Skip to main content
NCBI home page
Biophysical Journal logoLink to Biophysical Journal
. 2002 Apr;82(4):1756–1772. doi: 10.1016/s0006-3495(02)75527-6

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

Ranjan Mukhopadhyay 1, Gerald Lim H W 1, Michael Wortis 1
PMCID: PMC1301974  PMID: 11916836

Abstract

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.

Full Text

The Full Text of this article is available as a PDF (184.2 KB).

Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Backman L. Shape control in the human red cell. J Cell Sci. 1986 Feb;80:281–298. doi: 10.1242/jcs.80.1.281. [DOI] [PubMed] [Google Scholar]
  2. Bennett V. Spectrin-based membrane skeleton: a multipotential adaptor between plasma membrane and cytoplasm. Physiol Rev. 1990 Oct;70(4):1029–1065. doi: 10.1152/physrev.1990.70.4.1029. [DOI] [PubMed] [Google Scholar]
  3. Bessis M., Prenant M. Topographie de l'apparition des spicules dans les érythrocytes crénelés (échinocytes. Nouv Rev Fr Hematol. 1972 May-Jun;12(3):351–364. [PubMed] [Google Scholar]
  4. Boal D. H. Computer simulation of a model network for the erythrocyte cytoskeleton. Biophys J. 1994 Aug;67(2):521–529. doi: 10.1016/S0006-3495(94)80511-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Bozic B., Svetina S., Zeks B., Waugh R. E. Role of lamellar membrane structure in tether formation from bilayer vesicles. Biophys J. 1992 Apr;61(4):963–973. doi: 10.1016/S0006-3495(92)81903-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Brecher G., Bessis M. Present status of spiculed red cells and their relationship to the discocyte-echinocyte transformation: a critical review. Blood. 1972 Sep;40(3):333–344. [PubMed] [Google Scholar]
  7. Byers T. J., Branton D. Visualization of the protein associations in the erythrocyte membrane skeleton. Proc Natl Acad Sci U S A. 1985 Sep;82(18):6153–6157. doi: 10.1073/pnas.82.18.6153. [DOI] [PMC free article] [PubMed] [Google Scholar]
  8. 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. 1970 Jan;26(1):61–81. doi: 10.1016/s0022-5193(70)80032-7. [DOI] [PubMed] [Google Scholar]
  9. Chailley B., Weed R. I., Leblond P. F., Maigné J. Formes échinocytaires et stomatocytaires du globule rouge; leur réversibilit et leur convertibilité. Nouv Rev Fr Hematol. 1973 Jan-Feb;13(1):71–87. [PubMed] [Google Scholar]
  10. Christiansson A., Kuypers F. A., Roelofsen B., Op den Kamp J. A., van Deenen L. L. 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. J Cell Biol. 1985 Oct;101(4):1455–1462. doi: 10.1083/jcb.101.4.1455. [DOI] [PMC free article] [PubMed] [Google Scholar]
  11. Deuticke B. Transformation and restoration of biconcave shape of human erythrocytes induced by amphiphilic agents and changes of ionic environment. Biochim Biophys Acta. 1968 Dec 10;163(4):494–500. doi: 10.1016/0005-2736(68)90078-3. [DOI] [PubMed] [Google Scholar]
  12. Discher D. E., Mohandas N., Evans E. A. Molecular maps of red cell deformation: hidden elasticity and in situ connectivity. Science. 1994 Nov 11;266(5187):1032–1035. doi: 10.1126/science.7973655. [DOI] [PubMed] [Google Scholar]
  13. Elgsaeter A., Stokke B. T., Mikkelsen A., Branton D. The molecular basis of erythrocyte shape. Science. 1986 Dec 5;234(4781):1217–1223. doi: 10.1126/science.3775380. [DOI] [PubMed] [Google Scholar]
  14. Evans E. A. A new material concept for the red cell membrane. Biophys J. 1973 Sep;13(9):926–940. doi: 10.1016/S0006-3495(73)86035-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  15. Evans E. A. Bending resistance and chemically induced moments in membrane bilayers. Biophys J. 1974 Dec;14(12):923–931. doi: 10.1016/S0006-3495(74)85959-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  16. Evans E. A. New membrane concept applied to the analysis of fluid shear- and micropipette-deformed red blood cells. Biophys J. 1973 Sep;13(9):941–954. doi: 10.1016/S0006-3495(73)86036-9. [DOI] [PMC free article] [PubMed] [Google Scholar]
  17. Ferrell J. E., Jr, Lee K. J., Huestis W. H. Membrane bilayer balance and erythrocyte shape: a quantitative assessment. Biochemistry. 1985 Jun 4;24(12):2849–2857. doi: 10.1021/bi00333a006. [DOI] [PubMed] [Google Scholar]
  18. Fourcade B, Miao L, Rao M, Wortis M, Zia RK. Scaling analysis of narrow necks in curvature models of fluid lipid-bilayer vesicles. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Jun;49(6):5276–5286. doi: 10.1103/physreve.49.5276. [DOI] [PubMed] [Google Scholar]
  19. Fung Y. C., Tong P. Theory of the sphering of red blood cells. Biophys J. 1968 Feb;8(2):175–198. doi: 10.1016/S0006-3495(68)86484-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  20. Gedde M. M., Davis D. K., Huestis W. H. Cytoplasmic pH and human erythrocyte shape. Biophys J. 1997 Mar;72(3):1234–1246. doi: 10.1016/S0006-3495(97)78770-8. [DOI] [PMC free article] [PubMed] [Google Scholar]
  21. Gedde M. M., Huestis W. H. Membrane potential and human erythrocyte shape. Biophys J. 1997 Mar;72(3):1220–1233. doi: 10.1016/S0006-3495(97)78769-1. [DOI] [PMC free article] [PubMed] [Google Scholar]
  22. Gedde M. M., Yang E., Huestis W. H. Resolution of the paradox of red cell shape changes in low and high pH. Biochim Biophys Acta. 1999 Mar 4;1417(2):246–253. doi: 10.1016/s0005-2736(99)00007-3. [DOI] [PubMed] [Google Scholar]
  23. Gedde M. M., Yang E., Huestis W. H. Shape response of human erythrocytes to altered cell pH. Blood. 1995 Aug 15;86(4):1595–1599. [PubMed] [Google Scholar]
  24. Gimsa J. A possible molecular mechanism governing human erythrocyte shape. Biophys J. 1998 Jul;75(1):568–569. doi: 10.1016/S0006-3495(98)77546-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  25. Gimsa J., Ried C. Do band 3 protein conformational changes mediate shape changes of human erythrocytes? Mol Membr Biol. 1995 Jul-Sep;12(3):247–254. doi: 10.3109/09687689509072424. [DOI] [PubMed] [Google Scholar]
  26. Helfrich W. Elastic properties of lipid bilayers: theory and possible experiments. Z Naturforsch C. 1973 Nov-Dec;28(11):693–703. doi: 10.1515/znc-1973-11-1209. [DOI] [PubMed] [Google Scholar]
  27. Hägerstrand H., Danieluk M., Bobrowska-Hägerstrand M., Iglic A., Wróbel A., Isomaa B., Nikinmaa M. 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. Biochim Biophys Acta. 2000 Jun 1;1466(1-2):125–138. doi: 10.1016/s0005-2736(00)00184-x. [DOI] [PubMed] [Google Scholar]
  28. Hénon S., Lenormand G., Richert A., Gallet F. A new determination of the shear modulus of the human erythrocyte membrane using optical tweezers. Biophys J. 1999 Feb;76(2):1145–1151. doi: 10.1016/S0006-3495(99)77279-6. [DOI] [PMC free article] [PubMed] [Google Scholar]
  29. Iglic A. A possible mechanism determining the stability of spiculated red blood cells. J Biomech. 1997 Jan;30(1):35–40. doi: 10.1016/s0021-9290(96)00100-5. [DOI] [PubMed] [Google Scholar]
  30. Iglic A., Kralj-Iglic V., Hägerstrand H. Amphiphile induced echinocyte-spheroechinocyte transformation of red blood cell shape. Eur Biophys J. 1998;27(4):335–339. doi: 10.1007/s002490050140. [DOI] [PubMed] [Google Scholar]
  31. Iglic A., Kralj-Iglic V., Hägerstrand H. Stability of spiculated red blood cells induced by intercalation of amphiphiles in cell membrane. Med Biol Eng Comput. 1998 Mar;36(2):251–255. doi: 10.1007/BF02510754. [DOI] [PubMed] [Google Scholar]
  32. Iglic A., Svetina S., Zeks B. Depletion of membrane skeleton in red blood cell vesicles. Biophys J. 1995 Jul;69(1):274–279. doi: 10.1016/S0006-3495(95)79899-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  33. Isomaa B., Hägerstrand H., Paatero G. Shape transformations induced by amphiphiles in erythrocytes. Biochim Biophys Acta. 1987 May 12;899(1):93–103. doi: 10.1016/0005-2736(87)90243-4. [DOI] [PubMed] [Google Scholar]
  34. Jay D. G. Role of band 3 in homeostasis and cell shape. Cell. 1996 Sep 20;86(6):853–854. doi: 10.1016/s0092-8674(00)80160-9. [DOI] [PubMed] [Google Scholar]
  35. Landman K. A. A continuum model for a red blood cell transformation: sphere to crenated sphere. J Theor Biol. 1984 Feb 7;106(3):329–351. doi: 10.1016/0022-5193(84)90034-1. [DOI] [PubMed] [Google Scholar]
  36. Lange Y., Gough A., Steck T. L. Role of the bilayer in the shape of the isolated erythrocyte membrane. J Membr Biol. 1982;69(2):113–123. doi: 10.1007/BF01872271. [DOI] [PubMed] [Google Scholar]
  37. Lange Y., Slayton J. M. Interaction of cholesterol and lysophosphatidylcholine in determining red cell shape. J Lipid Res. 1982 Nov;23(8):1121–1127. [PubMed] [Google Scholar]
  38. Lee J. C., Wong D. T., Discher D. E. Direct measures of large, anisotropic strains in deformation of the erythrocyte cytoskeleton. Biophys J. 1999 Aug;77(2):853–864. doi: 10.1016/S0006-3495(99)76937-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  39. 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. 2001 Jul;81(1):43–56. doi: 10.1016/S0006-3495(01)75678-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  40. Liu S. C., Derick L. H., Palek J. Visualization of the hexagonal lattice in the erythrocyte membrane skeleton. J Cell Biol. 1987 Mar;104(3):527–536. doi: 10.1083/jcb.104.3.527. [DOI] [PMC free article] [PubMed] [Google Scholar]
  41. Low P. S., Willardson B. M., Mohandas N., Rossi M., Shohet S. Contribution of the band 3-ankyrin interaction to erythrocyte membrane mechanical stability. Blood. 1991 Apr 1;77(7):1581–1586. [PubMed] [Google Scholar]
  42. Miao L, Seifert U, Wortis M, Döbereiner HG. Budding transitions of fluid-bilayer vesicles: The effect of area-difference elasticity. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994 Jun;49(6):5389–5407. doi: 10.1103/physreve.49.5389. [DOI] [PubMed] [Google Scholar]
  43. NAKAO K., WADA T., KAMIYAMA T., NAKAO M., NAGANO K. A direct relationship between adenosine triphosphate-level and in vivo viability of erythrocytes. Nature. 1962 Jun 2;194:877–878. doi: 10.1038/194877a0. [DOI] [PubMed] [Google Scholar]
  44. NAKAO M., NAKAO T., YAMAZOE S. Adenosine triphosphate and maintenance of shape of the human red cells. Nature. 1960 Sep 10;187:945–946. doi: 10.1038/187945a0. [DOI] [PubMed] [Google Scholar]
  45. NAKAO M., NAKAO T., YAMAZOE S., YOSHIKAWA H. Adenosine triphosphate and shape of erythrocytes. J Biochem. 1961 Jun;49:487–492. doi: 10.1093/oxfordjournals.jbchem.a127333. [DOI] [PubMed] [Google Scholar]
  46. Pralle A., Keller P., Florin E. L., Simons K., Hörber J. K. Sphingolipid-cholesterol rafts diffuse as small entities in the plasma membrane of mammalian cells. J Cell Biol. 2000 Mar 6;148(5):997–1008. doi: 10.1083/jcb.148.5.997. [DOI] [PMC free article] [PubMed] [Google Scholar]
  47. Schwarz S., Deuticke B., Haest C. W. Passive transmembrane redistributions of phospholipids as a determinant of erythrocyte shape change. Studies on electroporated cells. Mol Membr Biol. 1999 Jul-Sep;16(3):247–255. doi: 10.1080/096876899294562. [DOI] [PubMed] [Google Scholar]
  48. Schwarz S., Haest C. W., Deuticke B. Extensive electroporation abolishes experimentally induced shape transformations of erythrocytes: a consequence of phospholipid symmetrization? Biochim Biophys Acta. 1999 Oct 15;1421(2):361–379. doi: 10.1016/s0005-2736(99)00138-8. [DOI] [PubMed] [Google Scholar]
  49. Sheetz M. P. DNase-I-dependent dissociation of erythrocyte cytoskeletons. J Cell Biol. 1979 Apr;81(1):266–270. doi: 10.1083/jcb.81.1.266. [DOI] [PMC free article] [PubMed] [Google Scholar]
  50. Sheetz M. P., Singer S. J. Biological membranes as bilayer couples. A molecular mechanism of drug-erythrocyte interactions. Proc Natl Acad Sci U S A. 1974 Nov;71(11):4457–4461. doi: 10.1073/pnas.71.11.4457. [DOI] [PMC free article] [PubMed] [Google Scholar]
  51. Simons K., Toomre D. Lipid rafts and signal transduction. Nat Rev Mol Cell Biol. 2000 Oct;1(1):31–39. doi: 10.1038/35036052. [DOI] [PubMed] [Google Scholar]
  52. Smith J. E., Mohandas N., Shohet S. B. Interaction of amphipathic drugs with erythrocytes from various species. Am J Vet Res. 1982 Jun;43(6):1041–1048. [PubMed] [Google Scholar]
  53. Stokke B. T., Mikkelsen A., Elgsaeter A. Spectrin, human erythrocyte shapes, and mechanochemical properties. Biophys J. 1986 Jan;49(1):319–327. doi: 10.1016/S0006-3495(86)83644-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  54. Strey H., Peterson M., Sackmann E. Measurement of erythrocyte membrane elasticity by flicker eigenmode decomposition. Biophys J. 1995 Aug;69(2):478–488. doi: 10.1016/S0006-3495(95)79921-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  55. Svoboda K., Schmidt C. F., Branton D., Block S. M. Conformation and elasticity of the isolated red blood cell membrane skeleton. Biophys J. 1992 Sep;63(3):784–793. doi: 10.1016/S0006-3495(92)81644-2. [DOI] [PMC free article] [PubMed] [Google Scholar]
  56. Waugh R. E., Bauserman R. G. Physical measurements of bilayer-skeletal separation forces. Ann Biomed Eng. 1995 May-Jun;23(3):308–321. doi: 10.1007/BF02584431. [DOI] [PubMed] [Google Scholar]
  57. Waugh R. E. Elastic energy of curvature-driven bump formation on red blood cell membrane. Biophys J. 1996 Feb;70(2):1027–1035. doi: 10.1016/S0006-3495(96)79648-0. [DOI] [PMC free article] [PubMed] [Google Scholar]
  58. Waugh R., Evans E. A. Thermoelasticity of red blood cell membrane. Biophys J. 1979 Apr;26(1):115–131. doi: 10.1016/S0006-3495(79)85239-X. [DOI] [PMC free article] [PubMed] [Google Scholar]
  59. Weed R. I., Chailley B. Calcium-pH interactions in the production of shape change in erythrocytes. Nouv Rev Fr Hematol. 1972 Nov-Dec;12(6):775–788. [PubMed] [Google Scholar]
  60. Wong P. A basis of echinocytosis and stomatocytosis in the disc-sphere transformations of the erythrocyte. J Theor Biol. 1999 Feb 7;196(3):343–361. doi: 10.1006/jtbi.1998.0845. [DOI] [PubMed] [Google Scholar]
  61. Wong P. Mechanism of control of erythrocyte shape: a possible relationship to band 3. J Theor Biol. 1994 Nov 21;171(2):197–205. doi: 10.1006/jtbi.1994.1223. [DOI] [PubMed] [Google Scholar]
  62. Zarda P. R., Chien S., Skalak R. Elastic deformations of red blood cells. J Biomech. 1977;10(4):211–221. doi: 10.1016/0021-9290(77)90044-6. [DOI] [PubMed] [Google Scholar]

Articles from Biophysical Journal are provided here courtesy of The Biophysical Society

RESOURCES