Echinocyte shapes: bending, stretching, and shear determine spicule shape and spacing.

We study the shapes of human red blood cells using continuum mechanics. In particular, we model the crenated, echinocytic shapes and show how they may arise from a competition between the bending energy of the plasma membrane and the stretching/shear elastic energies of the membrane skeleton. In contrast to earlier work, we calculate spicule shapes exactly by solving the equations of continuum mechanics subject to appropriate boundary conditions. A simple scaling analysis of this competition reveals an elastic length Lambda(el), which sets the length scale for the spicules and is, thus, related to the number of spicules experimentally observed on the fully developed echinocyte.

[1]  Y. Lange,et al.  Interaction of cholesterol and lysophosphatidylcholine in determining red cell shape. , 1982, Journal of lipid research.

[2]  M. Bessis,et al.  Present status of spiculed red cells and their relationship to the discocyte-echinocyte transformation: a critical review. , 1972, Blood.

[3]  E. Ponder,et al.  Disk-Sphere Transformation in Mammalian Red Cells. II.The Nature of the Anti-Sphering Factor. , 1940 .

[4]  B. Isomaa,et al.  Influence of band 3 protein absence and skeletal structures on amphiphile- and Ca(2+)-induced shape alterations in erythrocytes: a study with lamprey (Lampetra fluviatilis), trout (Onchorhynchus mykiss) and human erythrocytes. , 2000, Biochimica et biophysica acta.

[5]  W. Helfrich.  Elastic Properties of Lipid Bilayers: Theory and Possible Experiments , 1973, Zeitschrift fur Naturforschung. Teil C: Biochemie, Biophysik, Biologie, Virologie.

[6]  B. Deuticke.  Transformation and restoration of biconcave shape of human erythrocytes induced by amphiphilic agents and changes of ionic environment. , 1968, Biochimica et biophysica acta.

[7]  M. Nakao,et al.  Adenosine triphosphate and shape of erythrocytes. , 1961, Journal of biochemistry.

[8]  Robert B. Gennis,et al.  Biomembranes: Molecular Structure and Function , 1988 .

[9]  Seifert,et al.  Budding transitions of fluid-bilayer vesicles: The effect of area-difference elasticity. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[10]  L. Derick,et al.  Visualization of the hexagonal lattice in the erythrocyte membrane skeleton , 1987, The Journal of cell biology.

[11]  D. Discher,et al.  Direct measures of large, anisotropic strains in deformation of the erythrocyte cytoskeleton. , 1999, Biophysical journal.

[12]  W. Helfrich,et al.  Budding of lipid bilayer vesicles and flat membranes , 1992 .

[13]  A. Iglič,et al.  Depletion of membrane skeleton in red blood cell vesicles. , 1995, Biophysical journal.

[14]  C. Haest,et al.  Passive transmembrane redistributions of phospholipids as a determinant of erythrocyte shape change. Studies on electroporated cells. , 1999, Molecular membrane biology.

[15]  M. Gedde,et al.  Membrane potential and human erythrocyte shape. , 1997, Biophysical journal.

[16]  P. Low,et al.  Contribution of the band 3-ankyrin interaction to erythrocyte membrane mechanical stability. , 1991, Blood.

[17]  E. Evans,et al.  Bending resistance and chemically induced moments in membrane bilayers. , 1974, Biophysical journal.

[18]  M. Gedde,et al.  Shape response of human erythrocytes to altered cell pH. , 1995, Blood.

[19]  J. Gimsa.  A possible molecular mechanism governing human erythrocyte shape. , 1998, Biophysical journal.

[20]  P. Canham.  The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell. , 1970, Journal of theoretical biology.

[21]  Wilfred D. Stein,et al.  Cell Shape: Determinants, Regulation, and Regulatory Role , 1989 .

[22]  R. Waugh.  Elastic energy of curvature-driven bump formation on red blood cell membrane. , 1996, Biophysical journal.

[23]  M. Sheetz,et al.  Biological membranes as bilayer couples. A molecular mechanism of drug-erythrocyte interactions. , 1974, Proceedings of the National Academy of Sciences of the United States of America.

[24]  A. Iglič.  A possible mechanism determining the stability of spiculated red blood cells. , 1997, Journal of biomechanics.

[25]  D. Boal,et al.  Computer simulation of a model network for the erythrocyte cytoskeleton. , 1994, Biophysical journal.

[26]  R. Waugh,et al.  Role of lamellar membrane structure in tether formation from bilayer vesicles. , 1992, Biophysical journal.

[27]  J. Gimsa,et al.  Do band 3 protein conformational changes mediate shape changes of human erythrocytes? , 1995, Molecular membrane biology.

[28]  K. J. Lee,et al.  Membrane bilayer balance and erythrocyte shape: a quantitative assessment. , 1985, Biochemistry.

[29]  R. Furchgott.  Disk-Sphere Transformation in Mammalian Red Cells , 1940 .

[30]  J. Simeon,et al.  Direct measurement of the area expansion and shear moduli of the human red blood cell membrane skeleton. , 2001, Biophysical journal.

[31]  M. Sheetz.  DNase-I-dependent dissociation of erythrocyte cytoskeletons , 1979, The Journal of cell biology.

[32]  M. Gedde,et al.  Resolution of the paradox of red cell shape changes in low and high pH. , 1999, Biochimica et biophysica acta.

[33]  A. Iglič,et al.  A role of membrane skeleton in discontinuous red blood cell shape transformations , 1996 .

[34]  W. Helfrich,et al.  The curvature elasticity of fluid membranes : A catalogue of vesicle shapes , 1976 .

[35]  S. Hénon,et al.  A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers. , 1999, Biophysical journal.

[36]  Christoph F. Schmidt,et al.  Conformation and elasticity of the isolated red blood cell membrane skeleton. , 1992, Biophysical journal.

[37]  U. Seifert,et al.  Thermal shape fluctuations of fluid-phase phospholipid-bilayer membranes and vesicles , 1997 .

[38]  S Chien,et al.  Elastic deformations of red blood cells. , 1977, Journal of Biomechanics.

[39]  D. Branton,et al.  The molecular basis of erythrocyte shape. , 1986, Science.

[40]  B. Chailley,et al.  Calcium-pH Interactions in the Production of Shape Change in Erythrocytes , 1973 .

[41]  M. Nakao,et al.  Adenosine Triphosphate and Maintenance of Shape of the Human Red Cells , 1960, Nature.

[42]  E. Evans,et al.  New membrane concept applied to the analysis of fluid shear- and micropipette-deformed red blood cells. , 1973, Biophysical journal.

[43]  U. Seifert,et al.  Mapping vesicle shapes into the phase diagram: A comparison of experiment and theory , 1996, cond-mat/9612151.

[44]  P. Wong.  A basis of echinocytosis and stomatocytosis in the disc-sphere transformations of the erythrocyte. , 1999, Journal of theoretical biology.

[45]  A. Mikkelsen,et al.  Spectrin, human erythrocyte shapes, and mechanochemical properties. , 1986, Biophysical journal.

[46]  E. Evans,et al.  Molecular maps of red cell deformation: hidden elasticity and in situ connectivity. , 1994, Science.

[47]  E. Evans.  A new material concept for the red cell membrane. , 1973, Biophysical journal.

[48]  Y C Fung,et al.  Theory of the sphering of red blood cells. , 1968, Biophysical journal.

[49]  N. Mohandas,et al.  Interaction of amphipathic drugs with erythrocytes from various species. , 1982, American journal of veterinary research.

[50]  D. Branton,et al.  Visualization of the protein associations in the erythrocyte membrane skeleton. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[51]  J. Hörber,et al.  Sphingolipid–Cholesterol Rafts Diffuse as Small Entities in the Plasma Membrane of Mammalian Cells , 2000, The Journal of cell biology.

[52]  R. Waugh,et al.  Thermoelasticity of red blood cell membrane. , 1979, Biophysical journal.

[53]  B. Roelofsen,et al.  Lipid molecular shape affects erythrocyte morphology: a study involving replacement of native phosphatidylcholine with different species followed by treatment of cells with sphingomyelinase C or phospholipase A2 , 1985, The Journal of cell biology.

[54]  E. Sackmann,et al.  Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition. , 1995, Biophysical journal.

[55]  E. Ponder.  Red cell structure and its breakdown , 1955 .

[56]  JOSEPH M. Hill,et al.  Hemolysis and Related Phenomena , 1949 .

[57]  Marcel Bessis,et al.  Living Blood Cells and Their Ultrastructure , 1972 .

[58]  R. Furchgott.  OBSERVATIONS ON THE STRUCTURE OF RED CELL GHOSTS , 1940 .

[59]  M. Gedde,et al.  Cytoplasmic pH and human erythrocyte shape. , 1997, Biophysical journal.

[60]  H. Hägerstrand,et al.  Amphiphile induced echinocyte-spheroechinocyte transformation of red blood cell shape , 1998, European Biophysics Journal.

[61]  R. Zia,et al.  Scaling analysis of narrow necks in curvature models of fluid lipid-bilayer vesicles. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[62]  L. Backman.  Shape control in the human red cell. , 1986, Journal of cell science.

[63]  M. Peterson.  An instability of the red blood cell shape , 1985 .

[64]  B. Isomaa,et al.  Shape transformations induced by amphiphiles in erythrocytes. , 1987, Biochimica et biophysica acta.

[65]  C. Haest,et al.  Extensive electroporation abolishes experimentally induced shape transformations of erythrocytes: a consequence of phospholipid symmetrization? , 1999, Biochimica et biophysica acta.

[66]  D. Jay.  Role of Band 3 in Homeostasis and Cell Shape , 1996, Cell.

[67]  K. Nagano,et al.  A Direct Relationship between Adenosine Triphosphate-level and in vivo Viability of Erythrocytes , 1962, Nature.

[68]  V. Bennett,et al.  Spectrin-based membrane skeleton: a multipotential adaptor between plasma membrane and cytoplasm. , 1990, Physiological reviews.

[69]  Marcel Bessis,et al.  Red cell shape : physiology, pathology, ultrastructure , 1973 .

[70]  M. Prenant,et al.  Topographie de l'apparition des spicules dans les érythrocytes crénelés (échinocytes. , 1972 .

[71]  Kai Simons,et al.  Lipid rafts and signal transduction , 2000, Nature Reviews Molecular Cell Biology.

[72]  K. Landman.  A continuum model for a red blood cell transformation: sphere to crenated sphere. , 1984, Journal of theoretical biology.