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Nonlinear Osmotic Properties of the Cell Nucleus

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Abstract

In the absence of active volume regulation processes, cell volume is inversely proportional to osmolarity, as predicted by the Boyle Van’t Hoff relation. In this study, we tested the hypothesis that nuclear volume has a similar relationship with extracellular osmolarity in articular chondrocytes, cells that are exposed to changes in the osmotic environment in vivo. Furthermore, we explored the mechanism of the relationships between osmolarity and nuclear size and shape. Nuclear size was quantified using two independent techniques, confocal laser scanning microscopy and angle-resolved low coherence interferometry. Nuclear volume was osmotically sensitive but this relationship was not linear, showing a decline in the osmotic sensitivity in the hypo-osmotic range. Nuclear shape was also influenced by extracellular osmolarity, becoming smoother as the osmolarity decreased. The osmotically induced changes in nuclear size paralleled the changes in nuclear shape, suggesting that shape and volume are interdependent. The osmotic sensitivity of shape and volume persisted after disruption of the actin cytoskeleton. Isolated nuclei contracted in response to physiologic changes in macromolecule concentration but not in response to physiologic changes in ion concentration, suggesting solute size has an important influence on the osmotic pressurization of the nucleus. This finding in turn implies that the diffusion barrier that causes osmotic effects is not a semi-permeable membrane, but rather due to size constraints that prevent large solute molecules from entering small spaces in the nucleus. As nuclear morphology has been associated previously with cell phenotype, these findings may provide new insight into the role of mechanical and osmotic signals in regulating cell physiology.

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References

  1. Albiez H., M. Cremer, C. Tiberi, L. Vecchio, L. Schermelleh, S. Dittrich, K. Kupper, B. Joffe, T. Thormeyer, J. von Hase, S. Yang, K. Rohr, H. Leonhardt, I. Solovei, C. Cremer, S. Fakan, T. Cremer 2006 Chromatin domains and the interchromatin compartment form structurally defined and functionally interacting nuclear networks. Chromosome Res. 14(7), 707–733. doi:10.1007/s10577-006-1086-x

    Article  PubMed  CAS  Google Scholar 

  2. Albro M. B., N. O. Chahine, M. Caligaris, V. I. Wei, M. Likhitpanichkul, K. W. Ng, C. T. Hung, G. A. Ateshian 2007 Osmotic loading of spherical gels: a biomimetic study of hindered transport in the cell protoplasm. J. Biomech. Eng. 129(4), 503–510. doi:10.1115/1.2746371

    Article  PubMed  Google Scholar 

  3. Alexopoulos L. G., G. R. Erickson, F. Guilak 2002 A method for quantifying cell size from differential interference contrast images: validation and application to osmotically stressed chondrocytes. J. Microsc. 205(Pt 2), 125–135. doi:10.1046/j.0022-2720.2001.00976.x

    Article  PubMed  CAS  Google Scholar 

  4. Ateshian G. A., M. Likhitpanichicul, C. T. Hung 2006 A mixture theory analysis for passive transport in osmotic loading of cells. J. Biomech. 39(3), 464–475

    PubMed  Google Scholar 

  5. Backman V., M. B. Wallace, L. T. Perelman, J. T. Arendt, R. Gurjar, M. G. Muller, Q. Zhang, G. Zonios, E. Kline, J. A. McGilligan, S. Shapshay, T. Valdez, K. Badizadegan, J. M. Crawford, M. Fitzmaurice, S. Kabani, H. S. Levin, M. Seiler, R. R. Dasari, I. Itzkan, J. Van Dam, M. S. Feld 2000 Detection of preinvasive cancer cells. Nature 406(6791), 35–36. doi:10.1038/35017638

    Article  PubMed  CAS  Google Scholar 

  6. Borghetti P., L. Della Salda, E. De Angelis, M. C. Maltarello, P. G. Petronini, E. Cabassi, P. S. Marcato, N. M. Maraldi, A. F. Borghetti 1995 Adaptive cellular response to osmotic stress in pig articular chondrocytes. Tissue Cell 27(2), 173–183. doi:10.1016/S0040-8166(95)80020-4

    Article  PubMed  CAS  Google Scholar 

  7. Broers J. L., B. M. Machiels, H. J. Kuijpers, F. Smedts, R. van den Kieboom, Y. Raymond, F. C. Ramaekers 1997 A- and B-type lamins are differentially expressed in normal human tissues. Histochem. Cell Biol. 107(6), 505–517. doi:10.1007/s004180050138

    Article  PubMed  CAS  Google Scholar 

  8. Broers J. L., E. A. Peeters, H. J. Kuijpers, J. Endert, C. V. Bouten, C. W. Oomens, F. P. Baaijens, F. C. Ramaekers 2004 Decreased mechanical stiffness in LMNA-/- cells is caused by defective nucleo-cytoskeletal integrity: implications for the development of laminopathies. Hum. Mol. Genet. 13(21), 2567–2580. doi:10.1093/hmg/ddh295

    Article  PubMed  CAS  Google Scholar 

  9. Bruce A., A. Johnson J. Lewis M. Raff K. Roberts P. Walter (2002) Molecular Biology of the Cell. 4 ed. Garland Science, New York

    Google Scholar 

  10. Buschmann M. D., E. B. Hunziker, Y. J. Kim, A. J. Grodzinsky 1996 Altered aggrecan synthesis correlates with cell and nucleus structure in statically compressed cartilage. J. Cell Sci. 109, 499–508

    PubMed  CAS  Google Scholar 

  11. Bush P. G., A. C. Hall 2001 The osmotic sensitivity of isolated and in situ bovine articular chondrocytes. J. Orthop. Res. 19(5), 768–778. doi:10.1016/S0736-0266(01)00013-4

    Article  PubMed  CAS  Google Scholar 

  12. Caille N., O. Thoumine, Y. Tardy, J. J. Meister 2002 Contribution of the nucleus to the mechanical properties of endothelial cells. J. Biomech. 35(2), 177–187. doi:10.1016/S0021-9290(01)00201-9

    Article  PubMed  Google Scholar 

  13. Chalut, K., S. Chen, J. Finan, M. Giacomelli, F. Guilak, K. Leong, and A. Wax. Label-free, high-throughput measurements of dynamic changes in cell nuclei using angle-resolved low coherence interferometry. Biophys. J. 94(12):4948–4956, 2008. doi:10.1529/biophysj.107.124107

    Google Scholar 

  14. Chalut K. J., L. A. Kresty, J. W. Pyhtila, R. Nines, M. Baird, V. E. Steele, A. Wax 2007 In situ assessment of intraepithelial neoplasia in hamster trachea epithelium using angle-resolved low-coherence interferometry. Cancer Epidemiol. Biomarkers Prev. 16(2), 223–227. doi:10.1158/1055-9965.EPI-06-0418

    Article  PubMed  Google Scholar 

  15. Chao P. H., A. C. West, C. T. Hung 2006 Chondrocyte intracellular calcium, cytoskeletal organization, and gene expression responses to dynamic osmotic loading. Am. J. Physiol. Cell. Physiol. 291(4), C718–C725. doi:10.1152/ajpcell.00127.2005

    Article  PubMed  CAS  Google Scholar 

  16. Chen C. S., D. E. Ingber 1999 Tensegrity and mechanoregulation: from skeleton to cytoskeleton. Osteoarthr. Cartil. 7(1), 81–94. doi:10.1053/joca.1998.0164

    Article  PubMed  CAS  Google Scholar 

  17. Chen K. D., Y. S. Li, M. Kim, S. Li, S. Yuan, S. Chien, J. Y. J. Shyy 1999 Mechanotransduction in response to shear stress—roles of receptor tyrosine kinases, integrins, and Shc. J. Biol. Chem. 274(26), 18393–18400. doi:10.1074/jbc.274.26.18393

    Article  PubMed  CAS  Google Scholar 

  18. Constantinescu D., H. L. Gray, P. J. Sammak, G. P. Schatten, A. B. Csoka 2006 Lamin A/C expression is a marker of mouse and human embryonic stem cell differentiation. Stem Cells 24(1), 177–185. doi:10.1634/stemcells.2004-0159

    Article  PubMed  CAS  Google Scholar 

  19. Correa-Meyer E., L. Pesce, C. Guerrero, J. I. Sznajder 2002 Cyclic stretch activates ERK1/2 via G proteins and EGFR in alveolar epithelial cells. Am. J. Physiol. Lung Cell. Mol. Physiol. 282(5), L883–L891. doi:10.1152/ajplung.00203.2001

    PubMed  CAS  Google Scholar 

  20. Dahl K. N., A. J. Engler, J. D. Pajerowski, D. E. Discher 2005 Power-law rheology of isolated nuclei with deformation mapping of nuclear substructures. Biophys. J. 89(4), 2855–2864. doi:10.1529/biophysj.105.062554

    Article  PubMed  CAS  Google Scholar 

  21. Dahl K. N., P. Scaffidi, M. F. Islam, A. G. Yodh, K. L. Wilson, T. Misteli 2006 Distinct structural and mechanical properties of the nuclear lamina in Hutchinson-Gilford progeria syndrome. Proc. Natl. Acad. Sci. USA 103(27), 10271–10276. doi:10.1073/pnas.0601058103

    Article  PubMed  CAS  Google Scholar 

  22. de Freitas R. C., K. R. Diller, J. R. Lakey, R. V. Rajotte 1997 Osmotic behavior and transport properties of human islets in a dimethyl sulfoxide solution. Cryobiology 35(3), 230–239. doi:10.1006/cryo.1997.2045

    Article  PubMed  Google Scholar 

  23. de Vries A. H., B. E. Krenn, R. van Driel, V. Subramaniam, J. S. Kanger 2007 Direct observation of nanomechanical properties of chromatin in living cells. Nano. Lett. 7(5), 1424–1427. doi:10.1021/nl070603+

    Article  PubMed  CAS  Google Scholar 

  24. Dmitrieva N. I., Q. Cai, M. B. Burg 2004 Cells adapted to high NaCl have many DNA breaks and impaired DNA repair both in cell culture and in vivo. Proc. Natl. Acad. Sci. USA 101(8), 2317–2322. doi:10.1073/pnas.0308463100

    Article  PubMed  CAS  Google Scholar 

  25. Dong C., R. Skalak, K. L. Sung 1991 Cytoplasmic rheology of passive neutrophils. Biorheology 28(6), 557–567

    PubMed  CAS  Google Scholar 

  26. Erickson G. R., L. G. Alexopoulos, F. Guilak 2001 Hyper-osmotic stress induces volume change and calcium transients in chondrocytes by transmembrane, phospholipid, and G-protein pathways. J. Biomech. 34(12), 1527–1535. doi:10.1016/S0021-9290(01)00156-7

    Article  PubMed  CAS  Google Scholar 

  27. Erickson G. R., D. L. Northrup, F. Guilak 2003 Hypo-osmotic stress induces calcium-dependent actin reorganization in articular chondrocytes. Osteoarthr. Cartil. 11(3), 187–197. doi:10.1053/S1063-4584(02)00347-3

    Article  PubMed  CAS  Google Scholar 

  28. Feldherr C. M., D. Akin 1993 Regulation of nuclear transport in proliferating and quiescent cells. Exp. Cell. Res. 205(1), 179–186. doi:10.1006/excr.1993.1073

    Article  PubMed  CAS  Google Scholar 

  29. Gieni, R. S., and M. J. Hendzel. Mechanotransduction from the ECM to the genome: are the pieces now in place? J. Cell. Biochem. 104(6):1964–1987, 2008

    Google Scholar 

  30. Goldman R. D., Y. Gruenbaum, R. D. Moir, D. K. Shumaker, T. P. Spann 2002 Nuclear lamins: building blocks of nuclear architecture. Genes Dev. 16(5), 533–547. doi:10.1101/gad.960502

    Article  PubMed  CAS  Google Scholar 

  31. Goldman R. D., D. K. Shumaker, M. R. Erdos, M. Eriksson, A. E. Goldman, L. B. Gordon, Y. Gruenbaum, S. Khuon, M. Mendez, R. Varga, F. S. Collins 2004 Accumulation of mutant lamin A causes progressive changes in nuclear architecture in Hutchinson-Gilford progeria syndrome. Proc. Natl. Acad. Sci. USA 101(24), 8963–8968. doi:10.1073/pnas.0402943101

    Article  PubMed  CAS  Google Scholar 

  32. Guharay F., F. Sachs 1984 Stretch-activated single ion channel currents in tissue-cultured embryonic chick skeletal muscle. J. Physiol. 352, 685–701

    PubMed  CAS  Google Scholar 

  33. Guilak F. 1995 Compression-induced changes in the shape and volume of the chondrocyte nucleus. J. Biomech. 28(12), 1529–1541. doi:10.1016/0021-9290(95)00100-X

    Article  PubMed  CAS  Google Scholar 

  34. Guilak F., G. R. Erickson, H. P. Ting-Beall 2002 The effects of osmotic stress on the viscoelastic and physical properties of articular chondrocytes. Biophys. J. 82(2), 720–727

    Article  PubMed  CAS  Google Scholar 

  35. Guilak F., J. R. Tedrow, R. Burgkart 2000 Viscoelastic properties of the cell nucleus. Biochem. Biophys. Res. Commun. 269(3), 781–786. doi:10.1006/bbrc.2000.2360

    Article  PubMed  CAS  Google Scholar 

  36. Hamill O. P., B. Martinac 2001 Molecular basis of mechanotransduction in living cells. Physiol. Rev. 81(2), 685–740

    PubMed  CAS  Google Scholar 

  37. Hu S., J. Chen, J. P. Butler, N. Wang 2005 Prestress mediates force propagation into the nucleus. Biochem. Biophys. Res. Commun. 329(2), 423–428. doi:10.1016/j.bbrc.2005.02.026

    Article  PubMed  CAS  Google Scholar 

  38. Huang D., E. A. Swanson, C. P. Lin, J. S. Schuman, W. G. Stinson, W. Chang, M. R. Hee, T. Flotte, K. Gregory, C. A. Puliafito, J. G. Fujimoto 1991 Optical coherence tomography. Science 254(5035), 1178–1181. doi:10.1126/science.1957169

    Article  PubMed  CAS  Google Scholar 

  39. Hung C. T., M. A. LeRoux, G. D. Palmer, P. H. G. Chao, S. Lo, W. B. Valhmu 2003 Disparate aggrecan gene expression in chondrocytes subjected to hypotonic and hypertonic loading in 2D and 3D culture. Biorheology 40(1–3), 61–72

    PubMed  CAS  Google Scholar 

  40. Huyghe J. M., J. D. Janssen 1997 Quadriphasic mechanics of swelling incompressible porous media. Int. J. Eng. Sci. 35(8), 793–802. doi:10.1016/S0020-7225(96)00119-X

    Article  Google Scholar 

  41. Ji J. Y., R. T. Lee, L. Vergnes, L. G. Fong, C. L. Stewart, K. Reue, S. G. Young, Q. Zhang, C. M. Shanahan, J. Lammerding 2007 Cell nuclei spin in the absence of lamin b1. J. Biol. Chem. 282(27), 20015–20026. doi:10.1074/jbc.M611094200

    Article  PubMed  CAS  Google Scholar 

  42. Kerr J. F., A. H. Wyllie, A. R. Currie 1972 Apoptosis: a basic biological phenomenon with wide-ranging implications in tissue kinetics. Br. J. Cancer 26(4), 239–257

    PubMed  CAS  Google Scholar 

  43. Knight M. M., J. V. D. B. Bravenboer, D. A. Lee, G. J. V. M. van Osch, H. Weinans, D. L. Bader 2002 Cell and nucleus deformation in compressed chondrocyte-alginate constructs: temporal changes and calculation of cell modulus. BBA-Gen Subjects 1570(1), 1–8. doi:10.1016/S0304-4165(02)00144-7

    Article  CAS  Google Scholar 

  44. Lai W. M., J. S. Hou, V. C. Mow 1991 A triphasic theory for the swelling and deformation behaviors of articular cartilage. J. Biomech. Eng. 113(3), 245–258. doi:10.1115/1.2894880

    Article  PubMed  CAS  Google Scholar 

  45. Lammerding J., L. G. Fong, J. Y. Ji, K. Reue, C. L. Stewart, S. G. Young, R. T. Lee 2006 Lamins A and C but not lamin B1 regulate nuclear mechanics. J. Biol. Chem. 281(35), 25768–25780. doi:10.1074/jbc.M513511200

    Article  PubMed  CAS  Google Scholar 

  46. Lansman J. B., T. J. Hallam, T. J. Rink 1987 Single stretch-activated ion channels in vascular endothelial cells as mechanotransducers? Nature. 325(6107), 811–813. doi:10.1038/325811a0

    Article  PubMed  CAS  Google Scholar 

  47. Maniotis A. J., C. S. Chen, D. E. Ingber 1997 Demonstration of mechanical connections between integrins, cytoskeletal filaments, and nucleoplasm that stabilize nuclear structure. Proc. Natl. Acad. Sci. USA 94(3), 849–854. doi:10.1073/pnas.94.3.849

    Article  PubMed  CAS  Google Scholar 

  48. Maroudas A., C. Bannon 1981 Measurement of swelling pressure in cartilage and comparison with the osmotic pressure of constituent proteoglycans. Biorheology 18(3–6), 619–632

    PubMed  CAS  Google Scholar 

  49. Maroudas A. I. 1976 Balance between swelling pressure and collagen tension in normal and degenerate cartilage. Nature 260(5554), 808–809. doi:10.1038/260808a0

    Article  PubMed  CAS  Google Scholar 

  50. Misteli T. 2004 Spatial positioning; a new dimension in genome function. Cell 119(2), 153–156. doi:10.1016/j.cell.2004.09.035

    Article  PubMed  CAS  Google Scholar 

  51. Misteli T. 2007 Beyond the sequence: cellular organization of genome function. Cell 128(4), 787–800. doi:10.1016/j.cell.2007.01.028

    Article  PubMed  CAS  Google Scholar 

  52. Mow V. C., G. A. Ateshian, W. M. Lai, W. Y. Gu 1998 Effects of fixed charges on the stress-relaxation behavior of hydrated soft tissues in a confined compression problem. Int. J. Solids Struct. 35(34–35), 4945–4962. doi:10.1016/S0020-7683(98)00103-6

    Article  Google Scholar 

  53. Mow V. C., S. C. Kuei, W. M. Lai, C. G. Armstrong 1980 Biphasic creep and stress relaxation of articular cartilage in compression? Theory and experiments. J. Biomech. Eng. 102(1), 73–84

    PubMed  CAS  Google Scholar 

  54. Mow V. C., C. C. Wang, C. T. Hung 1999 The extracellular matrix, interstitial fluid and ions as a mechanical signal transducer in articular cartilage. Osteoarthr. Cartil. 7(1), 41–58. doi:10.1053/joca.1998.0161

    Article  PubMed  CAS  Google Scholar 

  55. Nobel P. S. (1969) Boyle-Vant Hoff relation. J. Theor. Biol. 23(3):375–379

    Article  PubMed  CAS  Google Scholar 

  56. Oswald E. S., P. G. Chao, J. C. Bulinski, G. A. Ateshian, C. T. Hung 2006 Chondrocyte nuclear response to osmotic loading. Conf. Proc. IEEE Eng. Med. Biol. Soc. 1, 3659–3661

    Article  PubMed  Google Scholar 

  57. Paine P. L., L. C. Moore, S. B. Horowitz 1975 Nuclear envelope permeability. Nature 254(5496), 109–114. doi:10.1038/254109a0

    Article  PubMed  CAS  Google Scholar 

  58. Pajerowski J. D., K. N. Dahl, F. L. Zhong, P. J. Sammak, D. E. Discher 2007 Physical plasticity of the nucleus in stem cell differentiation. Proc. Natl. Acad. Sci. USA 104(40), 15619–15624. doi:10.1073/pnas.0702576104

    Article  PubMed  CAS  Google Scholar 

  59. Pyhtila J. W., A. Wax 2004 Rapid, depth-resolved light scattering measurements using Fourier domain, angle-resolved low coherence interferometry. Opt. Express 12(25), 6178–6183. doi:10.1364/OPEX.12.006178

    Article  PubMed  Google Scholar 

  60. Reinehr R., D. Haussinger 2006 Hyperosmotic activation of the CD95 death receptor system. Acta Physiol. (Oxf) 187(1–2), 199–203. doi:10.1111/j.1748-1716.2006.01541.x

    Article  CAS  Google Scholar 

  61. Richter K., M. Nessling, P. Lichter 2007 Experimental evidence for the influence of molecular crowding on nuclear architecture. J. Cell Sci. 120(Pt 9), 1673–1680. doi:10.1242/jcs.03440

    Article  PubMed  CAS  Google Scholar 

  62. Rober R. A., K. Weber, M. Osborn 1989 Differential timing of nuclear lamin A/C expression in the various organs of the mouse embryo and the young animal: a developmental study. Development 105(2), 365–378

    PubMed  CAS  Google Scholar 

  63. Rowat A. C., J. Lammerding, J. H. Ipsen 2006 Mechanical properties of the cell nucleus and the effect of emerin deficiency. Biophys. J. 91(12), 4649–4664. doi:10.1529/biophysj.106.086454

    Article  PubMed  CAS  Google Scholar 

  64. Sackin H. 1995 Mechanosensitive channels. Annu. Rev. Physiol. 57, 333–353

    PubMed  CAS  Google Scholar 

  65. Scaffidi P., T. Misteli 2006 Lamin A-dependent nuclear defects in human aging. Science 312(5776), 1059–1063. doi:10.1126/science.1127168

    Article  PubMed  CAS  Google Scholar 

  66. Sun D. D., X. E. Guo, M. Likhitpanichkul, W. M. Lai, V. C. Mow 2004 The influence of the fixed negative charges on mechanical and electrical behaviors of articular cartilage under unconfined compression. J. Biomech. Eng. Trans. ASME 126(1), 6–16. doi:10.1115/1.1644562

    Article  CAS  Google Scholar 

  67. Thoma F., T. Koller 1977 Influence of histone-H1 on chromatin structure. Cell 12(1), 101–107. doi:10.1016/0092-8674(77)90188-X

    Article  PubMed  CAS  Google Scholar 

  68. Thoma F., T. Koller 1981 Unravelled nucleosomes, nucleosome beads and higher-order structures of chromatin—influence of non-histone components and histone H-1. J. Mol. Biol. 149(4), 709–733. doi:10.1016/0022-2836(81)90354-5

    Article  PubMed  CAS  Google Scholar 

  69. Thoma F., T. Koller, A. Klug 1979 Involvement of histone H1 in the organization of the nucleosome and of the salt-dependent superstructures of chromatin. J. Cell. Biol. 83(2 Pt 1), 403–427. doi:10.1083/jcb.83.2.403

    Article  PubMed  CAS  Google Scholar 

  70. Ting-Beall H. P., D. Needham, R. M. Hochmuth 1993 Volume and osmotic properties of human neutrophils. Blood 81(10), 2774–2780

    PubMed  CAS  Google Scholar 

  71. Urban J. P., A. C. Hall, K. A. Gehl 1993 Regulation of matrix synthesis rates by the ionic and osmotic environment of articular chondrocytes. J. Cell Physiol. 154(2), 262–270. doi:10.1002/jcp.1041540208

    Article  PubMed  CAS  Google Scholar 

  72. Urban J. P., A. Maroudas, M. T. Bayliss, J. Dillon 1979 Swelling pressures of proteoglycans at the concentrations found in cartilaginous tissues. Biorheology 16(6), 447–464

    PubMed  CAS  Google Scholar 

  73. Vaziri A., M. R. Mofrad 2007 Mechanics and deformation of the nucleus in micropipette aspiration experiment. J. Biomech. 40(9), 2053–2062. doi:10.1016/j.jbiomech.2006.09.023

    Article  PubMed  Google Scholar 

  74. Wang N., J. P. Butler, D. E. Ingber 1993 Mechanotransduction across the cell surface and through the cytoskeleton. Science 260(5111), 1124–1127. doi:10.1126/science.7684161

    Article  PubMed  CAS  Google Scholar 

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Acknowledgments

Supported by NIH Grants AR50245, AR48182, AG15768, and AR48852. We thank Dr. Mansoor Haider for many important discussions.

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Correspondence to Farshid Guilak.

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Finan, J.D., Chalut, K.J., Wax, A. et al. Nonlinear Osmotic Properties of the Cell Nucleus. Ann Biomed Eng 37, 477–491 (2009). https://doi.org/10.1007/s10439-008-9618-5

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