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Equilibrium physics breakdown reveals the active nature of red blood cell flickering

Abstract

Red blood cells, or erythrocytes, are seen to flicker under optical microscopy, a phenomenon initially described as thermal fluctuations of the cell membrane. But recent studies have suggested the involvement of non-equilibrium processes, without definitively ruling out equilibrium interpretations. Using active and passive microrheology to directly compare the membrane response and fluctuations on single erythrocytes, we report here a violation of the fluctuation–dissipation relation, which is a direct demonstration of the non-equilibrium nature of flickering. With an analytical model of the composite erythrocyte membrane and realistic stochastic simulations, we show that several molecular mechanisms may explain the active fluctuations, and we predict their kinetics. We demonstrate that tangential metabolic activity in the network formed by spectrin, a cytoskeletal protein, can generate curvature-mediated active membrane motions. We also show that other active membrane processes represented by direct normal force dipoles may explain the observed membrane activity. Our findings provide solid experimental and theoretical frameworks for future investigations of the origin and function of active motion in cells.

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Figure 1: Experimental set-up.
Figure 2: Membrane fluctuations and apparent response.
Figure 3: Analytic composite model of the red blood cell membrane.
Figure 4: Simulations mimicking the experimental conditions.

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References

  1. Browicz, T. Further observation of motion phenomena on red blood cells in pathological states. Zbl Med. Wiss. 28, 625–627 (1890).

    Google Scholar 

  2. Evans, E. A. & Parsegian, V. A. Thermal–mechanical fluctuations enhance repulsion between bimolecular layers. Proc. Natl Acad. Sci. USA 83, 7132–7136 (1986).

    ADS  Google Scholar 

  3. Lin, L. C.-L. & Brown, F. L. H. Dynamics of pinned membranes with application to protein diffusion on the surface of red blood cells. Biophys. J. 86, 764–780 (2004).

    ADS  Google Scholar 

  4. Cojoc, D. et al. Toward fast malaria detection by secondary speckle sensing microscopy. Biomed. Opt. Express 3, 991–1005 (2012).

    Google Scholar 

  5. Strey, H., Peterson, M. & Sackmann, E. Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition. Biophys. J. 69, 478–488 (1995).

    ADS  Google Scholar 

  6. Betz, T., Lenz, M., Joanny, J.-F. & Sykes, C. ATP-dependent mechanics of red blood cells. Proc. Natl Acad. Sci. USA 106, 15320–15325 (2009).

    ADS  Google Scholar 

  7. Yoon, Y.-Z. et al. Flickering analysis of erythrocyte mechanical properties: dependence on oxygenation level, cell shape, and hydration level. Biophys. J. 97, 1606–1615 (2009).

    ADS  Google Scholar 

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

    Google Scholar 

  9. Evans, J., Gratzer, W., Mohandas, N., Parker, K. & Sleep, J. Fluctuations of the red blood cell membrane: relation to mechanical properties and lack of ATP dependence. Biophys. J. 94, 4134–4144 (2008).

    ADS  Google Scholar 

  10. Yoon, Y. Z., Kotar, J., Brown, A. T. & Cicuta, P. Red blood cell dynamics: from spontaneous fluctuations to non-linear response. Soft Matter 7, 2042–2051 (2011).

    ADS  Google Scholar 

  11. Boss, D. et al. Spatially-resolved eigenmode decomposition of red blood cells membrane fluctuations questions the role of ATP in flickering. PLoS ONE 7, e40667 (2012).

    ADS  Google Scholar 

  12. Puckeridge, M., Chapman, B. E., Conigrave, A. D. & Kuchel, P. W. Membrane flickering of the human erythrocyte: physical and chemical effectors. Eur. Biophys. J. 43, 169–177 (2014).

    Google Scholar 

  13. Blowers, R., Clarkson, E. M. & Maizels, M. Flicker phenomenon in human erythrocytes. J. Physiol. 113, 228–239 (1951).

    Google Scholar 

  14. Tuvia, S. et al. Cell membrane fluctuations are regulated by medium macroviscosity: evidence for a metabolic driving force. Proc. Natl Acad. Sci. USA 94, 5045–5049 (1997).

    ADS  Google Scholar 

  15. Park, Y. et al. Metabolic remodeling of the human red blood cell membrane. Proc. Natl Acad. Sci. USA 107, 1289–1294 (2010).

    ADS  Google Scholar 

  16. Rodríguez-García, R. et al. Direct cytoskeleton forces cause membrane softening in red blood cells. Biophys. J. 108, 2794–2806 (2015).

    ADS  Google Scholar 

  17. Weed, R. I., LaCelle, P. L. & Merrill, E. W. Metabolic dependence of red cell deformability. J. Clin. Invest. 48, 795–809 (1969).

    Google Scholar 

  18. Chabanel, A., Reinhart, W. & Chien, S. Increased resistance to membrane deformation of shape-transformed human red blood cells. Blood 69, 739–743 (1987).

    Google Scholar 

  19. Discher, D. E., Mohandas, N. & Evans, E. A. Molecular maps of red cell deformation: hidden elasticity and in situ connectivity. Science 266, 1032–1035 (1994).

    ADS  Google Scholar 

  20. Nakao, M., Nakao, T. & Yamazoe, S. Adenosine triphosphate and maintenance of shape of the human red cells. Nature 187, 945–946 (1960).

    ADS  Google Scholar 

  21. Sheetz, M. P. On the mechanism of ATP-induced shape changes in human erythrocyte membranes. I. The role of the spectrin complex. J. Cell Biol. 73, 638–646 (1977).

    Google Scholar 

  22. Manno, S., Takakuwa, Y., Nagao, K. & Mohandas, N. Modulation of erythrocyte membrane mechanical function by beta-spectrin phosphorylation and dephosphorylation. J. Biol. Chem. 270, 5659–5665 (1995).

    Google Scholar 

  23. Manno, S., Takakuwa, Y. & Mohandas, N. Modulation of erythrocyte membrane mechanical function by protein 4.1 phosphorylation. J. Biol. Chem. 280, 7581–7587 (2005).

    Google Scholar 

  24. Monzel, C. et al. Measuring fast stochastic displacements of bio-membranes with dynamic optical displacement spectroscopy. Nature Commun. 6, 8162 (2015).

    ADS  Google Scholar 

  25. Van Kampen, N. G. Fluctuation Phenomena in Solids (Academic Press, 1965).

    Google Scholar 

  26. Schmidt, D. et al. Signature of a nonharmonic potential as revealed from a consistent shape and fluctuation analysis of an adherent membrane. Phys. Rev. X 4, 021023 (2014).

    Google Scholar 

  27. Ben-Isaac, E. et al. Effective temperature of red-blood-cell membrane fluctuations. Phys. Rev. Lett. 106, 238103 (2011).

    ADS  Google Scholar 

  28. Callen, H. B. & Welton, T. A. Irreversibility and generalized noise. Phys. Rev. 83, 34–40 (1951).

    ADS  MathSciNet  MATH  Google Scholar 

  29. Martin, P., Hudspeth, A. J. & Julicher, F. Comparison of a hair bundle’s spontaneous oscillations with its response to mechanical stimulation reveals the underlying active process. Proc. Natl Acad. Sci. USA 98, 14380–14385 (2001).

    ADS  Google Scholar 

  30. Mizuno, D., Tardin, C., Schmidt, C. F. & MacKintosh, F. C. Nonequilibrium mechanics of active cytoskeletal networks. Science 315, 370–373 (2007).

    ADS  Google Scholar 

  31. Mizuno, D., Bacabac, R., Tardin, C., Head, D. & Schmidt, C. F. High-resolution probing of cellular force transmission. Phys. Rev. Lett. 102, 168102 (2009).

    ADS  Google Scholar 

  32. Hoffman, B. D., Massiera, G., Van Citters, K. M. & Crocker, J. C. The consensus mechanics of cultured mammalian cells. Proc. Natl Acad. Sci. USA 103, 10259–10264 (2006).

    ADS  Google Scholar 

  33. Discher, D. E., Boal, D. H. & Boey, S. K. Simulations of the erythrocyte cytoskeleton at large deformation. II. Micropipette aspiration. Biophys. J. 75, 1584–1597 (1998).

    Google Scholar 

  34. Engelhardt, H., Gaub, H. & Sackmann, E. Viscoelastic properties of erythrocyte membranes in high-frequency electric fields. Nature 307, 378–380 (1984).

    ADS  Google Scholar 

  35. Lenormand, G., Hénon, S., Richert, A., Siméon, J. & Gallet, F. Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton. Biophys. J. 81, 43–56 (2001).

    Google Scholar 

  36. Betz, T. & Sykes, C. Time resolved membrane fluctuation spectroscopy. Soft Matter 8, 5317–5326 (2012).

    ADS  Google Scholar 

  37. Chu, H. et al. Identification of cytoskeletal elements enclosing the ATP pools that fuel human red blood cell membrane cation pumps. Proc. Natl Acad. Sci. USA 109, 12794–12799 (2012).

    ADS  Google Scholar 

  38. Bandmann, U., Monti, M. & Wadsö, I. Clinical physiology: microcalorimetric measurements of heat production in whole blood and blood cells of normal persons. Scand. J. Clin. Lab. Invest. 35, 121–127 (1975).

    Google Scholar 

  39. Subrahmanyam, G., Bertics, P. J. & Anderson, R. A. Phosphorylation of protein 4.1 on tyrosine-418 modulates its function in vitro. Proc. Natl Acad. Sci. USA 88, 5222–5226 (1991).

    ADS  Google Scholar 

  40. Gauthier, E., Guo, X., Mohandas, N. & An, X. Phosphorylation-dependent perturbations of the 4.1R-associated multiprotein complex of the erythrocyte membrane. Biochemistry 50, 4561–4567 (2011).

    Google Scholar 

  41. Lu, P. W., Soong, C. J. & Tao, M. Phosphorylation of ankyrin decreases its affinity for spectrin tetramer. J. Biol. Chem. 260, 14958–14964 (1985).

    Google Scholar 

  42. Gov, N. S. & Safran, S. A. Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects. Biophys. J. 88, 1859–1874 (2005).

    Google Scholar 

  43. Gov, N. S. Active elastic network: cytoskeleton of the red blood cell. Phys. Rev. E 75, 011921 (2007).

    ADS  Google Scholar 

  44. Boal, D. H., Seifert, U. & Zilker, A. Dual network model for red blood cell membranes. Phys. Rev. Lett. 69, 3405–3408 (1992).

    ADS  Google Scholar 

  45. Peng, Z., Asaro, R. J. & Zhu, Q. Multiscale modelling of erythrocytes in Stokes flow. J. Fluid Mech. 686, 299–337 (2011).

    ADS  MathSciNet  MATH  Google Scholar 

  46. Li, H. & Lykotrafitis, G. Two-component coarse-grained molecular-dynamics model for the human erythrocyte membrane. Biophys. J. 102, 75–84 (2012).

    ADS  Google Scholar 

  47. Peng, Z. et al. Lipid bilayer and cytoskeletal interactions in a red blood cell. Proc. Natl Acad. Sci. USA 110, 13356–13361 (2013).

    ADS  Google Scholar 

  48. Fournier, J.-B., Lacoste, D. & Raphaël, E. Fluctuation spectrum of fluid membranes coupled to an elastic meshwork: jump of the effective surface tension at the mesh size. Phys. Rev. Lett. 92, 018102 (2004).

    ADS  Google Scholar 

  49. Dubus, C. & Fournier, J.-B. A Gaussian model for the membrane of red blood cells with cytoskeletal defects. Europhys. Lett. 75, 181–187 (2006).

    ADS  MathSciNet  Google Scholar 

  50. Zhang, R. & Brown, F. L. H. Cytoskeleton mediated effective elastic properties of model red blood cell membranes. J. Chem. Phys. 129, 065101 (2008).

    ADS  Google Scholar 

  51. Paulose, J., Vliegenthart, G. A., Gompper, G. & Nelson, D. R. Fluctuating shells under pressure. Proc. Natl Acad. Sci. USA 109, 19551–19556 (2012).

    ADS  Google Scholar 

  52. Kantor, Y. Entropic elasticity of tethered solids. Phys. Rev. A 39, 6582–6586 (1989).

    ADS  Google Scholar 

  53. Rochal, S. B., Lorman, V. L. & Mennessier, G. Viscoelastic dynamics of spherical composite vesicles. Phys. Rev. E 71, 021905 (2005).

    ADS  Google Scholar 

  54. Canham, P. B. The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. J. Theor. Biol. 26, 61–81 (1970).

    Google Scholar 

  55. Milner, S. T. & Safran, S. A. Dynamical fluctuations of droplet microemulsions and vesicles. Phys. Rev. A 36, 4371–4379 (1987).

    ADS  Google Scholar 

  56. Seifert, U. The concept of effective tension for fluctuating vesicles. Z. Phys. B 97, 299–309 (1995).

    ADS  Google Scholar 

  57. Loubet, B., Seifert, U. & Lomholt, M. A. Effective tension and fluctuations in active membranes. Phys. Rev. E 85, 031913 (2012).

    ADS  Google Scholar 

  58. Bihr, T., Seifert, U. & Smith, A.-S. Nucleation of ligand-receptor domains in membrane adhesion. Phys. Rev. Lett. 109, 258101 (2012).

    ADS  Google Scholar 

  59. Prost, J. & Bruinsma, R. Shape fluctuations of active membranes. Europhys. Lett. 33, 321–326 (1996).

    ADS  Google Scholar 

  60. Graham, T. R. Flippases and vesicle-mediated protein transport. Trends Cell Biol. 14, 670–677 (2004).

    Google Scholar 

  61. Hoogerbrugge, P. J. & Koelman, J. M. V. A. Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics. Europhys. Lett. 19, 155–160 (1992).

    ADS  Google Scholar 

  62. Español, P. & Warren, P. Statistical mechanics of dissipative particle dynamics. Europhys. Lett. 30, 191–196 (1995).

    ADS  Google Scholar 

  63. Fedosov, D. A., Caswell, B. & Karniadakis, G. E. A multiscale red blood cell model with accurate mechanics, rheology, and dynamics. Biophys. J. 98, 2215–2225 (2010).

    ADS  Google Scholar 

  64. Fedosov, D. A., Noguchi, H. & Gompper, G. Multiscale modeling of blood flow: from single cells to blood rheology. Biomech. Model. Mechanobiol. 13, 239–258 (2014).

    Google Scholar 

  65. Manneville, J.-B., Bassereau, P., Ramaswamy, S. & Prost, J. Active membrane fluctuations studied by micropipet aspiration. Phys. Rev. E 64, 021908 (2001).

    ADS  Google Scholar 

  66. Pierrat, S., Brochard-Wyart, F. & Nassoy, P. Enforced detachment of red blood cells adhering to surfaces: statics and dynamics. Biophys. J. 87, 2855–2869 (2004).

    ADS  Google Scholar 

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Acknowledgements

We thank V. L. Lorman and J. Prost for careful reading of the analytical model. T.B. was founded by ANR-11-JSV5-0002 and by the Deutsche Forschungsgemeinschaft (DFG), Cells-in-Motion Cluster of Excellence (EXC 1003—CiM), University of Münster, Germany. H.T. acknowledges funding from the EMBL Interdisciplinary Postdoc program under Marie Curie Actions FP7-PEOPLE-2011-COFUND and generous support from the Bettencourt Schueller Foundation. D.A.F. acknowledges funding by the Alexander von Humboldt Foundation. D.A.F., T.A. and G.G. gratefully acknowledge a CPU time grant by the Jülich Supercomputing Center. N.S.G. acknowledges the Institut Curie’s Mayent-Rothschild Visiting Professor fund and Labex CelTisPhyBio for their support during the stay at the Institut Curie. N.S.G. is the incumbent of the Lee and William Abramowitz Professorial Chair of Biophysics, and thanks ISF Grant 580/12 for support.

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T.B. and C.S. designed experiments; T.B. performed experiments; H.T., B.A. and J.-F.J. derived the analytical model; D.A.F., T.A. and G.G. designed the simulation set-up; D.A.F. performed simulations; T.B., H.T. and D.A.F. analysed the data; all authors discussed and interpreted results; all authors wrote the manuscript.

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Correspondence to T. Betz.

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Turlier, H., Fedosov, D., Audoly, B. et al. Equilibrium physics breakdown reveals the active nature of red blood cell flickering. Nature Phys 12, 513–519 (2016). https://doi.org/10.1038/nphys3621

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