Advertisement

Viscoelastic properties of doxorubicin-treated HT-29 cancer cells by atomic force microscopy: the fractional Zener model as an optimal viscoelastic model for cells

  • Maricela Rodríguez-Nieto
  • Priscila Mendoza-Flores
  • David García-Ortiz
  • Luis M. Montes-de-Oca
  • Marco Mendoza-Villa
  • Porfiria Barrón-González
  • Gabriel Espinosa
  • Jorge Luis MenchacaEmail author
Original Paper

Abstract

The malignancy of cancer cells and their response to drug treatments have been traditionally studied using solely their elastic properties. However, the study of the combined viscous and elastic properties provides a richer description of the mechanics of the cell, and achieves a more precise assessment of the effect exerted by anti-cancer treatments. We used an atomic force microscope to obtain the morphological, elastic and viscous properties of HT-29 colorectal cancer cells. Changes in these parameters were observed during exposure of the cells to doxorubicin at different times. The elastic properties were analyzed using the Hertz and Sneddon models. Furthermore, we analyzed the data to study the viscoelasticity of the cells comparing the models known as the standard linear solid, fractional Zener, generalized Maxwell, and power law. A discussion about the optimal model based in the accuracy and physical assumptions for this particular system is included. From the morphological data and viscoelasticity of HT-29 cells exposed to doxorubicin, we found that some parameters were affected differently at shorter or longer exposure times. For instance, the relaxation time suggests a measure of the cell to self-heal and it was observed to increase at shorter exposure times and then to reduce for longer exposure times to the drug. The fractional Zener model better described the mechanical properties of the cell due to the reduced number of parameters and the quality of the fit to experimental data.

Keywords

AFM in cells HT-29 cell line Young's modulus Viscoelastic properties Fractional viscoelastic models 

Notes

Acknowledgements

Authors acknowledge CONACYT for MRN, PM and DG doctoral scholarship, and a special acknowledgement to the Soft Condensed Matter Network for mobility financial support.

Funding:

This study was funded by Consejo Nacional de Ciencia y Tecnología (Grant Numbers 169319 and 220331).

Compliance with ethical standards

Conflicts of interest

The authors declare that they have no conflict of interest.

Supplementary material

10237_2019_1248_MOESM1_ESM.pdf (979 kb)
Supplementary material 1 (pdf 979 KB)

References

  1. Abràmoff MD, Magalhães PJ, Ram SJ (2004) Image processing with imageJ. arXiv:1081-8693
  2. Alcaraz J, Buscemi L, Grabulosa M, Trepat X, Fabry B, Farré R, Navajas D (2003) Microrheology of human lung epithelial cells measured by atomic force microscopy. Biophys J 84(3):2071–2079.  https://doi.org/10.1016/S0006-3495(03)75014-0 CrossRefGoogle Scholar
  3. Alessandrini A, Facci P (2005) AFM: a versatile tool in biophysics. Meas Sci Technol 16(6):R65–R92.  https://doi.org/10.1088/0957-0233/16/6/r01 CrossRefGoogle Scholar
  4. Alves AC, Magarkar A, Horta M, Lima JLFC, Bunker A, Nunes C, Reis S (2017) Influence of doxorubicin on model cell membrane properties: insights from in vitro and in silico studies. Sci Rep 7(1):6343.  https://doi.org/10.1038/s41598-017-06445-z CrossRefGoogle Scholar
  5. Arai F, Ando D, Fukuda T, Nonoda Y, Oota T (1995) Micro manipulation based on micro physics-strategy based on attractive force reduction and stress measurement. In: Proceedings 1995 IEEE/RSJ international conference on intelligent robots and systems. Human robot interaction and cooperative robots, vol 2. IEEE, pp 236–241.  https://doi.org/10.1109/IROS.1995.526166
  6. Arola OJ, Saraste A, Pulkki K, Kallajoki M, Parvinen M, Voipio-Pulkki LM (2000) Acute doxorubicin cardiotoxicity involves cardiomyocyte apoptosis. Cancer Res 60(7):1789–1792Google Scholar
  7. Berret JF (2016) Local viscoelasticity of living cells measured by rotational magnetic spectroscopy. Nat Commun 7:10134.  https://doi.org/10.1038/ncomms10134 CrossRefGoogle Scholar
  8. Birzle AM, Wall WA (2019) A viscoelastic nonlinear compressible material model of lung parenchyma-experiments and numerical identification. J Mech Behav Biomed Mater 94:164–175.  https://doi.org/10.1016/j.jmbbm.2019.02.024 CrossRefGoogle Scholar
  9. Cai X, Xing X, Cai J, Chen Q, Wu S, Huang F (2010) Connection between biomechanics and cytoskeleton structure of lymphocyte and Jurkat cells: an AFM study. Micron 41(3):257–262.  https://doi.org/10.1016/j.micron.2009.08.011 CrossRefGoogle Scholar
  10. Carmichael B, Babahosseini H, Mahmoodi SN, Agah M (2015) The fractional viscoelastic response of human breast tissue cells. Phys Biol 12(4):46001.  https://doi.org/10.1088/1478-3975/12/4/046001 CrossRefGoogle Scholar
  11. Chen J, Fabry B, Schiffrin EL, Wang N (2001) Twisting integrin receptors increases endothelin-1 gene expression in endothelial cells. Am J Physiol Cell Physiol 280(6):C1475–C1484.  https://doi.org/10.1152/ajpcell.2001.280.6.C1475 CrossRefGoogle Scholar
  12. Christensen R (1982) Chapter i—viscoelastic stress strain constitutive relations. In: Christensen R (ed) Theory of viscoelasticity, 2nd edn. Academic Press, New York, pp 1–34Google Scholar
  13. Cross SE, Jin YS, Rao J, Gimzewski JK (2007) Nanomechanical analysis of cells from cancer patients. Nat Nanotechnol 2(12):780.  https://doi.org/10.1038/nnano.2007.388 CrossRefGoogle Scholar
  14. Darling EM, Zauscher S, Guilak F (2006) Viscoelastic properties of zonal articular chondrocytes measured by atomic force microscopy. Osteoarthr Cartilage 14(6):571–579.  https://doi.org/10.1016/j.joca.2005.12.003 CrossRefGoogle Scholar
  15. Du M, Wang Z, Hu H (2013) Measuring memory with the order of fractional derivative. Sci Rep 3(1):3431.  https://doi.org/10.1038/srep03431 CrossRefGoogle Scholar
  16. Evans E, Yeung A (1989) Apparent viscosity and cortical tension of blood granulocytes determined by micropipet aspiration. Biophys J 56(1):151–160.  https://doi.org/10.1016/S0006-3495(89)82660-8 CrossRefGoogle Scholar
  17. Ferlay J, Colombet M, Soerjomataram I, Mathers C, Parkin D, Piñeros M, Znaor A, Bray F (2019) Estimating the global cancer incidence and mortality in 2018: globocan sources and methods. Int J Cancer 144(8):1941–1953.  https://doi.org/10.1002/ijc.31937 CrossRefGoogle Scholar
  18. Fraldi M, Cugno A, Carotenuto A, Cutolo A, Pugno N, Deseri L (2017) Small-on-large fractional derivative-based single-cell model incorporating cytoskeleton prestretch. J Eng Mech 143(5):D4016009.  https://doi.org/10.1061/(ASCE)EM.1943-7889.0001178 CrossRefGoogle Scholar
  19. Garcia PD, Guerrero CR, Garcia R (2017) Time-resolved nanomechanics of a single cell under the depolymerization of the cytoskeleton. Nanoscale 9:12051–12059.  https://doi.org/10.1039/C7NR03419A CrossRefGoogle Scholar
  20. Gavara N, Chadwick RS (2012) Determination of the elastic moduli of thin samples and adherent cells using conical atomic force microscope tips. Nat Nanotechnol 7(11):733–736.  https://doi.org/10.1038/nnano.2012.163 CrossRefGoogle Scholar
  21. Gorenflo R, Loutchko J, Luchko Y (2002) Computation of the Mittag–Leffler function E\(\alpha\),\(\beta\); and its derivative. Fractional Calculus and Applied Analysis 5Google Scholar
  22. Grady ME, Composto RJ, Eckmann DM (2016) Cell elasticity with altered cytoskeletal architectures across multiple cell types. J Mech Behav Biomed Mater 61:197–207.  https://doi.org/10.1016/j.jmbbm.2016.01.022 CrossRefGoogle Scholar
  23. Grzanka D, Domaniewski J, Grzanka A (2005) Effect of doxorubicin on actin reorganization in Chinese hamster ovary cells. Neoplasma 52:46–51Google Scholar
  24. Haubold HJ, Mathai AM, Saxena RK (2011) Mittag-leffler functions and their applications. J Appl Math 2011:1–51.  https://doi.org/10.1155/2011/298628. arXiv0909.0230MathSciNetCrossRefzbMATHGoogle Scholar
  25. Hayashi K, Iwata M (2015) Stiffness of cancer cells measured with an AFM indentation method. J Mech Behav Biomed Mater 49:105–111.  https://doi.org/10.1016/j.jmbbm.2015.04.030 CrossRefGoogle Scholar
  26. Heim LO, Rodrigues TS, Bonaccurso E (2014) Direct thermal noise calibration of colloidal probe cantilevers. Colloids Surf A Physicochem Eng Asp 443:377–383.  https://doi.org/10.1016/j.colsurfa.2013.11.018 CrossRefGoogle Scholar
  27. Hertz H, Jones DE, Schott GA (1896) Miscellaneous papers. Macmillan and Company, LondonGoogle Scholar
  28. Hildebrandt J (1969) Comparison of mathematical models for cat lung and viscoelastic balloon derived by Laplace transform methods from pressurevolume data. Bull Math Biophys 31(4):651–667.  https://doi.org/10.1007/BF02477779 CrossRefzbMATHGoogle Scholar
  29. Hiratsuka S, Mizutani Y, Toda A, Fukushima N (2009) Power-law stress and creep relaxations of single cells measured by colloidal probe atomic force microscopy. Jpn J Appl Phys 48(852):08JB17.  https://doi.org/10.1143/jjap.48.08jb17 CrossRefGoogle Scholar
  30. ISO E (1997) 4287-geometrical product specifications (gps)-surface texture: profile method-terms, definitions and surface texture parameters. International Organization for Standardization. Geneva, SwitzerlandGoogle Scholar
  31. Kim KS, Cho CH, Park EK, Jung MH, Yoon KS, Park HK (2012) AFM-detected apoptotic changes in morphology and biophysical property caused by paclitaxel in Ishikawa and HeLa cells. PLoS ONE 7(1):e30066.  https://doi.org/10.1371/journal.pone.0030066 CrossRefGoogle Scholar
  32. Kim SO, Kim J, Okajima T, Cho NJ (2017) Mechanical properties of paraformaldehyde-treated individual cells investigated by atomic force microscopy and scanning ion conductance microscopy. Nano Converg 4(1):5.  https://doi.org/10.1186/s40580-017-0099-9 CrossRefGoogle Scholar
  33. Koeller RC (1984) Applications of fractional calculus to the theory of viscoelasticity. J Appl Mech 51(2):299–307.  https://doi.org/10.1115/1.3167616 MathSciNetCrossRefzbMATHGoogle Scholar
  34. Kollmannsberger P, Fabry B (2011) Linear and nonlinear rheology of living cells. Ann Rev Mater Res 41:75–97.  https://doi.org/10.1146/annurev-matsci-062910-100351 CrossRefGoogle Scholar
  35. Kruskal WH, Wallis WA (1952) Use of ranks in one-criterion variance analysis. J Am Stat Assoc 47(260):583–621.  https://doi.org/10.1080/01621459.1952.10483441. arXiv:NIHMS150003 CrossRefzbMATHGoogle Scholar
  36. Landau L, Lifshitz E (1986) Theory of elasticity, 3rd edn. Pergamon Press, OxfordzbMATHGoogle Scholar
  37. Lekka M, Laidler P, Gil D, Lekki J, Stachura Z, Hrynkiewicz A (1999) Elasticity of normal and cancerous human bladder cells studied by scanning force microscopy. Eur Biophys J 28(4):312–316.  https://doi.org/10.1007/s002490050 CrossRefGoogle Scholar
  38. Lekka M, Pogoda K, Gostek J, Klymenko O, Prauzner-Bechcicki S, Wiltowska-Zuber J, Jaczewska J, Lekki J, Stachura Z (2012) Cancer cell recognition—mechanical phenotype. Micron 43(12):1259–1266.  https://doi.org/10.1016/j.micron.2012.01.019 CrossRefGoogle Scholar
  39. Li M, Liu L, Xiao X, Xi N, Wang Y (2016a) Effects of methotrexate on the viscoelastic properties of single cells probed by atomic force microscopy. J Biol Phys 42(4):551–569.  https://doi.org/10.1007/s10867-016-9423-6 CrossRefGoogle Scholar
  40. Li M, Liu L, Xiao X, Xi N, Wang Y (2016b) Viscoelastic properties measurement of human lymphocytes by atomic force microscopy based on magnetic beads cell isolation. IEEE Trans Nanobiosci 15(5):398–411.  https://doi.org/10.1109/TNB.2016.2547639 CrossRefGoogle Scholar
  41. Lin DC, Dimitriadis EK, Horkay F (2007) Robust strategies for automated AFM force curve analysis-I. non-adhesive indentation of soft, inhomogeneous materials. J Biomech Eng 129(6):430–440.  https://doi.org/10.1115/1.2720924 CrossRefGoogle Scholar
  42. Liu H, Wang N, Zhang Z, Wang H, Du J, Tang J (2017) Effects of tumor necrosis factor-\(\alpha\) on morphology and mechanical properties of HCT116 human colon cancer cells investigated by atomic force microscopy. Scanning.  https://doi.org/10.1155/2017/2027079 CrossRefGoogle Scholar
  43. Liu Y, Peterson DA, Kimura H, Schubert D (1997) Mechanism of cellular 3-(4, 5-dimethylthiazol-2-yl)-2, 5-diphenyltetrazolium bromide (mtt) reduction. J Neurochem 69(2):581–593.  https://doi.org/10.1046/j.1471-4159.1997.69020581.x CrossRefGoogle Scholar
  44. Mainardi F (2010) Fractional calculus and waves in linear viscoelasticity: an introduction to mathematical models. World Scientific, SingaporeCrossRefGoogle Scholar
  45. Marques SP, Creus GJ (2012) Computational viscoelasticity. 9783642253102, Springer. arXiv:1011.1669v3 CrossRefGoogle Scholar
  46. Molinari A, Calcabrini A, Crateri P, Arancia G (1990) Interaction of anthracyclinic antibiotics with cytoskeletal components of cultured carcinoma cells (CG5). Exp Mol Pathol 53(1):11–33.  https://doi.org/10.1016/0014-4800(90)90021-5 CrossRefGoogle Scholar
  47. Moreno-Flores S, Benitez R, dM Vivanco M, Toca-Herrera JL (2010) Stress relaxation microscopy: imaging local stress in cells. J Biomech 43(2):349–354.  https://doi.org/10.1016/j.jbiomech.2009.07.037 CrossRefGoogle Scholar
  48. Oudard S, Thierry A, Jorgensen TJ, Rahman A (1991) Sensitization of multidrug-resistant colon cancer cells to doxorubicin encapsulated in liposomes. Cancer Chemother Pharmacol 28(4):259–265.  https://doi.org/10.1007/BF00685532 CrossRefGoogle Scholar
  49. Pachenari M, Seyedpour SM, Janmaleki M, Shayan SB, Taranejoo S, Hosseinkhani H (2014) Mechanical properties of cancer cytoskeleton depend on actin filaments to microtubules content: investigating different grades of colon cancer cell lines. J Biomech 47(2):373–379.  https://doi.org/10.1016/j.jbiomech.2013.11.020 CrossRefGoogle Scholar
  50. Roylance D (2001) Engineering viscoelasticity. Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, pp 1–37Google Scholar
  51. Schiessel H, Metzler R, Blumen A, Nonnenmacher TF (1995) Generalized viscoelastic models: their fractional equations with solutions. J Phys A Math Gen 28(23):6567–6584.  https://doi.org/10.1088/0305-4470/28/23/012 CrossRefzbMATHGoogle Scholar
  52. Serpe L, Catalano MG, Cavalli R, Ugazio E, Bosco O, Canaparo R, Muntoni E, Frairia R, Gasco MR, Eandi M, Zara GP (2004) Cytotoxicity of anticancer drugs incorporated in solid lipid nanoparticles on HT-29 colorectal cancer cell line. European Journal of Pharmaceutics and Biopharmaceutics 58(3):673–680.  https://doi.org/10.1016/j.ejpb.2004.03.026 CrossRefGoogle Scholar
  53. Sneddon IN (1965) The relation between load and penetration in the axisymmetric boussinesq problem for a punch of arbitrary profile. Int J Eng Sci 3(1):47–57.  https://doi.org/10.1016/0020-7225(65)90019-4 MathSciNetCrossRefzbMATHGoogle Scholar
  54. Sousa JSD, Santos JAC, Barros EB, Alencar LMR, Cruz WT (2017) Analytical model of atomic-force-microscopy force curves in viscoelastic materials exhibiting power law relaxation. J Appl Phys 121(3):034901.  https://doi.org/10.1063/1.4974043 CrossRefGoogle Scholar
  55. Stiassnie M (1979) On the application of fractional calculus for the formulation of viscoelastic models. Appl Math Model 3(4):300–302.  https://doi.org/10.1016/S0307-904X(79)80063-3 CrossRefzbMATHGoogle Scholar
  56. Thorn CF, Oshiro C, Marsh S, Hernandez-Boussard T, McLeod H, Klein TE, Altman RB (2011) Doxorubicin pathways: pharmacodynamics and adverse effects. Pharmacogenet Genom 21(7):440.  https://doi.org/10.1097/FPC.0b013e32833ffb56 CrossRefGoogle Scholar
  57. Vargas-Pinto R, Gong H, Vahabikashi A, Johnson M (2013) The effect of the endothelial cell cortex on atomic force microscopy measurements. Biophys J 105(2):300–309.  https://doi.org/10.1016/j.bpj.2013.05.034 CrossRefGoogle Scholar
  58. Welch SW, Rorrer RA, Duren RG (1999) Application of time-based fractional calculus methods to viscoelastic creep and stress relaxation of materials. Mech Time-Dep Mater 3(3):279–303.  https://doi.org/10.1023/A:1009834317545 CrossRefGoogle Scholar
  59. Xiao L, Tang M, Li Q, Zhou A (2013) Non-invasive detection of biomechanical and biochemical responses of human lung cells to short time chemotherapy exposure using AFM and confocal Raman spectroscopy. Anal Methods 5(4):874–879.  https://doi.org/10.1039/C2AY25951F CrossRefGoogle Scholar
  60. Xu H, Jiang X (2017) Creep constitutive models for viscoelastic materials based on fractional derivatives. Comput Math Appl 73(6):1377–1384.  https://doi.org/10.1016/j.camwa.2016.05.002 MathSciNetCrossRefzbMATHGoogle Scholar
  61. Xu W, Mezencev R, Kim B, Wang L, McDonald J, Sulchek T (2012) Cell stiffness is a biomarker of the metastatic potential of ovarian cancer cells. PloS ONE 7(10):e46609.  https://doi.org/10.1371/journal.pone.0046609 CrossRefGoogle Scholar
  62. Yacoub TJ, Reddy AS, Szleifer I (2011) Structural effects and translocation of doxorubicin in a DPPC/Chol bilayer: the role of cholesterol. Biophys J 101(2):378–385.  https://doi.org/10.1016/j.bpj.2011.06.015 CrossRefGoogle Scholar
  63. Zhang H, zhe Zhang Q, Ruan L, Duan J, Wan M, Insana MF (2018) Modeling ramp-hold indentation measurements based on kelvin-voigt fractional derivative model. Meas Sci Technol 29(3):035701.  https://doi.org/10.1088/1361-6501/aa9daf CrossRefGoogle Scholar
  64. Zhang L, Jackson WJ, Bentil SA (2019) The mechanical behavior of brain surrogates manufactured from silicone elastomers. J Mech Behav Biomed Mater 95:180–190.  https://doi.org/10.1016/j.jmbbm.2019.04.005 CrossRefGoogle Scholar
  65. Zhao C, Yuan G, Jia D, Han CC (2012) Macrogel induced by microgel: bridging and depletion mechanisms. Soft Matter 8(26):7036–7043.  https://doi.org/10.1039/C2SM25409C CrossRefGoogle Scholar
  66. Zulfahmed (2015) Python implementation of Mittag-Leffler and its derivatives. URLhttps://zulfahmed.wordpress.com/2015/09/27/python-implementation-of-mittag-leffler-and-its-derivatives/

Copyright information

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

Authors and Affiliations

  • Maricela Rodríguez-Nieto
    • 1
  • Priscila Mendoza-Flores
    • 2
  • David García-Ortiz
    • 3
  • Luis M. Montes-de-Oca
    • 1
  • Marco Mendoza-Villa
    • 3
  • Porfiria Barrón-González
    • 2
  • Gabriel Espinosa
    • 1
  • Jorge Luis Menchaca
    • 3
    Email author
  1. 1.Instituto de Física y MatemáticasUniversidad Michoacana de San Nicolás de HidalgoMoreliaMexico
  2. 2.Facultad de Ciencias BiológicasUniversidad Autónoma de Nuevo LeónSan Nicolás de los GarzaMexico
  3. 3.Facultad de Ciencias Físico MatemáticasUniversidad Autónoma de Nuevo León, Centro de Investigación en Ciencias Físico MatemáticasSan Nicolás de los GarzaMexico

Personalised recommendations