Abstract
In contrast to most mechanical properties of the red cell, experimental information on stress relaxation (SR) of the membrane skeleton is scarce. On the other hand, many postulates or assumptions as to the value of the characteristic time of SR \((\tau _{\mathrm{SR}})\) can be found in the literature. Here, an experiment is presented that allows measurement of \(\tau _{\mathrm{SR}}\) up to values of about 10 h. The membrane skeleton was deformed passively by changing the spontaneous curvature of the bilayer thus transforming the natively biconcave red cells into echinocytes. This shape and the concomitant deformation of the skeleton were kept up to 4 h by incubation at 37 ℃. During this period, no plastic deformation (creep) was observed. After the incubation, the spontaneous curvature was returned to normal. The resulting shape was smooth showing no remnants of the echinocytic shape. Both observations indicate \(\tau _{\mathrm{SR}}\gtrapprox \) 10 h. This result is in gross disagreement to postulates or assumptions existing in the literature.
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An X, Lecomte MC, Chasis JA, Mohandas N, Gratzer W (2002) Shear-response of the spectrin dimer-tetramer equilibrium in the red blood cell membrane. J Biol Chem 277:31,796–31,800
Bessis M (1972) Red cell shapes. An illustrated classification and its rationale. Nouvelle Revue Française d’Hématologie 12:721–746
Brown FLH, M LD, McCammon J, Wilson KR (2000) Lateral diffusion of membrane proteins in the presence of static and dynamic corrals: Suggestions for appropriate observables. Biophys J 57:2257–2269
Chasis JA, Prenant M, Leung A, Mohandas N (1989) Membrane assembly and remodelling during reticulocyte maturation. Blood 74:1112–1120
Cordasco D, Yazdani A, Bagchi P (2014) Comparison of erythrocyte dynamics in shear flow under different stress-free configurations. Phys Fluids 26:041902
Discher DE, Mohandas N, Evans EA (1994) Molecular maps of red cell deformation: hidden elasticity and in situ connectivity. Science 226:1032–1035
Fai TG, Griffith BE, Mori Y, Peskin CS (2013) Immersed boundary method for variable viscosity and variable density problems using fast constant-coefficient linear solvers I: numerical method and results. SIAM J Sci Comput 35:B1132–B1161
Fischer TM (1986) Transcellular cross bonding of the red blood cell membrane. Biochim Biophys Acta 861:277–286
Fischer TM (2004) Shape memory of human red blood cells. Biophys J 86:3304–3313
Fischer TM, Haest CWM, Stöhr M, Kamp D, Deuticke B (1978a) Selective alteration of erythrocyte deformability by SH-reagents. Evidence for an involvement of spectrin in membrane shear elasticity. Biochim Biophys Acta 510:270–282
Fischer TM, Stöhr-Liesen M, Schmid-Schönbein H (1978b) The red cell as a fluid droplet: tank tread-like motion of the human erythrocyte membrane in shear flow. Science 202:894–896
Forsyth AM, Wan J, Owrutsky PD, Abkarian M, Stone HA (2011) Multiscale approach to link red blood cell dynamics, shear viscosity, and ATP release. Proc Nat Acad Sci USA 108:10,986–10,991
Freund JB (2013) The flow of red blood cells through a narrow spleen-like slit. Phys Fluids 25:110,807
Gokhin DS, Nowak RB, Khoory JA, de la Piedra A, Ghiran IC, Fowler VM (2015) Dynamic actin filaments control the mechanical behavior of the human red blood cell membrane. Mol Biol Cell 26:1699–1710
Gov NS, Safran SA (2005) Red blood cell membrane fluctuations and shape controlled by ATP-induced cytoskeletal defects. Biophys J 89:1859–1874
Haest CWM, Fischer TM, Plasa G, Deuticke B (1980) Stabilization of erythrocyte shape by a chemical increase in membrane shear stiffness. Blood Cells 6:539–553
Jay AWL (1975) Geometry of the human erythrocyte. I. Effect of albumin on cell geometry. Biophys J 15:205–222
Lange Y, Hadesman RA, Steck TL (1982) Role of the reticulum in the stability and shape of the isolated human erythrocyte membrane. J Cell Biol 92:714–721
Lazaro GR, Melzak KA, Toca-Herrera JL, Pagonabarraga I, Hernandez-Machado A (2013) Elastic energies and morphologies of the first stages of the discoechinocyte transition. Soft Matter 9:6430–6441
Li J, Dao M, Lim C, Suresh S (2005) Spectrin-level modeling of the cytoskeleton and optical tweezers stretching of the erythrocyte. Biophys J 88:3707–3719
Li J, Lykotrafitis G, Dao M, Suresh S (2007) Cytoskeletal dynamics of human erythrocyte. Proc Nat Acad Sci USA 104:4937–4942
Lim GHW, Wortis M, Mukhopadhyay R (2002) Stomatocyte-discocyte-echinocyte sequence of the human red blood cell: evidence for the bilayer-couple hypothesis from membrane mechanics. Proc Nat Acad Sci USA 99:16,766–16,769
Liu S, Derick L, Palek J (1993) Dependence of the permanent deformation of red blood cell membranes on spectrin dimer-tetramer equilibrium: implication for permanent membrane deformation of irreversibly sickled cells. Blood 81:522–528
Liu SC, Palek J (1984) Hemoglobin enhances the self-association of spectrin heterodimers in human erythrocytes. J Biol Chem 259:11556–11562
Markle DR, Evans EA, Hochmuth RM (1983) Force relaxation and permanent deformation of erythrocyte membrane. Biophys J 42:91–98
Mills JP, Qie L, Dao M, Lim CT, Suresh S (2004) Nonlinear elastic and viscoelastic deformation of the human red blood cell with optical tweezers. Mech Chem Biosys 1:169–180
Mohandas N (2013) An open-and-shut case? Blood 122:2928–2929
Mohandas N, Feo C (1975) A quantitative study of the red cell shape changes produced by anionic and cationic derivatives of phenothiazine. Blood Cells 1:375–384
Mohandas N, Greenquist AC, Shohet SB (1978) Bilayer balance and regulation of red cell shape changes. J Supramol Struct 9:453–458
Nans A, Mohandas N, Stokes DL (2011) Native ultrastructure of the red cell cytoskeleton by cryo-electron tomography. Biophys J 101:2341–2350
Park Y, Best CA, Auth T, Gov NS, Safran SA, Popescu G, Suresh S, Feld MS (2010) Metabolic remodeling of the human red blood cell membrane. Proc Nat Acad Sci USA 107:1289–1294
Salomao M, An X, Guo X, Gratzer WB, Mohandas N, Baines AJ (2006) Mammalian \(\alpha \)i-spectrin is a neofunctionalized polypeptide adapted to small highly deformable erythrocytes. Proc Nat Acad Sci USA 103:643–648
Saxton MJ (1990) The membrane skeleton of erythrocytes—a percolation model. Biophys J 57:1167–1177
Sheetz MP, Singer SJ (1974) Biological membranes as bilayer couples. A molecular mechanism of drug-erythrocyte interactions. Proc Nat Acad Sci USA 71:4457–4461
Waugh RE, Mantalaris A, Bauserman RG, Hwang WC, Wu JHD (2001) Membrane instability in late-stage erythropoiesis. Blood 97:1869–1875
Weaver FE, Polster H, Febboriello P, Sheetz MP, Schmid-Schönbein H, Koppel DE (1990) Normal band 3-cytoskeletal interactions are maintained on tanktreading erythrocytes. Biophys J 58:1427–1436
Wojdyla M, Raj S, Petrov D (2013) Nonequilibrium fluctuations of mechanically stretched single red blood cells detected by optical tweezers. Eur Biophys J 42:539–547. doi:10.1007/s00249-013-0903-3
Yoon YZ, Hong H, Brown A, Kim DC, Kang DJ, Lew VL, Cicuta P (2009a) Flickering analysis of erythrocyte mechanical properties: dependence on oxygenation level, cell shape, and hydration level. Biophys J 97:1606–1615
Yoon YZ, Kotar J, Yoon G, Cicuta P (2009b) The nonlinear mechanical response of the red blood cell. Phys Biol 5:036007
Yoon YZ, Kotar J, Brown AT, Cicuta P (2011) Red blood cell dynamics: from spontaneous fluctuations to non-linear response. Soft Matter 7:2042–2051
Zhang R, Brown FLH (2000) Cytoskeleton mediated effective elastic properties of model red blood cell membranes. J Chem Phys 129:065101
Zhu Q, Asaro RJ (2008) Spectrin folding versus unfolding reactions and RBC membrane stiffness. Biophys J 94:2529–2545
Ziparo E, Lemay A, Marchesi VT (1978) The distribution of spectrin along the membranes of normal and echinocytic human erythrocytes. J Cell Sci 34:91–101
Acknowledgments
The author thanks the staff of the blood bank, Universitätsklinikum Aachen for their cooperation in placing the blood samples at our disposal, Rosi Degenhardt for excellent technical help, and Chaouqi Misbah, Université J. Fourier Grenoble I, France, for reading the manuscript.
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Fischer, T.M. Creep and stress relaxation of human red cell membrane. Biomech Model Mechanobiol 16, 239–247 (2017). https://doi.org/10.1007/s10237-016-0813-2
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DOI: https://doi.org/10.1007/s10237-016-0813-2