Abstract

Intracellular motion can be quantitatively monitored in tissues using coherence-gated microscopic techniques. With full-field optical coherence tomography (FFOCT), the use of high numerical aperture microscope objectives provides a high resolution mapping of intracellular dynamics that are probed with subwavelength sensitivity. In the upper temporal bandwidth that we have used (1-6 Hz) the main contribution to the dynamic signal arises from the overall dynamical, optically heterogeneous cytoplasm. We propose a method to specifically study the impact of actomyosin contractility on the intracellular dynamic signal by performing high throughput, comparative measurements of multicellular aggregates with and without blebbistatin action, a selective inhibitor of class-II myosins that disrupts actomyosin contractile activity. Our results indicate a significant increase in the fraction of the signal that decorrelates within 1 second after inhibition of contractility. This observation mitigates the anticipated importance of actomyosin contractile forces to directly move organelles, but highlights their role in hindering organelle transport via their stiffening effect of the viscoelastic cytoplasm.

© 2016 Optical Society of America

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References

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2016 (1)

C. Apelian, F. Harms, O. Thouvenin, and A. C. Boccara, “Dynamic full field optical coherence tomography: subcellular metabolic contrast revealed in tissues by temporal analysis of interferometric signals,” Biomed. Opt. Express 7(3), 455–468 (2016).
[PubMed]

2015 (2)

2014 (1)

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

2013 (6)

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

F. Höfling and T. Franosch, “Anomalous transport in the crowded world of biological cells,” Rep. Prog. Phys. 76(4), 046602 (2013).
[Crossref] [PubMed]

M. Delarue, F. Montel, O. Caen, J. Elgeti, J. M. Siaugue, D. Vignjevic, J. Prost, J. F. Joanny, and G. Cappello, “Mechanical control of cell flow in multicellular spheroids,” Phys. Rev. Lett. 110(13), 138103 (2013).
[Crossref] [PubMed]

R. An, J. Turek, D. E. Matei, and D. Nolte, “Live tissue viability and chemosensitivity assays using digital holographic motility contrast imaging,” Appl. Opt. 52(1), A300–A309 (2013).
[Crossref] [PubMed]

A. L. Oldenburg, R. K. Chhetri, J. M. Cooper, W. C. Wu, M. A. Troester, and J. B. Tracy, “Motility-, autocorrelation-, and polarization-sensitive optical coherence tomography discriminates cells and gold nanorods within 3D tissue cultures,” Opt. Lett. 38(15), 2923–2926 (2013).
[Crossref] [PubMed]

2012 (3)

D. D. Nolte, R. An, J. Turek, and K. Jeong, “Tissue dynamics spectroscopy for phenotypic profiling of drug effects in three-dimensional culture,” Biomed. Opt. Express 3(11), 2825–2841 (2012).
[Crossref] [PubMed]

G. Mehta, A. Y. Hsiao, M. Ingram, G. D. Luker, and S. Takayama, “Opportunities and challenges for use of tumor spheroids as models to test drug delivery and efficacy,” J. Control. Release 164(2), 192–204 (2012).
[Crossref] [PubMed]

E. M. Balzer, Z. Tong, C. D. Paul, W. C. Hung, K. M. Stroka, A. E. Boggs, S. S. Martin, and K. Konstantopoulos, “Physical confinement alters tumor cell adhesion and migration phenotypes,” FASEB J. 26(10), 4045–4056 (2012).
[Crossref] [PubMed]

2011 (1)

O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, “Intermittent search strategies,” Rev. Mod. Phys. 83(1), 81–129 (2011).
[Crossref]

2009 (3)

B. D. Hoffman and J. C. Crocker, “Cell mechanics: dissecting the physical responses of cells to force,” Annu. Rev. Biomed. Eng. 11(1), 259–288 (2009).
[Crossref] [PubMed]

C. P. Brangwynne, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, “Intracellular transport by active diffusion,” Trends Cell Biol. 19(9), 423–427 (2009).
[Crossref] [PubMed]

F. Gallet, D. Arcizet, P. Bohec, and A. Richert, “Power spectrum of out-of-equilibrium forces in living cells: amplitude and frequency dependence,” Soft Matter 5(15), 2947–2953 (2009).
[Crossref]

2007 (2)

2004 (1)

M. Kovács, J. Tóth, C. Hetényi, A. Málnási-Csizmadia, and J. R. Sellers, “Mechanism of blebbistatin inhibition of myosin II,” J. Biol. Chem. 279(34), 35557–35563 (2004).
[Crossref] [PubMed]

1998 (1)

1991 (1)

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

1986 (1)

J. P. Freyer and R. M. Sutherland, “Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply,” Cancer Res. 46(7), 3504–3512 (1986).
[PubMed]

1971 (1)

R. Nossal, S. H. Chen, and C. C. Lai, “Use of laser scattering for quantitative determinations of bacterial motility,” Opt. Commun. 4(1), 35–39 (1971).
[Crossref]

Alabi, O.

Alessandri, K.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

An, R.

Apelian, C.

C. Apelian, F. Harms, O. Thouvenin, and A. C. Boccara, “Dynamic full field optical coherence tomography: subcellular metabolic contrast revealed in tissues by temporal analysis of interferometric signals,” Biomed. Opt. Express 7(3), 455–468 (2016).
[PubMed]

Arcizet, D.

F. Gallet, D. Arcizet, P. Bohec, and A. Richert, “Power spectrum of out-of-equilibrium forces in living cells: amplitude and frequency dependence,” Soft Matter 5(15), 2947–2953 (2009).
[Crossref]

Balzer, E. M.

E. M. Balzer, Z. Tong, C. D. Paul, W. C. Hung, K. M. Stroka, A. E. Boggs, S. S. Martin, and K. Konstantopoulos, “Physical confinement alters tumor cell adhesion and migration phenotypes,” FASEB J. 26(10), 4045–4056 (2012).
[Crossref] [PubMed]

Beaurepaire, E.

Bénichou, O.

O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, “Intermittent search strategies,” Rev. Mod. Phys. 83(1), 81–129 (2011).
[Crossref]

Bibette, J.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Blanchot, L.

Boccara, A. C.

C. Apelian, F. Harms, O. Thouvenin, and A. C. Boccara, “Dynamic full field optical coherence tomography: subcellular metabolic contrast revealed in tissues by temporal analysis of interferometric signals,” Biomed. Opt. Express 7(3), 455–468 (2016).
[PubMed]

E. Beaurepaire, A. C. Boccara, M. Lebec, L. Blanchot, and H. Saint-Jalmes, “Full-field optical coherence microscopy,” Opt. Lett. 23(4), 244–246 (1998).
[Crossref] [PubMed]

Boggs, A. E.

E. M. Balzer, Z. Tong, C. D. Paul, W. C. Hung, K. M. Stroka, A. E. Boggs, S. S. Martin, and K. Konstantopoulos, “Physical confinement alters tumor cell adhesion and migration phenotypes,” FASEB J. 26(10), 4045–4056 (2012).
[Crossref] [PubMed]

Bohec, P.

F. Gallet, D. Arcizet, P. Bohec, and A. Richert, “Power spectrum of out-of-equilibrium forces in living cells: amplitude and frequency dependence,” Soft Matter 5(15), 2947–2953 (2009).
[Crossref]

Brangwynne, C. P.

C. P. Brangwynne, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, “Intracellular transport by active diffusion,” Trends Cell Biol. 19(9), 423–427 (2009).
[Crossref] [PubMed]

Bremond, N.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Caen, O.

M. Delarue, F. Montel, O. Caen, J. Elgeti, J. M. Siaugue, D. Vignjevic, J. Prost, J. F. Joanny, and G. Cappello, “Mechanical control of cell flow in multicellular spheroids,” Phys. Rev. Lett. 110(13), 138103 (2013).
[Crossref] [PubMed]

Cappello, G.

M. Delarue, F. Montel, O. Caen, J. Elgeti, J. M. Siaugue, D. Vignjevic, J. Prost, J. F. Joanny, and G. Cappello, “Mechanical control of cell flow in multicellular spheroids,” Phys. Rev. Lett. 110(13), 138103 (2013).
[Crossref] [PubMed]

Chang, W.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Charras, G. T.

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

Chen, S. H.

R. Nossal, S. H. Chen, and C. C. Lai, “Use of laser scattering for quantitative determinations of bacterial motility,” Opt. Commun. 4(1), 35–39 (1971).
[Crossref]

Chhetri, R. K.

Cooper, J. M.

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(1), 259–288 (2009).
[Crossref] [PubMed]

Delarue, M.

M. Delarue, F. Montel, O. Caen, J. Elgeti, J. M. Siaugue, D. Vignjevic, J. Prost, J. F. Joanny, and G. Cappello, “Mechanical control of cell flow in multicellular spheroids,” Phys. Rev. Lett. 110(13), 138103 (2013).
[Crossref] [PubMed]

Doméjean, H.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Ehrlicher, A. J.

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

Elgeti, J.

M. Delarue, F. Montel, O. Caen, J. Elgeti, J. M. Siaugue, D. Vignjevic, J. Prost, J. F. Joanny, and G. Cappello, “Mechanical control of cell flow in multicellular spheroids,” Phys. Rev. Lett. 110(13), 138103 (2013).
[Crossref] [PubMed]

Fetler, L.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Flotte, T.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Franosch, T.

F. Höfling and T. Franosch, “Anomalous transport in the crowded world of biological cells,” Rep. Prog. Phys. 76(4), 046602 (2013).
[Crossref] [PubMed]

Freyer, J. P.

J. P. Freyer and R. M. Sutherland, “Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply,” Cancer Res. 46(7), 3504–3512 (1986).
[PubMed]

Fritzsche, M.

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

Fujimoto, J. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Funfak, A.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Gallet, F.

F. Gallet, D. Arcizet, P. Bohec, and A. Richert, “Power spectrum of out-of-equilibrium forces in living cells: amplitude and frequency dependence,” Soft Matter 5(15), 2947–2953 (2009).
[Crossref]

Geraldo, S.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Gilliss, T.

Goldman, R. D.

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

Gregory, K.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Guo, M.

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

Gurchenkov, V. V.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Harms, F.

C. Apelian, F. Harms, O. Thouvenin, and A. C. Boccara, “Dynamic full field optical coherence tomography: subcellular metabolic contrast revealed in tissues by temporal analysis of interferometric signals,” Biomed. Opt. Express 7(3), 455–468 (2016).
[PubMed]

Harris, A. R.

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

Hee, M. R.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Hetényi, C.

M. Kovács, J. Tóth, C. Hetényi, A. Málnási-Csizmadia, and J. R. Sellers, “Mechanism of blebbistatin inhibition of myosin II,” J. Biol. Chem. 279(34), 35557–35563 (2004).
[Crossref] [PubMed]

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(1), 259–288 (2009).
[Crossref] [PubMed]

Höfling, F.

F. Höfling and T. Franosch, “Anomalous transport in the crowded world of biological cells,” Rep. Prog. Phys. 76(4), 046602 (2013).
[Crossref] [PubMed]

Hsiao, A. Y.

G. Mehta, A. Y. Hsiao, M. Ingram, G. D. Luker, and S. Takayama, “Opportunities and challenges for use of tumor spheroids as models to test drug delivery and efficacy,” J. Control. Release 164(2), 192–204 (2012).
[Crossref] [PubMed]

Huang, D.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Hung, W. C.

E. M. Balzer, Z. Tong, C. D. Paul, W. C. Hung, K. M. Stroka, A. E. Boggs, S. S. Martin, and K. Konstantopoulos, “Physical confinement alters tumor cell adhesion and migration phenotypes,” FASEB J. 26(10), 4045–4056 (2012).
[Crossref] [PubMed]

Ingram, M.

G. Mehta, A. Y. Hsiao, M. Ingram, G. D. Luker, and S. Takayama, “Opportunities and challenges for use of tumor spheroids as models to test drug delivery and efficacy,” J. Control. Release 164(2), 192–204 (2012).
[Crossref] [PubMed]

Jensen, M. H.

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

Jeong, K.

Joanny, J. F.

M. Delarue, F. Montel, O. Caen, J. Elgeti, J. M. Siaugue, D. Vignjevic, J. Prost, J. F. Joanny, and G. Cappello, “Mechanical control of cell flow in multicellular spheroids,” Phys. Rev. Lett. 110(13), 138103 (2013).
[Crossref] [PubMed]

Kießling, T. R.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Koenderink, G. H.

C. P. Brangwynne, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, “Intracellular transport by active diffusion,” Trends Cell Biol. 19(9), 423–427 (2009).
[Crossref] [PubMed]

Konstantopoulos, K.

E. M. Balzer, Z. Tong, C. D. Paul, W. C. Hung, K. M. Stroka, A. E. Boggs, S. S. Martin, and K. Konstantopoulos, “Physical confinement alters tumor cell adhesion and migration phenotypes,” FASEB J. 26(10), 4045–4056 (2012).
[Crossref] [PubMed]

Kovács, M.

M. Kovács, J. Tóth, C. Hetényi, A. Málnási-Csizmadia, and J. R. Sellers, “Mechanism of blebbistatin inhibition of myosin II,” J. Biol. Chem. 279(34), 35557–35563 (2004).
[Crossref] [PubMed]

Lai, C. C.

R. Nossal, S. H. Chen, and C. C. Lai, “Use of laser scattering for quantitative determinations of bacterial motility,” Opt. Commun. 4(1), 35–39 (1971).
[Crossref]

Lamaze, C.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Lebec, M.

Lin, C. P.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Lippincott-Schwartz, J.

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

Loverdo, C.

O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, “Intermittent search strategies,” Rev. Mod. Phys. 83(1), 81–129 (2011).
[Crossref]

Luker, G. D.

G. Mehta, A. Y. Hsiao, M. Ingram, G. D. Luker, and S. Takayama, “Opportunities and challenges for use of tumor spheroids as models to test drug delivery and efficacy,” J. Control. Release 164(2), 192–204 (2012).
[Crossref] [PubMed]

Machaty, Z.

Mackintosh, F. C.

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

C. P. Brangwynne, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, “Intracellular transport by active diffusion,” Trends Cell Biol. 19(9), 423–427 (2009).
[Crossref] [PubMed]

Mahadevan, L.

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

Málnási-Csizmadia, A.

M. Kovács, J. Tóth, C. Hetényi, A. Málnási-Csizmadia, and J. R. Sellers, “Mechanism of blebbistatin inhibition of myosin II,” J. Biol. Chem. 279(34), 35557–35563 (2004).
[Crossref] [PubMed]

Martin, S. S.

E. M. Balzer, Z. Tong, C. D. Paul, W. C. Hung, K. M. Stroka, A. E. Boggs, S. S. Martin, and K. Konstantopoulos, “Physical confinement alters tumor cell adhesion and migration phenotypes,” FASEB J. 26(10), 4045–4056 (2012).
[Crossref] [PubMed]

Matei, D. E.

Mehta, G.

G. Mehta, A. Y. Hsiao, M. Ingram, G. D. Luker, and S. Takayama, “Opportunities and challenges for use of tumor spheroids as models to test drug delivery and efficacy,” J. Control. Release 164(2), 192–204 (2012).
[Crossref] [PubMed]

Moeendarbary, E.

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

Montel, F.

M. Delarue, F. Montel, O. Caen, J. Elgeti, J. M. Siaugue, D. Vignjevic, J. Prost, J. F. Joanny, and G. Cappello, “Mechanical control of cell flow in multicellular spheroids,” Phys. Rev. Lett. 110(13), 138103 (2013).
[Crossref] [PubMed]

Moore, J. R.

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

Moreau, M.

O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, “Intermittent search strategies,” Rev. Mod. Phys. 83(1), 81–129 (2011).
[Crossref]

Moulding, D. A.

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

Nassoy, P.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Nolte, D.

Nolte, D. D.

Nossal, R.

R. Nossal, S. H. Chen, and C. C. Lai, “Use of laser scattering for quantitative determinations of bacterial motility,” Opt. Commun. 4(1), 35–39 (1971).
[Crossref]

Oldenburg, A. L.

Paul, C. D.

E. M. Balzer, Z. Tong, C. D. Paul, W. C. Hung, K. M. Stroka, A. E. Boggs, S. S. Martin, and K. Konstantopoulos, “Physical confinement alters tumor cell adhesion and migration phenotypes,” FASEB J. 26(10), 4045–4056 (2012).
[Crossref] [PubMed]

Prost, J.

M. Delarue, F. Montel, O. Caen, J. Elgeti, J. M. Siaugue, D. Vignjevic, J. Prost, J. F. Joanny, and G. Cappello, “Mechanical control of cell flow in multicellular spheroids,” Phys. Rev. Lett. 110(13), 138103 (2013).
[Crossref] [PubMed]

Puliafito, C. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Renz, M.

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

Richert, A.

F. Gallet, D. Arcizet, P. Bohec, and A. Richert, “Power spectrum of out-of-equilibrium forces in living cells: amplitude and frequency dependence,” Soft Matter 5(15), 2947–2953 (2009).
[Crossref]

Rico, F.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Rolland, L.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Saint-Jalmes, H.

Sarangi, B. R.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Scheuring, S.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Schuman, J. S.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Sellers, J. R.

M. Kovács, J. Tóth, C. Hetényi, A. Málnási-Csizmadia, and J. R. Sellers, “Mechanism of blebbistatin inhibition of myosin II,” J. Biol. Chem. 279(34), 35557–35563 (2004).
[Crossref] [PubMed]

Siaugue, J. M.

M. Delarue, F. Montel, O. Caen, J. Elgeti, J. M. Siaugue, D. Vignjevic, J. Prost, J. F. Joanny, and G. Cappello, “Mechanical control of cell flow in multicellular spheroids,” Phys. Rev. Lett. 110(13), 138103 (2013).
[Crossref] [PubMed]

Simon, A.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Sinha, B.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

Stinson, W. G.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Stride, E.

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

Stroka, K. M.

E. M. Balzer, Z. Tong, C. D. Paul, W. C. Hung, K. M. Stroka, A. E. Boggs, S. S. Martin, and K. Konstantopoulos, “Physical confinement alters tumor cell adhesion and migration phenotypes,” FASEB J. 26(10), 4045–4056 (2012).
[Crossref] [PubMed]

Sutherland, R. M.

J. P. Freyer and R. M. Sutherland, “Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply,” Cancer Res. 46(7), 3504–3512 (1986).
[PubMed]

Swanson, E. A.

D. Huang, E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, and J. G. Fujimoto, “Optical Coherence Tomography,” Science 254(5035), 1178–1181 (1991).
[Crossref] [PubMed]

Takayama, S.

G. Mehta, A. Y. Hsiao, M. Ingram, G. D. Luker, and S. Takayama, “Opportunities and challenges for use of tumor spheroids as models to test drug delivery and efficacy,” J. Control. Release 164(2), 192–204 (2012).
[Crossref] [PubMed]

Taylor, R. M.

Thouvenin, O.

C. Apelian, F. Harms, O. Thouvenin, and A. C. Boccara, “Dynamic full field optical coherence tomography: subcellular metabolic contrast revealed in tissues by temporal analysis of interferometric signals,” Biomed. Opt. Express 7(3), 455–468 (2016).
[PubMed]

Thrasher, A. J.

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

Tong, Z.

E. M. Balzer, Z. Tong, C. D. Paul, W. C. Hung, K. M. Stroka, A. E. Boggs, S. S. Martin, and K. Konstantopoulos, “Physical confinement alters tumor cell adhesion and migration phenotypes,” FASEB J. 26(10), 4045–4056 (2012).
[Crossref] [PubMed]

Tóth, J.

M. Kovács, J. Tóth, C. Hetényi, A. Málnási-Csizmadia, and J. R. Sellers, “Mechanism of blebbistatin inhibition of myosin II,” J. Biol. Chem. 279(34), 35557–35563 (2004).
[Crossref] [PubMed]

Tracy, J. B.

Troester, M. A.

Turek, J.

Turek, J. J.

Valon, L.

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

Vignjevic, D.

K. Alessandri, B. R. Sarangi, V. V. Gurchenkov, B. Sinha, T. R. Kießling, L. Fetler, F. Rico, S. Scheuring, C. Lamaze, A. Simon, S. Geraldo, D. Vignjevic, H. Doméjean, L. Rolland, A. Funfak, J. Bibette, N. Bremond, and P. Nassoy, “Cellular capsules as a tool for multicellular spheroid production and for investigating the mechanics of tumor progression in vitro,” Proc. Natl. Acad. Sci. U.S.A. 110(37), 14843–14848 (2013).
[Crossref] [PubMed]

M. Delarue, F. Montel, O. Caen, J. Elgeti, J. M. Siaugue, D. Vignjevic, J. Prost, J. F. Joanny, and G. Cappello, “Mechanical control of cell flow in multicellular spheroids,” Phys. Rev. Lett. 110(13), 138103 (2013).
[Crossref] [PubMed]

Voituriez, R.

O. Bénichou, C. Loverdo, M. Moreau, and R. Voituriez, “Intermittent search strategies,” Rev. Mod. Phys. 83(1), 81–129 (2011).
[Crossref]

Wang, C.

Weitz, D. A.

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

C. P. Brangwynne, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, “Intracellular transport by active diffusion,” Trends Cell Biol. 19(9), 423–427 (2009).
[Crossref] [PubMed]

Wu, W. C.

Yu, X.

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(1), 259–288 (2009).
[Crossref] [PubMed]

Appl. Opt. (2)

Biomed. Opt. Express (3)

Cancer Res. (1)

J. P. Freyer and R. M. Sutherland, “Regulation of growth saturation and development of necrosis in EMT6/Ro multicellular spheroids by the glucose and oxygen supply,” Cancer Res. 46(7), 3504–3512 (1986).
[PubMed]

Cell (1)

M. Guo, A. J. Ehrlicher, M. H. Jensen, M. Renz, J. R. Moore, R. D. Goldman, J. Lippincott-Schwartz, F. C. Mackintosh, and D. A. Weitz, “Probing the stochastic, motor-driven properties of the cytoplasm using force spectrum microscopy,” Cell 158(4), 822–832 (2014).
[Crossref] [PubMed]

FASEB J. (1)

E. M. Balzer, Z. Tong, C. D. Paul, W. C. Hung, K. M. Stroka, A. E. Boggs, S. S. Martin, and K. Konstantopoulos, “Physical confinement alters tumor cell adhesion and migration phenotypes,” FASEB J. 26(10), 4045–4056 (2012).
[Crossref] [PubMed]

J. Biol. Chem. (1)

M. Kovács, J. Tóth, C. Hetényi, A. Málnási-Csizmadia, and J. R. Sellers, “Mechanism of blebbistatin inhibition of myosin II,” J. Biol. Chem. 279(34), 35557–35563 (2004).
[Crossref] [PubMed]

J. Control. Release (1)

G. Mehta, A. Y. Hsiao, M. Ingram, G. D. Luker, and S. Takayama, “Opportunities and challenges for use of tumor spheroids as models to test drug delivery and efficacy,” J. Control. Release 164(2), 192–204 (2012).
[Crossref] [PubMed]

Nat. Mater. (1)

E. Moeendarbary, L. Valon, M. Fritzsche, A. R. Harris, D. A. Moulding, A. J. Thrasher, E. Stride, L. Mahadevan, and G. T. Charras, “The cytoplasm of living cells behaves as a poroelastic material,” Nat. Mater. 12(3), 253–261 (2013).
[Crossref] [PubMed]

Opt. Commun. (1)

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Figures (8)

Fig. 1
Fig. 1

Experimental setup to image encapsulated spheroids. A spatially and temporally incoherent light source is imaged at the back focal plane BF of two identical microscope objectives using an illumination lens. The spatial extend of the source generates small and isotropic (1μm3) observation volumes (voxel) from which light is backscattered and interferes with the beam reflected by a silicon reference mirror. Encapsulated spheroids are mechanically stabilized in an agarose gel, and maintained at 37°C temperature via an active temperature control performed at the lower glass side, which is coated with ITO.

Fig. 2
Fig. 2

Dynamic contrast with FFOCT provided by the fast decay of the ACF, Mij. (a) Spheroid imaged at the 60 μm imaging depth of this study, with the LLTECH setup. (b) Individual cells imaged with the LLTECH setup (linear gray map with 2 dynamic range).

Fig. 3
Fig. 3

The near zero lag amplitude of the ACFij(dt) carries the information of signal strength: (a) Histograms of the fast decorrelation Mij and the zero lag amplitude of correlation ACFij(dt), for the same spheroid at 20°C and 37°C. ACFij(dt) is not affected by change in temperature that promotes intracellular motion. (b) ACFij(dt) is strongly correlated to signal strength Sij.

Fig. 4
Fig. 4

(a) Spatially-averaged ACF function of the same spheroid at 37°C and 20°C. The ACF are not normalized to illustrate that increased intracellular motion does not modify the near zero lag amplitude, which is a measure of signal strength. Temperature control at 37°C increases α (0.08 to 0.13), and reduce the fast T1 (0.7 to 0.36 s) and slow T2 (9 to 3.4 s) decorrelation times. (b) Typical residual from the biexponential fit, which show fluctuations of normalized amplitude 1%. (c) Same data as (a) in the frequency domain. Increased intracellular motion at 37° increase the slope of the spectrum in the [0.1-1] Hz band, and its high frequency plateau by 5dB.

Fig. 5
Fig. 5

Distribution of the α values with and without blebbistatin for two cell types. (71 and 75 CT26 spheroids were measured in the control and in the experiment with blebbistatin respectively. 57 and 47 HT29 spheroids were measured in the same experimental conditions).

Fig. 6
Fig. 6

(a) Population-averaged α response to blebbistatin treatment for CT26 aggregates, as a function of the normalized scattering strength. Error bars represent the 66% quantile, for 71 (control) and 75 (with blebbistatin) CT26 spheroids. All cellular components probed with FFOCT undergo faster transport after blebbistatin treatment (α values are higher with blebbistatin, for all values of signal strength. Inset: The transport of strongly scattering, most probably larger, cellular components is more affected by blebbistatin treatment. (b-c) Processing steps to plot (a): (b) sort pixels in bin of signal strength, normalized by the overall signal strength of the acquisition; (c) adjust biexponential parameters for each spheroid, at a given normalized signal strength.

Fig. 7
Fig. 7

Dynamic contrast with FFOCT provided by the fast decay of the ACF, Mij. (a) Spheroid imaged at the 60 μm imaging depth of this study with the 0.8 numerical aperture FFOCT prototype. (b) Individual cells imaged with the prototype (linear gray map with 2 dynamic range).

Fig. 8
Fig. 8

(a-c) Fit parameters measured during the first week after aggregate synthesis, for the CT26 cells. Median values are represented, and the error bars limits the 66% quantiles. (d) Estimated diameter of the CT26 spheroid during one week. Numbers of measured CT26 spheroids are 38, 71, and 44 for the control experiment on days 4, 7, and 10. We measured 75 spheroids for the blebbistatin experiment on day 9.

Equations (4)

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OC T ij ( t )2 I ij r × I ij s ( t ) cos( ϕ ij ( t ) )
AC F ij (τ=m×dt)= 1 Nm k=0 k=N1m OC T ij (k)×OC T ij (k+m)
S ij 2 = 2 π ( AC F ij (dt)+ n 2 )
ACF( τ ) ACF(dt) =α e τ/ T 1 +( 1α ) e τ/ T 2

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