Abstract

We present optical measurements of nanoscale red blood cell fluctuations obtained by highly sensitive quantitative phase imaging. These spatio-temporal fluctuations are modeled in terms of the bulk viscoelastic response of the cell. Relating the displacement distribution to the storage and loss moduli of the bulk has the advantage of incorporating all geometric and cortical effects into a single effective medium behavior. The results on normal cells indicate that the viscous modulus is much larger than the elastic one throughout the entire frequency range covered by the measurement, indicating fluid behavior.

© 2011 OSA

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    [CrossRef] [PubMed]
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    [CrossRef]

2010 (2)

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]

H. Ding, L. J. Millet, M. U. Gillette, and G. Popescu, “Actin-driven cell dynamics probed by Fourier transform light scattering,” Biomed. Opt. Express 1(1), 260–267 (2010).
[CrossRef] [PubMed]

2008 (4)

H. 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]

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]

J. D. Wan, W. D. Ristenpart, and H. A. Stone, “Dynamics of shear-induced ATP release from red blood cells,” Proc. Natl. Acad. Sci. U.S.A. 105(43), 16432–16437 (2008).
[CrossRef] [PubMed]

N. Mohandas and P. G. Gallagher, “Red cell membrane: past, present, and future,” Blood 112(10), 3939–3948 (2008).
[CrossRef] [PubMed]

2007 (2)

M. Puig-de-Morales, K. T. Turner, J. P. Butler, J. J. Fredberg, and S. Suresh, “Viscoelasticity of the human red blood cell,” J. Appl. Physiol. 293, 597–605 (2007).

M. S. Amin, Y. K. Park, N. Lue, R. R. Dasari, K. Badizadegan, M. S. Feld, and G. Popescu, “Microrheology of red blood cell membranes using dynamic scattering microscopy,” Opt. Express 15(25), 17001–17009 (2007).
[CrossRef] [PubMed]

2006 (3)

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]

L. C. L. Lin, N. Gov, and F. L. H. Brown, “Nonequilibrium membrane fluctuations driven by active proteins,” J. Chem. Phys. 124(7), 074903 (2006).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006).
[CrossRef] [PubMed]

2005 (1)

N. S. Gov and S. A. Safran, “Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects,” Biophys. J. 88(3), 1859–1874 (2005).
[CrossRef] [PubMed]

2004 (2)

N. Gov, “Membrane undulations driven by force fluctuations of active proteins,” Phys. Rev. Lett. 93(26), 268104 (2004).
[CrossRef] [PubMed]

L. C. L. Lin and F. L. H. Brown, “Brownian dynamics in Fourier space: membrane simulations over long length and time scales,” Phys. Rev. Lett. 93(25), 256001 (2004).
[CrossRef] [PubMed]

2003 (4)

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[CrossRef]

G. Bao and S. Suresh, “Cell and molecular mechanics of biological materials,” Nat. Mater. 2(11), 715–725 (2003).
[CrossRef] [PubMed]

N. Gov, A. G. Zilman, and S. Safran, “Cytoskeleton confinement and tension of red blood cell membranes,” Phys. Rev. Lett. 90(22), 228101 (2003).
[CrossRef] [PubMed]

N. Gov, A. Zilman, and S. Safran, “Cytoskeleton confinement of red blood cell membrane fluctuations,” Biophys. J. 84, 486A (2003).

2002 (2)

A. J. Levine and F. C. MacKintosh, “Dynamics of viscoelastic membranes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 061606 (2002).
[CrossRef] [PubMed]

G. Popescu, A. Dogariu, and R. Rajagopalan, “Spatially resolved microrheology using localized coherence volumes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 041504 (2002).
[CrossRef] [PubMed]

1999 (1)

J. Sleep, D. Wilson, R. Simmons, and W. Gratzer, “Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study,” Biophys. J. 77(6), 3085–3095 (1999).
[CrossRef] [PubMed]

1998 (1)

F. Gittes and F. C. MacKintosh, “Dynamic shear modulus of a semiflexible polymer network,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(2), R1241–R1244 (1998).
[CrossRef]

1997 (1)

S. Tuvia, A. Almagor, A. Bitler, S. Levin, R. Korenstein, and S. Yedgar, “Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 5045–5049 (1997).
[CrossRef] [PubMed]

1996 (1)

A. G. Zilman and R. Granek, “Undulations and dynamic structure factor of membranes,” Phys. Rev. Lett. 77(23), 4788–4791 (1996).
[CrossRef] [PubMed]

1995 (1)

T. G. Mason and D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74(7), 1250–1253 (1995).
[CrossRef] [PubMed]

1994 (1)

D. E. Discher, N. Mohandas, and E. A. Evans, “Molecular maps of red cell deformation: hidden elasticity and in situ connectivity,” Science 266(5187), 1032–1035 (1994).
[CrossRef] [PubMed]

1992 (2)

D. H. Boal, U. Seifert, and A. Zilker, “Dual network model for red blood cell membranes,” Phys. Rev. Lett. 69(23), 3405–3408 (1992).
[CrossRef] [PubMed]

S. Tuvia, S. Levin, and R. Korenstein, “Correlation between local cell membrane displacements and filterability of human red blood cells,” FEBS Lett. 304(1), 32–36 (1992).
[CrossRef] [PubMed]

1991 (1)

S. Levin and R. Korenstein, “Membrane fluctuations in erythrocytes are linked to MgATP-dependent dynamic assembly of the membrane skeleton,” Biophys. J. 60(3), 733–737 (1991).
[CrossRef] [PubMed]

1990 (1)

R. Lipowsky and M. Girardet, “Shape fluctuations of polymerized or solidlike membranes,” Phys. Rev. Lett. 65(23), 2893–2896 (1990).
[CrossRef] [PubMed]

1985 (1)

M. A. Peterson, “Geometrical methods for the elasticity theory of membranes,” J. Math. Phys. 26(4), 711–717 (1985).
[CrossRef]

1984 (1)

H. Engelhardt, H. Gaub, and E. Sackmann, “Viscoelastic properties of erythrocyte membranes in high-frequency electric fields,” Nature 307(5949), 378–380 (1984).
[CrossRef] [PubMed]

1975 (1)

F. Brochard and J. F. Lennon, “Frequency spectrum of the flicker phenomenon in erythrocytes,” J. Phys. 36, 1035–1047 (1975).

Almagor, A.

S. Tuvia, A. Almagor, A. Bitler, S. Levin, R. Korenstein, and S. Yedgar, “Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 5045–5049 (1997).
[CrossRef] [PubMed]

Amin, M. S.

Auth, T.

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]

Badizadegan, K.

M. S. Amin, Y. K. Park, N. Lue, R. R. Dasari, K. Badizadegan, M. S. Feld, and G. Popescu, “Microrheology of red blood cell membranes using dynamic scattering microscopy,” Opt. Express 15(25), 17001–17009 (2007).
[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]

Bao, G.

G. Bao and S. Suresh, “Cell and molecular mechanics of biological materials,” Nat. Mater. 2(11), 715–725 (2003).
[CrossRef] [PubMed]

Best, C. 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]

Best-Popescu, C. A.

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]

Bitler, A.

S. Tuvia, A. Almagor, A. Bitler, S. Levin, R. Korenstein, and S. Yedgar, “Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 5045–5049 (1997).
[CrossRef] [PubMed]

Boal, D. H.

D. H. Boal, U. Seifert, and A. Zilker, “Dual network model for red blood cell membranes,” Phys. Rev. Lett. 69(23), 3405–3408 (1992).
[CrossRef] [PubMed]

Boppart, S. A.

H. 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]

Brochard, F.

F. Brochard and J. F. Lennon, “Frequency spectrum of the flicker phenomenon in erythrocytes,” J. Phys. 36, 1035–1047 (1975).

Brown, F. L. H.

L. C. L. Lin, N. Gov, and F. L. H. Brown, “Nonequilibrium membrane fluctuations driven by active proteins,” J. Chem. Phys. 124(7), 074903 (2006).
[CrossRef] [PubMed]

L. C. L. Lin and F. L. H. Brown, “Brownian dynamics in Fourier space: membrane simulations over long length and time scales,” Phys. Rev. Lett. 93(25), 256001 (2004).
[CrossRef] [PubMed]

Butler, J. P.

M. Puig-de-Morales, K. T. Turner, J. P. Butler, J. J. Fredberg, and S. Suresh, “Viscoelasticity of the human red blood cell,” J. Appl. Physiol. 293, 597–605 (2007).

Choi, W.

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]

Dao, M.

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[CrossRef]

Dasari, R. R.

Diez-Silva, M.

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]

Ding, H.

H. Ding, L. J. Millet, M. U. Gillette, and G. Popescu, “Actin-driven cell dynamics probed by Fourier transform light scattering,” Biomed. Opt. Express 1(1), 260–267 (2010).
[CrossRef] [PubMed]

H. 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]

Discher, D. E.

D. E. Discher, N. Mohandas, and E. A. Evans, “Molecular maps of red cell deformation: hidden elasticity and in situ connectivity,” Science 266(5187), 1032–1035 (1994).
[CrossRef] [PubMed]

Dogariu, A.

G. Popescu, A. Dogariu, and R. Rajagopalan, “Spatially resolved microrheology using localized coherence volumes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 041504 (2002).
[CrossRef] [PubMed]

Engelhardt, H.

H. Engelhardt, H. Gaub, and E. Sackmann, “Viscoelastic properties of erythrocyte membranes in high-frequency electric fields,” Nature 307(5949), 378–380 (1984).
[CrossRef] [PubMed]

Evans, E. A.

D. E. Discher, N. Mohandas, and E. A. Evans, “Molecular maps of red cell deformation: hidden elasticity and in situ connectivity,” Science 266(5187), 1032–1035 (1994).
[CrossRef] [PubMed]

Feld, M. S.

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]

M. S. Amin, Y. K. Park, N. Lue, R. R. Dasari, K. Badizadegan, M. S. Feld, and G. Popescu, “Microrheology of red blood cell membranes using dynamic scattering microscopy,” Opt. Express 15(25), 17001–17009 (2007).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006).
[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]

Fredberg, J. J.

M. Puig-de-Morales, K. T. Turner, J. P. Butler, J. J. Fredberg, and S. Suresh, “Viscoelasticity of the human red blood cell,” J. Appl. Physiol. 293, 597–605 (2007).

Gallagher, P. G.

N. Mohandas and P. G. Gallagher, “Red cell membrane: past, present, and future,” Blood 112(10), 3939–3948 (2008).
[CrossRef] [PubMed]

Gaub, H.

H. Engelhardt, H. Gaub, and E. Sackmann, “Viscoelastic properties of erythrocyte membranes in high-frequency electric fields,” Nature 307(5949), 378–380 (1984).
[CrossRef] [PubMed]

Gillette, M. U.

Girardet, M.

R. Lipowsky and M. Girardet, “Shape fluctuations of polymerized or solidlike membranes,” Phys. Rev. Lett. 65(23), 2893–2896 (1990).
[CrossRef] [PubMed]

Gittes, F.

F. Gittes and F. C. MacKintosh, “Dynamic shear modulus of a semiflexible polymer network,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(2), R1241–R1244 (1998).
[CrossRef]

Goda, K.

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]

Gov, N.

L. C. L. Lin, N. Gov, and F. L. H. Brown, “Nonequilibrium membrane fluctuations driven by active proteins,” J. Chem. Phys. 124(7), 074903 (2006).
[CrossRef] [PubMed]

N. Gov, “Membrane undulations driven by force fluctuations of active proteins,” Phys. Rev. Lett. 93(26), 268104 (2004).
[CrossRef] [PubMed]

N. Gov, A. G. Zilman, and S. Safran, “Cytoskeleton confinement and tension of red blood cell membranes,” Phys. Rev. Lett. 90(22), 228101 (2003).
[CrossRef] [PubMed]

N. Gov, A. Zilman, and S. Safran, “Cytoskeleton confinement of red blood cell membrane fluctuations,” Biophys. J. 84, 486A (2003).

Gov, N. S.

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]

N. S. Gov and S. A. Safran, “Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects,” Biophys. J. 88(3), 1859–1874 (2005).
[CrossRef] [PubMed]

Granek, R.

A. G. Zilman and R. Granek, “Undulations and dynamic structure factor of membranes,” Phys. Rev. Lett. 77(23), 4788–4791 (1996).
[CrossRef] [PubMed]

Gratzer, W.

J. Sleep, D. Wilson, R. Simmons, and W. Gratzer, “Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study,” Biophys. J. 77(6), 3085–3095 (1999).
[CrossRef] [PubMed]

Ikeda, T.

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006).
[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]

Korenstein, R.

S. Tuvia, A. Almagor, A. Bitler, S. Levin, R. Korenstein, and S. Yedgar, “Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 5045–5049 (1997).
[CrossRef] [PubMed]

S. Tuvia, S. Levin, and R. Korenstein, “Correlation between local cell membrane displacements and filterability of human red blood cells,” FEBS Lett. 304(1), 32–36 (1992).
[CrossRef] [PubMed]

S. Levin and R. Korenstein, “Membrane fluctuations in erythrocytes are linked to MgATP-dependent dynamic assembly of the membrane skeleton,” Biophys. J. 60(3), 733–737 (1991).
[CrossRef] [PubMed]

Laposata, M.

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]

Lennon, J. F.

F. Brochard and J. F. Lennon, “Frequency spectrum of the flicker phenomenon in erythrocytes,” J. Phys. 36, 1035–1047 (1975).

Levin, S.

S. Tuvia, A. Almagor, A. Bitler, S. Levin, R. Korenstein, and S. Yedgar, “Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 5045–5049 (1997).
[CrossRef] [PubMed]

S. Tuvia, S. Levin, and R. Korenstein, “Correlation between local cell membrane displacements and filterability of human red blood cells,” FEBS Lett. 304(1), 32–36 (1992).
[CrossRef] [PubMed]

S. Levin and R. Korenstein, “Membrane fluctuations in erythrocytes are linked to MgATP-dependent dynamic assembly of the membrane skeleton,” Biophys. J. 60(3), 733–737 (1991).
[CrossRef] [PubMed]

Levine, A. J.

A. J. Levine and F. C. MacKintosh, “Dynamics of viscoelastic membranes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 061606 (2002).
[CrossRef] [PubMed]

Lim, C. T.

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[CrossRef]

Lin, L. C. L.

L. C. L. Lin, N. Gov, and F. L. H. Brown, “Nonequilibrium membrane fluctuations driven by active proteins,” J. Chem. Phys. 124(7), 074903 (2006).
[CrossRef] [PubMed]

L. C. L. Lin and F. L. H. Brown, “Brownian dynamics in Fourier space: membrane simulations over long length and time scales,” Phys. Rev. Lett. 93(25), 256001 (2004).
[CrossRef] [PubMed]

Lipowsky, R.

R. Lipowsky and M. Girardet, “Shape fluctuations of polymerized or solidlike membranes,” Phys. Rev. Lett. 65(23), 2893–2896 (1990).
[CrossRef] [PubMed]

Lue, N.

Lykotrafitis, G.

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]

MacKintosh, F. C.

A. J. Levine and F. C. MacKintosh, “Dynamics of viscoelastic membranes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 061606 (2002).
[CrossRef] [PubMed]

F. Gittes and F. C. MacKintosh, “Dynamic shear modulus of a semiflexible polymer network,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(2), R1241–R1244 (1998).
[CrossRef]

Manley, S.

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]

Mason, T. G.

T. G. Mason and D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74(7), 1250–1253 (1995).
[CrossRef] [PubMed]

Millet, L. J.

Mohandas, N.

N. Mohandas and P. G. Gallagher, “Red cell membrane: past, present, and future,” Blood 112(10), 3939–3948 (2008).
[CrossRef] [PubMed]

D. E. Discher, N. Mohandas, and E. A. Evans, “Molecular maps of red cell deformation: hidden elasticity and in situ connectivity,” Science 266(5187), 1032–1035 (1994).
[CrossRef] [PubMed]

Nguyen, F.

H. 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]

Park, Y. K.

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]

M. S. Amin, Y. K. Park, N. Lue, R. R. Dasari, K. Badizadegan, M. S. Feld, and G. Popescu, “Microrheology of red blood cell membranes using dynamic scattering microscopy,” Opt. Express 15(25), 17001–17009 (2007).
[CrossRef] [PubMed]

Peterson, M. A.

M. A. Peterson, “Geometrical methods for the elasticity theory of membranes,” J. Math. Phys. 26(4), 711–717 (1985).
[CrossRef]

Popescu, G.

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]

H. Ding, L. J. Millet, M. U. Gillette, and G. Popescu, “Actin-driven cell dynamics probed by Fourier transform light scattering,” Biomed. Opt. Express 1(1), 260–267 (2010).
[CrossRef] [PubMed]

H. 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]

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]

M. S. Amin, Y. K. Park, N. Lue, R. R. Dasari, K. Badizadegan, M. S. Feld, and G. Popescu, “Microrheology of red blood cell membranes using dynamic scattering microscopy,” Opt. Express 15(25), 17001–17009 (2007).
[CrossRef] [PubMed]

G. Popescu, T. Ikeda, R. R. Dasari, and M. S. Feld, “Diffraction phase microscopy for quantifying cell structure and dynamics,” Opt. Lett. 31(6), 775–777 (2006).
[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]

G. Popescu, A. Dogariu, and R. Rajagopalan, “Spatially resolved microrheology using localized coherence volumes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 041504 (2002).
[CrossRef] [PubMed]

Puig-de-Morales, M.

M. Puig-de-Morales, K. T. Turner, J. P. Butler, J. J. Fredberg, and S. Suresh, “Viscoelasticity of the human red blood cell,” J. Appl. Physiol. 293, 597–605 (2007).

Rajagopalan, R.

G. Popescu, A. Dogariu, and R. Rajagopalan, “Spatially resolved microrheology using localized coherence volumes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 041504 (2002).
[CrossRef] [PubMed]

Ristenpart, W. D.

J. D. Wan, W. D. Ristenpart, and H. A. Stone, “Dynamics of shear-induced ATP release from red blood cells,” Proc. Natl. Acad. Sci. U.S.A. 105(43), 16432–16437 (2008).
[CrossRef] [PubMed]

Sackmann, E.

H. Engelhardt, H. Gaub, and E. Sackmann, “Viscoelastic properties of erythrocyte membranes in high-frequency electric fields,” Nature 307(5949), 378–380 (1984).
[CrossRef] [PubMed]

Safran, S.

N. Gov, A. G. Zilman, and S. Safran, “Cytoskeleton confinement and tension of red blood cell membranes,” Phys. Rev. Lett. 90(22), 228101 (2003).
[CrossRef] [PubMed]

N. Gov, A. Zilman, and S. Safran, “Cytoskeleton confinement of red blood cell membrane fluctuations,” Biophys. J. 84, 486A (2003).

Safran, 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]

N. S. Gov and S. A. Safran, “Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects,” Biophys. J. 88(3), 1859–1874 (2005).
[CrossRef] [PubMed]

Seifert, U.

D. H. Boal, U. Seifert, and A. Zilker, “Dual network model for red blood cell membranes,” Phys. Rev. Lett. 69(23), 3405–3408 (1992).
[CrossRef] [PubMed]

Simmons, R.

J. Sleep, D. Wilson, R. Simmons, and W. Gratzer, “Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study,” Biophys. J. 77(6), 3085–3095 (1999).
[CrossRef] [PubMed]

Sleep, J.

J. Sleep, D. Wilson, R. Simmons, and W. Gratzer, “Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study,” Biophys. J. 77(6), 3085–3095 (1999).
[CrossRef] [PubMed]

Stone, H. A.

J. D. Wan, W. D. Ristenpart, and H. A. Stone, “Dynamics of shear-induced ATP release from red blood cells,” Proc. Natl. Acad. Sci. U.S.A. 105(43), 16432–16437 (2008).
[CrossRef] [PubMed]

Suresh, S.

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]

M. Puig-de-Morales, K. T. Turner, J. P. Butler, J. J. Fredberg, and S. Suresh, “Viscoelasticity of the human red blood cell,” J. Appl. Physiol. 293, 597–605 (2007).

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[CrossRef]

G. Bao and S. Suresh, “Cell and molecular mechanics of biological materials,” Nat. Mater. 2(11), 715–725 (2003).
[CrossRef] [PubMed]

Turner, K. T.

M. Puig-de-Morales, K. T. Turner, J. P. Butler, J. J. Fredberg, and S. Suresh, “Viscoelasticity of the human red blood cell,” J. Appl. Physiol. 293, 597–605 (2007).

Tuvia, S.

S. Tuvia, A. Almagor, A. Bitler, S. Levin, R. Korenstein, and S. Yedgar, “Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 5045–5049 (1997).
[CrossRef] [PubMed]

S. Tuvia, S. Levin, and R. Korenstein, “Correlation between local cell membrane displacements and filterability of human red blood cells,” FEBS Lett. 304(1), 32–36 (1992).
[CrossRef] [PubMed]

Wan, J. D.

J. D. Wan, W. D. Ristenpart, and H. A. Stone, “Dynamics of shear-induced ATP release from red blood cells,” Proc. Natl. Acad. Sci. U.S.A. 105(43), 16432–16437 (2008).
[CrossRef] [PubMed]

Wang, Z.

H. 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]

Weitz, D. A.

T. G. Mason and D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74(7), 1250–1253 (1995).
[CrossRef] [PubMed]

Wilson, D.

J. Sleep, D. Wilson, R. Simmons, and W. Gratzer, “Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study,” Biophys. J. 77(6), 3085–3095 (1999).
[CrossRef] [PubMed]

Yedgar, S.

S. Tuvia, A. Almagor, A. Bitler, S. Levin, R. Korenstein, and S. Yedgar, “Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 5045–5049 (1997).
[CrossRef] [PubMed]

Zilker, A.

D. H. Boal, U. Seifert, and A. Zilker, “Dual network model for red blood cell membranes,” Phys. Rev. Lett. 69(23), 3405–3408 (1992).
[CrossRef] [PubMed]

Zilman, A.

N. Gov, A. Zilman, and S. Safran, “Cytoskeleton confinement of red blood cell membrane fluctuations,” Biophys. J. 84, 486A (2003).

Zilman, A. G.

N. Gov, A. G. Zilman, and S. Safran, “Cytoskeleton confinement and tension of red blood cell membranes,” Phys. Rev. Lett. 90(22), 228101 (2003).
[CrossRef] [PubMed]

A. G. Zilman and R. Granek, “Undulations and dynamic structure factor of membranes,” Phys. Rev. Lett. 77(23), 4788–4791 (1996).
[CrossRef] [PubMed]

Biomed. Opt. Express (1)

Biophys. J. (4)

J. Sleep, D. Wilson, R. Simmons, and W. Gratzer, “Elasticity of the red cell membrane and its relation to hemolytic disorders: an optical tweezers study,” Biophys. J. 77(6), 3085–3095 (1999).
[CrossRef] [PubMed]

S. Levin and R. Korenstein, “Membrane fluctuations in erythrocytes are linked to MgATP-dependent dynamic assembly of the membrane skeleton,” Biophys. J. 60(3), 733–737 (1991).
[CrossRef] [PubMed]

N. S. Gov and S. A. Safran, “Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects,” Biophys. J. 88(3), 1859–1874 (2005).
[CrossRef] [PubMed]

N. Gov, A. Zilman, and S. Safran, “Cytoskeleton confinement of red blood cell membrane fluctuations,” Biophys. J. 84, 486A (2003).

Blood (1)

N. Mohandas and P. G. Gallagher, “Red cell membrane: past, present, and future,” Blood 112(10), 3939–3948 (2008).
[CrossRef] [PubMed]

FEBS Lett. (1)

S. Tuvia, S. Levin, and R. Korenstein, “Correlation between local cell membrane displacements and filterability of human red blood cells,” FEBS Lett. 304(1), 32–36 (1992).
[CrossRef] [PubMed]

J. Appl. Physiol. (1)

M. Puig-de-Morales, K. T. Turner, J. P. Butler, J. J. Fredberg, and S. Suresh, “Viscoelasticity of the human red blood cell,” J. Appl. Physiol. 293, 597–605 (2007).

J. Chem. Phys. (1)

L. C. L. Lin, N. Gov, and F. L. H. Brown, “Nonequilibrium membrane fluctuations driven by active proteins,” J. Chem. Phys. 124(7), 074903 (2006).
[CrossRef] [PubMed]

J. Math. Phys. (1)

M. A. Peterson, “Geometrical methods for the elasticity theory of membranes,” J. Math. Phys. 26(4), 711–717 (1985).
[CrossRef]

J. Mech. Phys. Solids (1)

M. Dao, C. T. Lim, and S. Suresh, “Mechanics of the human red blood cell deformed by optical tweezers,” J. Mech. Phys. Solids 51(11-12), 2259–2280 (2003).
[CrossRef]

J. Phys. (1)

F. Brochard and J. F. Lennon, “Frequency spectrum of the flicker phenomenon in erythrocytes,” J. Phys. 36, 1035–1047 (1975).

Nat. Mater. (1)

G. Bao and S. Suresh, “Cell and molecular mechanics of biological materials,” Nat. Mater. 2(11), 715–725 (2003).
[CrossRef] [PubMed]

Nature (1)

H. Engelhardt, H. Gaub, and E. Sackmann, “Viscoelastic properties of erythrocyte membranes in high-frequency electric fields,” Nature 307(5949), 378–380 (1984).
[CrossRef] [PubMed]

Opt. Express (1)

Opt. Lett. (1)

Phys. Rev. E Stat. Nonlin. Soft Matter Phys. (2)

G. Popescu, A. Dogariu, and R. Rajagopalan, “Spatially resolved microrheology using localized coherence volumes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 65(4), 041504 (2002).
[CrossRef] [PubMed]

A. J. Levine and F. C. MacKintosh, “Dynamics of viscoelastic membranes,” Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 66(6), 061606 (2002).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics (1)

F. Gittes and F. C. MacKintosh, “Dynamic shear modulus of a semiflexible polymer network,” Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 58(2), R1241–R1244 (1998).
[CrossRef]

Phys. Rev. Lett. (9)

R. Lipowsky and M. Girardet, “Shape fluctuations of polymerized or solidlike membranes,” Phys. Rev. Lett. 65(23), 2893–2896 (1990).
[CrossRef] [PubMed]

H. 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]

A. G. Zilman and R. Granek, “Undulations and dynamic structure factor of membranes,” Phys. Rev. Lett. 77(23), 4788–4791 (1996).
[CrossRef] [PubMed]

T. G. Mason and D. A. Weitz, “Optical measurements of frequency-dependent linear viscoelastic moduli of complex fluids,” Phys. Rev. Lett. 74(7), 1250–1253 (1995).
[CrossRef] [PubMed]

D. H. Boal, U. Seifert, and A. Zilker, “Dual network model for red blood cell membranes,” Phys. Rev. Lett. 69(23), 3405–3408 (1992).
[CrossRef] [PubMed]

N. Gov, A. G. Zilman, and S. Safran, “Cytoskeleton confinement and tension of red blood cell membranes,” Phys. Rev. Lett. 90(22), 228101 (2003).
[CrossRef] [PubMed]

N. Gov, “Membrane undulations driven by force fluctuations of active proteins,” Phys. Rev. Lett. 93(26), 268104 (2004).
[CrossRef] [PubMed]

L. C. L. Lin and F. L. H. Brown, “Brownian dynamics in Fourier space: membrane simulations over long length and time scales,” Phys. Rev. Lett. 93(25), 256001 (2004).
[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]

Proc. Natl. Acad. Sci. U.S.A. (4)

S. Tuvia, A. Almagor, A. Bitler, S. Levin, R. Korenstein, and S. Yedgar, “Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force,” Proc. Natl. Acad. Sci. U.S.A. 94(10), 5045–5049 (1997).
[CrossRef] [PubMed]

J. D. Wan, W. D. Ristenpart, and H. A. Stone, “Dynamics of shear-induced ATP release from red blood cells,” Proc. Natl. Acad. Sci. U.S.A. 105(43), 16432–16437 (2008).
[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, 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]

Science (1)

D. E. Discher, N. Mohandas, and E. A. Evans, “Molecular maps of red cell deformation: hidden elasticity and in situ connectivity,” Science 266(5187), 1032–1035 (1994).
[CrossRef] [PubMed]

Other (4)

R. Cotran, V. Kumar, T. Collins, and S. Robbins, Robbins Pathologic Basis of Disease (WB Saunders Company, 2004).

G. Popescu, “Quantitative phase imaging of nanoscale cell structure and dynamics.methods in cell biology.” in Methods in Nano Cell Biology, B. P.Jena, ed. (Elsevier. 2008) pp. 87–115.

D. Langevin, Light Scattering by Liquid Surfaces and Complementary Techniques (M. Dekker, New York, 1992).

Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues (Springer-Verlag, New York, 1993).

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Figures (3)

Fig. 1
Fig. 1

a) RBC topography map; color bar indicates thickness in microns. b) Instant displacement map; color bar in nm. c) Background displacement; color bar in nm. d) Histogram of displacements associated with the mps in b and c.

Fig. 2
Fig. 2

(a) Power spectra of membrane fluctuations for 7 RBCs, their average, and background, as indicated. Dash line indicates a power law of exponent −1.7. (b). RBC viscous and elastic moduli vs. frequency, as indicated. Dash lines show the liquid and solid behavior.

Fig. 3
Fig. 3

Instantaneous displacement map associated with an RBC at a spatial wavelength, Λ = 2π/q, centered around 1 μm. Color bar in nanometers indicates displacements in nanometers. b) Schematics of how the membrane ripples deform the membrane material like a bead of size comparable with Λ. The spectrin molecules are depicted in red and connected to the lipid bilayer.

Equations (5)

Equations on this page are rendered with MathJax. Learn more.

Δ h 2 ( q , ω ) = k B T π ω q τ 0 2 ρ Im ( 1 β + ( 1 + α ) 2 1 + 2 α ) | α = i ω τ 0
Δ h 2 ( q , ω ) k B T 2 π q ω 2 1 η ( ω )
χ ' ' ( q , ω ) = π ω k B T Δ h 2 ( q , ω )
χ ¯ ' ( ω ) = 2 π P + χ ¯ ' ' ( ω ' ) ω ' ω d ω ' ,
G ( ω ) G S E R = 1 6 π a 1 χ ( ω ) ,

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