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In silico approach to quantify nucleus self-deformation on micropillared substrates

  • Solenne Mondésert-Deveraux
  • Denis Aubry
  • Rachele AllenaEmail author
Original Paper
  • 54 Downloads

Abstract

Considering the major role of confined cell migration in biological processes and diseases, such as embryogenesis or metastatic cancer, it has become increasingly important to design relevant experimental set-ups for in vitro studies. Microfluidic devices have recently presented great opportunities in their respect since they offer the possibility to study all the steps from a suspended to a spread, and eventually crawling cell or a cell with highly deformed nucleus. Here, we focus on the nucleus self-deformation over a micropillared substrate. Actin networks have been observed at two locations in this set-up: above the nucleus, forming the perinuclear actin cap (PAC), and below the nucleus, surrounding the pillars. We can then wonder which of these contractile networks is responsible for nuclear deformation. The cytoplasm and the nucleus are represented through the superposition of a viscous and a hyperelastic material and follow a series of processes. First, the suspended cell settles on the pillars due to gravity. Second, an adhesive spreading force comes into play, and then, active deformations contract one or both actin domains and consequently the nucleus. Our model is first tested on a flat substrate to validate its global behaviour before being confronted to a micropillared substrate. Overall, the nucleus appears to be mostly pulled towards the pillars, while the mechanical action of the PAC is weak. Eventually, we test the influence of gravity and prove that the gravitational force does not play a role in the final deformation of the nucleus.

Keywords

Mechanical forces Nucleus self-deformation Micropillared substrate In silico model 

Notes

Acknowledgements

This work was funded by a PhD fellowship of the French Government. We thank the editor of the Biomechanics and Modeling in Mechanobiology and the reviewers for their very interesting comments and suggestions.

Supplementary material

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Supplementary material 1 (GIF 302 kb)
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Supplementary material 2 (GIF 295 kb)
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Supplementary material 3 (GIF 311 kb)

References

  1. Abercrombie M, Heaysman JEM, Pegrum SM (1970) The locomotion of fibroblasts in culture I. Movements of the leading edge. Exp Cell Res 59:393–398.  https://doi.org/10.1016/0014-4827(70)90646-4 CrossRefGoogle Scholar
  2. Allena R, Aubry D (2012) “Run-and-tumble” or “look-and-run”? A mechanical model to explore the behavior of a migrating amoeboid cell. J Theor Biol 306:15–31.  https://doi.org/10.1016/j.jtbi.2012.03.041 MathSciNetCrossRefzbMATHGoogle Scholar
  3. Allena R, Mouronval A-S, Aubry D (2010) Simulation of multiple morphogenetic movements in the Drosophila embryo by a single 3D finite element model. J Mech Behav Biomed Mater 3:313–323.  https://doi.org/10.1016/j.jmbbm.2010.01.001 CrossRefGoogle Scholar
  4. Allena R, Muñoz JJ, Aubry D (2013) Diffusion-reaction model for Drosophila embryo development. Comput Methods Biomech Biomed Eng 16:235–248.  https://doi.org/10.1080/10255842.2011.616944 CrossRefGoogle Scholar
  5. Ambrosi D, Pezzuto S (2011) Active stress vs. active strain in mechanobiology: constitutive issues. J Elast 107:199–212.  https://doi.org/10.1007/s10659-011-9351-4 MathSciNetCrossRefzbMATHGoogle Scholar
  6. Ambrosi D, Arioli G, Nobile F, Quarteroni A (2011) Electromechanical coupling in cardiac dynamics: the active strain approach. SIAM J Appl Math 71:605–621.  https://doi.org/10.1137/100788379 MathSciNetCrossRefzbMATHGoogle Scholar
  7. Badique F, Stamov DR, Davidson PM et al (2013) Directing nuclear deformation on micropillared surfaces by substrate geometry and cytoskeleton organization. Biomaterials 34:2991–3001.  https://doi.org/10.1016/j.biomaterials.2013.01.018 CrossRefGoogle Scholar
  8. Bao G, Suresh S (2003) Cell and molecular mechanics of biological materials. Nat Mater 2:715–725.  https://doi.org/10.1038/nmat1001 CrossRefGoogle Scholar
  9. Bell ES, Lammerding J (2016) Causes and consequences of nuclear envelope alterations in tumour progression. Eur J Cell Biol 95:449–464.  https://doi.org/10.1016/j.ejcb.2016.06.007 CrossRefGoogle Scholar
  10. Benjamin M, Hillen B (2003) Mechanical influences on cells, tissues and organs—“Mechanical Morphogenesis”. Eur J Morphol 41:3–7.  https://doi.org/10.1076/ejom.41.1.3.28102 CrossRefGoogle Scholar
  11. Bonet J, Gil AJ, Ortigosa R (2015) A computational framework for polyconvex large strain elasticity. Comput Methods Appl Mech Eng 283:1061–1094.  https://doi.org/10.1016/j.cma.2014.10.002 MathSciNetCrossRefzbMATHGoogle Scholar
  12. Caille N, Thoumine O, Tardy Y, Meister J-J (2002) Contribution of the nucleus to the mechanical properties of endothelial cells. J Biomech 35:177–187CrossRefGoogle Scholar
  13. Cao X, Lin Y, Driscoll TP et al (2015) A chemomechanical model of matrix and nuclear rigidity regulation of focal adhesion size. Biophys J 109:1807–1817.  https://doi.org/10.1016/j.bpj.2015.08.048 CrossRefGoogle Scholar
  14. Cherubini C, Filippi S, Nardinocchi P, Teresi L (2008) An electromechanical model of cardiac tissue: constitutive issues and electrophysiological effects. Prog Biophys Mol Biol 97:562–573.  https://doi.org/10.1016/j.pbiomolbio.2008.02.001 CrossRefGoogle Scholar
  15. Cuvelier D, Théry M, Chu Y-S et al (2007) The universal dynamics of cell spreading. Curr Biol 17:694–699.  https://doi.org/10.1016/j.cub.2007.02.058 CrossRefGoogle Scholar
  16. Davidson PM, Özçelik H, Hasirci V et al (2009) Microstructured surfaces cause severe but non-detrimental deformation of the cell nucleus. Adv Mater 21:3586–3590.  https://doi.org/10.1002/adma.200900582 CrossRefGoogle Scholar
  17. Davidson PM, Fromigué O, Marie PJ et al (2010) Topographically induced self-deformation of the nuclei of cells: dependence on cell type and proposed mechanisms. J Mater Sci Mater Med 21:939–946.  https://doi.org/10.1007/s10856-009-3950-7 CrossRefGoogle Scholar
  18. Davidson PM, Sliz J, Isermann P et al (2015) Design of a microfluidic device to quantify dynamic intra-nuclear deformation during cell migration through confining environments. Integr Biol Quant Biosci Nano Macro 7:1534–1546.  https://doi.org/10.1039/c5ib00200a Google Scholar
  19. Denais CM, Gilbert RM, Isermann P et al (2016) Nuclear envelope rupture and repair during cancer cell migration. Science 352:353–358.  https://doi.org/10.1126/science.aad7297 CrossRefGoogle Scholar
  20. Deveraux S, Allena R, Aubry D (2017) A numerical model suggests the interplay between nuclear plasticity and stiffness during a perfusion assay. J Theor Biol.  https://doi.org/10.1016/j.jtbi.2017.09.007 MathSciNetzbMATHGoogle Scholar
  21. du Roure O, Saez A, Buguin A et al (2005) Force mapping in epithelial cell migration. Proc Natl Acad Sci 102:2390–2395.  https://doi.org/10.1073/pnas.0408482102 CrossRefGoogle Scholar
  22. Erk KA, Henderson KJ, Shull KR (2010) Strain stiffening in synthetic and biopolymer networks. Biomacromol 11:1358–1363.  https://doi.org/10.1021/bm100136y CrossRefGoogle Scholar
  23. Ermis M, Akkaynak D, Chen P et al (2016) A high throughput approach for analysis of cell nuclear deformability at single cell level. Sci Rep 6:36917.  https://doi.org/10.1038/srep36917 CrossRefGoogle Scholar
  24. Étienne J, Duperray A (2011) Initial dynamics of cell spreading are governed by dissipation in the actin cortex. Biophys J 101:611–621.  https://doi.org/10.1016/j.bpj.2011.06.030 CrossRefGoogle Scholar
  25. Fan H, Li S (2015a) Modeling microtubule cytoskeleton via an active liquid crystal elastomer model. Comput Mater Sci 96:559–566.  https://doi.org/10.1016/j.commatsci.2014.04.041 CrossRefGoogle Scholar
  26. Fan H, Li S (2015b) Modeling universal dynamics of cell spreading on elastic substrates. Biomech Model Mechanobiol 14:1265–1280.  https://doi.org/10.1007/s10237-015-0673-1 CrossRefGoogle Scholar
  27. Fang Y, Lai KWC (2016) Modeling the mechanics of cells in the cell-spreading process driven by traction forces. Phys Rev E 93:042404.  https://doi.org/10.1103/physreve.93.042404 CrossRefGoogle Scholar
  28. Fried I, Johnson AR (1988) A note on elastic energy density functions for largely deformed compressible rubber solids. Comput Methods Appl Mech Eng 69:53–64.  https://doi.org/10.1016/0045-7825(88)90166-1 MathSciNetCrossRefzbMATHGoogle Scholar
  29. Friedl P, Wolf K, Lammerding J (2011) Nuclear mechanics during cell migration. Curr Opin Cell Biol 23:55–64.  https://doi.org/10.1016/j.ceb.2010.10.015 CrossRefGoogle Scholar
  30. Geiger B, Spatz JP, Bershadsky AD (2009) Environmental sensing through focal adhesions. Nat Rev Mol Cell Biol 10:21–33.  https://doi.org/10.1038/nrm2593 CrossRefGoogle Scholar
  31. Ghibaudo M, Di Meglio J-M, Hersen P, Ladoux B (2011) Mechanics of cell spreading within 3D-micropatterned environments. Lab Chip 11:805–812.  https://doi.org/10.1039/c0lc00221f CrossRefGoogle Scholar
  32. Golestaneh AF, Nadler B (2016) Modeling of cell adhesion and deformation mediated by receptor–ligand interactions. Biomech Model Mechanobiol 15:371–387.  https://doi.org/10.1007/s10237-015-0694-9 CrossRefGoogle Scholar
  33. Hanson L, Zhao W, Lou H-Y et al (2015) Vertical nanopillars for in situ probing of nuclear mechanics in adherent cells. Nat Nanotechnol 10:554–562.  https://doi.org/10.1038/nnano.2015.88 CrossRefGoogle Scholar
  34. Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering, 1st edn. Wiley, HobokenzbMATHGoogle Scholar
  35. Ingber DE (2003) Tensegrity I. Cell structure and hierarchical systems biology. J Cell Sci 116:1157–1173.  https://doi.org/10.1242/jcs.00359 CrossRefGoogle Scholar
  36. Jean RP, Chen CS, Spector AA (2003) Analysis of the deformation of the nucleus as a result of alterations of the cell adhesion area, pp 121–122.  https://doi.org/10.1115/imece2003-42905
  37. Keren K (2011) Membrane tension leads the way. Proc Natl Acad Sci 108:14379–14380.  https://doi.org/10.1073/pnas.1111671108 CrossRefGoogle Scholar
  38. Khatau SB, Hale CM, Stewart-Hutchinson PJ et al (2009) A perinuclear actin cap regulates nuclear shape. Proc Natl Acad Sci USA 106:19017–19022.  https://doi.org/10.1073/pnas.0908686106 CrossRefGoogle Scholar
  39. Kim D-H, Khatau SB, Feng Y et al (2012) Actin cap associated focal adhesions and their distinct role in cellular mechanosensing. Sci Rep 2:555.  https://doi.org/10.1038/srep00555 CrossRefGoogle Scholar
  40. Kim D-H, Cho S, Wirtz D (2014) Tight coupling between nucleus and cell migration through the perinuclear actin cap. J Cell Sci 127:2528–2541.  https://doi.org/10.1242/jcs.144345 CrossRefGoogle Scholar
  41. Liu P, Zhang YW, Cheng QH, Lu C (2007) Simulations of the spreading of a vesicle on a substrate surface mediated by receptor–ligand binding. J Mech Phys Solids 55:1166–1181.  https://doi.org/10.1016/j.jmps.2006.12.001 CrossRefzbMATHGoogle Scholar
  42. Liu X, Liu R, Gu Y, Ding J (2017) Nonmonotonic self-deformation of cell nuclei on topological surfaces with micropillar array. ACS Appl Mater Interfaces 9:18521–18530.  https://doi.org/10.1021/acsami.7b04027 CrossRefGoogle Scholar
  43. Liu R, Yao X, Liu X, Ding J (2018) Proliferation of cells with severe nuclear deformation on a micropillar array. Langmuir.  https://doi.org/10.1021/acs.langmuir.8b03452 Google Scholar
  44. Lu H, Koo LY, Wang WM et al (2004) Microfluidic shear devices for quantitative analysis of cell adhesion. Anal Chem 76:5257–5264.  https://doi.org/10.1021/ac049837t CrossRefGoogle Scholar
  45. Lubarda V (2004) Constitutive theories based on the multiplicative decomposition of deformation gradient: thermoelasticity, elastoplasticity, and biomechanics. Appl Mech Rev 57:95–109CrossRefGoogle Scholar
  46. Mammoto T, Ingber DE (2010) Mechanical control of tissue and organ development. Dev Camb Engl 137:1407–1420.  https://doi.org/10.1242/dev.024166 Google Scholar
  47. Maninova M, Caslavsky J, Vomastek T (2017) The assembly and function of perinuclear actin cap in migrating cells. Protoplasma 254:1207–1218.  https://doi.org/10.1007/s00709-017-1077-0 CrossRefGoogle Scholar
  48. Milan J-L, Lavenus S, Pilet P et al (2013) Computational model combined with in vitro experiments to analyse mechanotransduction during mesenchymal stem cell adhesion. Eur Cell Mater 25:97–113CrossRefGoogle Scholar
  49. Mokbel M, Mokbel D, Mietke A et al (2017) Numerical simulation of real-time deformability cytometry to extract cell mechanical properties. ACS Biomater Sci Eng 3:2962–2973.  https://doi.org/10.1021/acsbiomaterials.6b00558 CrossRefGoogle Scholar
  50. Morgan MR, Humphries MJ, Bass MD (2007) Synergistic control of cell adhesion by integrins and syndecans. Nat Rev Mol Cell Biol 8:957–969.  https://doi.org/10.1038/nrm2289 CrossRefGoogle Scholar
  51. Muñoz JJ, Barrett K, Miodownik M (2007) A deformation gradient decomposition method for the analysis of the mechanics of morphogenesis. J Biomech 40:1372–1380.  https://doi.org/10.1016/j.jbiomech.2006.05.006 CrossRefGoogle Scholar
  52. Murtada S-I, Kroon M, Holzapfel GA (2010) A calcium-driven mechanochemical model for prediction of force generation in smooth muscle. Biomech Model Mechanobiol 9:749–762.  https://doi.org/10.1007/s10237-010-0211-0 CrossRefGoogle Scholar
  53. Nisenholz N, Rajendran K, Dang Q et al (2014) Active mechanics and dynamics of cell spreading on elastic substrates. Soft Matter 10:7234–7246.  https://doi.org/10.1039/c4sm00780h CrossRefGoogle Scholar
  54. Nobile F, Quarteroni A, Ruiz-Baier R (2012) An active strain electromechanical model for cardiac tissue. Int J Numer Methods Biomed Eng 28:52–71MathSciNetCrossRefzbMATHGoogle Scholar
  55. Nolan DR, Gower AL, Destrade M et al (2014) A robust anisotropic hyperelastic formulation for the modelling of soft tissue. J Mech Behav Biomed Mater 39:48–60.  https://doi.org/10.1016/j.jmbbm.2014.06.016 CrossRefGoogle Scholar
  56. Pan Z, Yan C, Peng R et al (2012) Control of cell nucleus shapes via micropillar patterns. Biomaterials 33:1730–1735.  https://doi.org/10.1016/j.biomaterials.2011.11.023 CrossRefGoogle Scholar
  57. Rodriguez EK, Hoger A, McCulloch AD (1994) Stress-dependent finite growth in soft elastic tissues. J Biomech 27:455–467CrossRefGoogle Scholar
  58. Rosenbluth MJ, Lam WA, Fletcher DA (2008) Analyzing cell mechanics in hematologic diseases with microfluidic biophysical flow cytometry. Lab Chip 8:1062–1070.  https://doi.org/10.1039/b802931h CrossRefGoogle Scholar
  59. Sarvestani AS, Jabbari E (2008) Modeling the kinetics of cell membrane spreading on substrates with ligand density gradient. J Biomech 41:921–925.  https://doi.org/10.1016/j.jbiomech.2007.11.004 CrossRefGoogle Scholar
  60. Sauer RA (2016) A survey of computational models for adhesion. J Adhes 92:81–120.  https://doi.org/10.1080/00218464.2014.1003210 CrossRefGoogle Scholar
  61. Schirmer EC, de las Heras JI (eds) (2014) Cancer biology and the nuclear envelope: recent advances may elucidate past paradoxes. Springer, New YorkGoogle Scholar
  62. Stålhand J, Klarbring A, Holzapfel GA (2008) Smooth muscle contraction: mechanochemical formulation for homogeneous finite strains. Prog Biophys Mol Biol 96:465–481.  https://doi.org/10.1016/j.pbiomolbio.2007.07.025 CrossRefGoogle Scholar
  63. Storm C, Pastore JJ, MacKintosh FC et al (2005) Nonlinear elasticity in biological gels. Nature 435:191–194.  https://doi.org/10.1038/nature03521 CrossRefGoogle Scholar
  64. Swift J, Ivanovska IL, Buxboim A et al (2013) Nuclear lamin-A scales with tissue stiffness and enhances matrix-directed differentiation. Science 341:1240104.  https://doi.org/10.1126/science.1240104 CrossRefGoogle Scholar
  65. Tan JL, Tien J, Pirone DM et al (2003) Cells lying on a bed of microneedles: an approach to isolate mechanical force. Proc Natl Acad Sci USA 100:1484–1489.  https://doi.org/10.1073/pnas.0235407100 CrossRefGoogle Scholar
  66. Versaevel M, Grevesse T, Gabriele S (2012) Spatial coordination between cell and nuclear shape within micropatterned endothelial cells. Nat Commun 3:671.  https://doi.org/10.1038/ncomms1668 CrossRefGoogle Scholar
  67. Wang H, Biao Y, Chunlai Y, Wen L (2017) Simulation of AFM indentation of soft biomaterials with hyperelasticity. In: 2017 IEEE 12th international conference on nano/micro engineered and molecular systems (NEMS), pp 550–553Google Scholar
  68. Wolf K, Te Lindert M, Krause M et al (2013) Physical limits of cell migration: control by ECM space and nuclear deformation and tuning by proteolysis and traction force. J Cell Biol 201:1069–1084.  https://doi.org/10.1083/jcb.201210152 CrossRefGoogle Scholar
  69. Yeoh OH (1993) Some forms of the strain energy function for rubber. Rubber Chem Technol 66:754–771.  https://doi.org/10.5254/1.3538343 CrossRefGoogle Scholar
  70. Zeng X, Li S (2011a) Modelling and simulation of substrate elasticity sensing in stem cells. Comput Methods Biomech Biomed Eng 14:447–458.  https://doi.org/10.1080/10255842.2011.557371 CrossRefGoogle Scholar
  71. Zeng X, Li S (2011b) Multiscale modeling and simulation of soft adhesion and contact of stem cells. J Mech Behav Biomed Mater 4:180–189.  https://doi.org/10.1016/j.jmbbm.2010.06.002 CrossRefGoogle Scholar
  72. Zeng X, Li S (2012) A three dimensional soft matter cell model for mechanotransduction. Soft Matter 8:5765–5776.  https://doi.org/10.1039/c2sm07138j CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Solenne Mondésert-Deveraux
    • 1
  • Denis Aubry
    • 1
  • Rachele Allena
    • 2
    Email author
  1. 1.Laboratoire MSSMat UMR CNRS 8579, CentraleSupélecUniversité Paris-SaclayParisFrance
  2. 2.LBM/Institut de Biomécanique Humaine Georges CharpakArts et Metiers ParisTechParisFrance

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