Advertisement

Biomechanics and Modeling in Mechanobiology

, Volume 16, Issue 6, pp 2063–2075 | Cite as

Cellular mechanosensitivity to substrate stiffness decreases with increasing dissimilarity to cell stiffness

  • Tamer Abdalrahman
  • Laura Dubuis
  • Jason Green
  • Neil Davies
  • Thomas Franz
Original Paper

Abstract

Computational modelling has received increasing attention to investigate multi-scale coupled problems in micro-heterogeneous biological structures such as cells. In the current study, we investigated for a single cell the effects of (1) different cell-substrate attachment (2) and different substrate modulus \(\textit{E}_\mathrm{s}\) on intracellular deformations. A fibroblast was geometrically reconstructed from confocal micrographs. Finite element models of the cell on a planar substrate were developed. Intracellular deformations due to substrate stretch of \(\lambda =1.1\), were assessed for: (1) cell-substrate attachment implemented as full basal contact (FC) and 124 focal adhesions (FA), respectively, and \(\textit{E}_\mathrm{s}\,=\,\)140 KPa and (2) \(\textit{E}_\mathrm{s}\,=\,10\), 140, 1000, and 10,000 KPa, respectively, and FA attachment. The largest strains in cytosol, nucleus and cell membrane were higher for FC (1.35\(\text {e}^{-2}\), 0.235\(\text {e}^{-2}\) and 0.6\(\text {e}^{-2}\)) than for FA attachment (0.0952\(\text {e}^{-2}\), 0.0472\(\text {e}^{-2}\) and 0.05\(\text {e}^{-2}\)). For increasing \(\textit{E}_\mathrm{s}\), the largest maximum principal strain was 4.4\(\text {e}^{-4}\), 5\(\text {e}^{-4}\), 5.3\(\text {e}^{-4}\) and 5.3\(\text {e}^{-4}\) in the membrane, 9.5\(\text {e}^{-4}\), 1.1\(\text {e}^{-4}\), 1.2\(\text {e}^{-3}\) and 1.2\(\text {e}^{-3}\) in the cytosol, and 4.5\(\text {e}^{-4}\), 5.3\(\text {e}^{-4}\), 5.7\(\text {e}^{-4}\) and 5.7\(\text {e}^{-4}\) in the nucleus. The results show (1) the importance of representing FA in cell models and (2) higher cellular mechanical sensitivity for substrate stiffness changes in the range of cell stiffness. The latter indicates that matching substrate stiffness to cell stiffness, and moderate variation of the former is very effective for controlled variation of cell deformation. The developed methodology is useful for parametric studies on cellular mechanics to obtain quantitative data of subcellular strains and stresses that cannot easily be measured experimentally.

Keywords

Cell mechanics Focal adhesion Substrate stiffness Finite element modelling 

Notes

Acknowledgements

The research reported in this publication was supported by the National Research Foundation of South Africa (UID 92531 and 93542), and the South African Medical Research Council under a Self-Initiated Research Grant (SIR 328148). Views and opinions expressed are not those of the NRF or MRC but of the authors.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. Ahmed WW, Kural MH, Saif TA (2010) A novel platform for in situ investigation of cells and tissues under mechanical strain. Acta Biomater 6:2979–2990CrossRefGoogle Scholar
  2. Altman G, Lu H, Horan R, Calabro T, Ryder D, Kaplan D, Stark P, Martin I, Richmond J, Vunjak-Novakovic G (2002) Advanced bioreactor with controlled application of multi-dimensional strain for tissue engineering. J Biomech Eng 124(6):742–749CrossRefGoogle Scholar
  3. Ando J, Yamamoto K (2011) Effects of shear stress and stretch on endothelial function. Antioxid Redox Signal 15:1389–1403CrossRefGoogle Scholar
  4. Baaijens FPT, Trickey WR, Laursen TA, Guilak F (2005) Large deformation finite element analysis of micropipette aspiration to determine the mechanical properties of the chondrocyte. Ann Biomed Eng 33:494–501CrossRefGoogle Scholar
  5. Bader R, Wagoner K (2010) Modulation of the response of rheumatoid arthritis synovial fibroblasts to proinflammatory stimulants with cyclic tensile strain. Cytokine 51(1):35–41CrossRefGoogle Scholar
  6. Balaban N, Schwarz U, Riveline D, Goichberg P, Tzur G, Sabanay I, Mahalu D, Safran S, Bershadsky A, Addadi L, Geiger B (2001) Force and focal adhesion assembly: a close relationship studied using elastic micropatterned substrates. Nat Cell Biol 3:466–472CrossRefGoogle Scholar
  7. Barreto S, Clausen CH, Perrault CM, Fletcher DA, Lacroix D (2013) A multi-structural single cell model of force-induced interactions of cytoskeletal components. Biomaterials 34:6119–6126CrossRefGoogle Scholar
  8. Barreto S, Perrault CM, Lacroix D (2014) Structural finite element analysis to explain cell mechanics variability. J Mech Behav Biomed Mater 38:219–231CrossRefGoogle Scholar
  9. Bartalena G, Grieder R, Sharma RI, Zambelli T, Muff R, Snedeker JG (2011) A novel method for assessing adherent single-cell stiffness in tension: design and testing of a substrate-based live cell functional imaging device. Biomed Microdevices 13:291–301CrossRefGoogle Scholar
  10. Birukova AA, Fu P, Xing J, Yakubov B, Cokic I, Birukov K (2010) Mechanotransduction by gefh1 as a novel mechanism of ventilator-induced vascular endothelial permeability. Am J Physiol Lung Cell Mol Physiol 298:L837–L848CrossRefGoogle Scholar
  11. Bracher M, Bezuidenhout D, Lutolf MP, Franz T, Sun M, Zilla P, Davies NH (2013) Cell specific ingrowth hydrogels. Biomaterials 34:6797–6803CrossRefGoogle Scholar
  12. Breuls RG, Sengers BG, Oomens CW, Bouten CV, Baaijens FP (2002) Predicting local cell deformations in engineered tissue constructs: a multilevel finite element approach. J Biomech Eng 124:198–207CrossRefGoogle Scholar
  13. Brown TD (2000) Techniques for mechanical stimulation of cells in vitro: a review. J Biomech 33:3–14CrossRefGoogle Scholar
  14. Butcher J, Nerem R (2006) Valvular endothelial cells regulate the phenotype of interstitial cells in co-culture: effects of steady shear stress. Tissue Eng 12:905–915CrossRefGoogle Scholar
  15. Caille N, Tardy Y, Meister J (1998) Assessment of strain field in endothelial cells subjected to uniaxial deformation of their substrate. Ann Biomed Eng 26:409–416CrossRefGoogle Scholar
  16. Chen A, Moy VT (2000) Cross-linking of cell surface receptors enhances cooperativity of molecular adhesion. Biophys J 78:2814–2820CrossRefGoogle Scholar
  17. Chien S, Li S, Shiu YT, Li YS (2005) Molecular basis of mechanical modulation of endothelial cell migration. Front Biosci 10:1985–2000CrossRefGoogle Scholar
  18. Dávila CG, Camanho PP, Turon A (2008) Effective simulation of delamination in aeronautical structures using shells and cohesive elements. J Aircr 45:663–672CrossRefGoogle Scholar
  19. Doyle A, Nerem R, Ahsan T (2009) Human mesenchymal stem cells form multicellular structures in response to applied cyclic strain. Ann Biomed Eng 37(4):783–793CrossRefGoogle Scholar
  20. Engler A, Griffin M, Sen S, Bönnemann C, Sweeney H, Discher D (2004) Myotubes differentiate optimally on substrates with tissue-like stiffness pathological implications for soft or stiff microenvironments. J Cell Biol 166:877–887CrossRefGoogle Scholar
  21. Forsyth AM, Wan J, Ristenpart W, Stone H (2010) The dynamic behavior of chemically stiffened? Red blood cells in microchannel flows. Microvasc Res 80(1):37–43CrossRefGoogle Scholar
  22. Fortino S, Zagari G, Mendicino AL, Dill-Langer G (2012) A simple approach for FEM simulation of Mode I cohesive crack growth in glued laminated timber under short-term loading. J Struct Mech 45:1–20Google Scholar
  23. Gerstmair A, Fois G, Innerbichler S, Dietl P, Felder E (2009) A device for simultaneous live cell imaging during uni-axial mechanical strain or compression. J Appl Physiol 107(2):613–620CrossRefGoogle Scholar
  24. Gu WY, Lai WM, Mow VC (1997) A triphasic analysis of negative osmotic flows through charged hydrated soft tissues. J Biomech 30:71–78CrossRefGoogle Scholar
  25. Hahn C, Schwartz M (2009) Mechanotransduction in vascular physiology and atherogenesis. Nat Rev Mol Cell Biol 10:53–62CrossRefGoogle Scholar
  26. Hashizume R, Fujimoto KL, Hong Y, Guan J, Toma C, Tobita K, Wagner WR (2013) Biodegradable elastic patch plasty ameliorates left ventricular adverse remodeling after ischemia-reperfusion injury: a preclinical study of a porous polyurethane material in a porcine model. J Thorac Cardiovasc Surg 146:391–399CrossRefGoogle Scholar
  27. Haudenschild A, Hsieh A, Kapila S, Lotz J (2009) Pressure and distortion regulate human mesenchymal stem cell gene expression. Ann Biomed Eng 37(3):492–502CrossRefGoogle Scholar
  28. Hine R (2009) The facts on file dictionary of biology. Infobase Publishing, New YorkGoogle Scholar
  29. Hochmuth RM, Mohandas N, Blackshear PL (1973) Measurement of the elastic modulus for red cell membrane using a fluid mechanical technique. Biophys J 13:747–762CrossRefGoogle Scholar
  30. Huang C, Ogawa R (2010) Mechanotransduction in bone repair and regeneration. FASEB J 24:3625–3632CrossRefGoogle Scholar
  31. Huang H, Kamm RD, Lee RT (2004) Cell mechanics and mechanotransduction: pathways, probes, and physiology. Am J Physiol Cell Physiol 287:C1–C11CrossRefGoogle Scholar
  32. Ishiko A, Shimizu H, Kikuchi A, Ebihara T, Hashimoto T, Nishikawa T (1993) Human autoantibodies against the 230-kD bullous pemphigoid antigen (BPAG1) bind only to the intracellular domain of the hemidesmosome, whereas those against the 180-kD bullous pemphigoid antigen (BPAG2) bind along the plasma membrane of the hemidesmosome in normal human and swine skin. J Clin Investig 91:1608–1615CrossRefGoogle Scholar
  33. Jean RP, Chen CS, Spector AA (2005) Finite-element analysis of the adhesion-cytoskeleton-nucleus mechanotransduction pathway during endothelial cell rounding: axisymmetric model. J Biomech Eng 127:594–600CrossRefGoogle Scholar
  34. Kortsmit J, Davies NH, Miller R, Macadangdang JR, Zilla P, Franz T (2013) The effect of hydrogel injection on cardiac function and myocardial mechanics in a computational post-infarction model. Comput Method Biomech Biomed Eng 16:1185–1195CrossRefGoogle Scholar
  35. Ku C, Johnson P, Batten P, Sarathchandra P, Chambers R, Taylor P, Yacoub M, Chester A (2006) Collagen synthesis by mesenchymal stem cells and aortic valve interstitial cells in response to mechanical stretch. Cardiovasc Res 71:548–556CrossRefGoogle Scholar
  36. Lai WM, Rubin DH, Rubin D, Krempl E (2009) Introduction to continuum mechanics, 4th edn. Butterworth-Heinemann, OxfordzbMATHGoogle Scholar
  37. Lau E, Lee W, Li J, Xiao A, Davies J, Wu Q, Wang L, You L (2011) Effect of low-magnitude, high-frequency vibration on osteogenic differentiation of rat mesenchymal stromal cells. J Orthop Res 29(7):1075–1080CrossRefGoogle Scholar
  38. Lavagnino M, Arnoczky SP, Kepich E, Caballero O, Haut RC (2008) A finite element model predicts the mechanotransduction response of tendon cells to cyclic tensile loading. Biomech Model Mechanobiol 7:405–416CrossRefGoogle Scholar
  39. Lee A, Delhaas T, Waldman L, MacKenna DA, Villarreal F, McCulloch A (1996) An equibiaxial strain system for cultured cells. Am J Physiol Cell Physiol 271:C1400–C1408Google Scholar
  40. Legner D, Skatulla S, MBewu J, Rama RR, Reddy BD, Sansour C, Davies NH, Franz T (2014) Studying the influence of hydrogel injections into the infarcted left ventricle using the element-free galerkin method. Int J Numer Methods Biomed Eng 30:416–429CrossRefGoogle Scholar
  41. Maul T, Hamilton D, Nieponice A, Soletti L, Vorp D (2007) A new experimental system for the extended application of cyclic hydrostatic pressure to cell culture. J Biomech Eng 129(1):110–116CrossRefGoogle Scholar
  42. Mazzag B, Barakat A (2011) The effect of noisy flow on endothelial cell mechanotransduction: a computational study. Ann Biomed Eng 39:911–921CrossRefGoogle Scholar
  43. Miller P, Hu L, Wang J (2010) Finite element simulation of cell-substrate decohesion by laser-induced stress waves. J Mech Behav Biomed Mater 3:268–277CrossRefGoogle Scholar
  44. Milner JS, Grol MW, Beaucage KL, Dixon SJ, Holdsworth DW (2012) Finite-element modeling of viscoelastic cells during high-frequency cyclic strain. J Funct Biomater 3:209–224CrossRefGoogle Scholar
  45. Morseth B, Emaus N, Jørgensen L (2011) Physical activity and bone: the importance of the various mechanical stimuli for bone mineral density. A review. Nor Epidemiol 20:173–178Google Scholar
  46. Mullen CA, Vaughan TJ, Voisin MC, Brennan MA, Layrolle P, McNamara LM (2014) Cell morphology and focal adhesion location alters internal cell stress. J R Soc Interface 11(20140):885Google Scholar
  47. Nakajima K, Fujita J, Matsui M, Tohyama S, Tamura N, Kanazawa H, Seki T, Kishino Y, Hirano A, Okada M, Tabei R, Sano M, Goto S, Tabata Y, Fukuda K (2015) Gelatin hydrogel enhances the engraftment of transplanted cardiomyocytes and angiogenesis to ameliorate cardiac function after myocardial infarction. PLoS ONE 10(e0133):308Google Scholar
  48. Nicolas A, Safran S (2006) Limitation of cell adhesion by the elasticity of the extracellular matrix. Biophys J 91:61–73CrossRefGoogle Scholar
  49. Nikander R, Sievänen H, Uusi-Rasi K, Heinonen A, Kannus P (2006) Loading modalities and bone structures at nonweight-bearing upper extremity and weight-bearing lower extremity: a pQCT study of adult female athletes. Bone 39:886–894CrossRefGoogle Scholar
  50. Pang Q, Zu J, Siu G, Li R (2010) Design and development of a novel biostretch apparatus for tissue engineering. J Biomech Eng 132(1):014–503CrossRefGoogle Scholar
  51. Park J, Chu J, Cheng C, Chen F, Chen D, Li S (2004) Differential effects of equiaxial and uniaxial strain on mesenchymal stem cells. Biotechnol Bioeng 88:359–368CrossRefGoogle Scholar
  52. Park K, Paulino GH (2012) Computational implementation of the PPR potential-based cohesive model in abaqus: educational perspective. Eng Fract Mech 93:239–262CrossRefGoogle Scholar
  53. Pečovnik-Balon B (2005) Cardiovascular calcification in patients with end-stage renal disease. Ther Apher Dial 9:208–210CrossRefGoogle Scholar
  54. Peeters EAG, Oomens CWJ, Bouten CVC, Bader DL, Baaijens FPT (2005) Mechanical and failure properties of single attached cells under compression. J Biomech 38:1685–1693CrossRefGoogle Scholar
  55. Seguin C, McLachlan J, Norton P, Lagugné-Labarthet F (2010) Surface modification of poly (dimethylsiloxane) for microfluidic assay applications. Appl Surf Sci 256(8):2524–2531CrossRefGoogle Scholar
  56. Simon BR, Kaufmann MV, McAfee MA, Baldwin AL (1993) Finite element models for arterial wall mechanics. J Biomech Eng 115:489–496CrossRefGoogle Scholar
  57. Sirry MS, Zilla P, Franz T (2010) A computational study of structural designs for a small-diameter composite vascular graft promoting tissue regeneration. Cardiovasc Eng Technol 1:269–281CrossRefGoogle Scholar
  58. Sirry MS, Davies NH, Kadner K, Dubuis L, Saleh MG, Meintjes EM, Spottiswoode BS, Zilla P, Franz T (2015) Micro-structurally detailed model of a therapeutic hydrogel injectate in a rat biventricular cardiac geometry for computational simulations. Comput Methods Biomech Biomed Eng 18:325–331CrossRefGoogle Scholar
  59. Sirry MS, Butler JR, Patnaik SS, Brazile B, Bertucci R, Claude A, McLaughlin R, Davies NH, Liao J, Franz T (2016) Characterisation of the mechanical properties of infarcted myocardium in the rat under biaxial tension and uniaxial compression. J Mech Behav Biomed Mater 63:252–264CrossRefGoogle Scholar
  60. Slomka N, Gefen A (2010) Confocal microscopy-based three-dimensional cell-specific modeling for large deformation analyses in cellular mechanics. J Biomech 43:1806–1816CrossRefGoogle Scholar
  61. Slomka N, Gefen A (2012) Relationship between strain levels and permeability of the plasma membrane in statically stretched myoblasts. Ann Biomed Eng 40:606–618CrossRefGoogle Scholar
  62. Stroetz RW, Vlahakis NE, Walters BJ, Schroeder MA, Hubmayr RD (2001) Validation of a new live cell strain system: characterization of plasma membrane stress failure. J Appl Physiol 90:2361–2370Google Scholar
  63. Suki B, Ito S, Stamenović D, Lutchen K, Ingenito E (2005) Biomechanics of the lung parenchyma: critical roles of collagen and mechanical forces. J Appl Physiol 98(5):1892–1899CrossRefGoogle Scholar
  64. Suresh S (2007) Biomechanics and biophysics of cancer cells. Acta Mater 55(12):3989–4014CrossRefGoogle Scholar
  65. Titushkin I, Shin J, Cho M (2010) A new perspective for stem-cell mechanobiology: biomechanical control of stem-cell behavior and fate. Crit Rev Biomed Eng 38(5):393–433CrossRefGoogle Scholar
  66. Van Rietbergen B, Müller R, Ulrich D, Rüegsegger P, Huiskes R (2008) Tissue stresses and strain in trabeculae of a canine proximal femur can be quantified from computer reconstructions. J Biomech 32:165–173CrossRefGoogle Scholar
  67. Venugopal JR, Prabhakaran MP, Mukherjee S, Ravichandran R, Dan K, Ramakrishna S (2012) Biomaterial strategies for alleviation of myocardial infarction. J R Soc Interface 9:1–19CrossRefGoogle Scholar
  68. Verbruggen SW, Vaughan TJ, McNamara LM (2012) Strain amplification in bone mechanobiology: a computational investigation of the in vivo mechanics of osteocytes. J R Soc Interface 9:2735–2744CrossRefGoogle Scholar
  69. Wall ME, Weinhold PS, Siu T, Brown TD, Banes AJ (2007) Comparison of cellular strain with applied substrate strain in vitro. J Biomech 40:173–181CrossRefGoogle Scholar
  70. Wang D, Xie Y, Yuan B, Xu J, Gong P, Jiang X (2010) A stretching device for imaging real-time molecular dynamics of live cells adhering to elastic membranes on inverted microscopes during the entire process of the stretch. Integr Biol 2(5–6):288–293CrossRefGoogle Scholar
  71. Wang JHC, Thampatty BP (2008) Mechanobiology of adult and stem cells. Int Rev Cell Mol Biol 271:301–346CrossRefGoogle Scholar
  72. Wang P, Chow H, Tsai W, Fang H (2009) Modulation of gene expression of rabbit chondrocytes by dynamic compression in polyurethane scaffolds with collagen gel encapsulation. J Biomater Appl 23:347–366CrossRefGoogle Scholar
  73. Weinbaum S, Duan Y, Satlin LM, Wang T, Weinstein AM (2010) Mechanotransduction in the renal tubule. Am J Physiol Renal Physiol 299(6):F1220–F1236CrossRefGoogle Scholar
  74. Wise P, Davies NH, Sirry MS, Kortsmit J, Dubuis L, Chai C, Baaijens F, Franz T (2016) Excessive volume of hydrogel injectates may compromise the efficacy for the treatment of acute myocardial infarction. Int J Numer Methods Biomed Eng 32(e02):772Google Scholar
  75. Wolchok J, Brokopp C, Underwood C, Tresco P (2009) The effect of bioreactor induced vibrational stimulation on extracellular matrix production from human derived fibroblasts. Biomaterials 30(3):327–335CrossRefGoogle Scholar
  76. Yao X, Liu Y, Gao J, Yang L, Mao D, Stefanitsch C, Li Y, Zhang J, Ou L, Kong D, Zhao Q, Li Z (2015) Nitric oxide releasing hydrogel enhances the therapeutic efficacy of mesenchymal stem cells for myocardial infarction. Biomaterials 60:130–140CrossRefGoogle Scholar
  77. Yao Y, Lacroix D, Mak AFT (2016) Effects of oxidative stress-induced changes in the actin cytoskeletal structure on myoblast damage under compressive stress: confocal-based cell-specific finite element analysis. Biomech Model Mechanobiol 15:1495–1508CrossRefGoogle Scholar
  78. Yokokawa M, Takeyasu K, Yoshimura SH (2008) Mechanical properties of plasma membrane and nuclear envelope measured by scanning probe microscope. J Microsc 232:82–90CrossRefMathSciNetGoogle Scholar
  79. Zeng Y, Sun H, Yu C, Lai Y, Liu X, Wu J, Chen H, Liu X (2011) CXCR1 and CXCR2 are novel mechano-sensors mediating laminar shear stress-induced endothelial cell migration. Cytokine 53(1):42–51CrossRefGoogle Scholar
  80. Zhang L, Kahn C, Chen H, Tran N, Wang X (2008) Effect of uniaxial stretching on rat bone mesenchymal stem cell: orientation and expressions of collagen types I and III and tenascin-C. Cell Biol Int 32(3):344–352CrossRefGoogle Scholar
  81. Zielinski R, Mihai C, Kniss D, Ghadiali SN (2013) Finite element analysis of traction force microscopy: influence of cell mechanics, adhesion, and morphology. J Biomech Eng 135(071):009Google Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Division of Biomedical Engineering, Department of Human Biology, Faculty of Health SciencesUniversity of Cape TownObservatorySouth Africa
  2. 2.Cardiovascular Research Unit, Chris Barnard Division of Cardiothoracic SurgeryUniversity of Cape TownObservatorySouth Africa
  3. 3.Bioengineering Science Research Group, Engineering Sciences, Faculty of Engineering and the EnvironmentUniversity of SouthamptonSouthamptonUK

Personalised recommendations