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. 1998 May;74(5):2227–2234. doi: 10.1016/S0006-3495(98)77932-9

Viscoelastic properties of living embryonic tissues: a quantitative study.

G Forgacs 1, R A Foty 1, Y Shafrir 1, M S Steinberg 1
PMCID: PMC1299566  PMID: 9591650

Abstract

A number of properties of certain living embryonic tissues can be explained by considering them as liquids. Tissue fragments left in a shaker bath round up to form spherical aggregates, as do liquid drops. When cells comprising two distinct embryonic tissues are mixed, typically a nucleation-like process takes place, and one tissue sorts out from the other. The equilibrium configurations at the end of such sorting out phenomena have been interpreted in terms of tissue surface tensions arising from the adhesive interactions between individual cells. In the present study we go beyond these equilibrium properties and study the viscoelastic behavior of a number of living embryonic tissues. Using a specifically designed apparatus, spherical cell aggregates are mechanically compressed and their viscoelastic response is followed. A generalized Kelvin model of viscoelasticity accurately describes the measured relaxation curves for each of the four tissues studied. Quantitative results are obtained for the characteristic relaxation times and elastic and viscous parameters. Our analysis demonstrates that the cell aggregates studied here, when subjected to mechanical deformations, relax as elastic materials on short time scales and as viscous liquids on long time scales.

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Selected References

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  1. Engelhardt H., Sackmann E. On the measurement of shear elastic moduli and viscosities of erythrocyte plasma membranes by transient deformation in high frequency electric fields. Biophys J. 1988 Sep;54(3):495–508. doi: 10.1016/S0006-3495(88)82982-5. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Folkman J., Moscona A. Role of cell shape in growth control. Nature. 1978 Jun 1;273(5661):345–349. doi: 10.1038/273345a0. [DOI] [PubMed] [Google Scholar]
  3. Foty R. A., Pfleger C. M., Forgacs G., Steinberg M. S. Surface tensions of embryonic tissues predict their mutual envelopment behavior. Development. 1996 May;122(5):1611–1620. doi: 10.1242/dev.122.5.1611. [DOI] [PubMed] [Google Scholar]
  4. Foty RA, Forgacs G, Pfleger CM, Steinberg MS. Liquid properties of embryonic tissues: Measurement of interfacial tensions. Phys Rev Lett. 1994 Apr 4;72(14):2298–2301. doi: 10.1103/PhysRevLett.72.2298. [DOI] [PubMed] [Google Scholar]
  5. Glazier JA, Graner F. Simulation of the differential adhesion driven rearrangement of biological cells. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1993 Mar;47(3):2128–2154. doi: 10.1103/physreve.47.2128. [DOI] [PubMed] [Google Scholar]
  6. Gordon R., Goel N. S., Steinberg M. S., Wiseman L. L. A rheological mechanism sufficient to explain the kinetics of cell sorting. J Theor Biol. 1972 Oct;37(1):43–73. doi: 10.1016/0022-5193(72)90114-2. [DOI] [PubMed] [Google Scholar]
  7. Heintzelman K. F., Phillips H. M., Davis G. S. Liquid-tissue behavior and differential cohesiveness during chick limb budding. J Embryol Exp Morphol. 1978 Oct;47:1–15. [PubMed] [Google Scholar]
  8. Hiramoto Y. Mechanical properties of the protoplasm of the sea urchin egg. I. Unfertilized egg. Exp Cell Res. 1969 Aug;56(2):201–208. doi: 10.1016/0014-4827(69)90003-2. [DOI] [PubMed] [Google Scholar]
  9. Hochmuth R. M., Ting-Beall H. P., Beaty B. B., Needham D., Tran-Son-Tay R. Viscosity of passive human neutrophils undergoing small deformations. Biophys J. 1993 May;64(5):1596–1601. doi: 10.1016/S0006-3495(93)81530-3. [DOI] [PMC free article] [PubMed] [Google Scholar]
  10. Janmey P. A. Mechanical properties of cytoskeletal polymers. Curr Opin Cell Biol. 1991 Feb;3(1):4–11. doi: 10.1016/0955-0674(91)90159-v. [DOI] [PubMed] [Google Scholar]
  11. Jay P. Y., Pasternak C., Elson E. L. Studies of mechanical aspects of amoeboid locomotion. Blood Cells. 1993;19(2):375–388. [PubMed] [Google Scholar]
  12. Luby-Phelps K., Taylor D. L., Lanni F. Probing the structure of cytoplasm. J Cell Biol. 1986 Jun;102(6):2015–2022. doi: 10.1083/jcb.102.6.2015. [DOI] [PMC free article] [PubMed] [Google Scholar]
  13. Magnani J. L., Thomas W. A., Steinberg M. S. Two distinct adhesion mechanisms in embryonic neural retina cells. I. A kinetic analysis. Dev Biol. 1981 Jan 15;81(1):96–105. doi: 10.1016/0012-1606(81)90351-1. [DOI] [PubMed] [Google Scholar]
  14. Mombach JC, Glazier JA, Raphael RC, Zajac M. Quantitative comparison between differential adhesion models and cell sorting in the presence and absence of fluctuations. Phys Rev Lett. 1995 Sep 11;75(11):2244–2247. doi: 10.1103/PhysRevLett.75.2244. [DOI] [PubMed] [Google Scholar]
  15. Moyer W. A., Steinberg M. S. Do rates of intercellular adhesion measure the cell affinities reflected in cell-sorting and tissue-spreading configurations? Dev Biol. 1976 Sep;52(2):246–262. doi: 10.1016/0012-1606(76)90244-x. [DOI] [PubMed] [Google Scholar]
  16. Phillips H. M., Steinberg M. S. Embryonic tissues as elasticoviscous liquids. I. Rapid and slow shape changes in centrifuged cell aggregates. J Cell Sci. 1978 Apr;30:1–20. doi: 10.1242/jcs.30.1.1. [DOI] [PubMed] [Google Scholar]
  17. Phillips H. M., Steinberg M. S., Lipton B. H. Embryonic tissues as elasticoviscous liquids. II. Direct evidence for cell slippage in centrifuged aggregates. Dev Biol. 1977 Sep;59(2):124–134. doi: 10.1016/0012-1606(77)90247-0. [DOI] [PubMed] [Google Scholar]
  18. Ragsdale G. K., Phelps J., Luby-Phelps K. Viscoelastic response of fibroblasts to tension transmitted through adherens junctions. Biophys J. 1997 Nov;73(5):2798–2808. doi: 10.1016/S0006-3495(97)78309-7. [DOI] [PMC free article] [PubMed] [Google Scholar]
  19. STEINBERG M. S. Reconstruction of tissues by dissociated cells. Some morphogenetic tissue movements and the sorting out of embryonic cells may have a common explanation. Science. 1963 Aug 2;141(3579):401–408. doi: 10.1126/science.141.3579.401. [DOI] [PubMed] [Google Scholar]
  20. Steinberg M. S. Does differential adhesion govern self-assembly processes in histogenesis? Equilibrium configurations and the emergence of a hierarchy among populations of embryonic cells. J Exp Zool. 1970 Apr;173(4):395–433. doi: 10.1002/jez.1401730406. [DOI] [PubMed] [Google Scholar]
  21. Takano Y., Sakanishi A. Effects of viscoelasticity of cytoplasm on the complex viscosity of red blood cell suspensions. Biorheology. 1988;25(1-2):123–128. doi: 10.3233/bir-1988-251-219. [DOI] [PubMed] [Google Scholar]
  22. Tempel M, Isenberg G, Sackmann E. Temperature-induced sol-gel transition and microgel formation in alpha -actinin cross-linked actin networks: A rheological study. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1996 Aug;54(2):1802–1810. doi: 10.1103/physreve.54.1802. [DOI] [PubMed] [Google Scholar]
  23. Valberg P. A., Albertini D. F. Cytoplasmic motions, rheology, and structure probed by a novel magnetic particle method. J Cell Biol. 1985 Jul;101(1):130–140. doi: 10.1083/jcb.101.1.130. [DOI] [PMC free article] [PubMed] [Google Scholar]
  24. Zaner K. S., Valberg P. A. Viscoelasticity of F-actin measured with magnetic microparticles. J Cell Biol. 1989 Nov;109(5):2233–2243. doi: 10.1083/jcb.109.5.2233. [DOI] [PMC free article] [PubMed] [Google Scholar]

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