We used quantitative phase imaging to measure the dispersion relation, i.e. decay rate vs. spatial mode, associated with mass transport in live cells. This approach applies equally well to both discrete and continuous mass distributions without the need for particle tracking. From the quadratic experimental curve specific to diffusion, we extracted the diffusion coefficient as the only fitting parameter. The linear portion of the dispersion relation reveals the deterministic component of the intracellular transport. Our data show a universal behavior where the intracellular transport is diffusive at small scales and deterministic at large scales. Measurements by our method and particle tracking show that, on average, the mass transport in the nucleus is slower than in the cytoplasm.

© 2011 OSA

1. R. B. Vallee and M. P. Sheetz, “Targeting of motor proteins,” Science271(5255), 1539–1544 (1996). [CrossRef] [PubMed]
2. F. C. MacKintosh and C. F. Schmidt, “Active cellular materials,” Curr. Opin. Cell Biol.22(1), 29–35 (2010). [CrossRef] [PubMed]
3. C. P. Brangwynne, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, “Cytoplasmic diffusion: molecular motors mix it up,” J. Cell Biol.183(4), 583–587 (2008). [CrossRef] [PubMed]
4. 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]
5. A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science300(5628), 2061–2065 (2003). [CrossRef] [PubMed]
6. X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature447, 592–595 (2007).
7. B. Fabry, G. N. Maksym, J. P. Butler, M. Glogauer, D. Navajas, and J. J. Fredberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett.87(14), 148102 (2001). [CrossRef] [PubMed]
8. A. Caspi, R. Granek, and M. Elbaum, “Enhanced diffusion in active intracellular transport,” Phys. Rev. Lett.85(26), 5655–5658 (2000). [CrossRef] [PubMed]
9. D. Mizuno, C. Tardin, C. F. Schmidt, and F. C. Mackintosh, “Nonequilibrium mechanics of active cytoskeletal networks,” Science315(5810), 370–373 (2007). [CrossRef] [PubMed]
10. B. Wang, S. M. Anthony, S. C. Bae, and S. Granick, “Anomalous yet Brownian,” Proc. Natl. Acad. Sci. U.S.A.106(36), 15160–15164 (2009). [CrossRef] [PubMed]
11. C. P. Brangwynne, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, “Nonequilibrium microtubule fluctuations in a model cytoskeleton,” Phys. Rev. Lett.100, 118104 (2008).
12. G. Popescu, in Methods in Cell Biology, 87–115, ed. Jena, B. P.), Academic Press, San Diego, 2008.
13. Y. K. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A.107(4), 1289–1294 (2010). [CrossRef] [PubMed]
14. Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A.105(37), 13730–13735 (2008). [CrossRef] [PubMed]
15. G. Popescu, T. Ikeda, K. Goda, C. A. Best-Popescu, M. Laposata, S. Manley, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Optical measurement of cell membrane tension,” Phys. Rev. Lett.97(21), 218101 (2006). [CrossRef] [PubMed]
16. Y. K. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A.107(15), 6731–6736 (2010). [CrossRef] [PubMed]
17. G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells Mol. Dis.41(1), 10–16 (2008). [CrossRef] [PubMed]
18. Z. Wang, L. J. Millet, M. Mir, H. Ding, S. Unarunotai, J. A. Rogers, M. U. Gillette, and G. Popescu, “Spatial light interference microscopy (SLIM),” Opt. Express19(2), 1016–1026 (2011). [CrossRef] [PubMed]
19. F. Zernike, “How I discovered phase contrast,” Science121(3141), 345–349 (1955). [CrossRef] [PubMed]
20. H. F. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, “Fourier transform light scattering of inhomogeneous and dynamic structures,” Phys. Rev. Lett.101(23), 238102 (2008). [CrossRef] [PubMed]
21. Z. Wang, I. S. Chun, X. L. Li, Z. Y. Ong, E. Pop, L. Millet, M. Gillette, and G. Popescu, “Topography and refractometry of nanostructures using spatial light interference microscopy,” Opt. Lett.35(2), 208–210 (2010). [CrossRef] [PubMed]
22. G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol.295(2), C538–C544 (2008). [CrossRef] [PubMed]
23. R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (John Wiley & Sons, 1960).
24. B. J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (Wiley, 1976).
25. D. L. Coy, M. Wagenbach, and J. Howard, “Kinesin takes one 8-nm step for each ATP that it hydrolyzes,” J. Biol. Chem.274(6), 3667–3671 (1999). [CrossRef] [PubMed]
26. I. F. Sbalzarini and P. Koumoutsakos, “Feature point tracking and trajectory analysis for video imaging in cell biology,” J. Struct. Biol.151(2), 182–195 (2005). [CrossRef] [PubMed]
27. R. Wang, Z. Wang, J. Leigh, N. Sobh, L. Millet, M. U. Gillette, A. J. Levine, and G. Popescu, “One-dimensional deterministic transport in neurons measured by dispersion-relation phase spectroscopy,” J. Phys. Condens. Matter23(37), 374107 (2011). [CrossRef] [PubMed]
28. M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A.107(42), 17864–17871 (2010). [CrossRef] [PubMed]
29. Y. Tseng, J. S. Lee, T. P. Kole, I. Jiang, and D. Wirtz, “Micro-organization and visco-elasticity of the interphase nucleus revealed by particle nanotracking,” J. Cell Sci.117(10), 2159–2167 (2004). [CrossRef] [PubMed]
30. P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett.30(5), 468–470 (2005). [CrossRef] [PubMed]
31. J. Frank, S. Altmeyer, and G. Wernicke, “Non-interferometric, non-iterative phase retrieval by Green’s functions,” J. Opt. Soc. Am. A27(10), 2244–2251 (2010). [CrossRef] [PubMed]
32. P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express17(15), 13080–13094 (2009). [CrossRef] [PubMed]

Am. J. Physiol. Cell Physiol.

• G. Popescu, Y. Park, N. Lue, C. Best-Popescu, L. Deflores, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Optical imaging of cell mass and growth dynamics,” Am. J. Physiol. Cell Physiol.295(2), C538–C544 (2008). [CrossRef] [PubMed]

Blood Cells Mol. Dis.

• G. Popescu, Y. Park, W. Choi, R. R. Dasari, M. S. Feld, and K. Badizadegan, “Imaging red blood cell dynamics by quantitative phase microscopy,” Blood Cells Mol. Dis.41(1), 10–16 (2008). [CrossRef] [PubMed]

Curr. Opin. Cell Biol.

• F. C. MacKintosh and C. F. Schmidt, “Active cellular materials,” Curr. Opin. Cell Biol.22(1), 29–35 (2010). [CrossRef] [PubMed]

J. Biol. Chem.

• D. L. Coy, M. Wagenbach, and J. Howard, “Kinesin takes one 8-nm step for each ATP that it hydrolyzes,” J. Biol. Chem.274(6), 3667–3671 (1999). [CrossRef] [PubMed]

J. Cell Biol.

• C. P. Brangwynne, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, “Cytoplasmic diffusion: molecular motors mix it up,” J. Cell Biol.183(4), 583–587 (2008). [CrossRef] [PubMed]

J. Cell Sci.

• Y. Tseng, J. S. Lee, T. P. Kole, I. Jiang, and D. Wirtz, “Micro-organization and visco-elasticity of the interphase nucleus revealed by particle nanotracking,” J. Cell Sci.117(10), 2159–2167 (2004). [CrossRef] [PubMed]

J. Opt. Soc. Am. A

• J. Frank, S. Altmeyer, and G. Wernicke, “Non-interferometric, non-iterative phase retrieval by Green’s functions,” J. Opt. Soc. Am. A27(10), 2244–2251 (2010). [CrossRef] [PubMed]

J. Phys. Condens. Matter

• R. Wang, Z. Wang, J. Leigh, N. Sobh, L. Millet, M. U. Gillette, A. J. Levine, and G. Popescu, “One-dimensional deterministic transport in neurons measured by dispersion-relation phase spectroscopy,” J. Phys. Condens. Matter23(37), 374107 (2011). [CrossRef] [PubMed]

J. Struct. Biol.

• I. F. Sbalzarini and P. Koumoutsakos, “Feature point tracking and trajectory analysis for video imaging in cell biology,” J. Struct. Biol.151(2), 182–195 (2005). [CrossRef] [PubMed]

Nature

• X. Trepat, L. H. Deng, S. S. An, D. Navajas, D. J. Tschumperlin, W. T. Gerthoffer, J. P. Butler, and J. J. Fredberg, “Universal physical responses to stretch in the living cell,” Nature447, 592–595 (2007).

Opt. Express

• Z. Wang, L. J. Millet, M. Mir, H. Ding, S. Unarunotai, J. A. Rogers, M. U. Gillette, and G. Popescu, “Spatial light interference microscopy (SLIM),” Opt. Express19(2), 1016–1026 (2011). [CrossRef] [PubMed]
• P. Bon, G. Maucort, B. Wattellier, and S. Monneret, “Quadriwave lateral shearing interferometry for quantitative phase microscopy of living cells,” Opt. Express17(15), 13080–13094 (2009). [CrossRef] [PubMed]

Opt. Lett.

• P. Marquet, B. Rappaz, P. J. Magistretti, E. Cuche, Y. Emery, T. Colomb, and C. Depeursinge, “Digital holographic microscopy: a noninvasive contrast imaging technique allowing quantitative visualization of living cells with subwavelength axial accuracy,” Opt. Lett.30(5), 468–470 (2005). [CrossRef] [PubMed]
• Z. Wang, I. S. Chun, X. L. Li, Z. Y. Ong, E. Pop, L. Millet, M. Gillette, and G. Popescu, “Topography and refractometry of nanostructures using spatial light interference microscopy,” Opt. Lett.35(2), 208–210 (2010). [CrossRef] [PubMed]

Phys. Rev. Lett.

• H. F. Ding, Z. Wang, F. Nguyen, S. A. Boppart, and G. Popescu, “Fourier transform light scattering of inhomogeneous and dynamic structures,” Phys. Rev. Lett.101(23), 238102 (2008). [CrossRef] [PubMed]
• G. Popescu, T. Ikeda, K. Goda, C. A. Best-Popescu, M. Laposata, S. Manley, R. R. Dasari, K. Badizadegan, and M. S. Feld, “Optical measurement of cell membrane tension,” Phys. Rev. Lett.97(21), 218101 (2006). [CrossRef] [PubMed]
• C. P. Brangwynne, G. H. Koenderink, F. C. MacKintosh, and D. A. Weitz, “Nonequilibrium microtubule fluctuations in a model cytoskeleton,” Phys. Rev. Lett.100, 118104 (2008).
• B. Fabry, G. N. Maksym, J. P. Butler, M. Glogauer, D. Navajas, and J. J. Fredberg, “Scaling the microrheology of living cells,” Phys. Rev. Lett.87(14), 148102 (2001). [CrossRef] [PubMed]
• A. Caspi, R. Granek, and M. Elbaum, “Enhanced diffusion in active intracellular transport,” Phys. Rev. Lett.85(26), 5655–5658 (2000). [CrossRef] [PubMed]

Proc. Natl. Acad. Sci. U.S.A.

• Y. K. Park, C. A. Best, T. Auth, N. S. Gov, S. A. Safran, G. Popescu, S. Suresh, and M. S. Feld, “Metabolic remodeling of the human red blood cell membrane,” Proc. Natl. Acad. Sci. U.S.A.107(4), 1289–1294 (2010). [CrossRef] [PubMed]
• Y. K. Park, M. Diez-Silva, G. Popescu, G. Lykotrafitis, W. Choi, M. S. Feld, and S. Suresh, “Refractive index maps and membrane dynamics of human red blood cells parasitized by Plasmodium falciparum,” Proc. Natl. Acad. Sci. U.S.A.105(37), 13730–13735 (2008). [CrossRef] [PubMed]
• Y. K. Park, C. A. Best, K. Badizadegan, R. R. Dasari, M. S. Feld, T. Kuriabova, M. L. Henle, A. J. Levine, and G. Popescu, “Measurement of red blood cell mechanics during morphological changes,” Proc. Natl. Acad. Sci. U.S.A.107(15), 6731–6736 (2010). [CrossRef] [PubMed]
• B. Wang, S. M. Anthony, S. C. Bae, and S. Granick, “Anomalous yet Brownian,” Proc. Natl. Acad. Sci. U.S.A.106(36), 15160–15164 (2009). [CrossRef] [PubMed]
• M. A. Thompson, J. M. Casolari, M. Badieirostami, P. O. Brown, and W. E. Moerner, “Three-dimensional tracking of single mRNA particles in Saccharomyces cerevisiae using a double-helix point spread function,” Proc. Natl. Acad. Sci. U.S.A.107(42), 17864–17871 (2010). [CrossRef] [PubMed]

Science

• F. Zernike, “How I discovered phase contrast,” Science121(3141), 345–349 (1955). [CrossRef] [PubMed]
• D. Mizuno, C. Tardin, C. F. Schmidt, and F. C. Mackintosh, “Nonequilibrium mechanics of active cytoskeletal networks,” Science315(5810), 370–373 (2007). [CrossRef] [PubMed]
• R. B. Vallee and M. P. Sheetz, “Targeting of motor proteins,” Science271(5255), 1539–1544 (1996). [CrossRef] [PubMed]
• A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, “Myosin V walks hand-over-hand: single fluorophore imaging with 1.5-nm localization,” Science300(5628), 2061–2065 (2003). [CrossRef] [PubMed]

Trends Cell Biol.

• 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]

Other

• G. Popescu, in Methods in Cell Biology, 87–115, ed. Jena, B. P.), Academic Press, San Diego, 2008.
• R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena (John Wiley & Sons, 1960).
• B. J. Berne and R. Pecora, Dynamic Light Scattering with Applications to Chemistry, Biology and Physics (Wiley, 1976).

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