organization,” Biophys. J. 86(5), 3186–3193 (2004).
[Crossref] [PubMed]

B. Blehm, Y. R. Chemla, and P. R. Selvin, “In vivo organelle tracking, calibration, and force measurement with an optical trap,” Biophys. J. 98(3), 722a (2010).
[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(2), 1074–1085 (1998).
[Crossref] [PubMed]

Cancer Metastasis Rev. (1)

S. Kumar and V. M. Weaver, “Mechanics, malignancy, and metastasis: the force journey of a tumor cell,” Cancer Metastasis Rev. 28(1-2), 113–127 (2009).
[Crossref] [PubMed]

Cell. Mol. Bioeng. (1)

J. R. Staunton, W. Vieira, K. L. Fung, R. Lake, A. Devine, and K. Tanner, “Mechanical properties of the tumor stromal microenvironment probed in vitro and ex vivo by in situ-calibrated optical trap-based active microrheology,” Cell. Mol. Bioeng. 9(3), 398–417 (2016).
[Crossref] [PubMed]

Curr. Biol. (1)

E. Paluch and C. P. Heisenberg, “Biology and physics of cell shape changes in development,” Curr. Biol. 19(17), R790–R799 (2009).
[Crossref] [PubMed]

Curr. Protoc. Cell Biol. (2)

V. V. Artym and K. Matsumoto, “Imaging cells in three-dimensional collagen matrix,” Curr. Protoc. Cell Biol. 10, 1–20 (2010).
[PubMed]

J. Kim and K. Tanner, “Three-dimensional patterning of the ECM microenvironment using magnetic nanoparticle self assembly,” Curr. Protoc. Cell Biol. 70, 1–14 (2016).
[PubMed]

Eur. Phys. J. (1)

G. Foffano, J. S. Lintuvuori, A. N. Morozov, K. Stratford, M. E. Cates, and D. Marenduzzo, “Bulk rheology and microrheology of active fluids,” Eur. Phys. J. 35(10), 98 (2012).
[Crossref] [PubMed]

Integr. Biol. (1)

E. Kniazeva, J. W. Weidling, R. Singh, E. L. Botvinick, M. A. Digman, E. Gratton, and A. J. Putnam, “Quantification of local matrix deformations and mechanical properties during capillary morphogenesis in 3D,” Integr. Biol. 4(4), 431–439 (2012).
[Crossref]

Interface Focus (1)

L. M. Browning, T. Huang, X. H. Xu, and X. N. Xu, “Real-time in vivo imaging of size-dependent transport and toxicity of gold nanoparticles in zebrafish embryos using single nanoparticle plasmonic spectroscopy,” Interface Focus 3(3), 20120098 (2013).
[Crossref] [PubMed]

J. Korean Phys. Soc. (1)

Y. Fujimura, M. Inoue, H. Kondoh, and S. Kinoshita, “Measurement of micro-elasticity within a fertilized egg by using Brillouin scattering spectroscopy,” J. Korean Phys. Soc. 51(2), 854–857 (2007).
[Crossref]

J. Opt. (1)

D. Preece, R. Warren, M. Tassieri, R. M. L. Evans, G. M. Gibson, M. J. Padgett, and J. M. Cooper, “Optical tweezers: wideband microrheology,” J. Opt. 13(4), 13 (2010).

J. Opt. A, Pure Appl. Opt. (3)

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. A, Pure Appl. Opt. 9(8), S103–S112 (2007).
[Crossref]

M. Fischer and K. Berg-sørensen, “Calibration of trapping force and response function of optical tweezers in viscoelastic media,” J. Opt. A, Pure Appl. Opt. 9(8), S239–S250 (2007).
[Crossref]

G. Pesce, A. C. De Luca, G. Rusciano, P. A. Netti, S. Fusco, and A. Sasso, “Microrheology of complex fluids using optical tweezers: a comparison with macrorheological measurements,” J. Opt. A, Pure Appl. Opt. 11(3), 034016 (2009).
[Crossref]

J. Rheol. (N.Y.N.Y.) (1)

J. P. Rich, G. H. McKinley, and P. S. Doyle, “Size dependence of microprobe dynamics during gelation of a discotic colloidal clay,” J. Rheol. (N.Y.N.Y.) 55(2), 273–299 (2011).
[Crossref]

J. Struct. Biol. (1)

P. Fratzl, K. Misof, I. Zizak, G. Rapp, H. Amenitsch, and S. Bernstorff, “Fibrillar structure and mechanical properties of collagen,” J. Struct. Biol. 122(1-2), 119–122 (1998).
[Crossref] [PubMed]

Lab Chip (1)

A. Yao, M. Tassieri, M. Padgett, and J. Cooper, “Microrheology with optical tweezers,” Lab Chip 9(17), 2568–2575 (2009).
[Crossref] [PubMed]

Langmuir (2)

T. M. Squires, “Nonlinear microrheology: bulk stresses versus direct interactions,” Langmuir 24(4), 1147–1159 (2008).
[Crossref] [PubMed]

Y. Song and L. L. Dai, “Two-particle interfacial microrheology at polymer-polymer interfaces,” Langmuir 26(16), 13044–13047 (2010).
[Crossref] [PubMed]

Nano Lett. (1)

A. Tuteja, M. E. Mackay, S. Narayanan, S. Asokan, and M. S. Wong, “Breakdown of the continuum stokes-einstein relation for nanoparticle diffusion,” Nano Lett. 7(5), 1276–1281 (2007).
[Crossref] [PubMed]

Nature (2)

S. M. Block, “Making light work with optical tweezers,” Nature 360(6403), 493–495 (1992).
[Crossref] [PubMed]

C. Storm, J. J. Pastore, F. C. MacKintosh, T. C. Lubensky, and P. A. Janmey, “Nonlinear elasticity in biological gels,” Nature 435(7039), 191–194 (2005).
[Crossref] [PubMed]

New J. Phys. (1)

H. Berthoumieux, J. Maître, C. Heisenberg, E. K. Paluch, F. Jülicher, and G. Salbreux, “Active elastic thin shell theory for cellular deformations,” New J. Phys. 16(6), 065005 (2014).
[Crossref]

Opt. Express (2)

Opt. Lett. (3)

Phys. Rev. E (1)

M. Tassieri, G. M. Gibson, R. M. L. Evans, A. M. Yao, R. Warren, M. J. Padgett, and J. M. Cooper, “Measuring storage and loss moduli using optical tweezers: broadband microrheology,” Phys. Rev. E 81(2), 026308 (2010).

Phys. Rev. Lett. (1)

P. Sollich, F. Lequeux, P. Hébraud, and M. Cates, “Rheology of soft glassy materials,” Phys. Rev. Lett. 78(10), 2020–2023 (1997).
[Crossref]

PLoS One (1)

M. A. Kotlarchyk, S. G. Shreim, M. B. Alvarez-Elizondo, L. C. Estrada, R. Singh, L. Valdevit, E. Kniazeva, E. Gratton, A. J. Putnam, and E. L. Botvinick, “Concentration independent modulation of local micromechanics in a fibrin gel,” PLoS One 6(5), e20201 (2011).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. U.S.A. (2)

B. H. Blehm, T. A. Schroer, K. M. Trybus, Y. R. Chemla, and P. R. Selvin, “In vivo optical trapping indicates kinesin’s stall force is reduced by dynein during intracellular transport,” Proc. Natl. Acad. Sci. U.S.A. 110(9), 3381–3386 (2013).
[Crossref] [PubMed]

C. A. R. Jones, M. Cibula, J. Feng, E. A. Krnacik, D. H. McIntyre, H. Levine, and B. Sun, “Micromechanics of cellularized biopolymer networks,” Proc. Natl. Acad. Sci. U.S.A. 112(37), E5117–E5122 (2015).
[Crossref] [PubMed]

Rev. Sci. Instrum. (5)

K. C. Vermeulen, J. Van Mameren, G. J. M. Stienen, E. J. G. Peterman, G. J. L. Wuite, and C. F. Schmidt, “Calibrating bead displacements in optical tweezers using acousto-optic deflectors,” Rev. Sci. Instrum. 77(1), 013704 (2006).
[Crossref]

M. Fischer, A. C. Richardson, S. N. S. Reihani, L. B. Oddershede, and K. Berg-Sørensen, “Active-passive calibration of optical tweezers in viscoelastic media,” Rev. Sci. Instrum. 81(1), 015103 (2010).
[Crossref] [PubMed]

K. C. Neuman and S. M. Block, “Optical trapping,” Rev. Sci. Instrum. 75(9), 2787–2809 (2004).
[Crossref] [PubMed]

S. F. Tolić-Nørrelykke, E. Schäffer, J. Howard, F. S. Pavone, F. Jülicher, and H. Flyvbjerg, “Calibration of optical tweezers with positional detection in the back focal plane,” Rev. Sci. Instrum. 77(10), 103101 (2006).
[Crossref]

K. Berg-Sørensen and H. Flyvbjerg, “Power spectrum analysis for optical tweezers,” Rev. Sci. Instrum. 75(3), 594–612 (2004).
[Crossref]

Rheol. Acta (1)

N. El Kissi, J. M. Piau, P. Attané, and G. Turrel, “Shear rheometry of polydimethylsiloxanes: master curves and testing of Gleissle and Yamamoto relations,” Rheol. Acta 310(3), 293–310 (1993).
[Crossref]

Sci. Rep. (1)

J. R. Staunton, B. L. Doss, S. Lindsay, and R. Ros, “Correlating confocal microscopy and atomic force indentation reveals metastatic cancer cells stiffen during invasion into collagen I matrices,” Sci. Rep. 6, 19686 (2016).
[Crossref] [PubMed]

Sci. Transl. Med. (1)

K. Tanner and M. M. Gottesman, “Beyond 3D culture models of cancer,” Sci. Transl. Med. 7(283), 283ps9 (2015).
[Crossref] [PubMed]

Science (1)

M. S. Kellermayer, S. B. Smith, H. L. Granzier, and C. Bustamante, “Folding-unfolding transitions in single titin molecules characterized with laser tweezers,” Science 276(5315), 1112–1116 (1997).
[Crossref] [PubMed]

Sens. Actuators B Chem. (1)

V. Raimbault, D. Rebière, C. Dejous, M. Guirardel, J. Pistré, and J. L. Lachaud, “High frequency microrheological measurements of PDMS fluids using saw microfluidic system,” Sens. Actuators B Chem. 144(2), 467–471 (2010).
[Crossref]

Other (5)

D. Kang, W. Wang, J. Lee, Y. C. Tai, and T. K. Hsiai, “Measurement of viscosity of adult zebrafish blood using a capillary pressure-driven viscometer,” in 18th International Conference on Solid-State Sensors, Actuators and Microsystems (IEEE, 2015), pp. 1661–1664.
[Crossref]

O. Campas, Department of Mechanical Engineering, University of California, Santa Barbara, Santa Barbara, CA 90314 (personal communication, 2016).

M. Westerfield, The Zebrafish Book. A Guide for the Laboratory Use of Zebrafish, 5th ed. (University of Oregon Press, 2007).

R. Cardinaels, J. Van De Velde, W. Mathues, P. Van Liedekerke, and P. Moldenaers, “A rheological characterisation of liquid egg albumen,” Insid. Food Symp.9–12 (2013).

A. J. Barlow, G. Harrison, and J. Lamb, “Viscoelastic relaxation of polydimethylsiloxane liquids,” Proc. R. Soc. A Math. Phys. Eng. Sci. 282(1389), (1964).
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (6)

Fig. 1
Fig. 1 Calibration for active microrheology in vivo. (a) Determining micromechanical properties requires calibration of the optical trap stiffness, k, and the inverse position detection sensitivity β (i.e. the V-nm conversion factor) of the detection system used to measure probe displacements. (b) in vivo (such as in the depicted zebrafish embryo), probes lie in different positions along the beam axis and in regions with different optical properties. Thus, both calibrations must be conducted for every probe measured. In some regions, probes may be free to fluctuate in position because they are not tightly confined (e.g. in the viscous yolk), or are subject to flow (as in perivasculature). (c) Two common methods used to calibrate β are (1) the thermal power spectral density (PSD) method and (2) the piezo stage stepping method. In the PSD method, the probe is trapped and allowed to fluctuate due to thermal motion while the voltage on the detector is recorded. Fluctuations in voltage are related by β to position fluctuations predicted by a fluctuation-dissipation model that requires knowledge of the probe radius and the drag coefficient. In the piezo stage stepping method, the probe is stepped through the detection beam as the stage is moved through known distances, while the voltage on the detector is recorded. This works well unless the probe and stage motions are not in tandem. (3) To calibrate under these conditions, the trap holds the probe stationary while the detection beam scans across it.
Fig. 2
Fig. 2 Schematic of the optical path of dual beam-steering optical trapping microscope. Both the primary trapping beam and the secondary detection beam have two-dimensional acousto-optical deflectors (AOD) in the optical path. Two telescope lens pairs collimate, expand and image the back focal plane of the objective onto both AODs. First, a probe is trapped and the secondary beam is steered across it while the detection QPD signal is recorded to calibrate β. Then the trap beam is alternately oscillated and held stationary in a sequential measurement for both the active-passive calibration of trap stiffness and for broadband active microrheology measurements.
Fig. 3
Fig. 3 Methods for calibrating the V-nm conversion factor β. In the piezo stage stepping method, QPD voltage is recorded while the stage is stepped through the detection beam in defined steps of 12 nm by moving the sample stage via the piezo controller. (a) In viscoelastic solids, the probe moves with the sample stage, so the recorded voltage correctly corresponds to the linear response of the detector to the interference pattern in the back focal plane of the condenser caused by the probe. Linear regression is used to get β from the voltage and position data. Data from the solid-like region in the tail of a zebrafish embryo. (b) In liquid or liquid-like samples, such as the zebrafish yolk, the probe may move freely and is not constrained to move in tandem with the stage, so the signal cannot be used to find the positional sensitivity. In the detection beam steering method, the probe is first trapped and held stationary. The detection beam is then steered using an acousto-optic deflector, oscillating across the probe center with an amplitude of 55 nm and frequency of 1 kHz while the QPD Voltage signal is recorded. To get β, the signal is Fourier transformed to find the voltage at the drive frequency. The method works in solid-like regions as in the tail of a zebrafish embryo (c) or in fluid-like regions as in the yolk (d).
Fig. 4
Fig. 4 Histograms comparing V-nm conversion factors (β) of carboxylated polystyrene microspheres in collagen hydrogel and water obtained by Piezo, PSD and FFT methods. (A) In a collagen hydrogel, β was determined for each probe consecutively by the Piezo and FFT methods. First, the probe was centered in the trap position with the trap off and stepped through the detection beam. Then the detection beam was oscillated across the probe center with frequency 1 kHz and amplitude 55 nm, Fourier transformed and used to calculate β. The ratios of the values are plotted in a histogram and the distribution of ratios was fitted to a normal distribution, giving 1.04 ± 0.09 (mean ± standard deviation). (B) In water, each probe was trapped and the passive motion was recorded, Fourier transformed and fitted to a Lorentzian power spectrum model with the drag coefficient of water to calculate β by the PSD method. Then the detection beam was oscillated across the probe center with frequency 1 kHz and amplitude 55 nm, Fourier transformed and used to calculate β. The ratios of the values are plotted in a histogram and the distribution of ratios was fitted to a normal distribution, giving 1.01 ± 0.03 (mean ± standard deviation). At the 5% significance level, Lilliefors statistical tests suggest the data in (A) and (B) were normally distributed (A: h = 0, p = 0.50; B: h = 0; p = 0.32).
Fig. 5
Fig. 5 Active Microrheology and small angle oscillatory shear (SAOS) bulk rheology data of probes in uncured PDMS. (A) Active microrheology measurements (red) were conducted from 2 Hz – 12,809 Hz, with multiplexed frequencies at stress-strain amplitudes of 20 nm trap displacement per frequency. Bulk rheology (black) frequency sweeps were conducted from 0.1 – 100 Hz at 1% shear strain. The elastic (G’, squares) and viscous (G”, triangles) components of the complex modulus calculated from both methods are shown. (B) The moduli in the overlapping frequency range (shaded in B). The moduli increased significantly with increasing stress-strain amplitude (p < 0.0001, two-way ANOVA). Values of G” are similar across length scales, whereas values of G’ in bulk are lower than microscopic values by three orders of magnitude at ~1 Hz and one order of magnitude at 100 Hz.
Fig. 6
Fig. 6 Microscale stress-strain behavior of zebrafish embryo yolk and uncured PDMS measured by active microrheology. (a) Sinusoidal oscillations of the trap position with increasing amplitudes of trap displacement increases applied force, stress, bead displacement and induced strain on the surrounding material. Probe displacements remain within the linear response regimes of both the detector and optical trapping potential but the material response is nonlinear. (b–e) Active microrheology measurements were conducted from 2 Hz – 12,8 kHz, with multiplexed frequencies at stress-strain amplitudes of 2 nm (blue), 5 nm (green) and 20 nm (red) trap displacement per frequency. (b, d) The elastic (G’, squares) and viscous (G”, triangles) components of the complex modulus are shown. (c, e) Corresponding complex viscosities η*. In both PDMS (b, c) and inside the yolks of living zebrafish embryos (d, e), the moduli show nonlinear viscoelasticity, increasing significantly with increasing stress-strain amplitude (p < 0.0001, two-way ANOVA).

Metrics