Research Papers

Simultaneous Analysis of Elastic and Nonspecific Adhesive Properties of Thin Sample and Biological Cell Considering Bottom Substrate Effect

[+] Author and Article Information
Vishwanath Managuli

Applied Mechanics Department,
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mail: vishwanath.sm123@gmail.com

Sitikantha Roy

Applied Mechanics Department,
Indian Institute of Technology Delhi,
New Delhi 110016, India
e-mail: sroy@am.iitd.ac.in

1Corresponding author.

Manuscript received August 10, 2016; final manuscript received June 30, 2017; published online July 28, 2017. Editor: Victor H. Barocas.

J Biomech Eng 139(9), 091008 (Jul 28, 2017) (10 pages) Paper No: BIO-16-1334; doi: 10.1115/1.4037289 History: Received August 10, 2016; Revised June 30, 2017

A new asymptotically correct contact model has been developed for conical tip based atomic force microscopy (AFM) nanoindentation. This new model provides both elastic and nonspecific adhesion properties of cells and soft gels by taking sample thickness at the point of indentation and its depth of indentation into consideration. The bottom substrate effect (BSE) is the most common source of error in the study of “AFM force maps” of the cellular sample. The present model incorporates an asymptotically correct correction term as a function of depth of indentation to eliminate the substrate effect in the analysis. Later, the model is extended to analyze the unloading portion of the indentation curve to extract the stiffness and adhesive properties simultaneously. A comparative study of the estimated material properties using other established contact models shows that the provided corrections effectively curb the errors coming from infinite thickness assumption. Nonspecific adhesive nature of a cell is represented in terms of adhesion parameter (γa) based on the “work of adhesion,” this is an alternative to the peak value of tip–sample attractive (negative) force commonly used as representative adhesion measurement. The simple analytical expression of the model can help in estimating more realistic and accurate biomechanical properties of cells from atomic force microscopy based indentation technique.

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Suresh, S. , 2007, “ Biomechanics and Biophysics of Cancer Cells,” Acta Biomater., 3(4), pp. 413–438. [CrossRef] [PubMed]
Li, Q. S. , Lee, G. Y. , Ong, C. N. , and Lim, C. T. , 2008, “ AFM Indentation Study of Breast Cancer Cells,” Biochem. Biophys. Res. Commun., 374(4), pp. 609–613. [CrossRef] [PubMed]
Palmieri, V. , Lucchetti, D. , Maiorana, A. , Papi, M. , Maulucci, G. , Calapa, F. , Ciasca, G. , Giordano, R. , Sgambato, A. , and De Spirito, M. , 2015, “ Mechanical and Structural Comparison Between Primary Tumor and Lymph Node Metastasis Cells in Colorectal Cancer,” Soft Matter, 11(8), pp. 5719–5726. [CrossRef] [PubMed]
Zhou, Z. , Zheng, C. , Li, S. , Zhou, X. , Liu, Z. , He, Q. , Zhang, N. , Ngan, A. , Tang, B. , and Wang, A. , 2013, “ AFM Nanoindentation Detection of the Elastic Modulus of Tongue Squamous Carcinoma Cells With Different Metastatic Potentials,” Nanomed. Nanotechnol. Biol. Med., 9(7), pp. 864–874. [CrossRef]
Cross, S. E. , Jin, Y.-S. , Rao, J. , and Gimzewski, J. K. , 2009, “ Applicability of AFM in Cancer Detection,” Nat. Nanotechnol., 4(2), pp. 72–73. [CrossRef] [PubMed]
Cross, S. E. , Jin, Y.-S. , Rao, J. , Tondre, J. , Wong, R. , and Gimzewski, J. K. , 2008, “ AFM-Based Analysis of Human Metastatic Cancer Cells,” Nanotechnology, 19(38), p. 384003. [CrossRef] [PubMed]
Hung, M.-S. , and Tsai, M.-F. , 2015, “ Investigating the Influence of Anti-Cancer Drugs on the Mechanics of Cells Using AFM,” BioNanoScience, 5(3), pp. 156–161. [CrossRef]
Efremov, Y. M. , Dokrunova, A. A. , Efremenko, A. V. , Kirpichnikov, M. P. , Shitan, K. V. , and Sokolova, O. S. , 2015, “ Distinct Impact of Targeted Actin Cytoskeleton Reorganization on Mechanical Properties of Normal and Malignant Cells,” Biochim. Biophys. Acta, 1853(11 Pt. B), pp. 3117–3125. [CrossRef] [PubMed]
Morton, K. C. , and Baker, L. A. , 2014, “ Atomic Force Microscopy-Based Bioanalysis for the Study of Disease,” Anal. Methods, 6(14), pp. 4932–4955. [CrossRef]
Banguy, X. , Suarez, F. , Argaw, A. , Bouchard, J.-F. , Hildgen, P. , and Giasson, S. , 2009, “ Effect of Mechanical Properties of Hydrogel Nanoparticles on Macrophage Cell Uptake,” Soft Matter, 5(20), pp. 3984–3991. [CrossRef]
Vasir, J. K. , and Labhasetwar, V. , 2008, “ Quantification of the Force of Nanoparticle-Cell Membrane Interactions and Its influence on Intracellular Trafficking of Nanoparticles,” Biomaterials, 29(31), pp. 4244–4252. [CrossRef] [PubMed]
Haga, H. , Sasaki, S. , Kawabata, K. , Ito, E. , Ushiki, T. , and Sambongi, T. , 2000, “ Elasticity Mapping of Living Fibroblasts by AFM and Immunofluorescence Observation of the Cytoskeleton,” Ultramicroscopy, 82(1–4), pp. 253–258. [CrossRef] [PubMed]
Wagh, A. A. , Roan, E. , Chapman, K. E. , Desai, L. P. , Rendon, D. A. , Eckstein, E. C. , and Waters, C. M. , 2008, “ Localized Elasticity Measured in Epithelial Cells Migrating at a Wound Edge Using Atomic Force Microscopy,” Lung Cell. Mol. Physiol., 295(1), pp. L54–L60. [CrossRef]
Hansen, J. C. , Lim, J. Y. , Xu, L. , Siedleckia, C. A. , Mauger, D. T. , and Donahu, H. J. , 2007, “ Effect of Surface Nanoscale Topography on Elastic Modulus of Individual Osteoblastic Cells as Determined by Atomic Force Microscopy,” J. Biomech., 40(13), pp. 2865–2871. [CrossRef] [PubMed]
Wang, B. , Guo, P. , and Auguste, D. T. , 2015, “ Mapping the CXCR4 Receptor on Breast Cancer Cells,” Biomaterials, 57, pp. 161–168. [CrossRef] [PubMed]
Almqvist, N. , Bhatia, R. , Primbs, G. , Desai, N. , Banerjee, S. , and Lal, R. , 2004, “ Elasticity and Adhesion Force Mapping Reveals Real-Time Clustering of Growth Factor Receptors and Associated Changes in Local Cellular Rheological Properties,” Biophys. J., 86(3), pp. 1753–1762. [CrossRef] [PubMed]
Zammaretti, P. S. , and Ubbink, J. , 2003, “ Imaging of Lactic Acid Bacteria With AFM—Elasticity and Adhesion Maps and Their Relationship to Biological and Structural Data,” Ultramicroscopy, 97(1–4), pp. 199–208. [CrossRef] [PubMed]
Sirghi, L. , Ponti, J. , Broggi, F. , and Rossi, F. , 2008, “ Probing Elasticity and Adhesion of Live Cells by Atomic Force Microscopy Indentation,” Eur. Biophys. J., 37(6), pp. 935–945. [CrossRef] [PubMed]
Johnson, K. L. , 2003, Contact Mechanics, Cambridge University Press, Cambridge, UK, Chap. 4.
Sneddon, I. N. , 1965, “ The Relation Between Load and Penetration in the Axisymmetric Boussinesq Problem for a Punch of Arbitrary Profile,” Int. J. Eng. Sci., 3(1), pp. 47–57. [CrossRef]
Sun, Y. , Akhremitchev, B. , and Walker, G. C. , 2004, “ Using the Adhesive Interaction Between Atomic Force Microscopy Tips and Polymer Surfaces to Measure the Elastic Modulus of Compliant Samples,” Langmuir, 20(14), pp. 5837–5845. [CrossRef] [PubMed]
Sen, S. , Subramanian, S. , and Discher, D. , 2005, “ Indentation and Adhesive Probing of a Cell Membrane With AFM: Theoretical Model and Experiments,” J. Biophys., 89(5), pp. 3203–3213. [CrossRef]
Johnson, K. L. , Kendall, K. , and Roberts, A. D. , 1971, “ Surface Energy and the Contact of Elastic Solids,” Proc. R. Soc. London, 324(1558), pp. 301–313. [CrossRef]
Sirghi, L. , 2010, “ Atomic Force Microscopy Indentation of Living Cells,” Microscopy: Science, Technology, Applications and Education, Formatex Research Center, Badajoz, Spain, pp. 433–440.
Sirghi, L. , and Rossi, F. , 2006, “ Adhesion and Elasticity in Nanoscale Indentation,” Appl. Phys. Lett., 89(24), p. 243118. [CrossRef]
Costa, K. D. , and Yin, F. C. P. , 1999, “ Analysis of Indentation: Implications for Measuring Mechanical Properties With Atomic Force Microscopy,” ASME J. Biomech. Eng., 121(5), pp. 462–471. [CrossRef]
Xu, W. , Mezencev, R. , Kim, B. , Wang, L. , McDonald, J. , and Sulchek, T. , 2012, “ Cell Stiffness Is a Biomarker of the Metastatic Potential of Ovarian Cancer Cells,” PLoS One, 7(10), p. e46609. [CrossRef] [PubMed]
Crick, S. L. , and Yin, F. C.-P. , 2007, “ Assessing Micromechanical Properties of Cells With Atomic Force Microscopy: Importance of the Contact Point,” Biomech. Modell. Mechanobiol., 6(3), pp. 199–210. [CrossRef]
Kim, Y. , Kim, M. , Shin, J. H. , and Kim, L. , 2011, “ Characterization of Cellular Elastic Modulus Using Structure Based Double Layer,” Med. Biol. Eng. Comput., 49(4), pp. 453–462. [CrossRef] [PubMed]
Dimitriadis, E. K. , Horkay, F. , Maresca, J. , Kachar, B. , and Chadwick, R. S. , 2002, “ Determination of Elastic Moduli of Thin Layers of Soft Material Using the Atomic Force Microscope,” J. Biophys., 82(5), pp. 2798–2810. [CrossRef]
Mahaffy, R. E. , Park, S. , Ferde, E. , Kas, J. , and Shih, C. K. , 2004, “ Quantitative Analysis of the Viscoelastic Properties of Thin Regions of Fibroblasts Using Atomic Force Microscopy,” Biophys. J., 86(3), pp. 1777–1793. [CrossRef] [PubMed]
Santos, J. A. C. , Rebelo, L. M. , Araujo, A. C. , Barros, E. B. , and De Sousa, J. S. , 2012, “ Thickness-Corrected Model for Nanoindentation of Thin Films With Conical Indenters,” Soft Matter, 8(16), pp. 4441–4148. [CrossRef]
Gavara, N. , and Chadwick, R. S. , 2012, “ Determination of the Elastic Moduli of Thin Samples and Adherent Cells Using Conical Atomic Force Microscope Tips,” Nat. Nanotechnol., 7(11), pp. 733–736. [CrossRef] [PubMed]
Lin, D. C. , and Horkay, F. , 2008, “ Nanomechanics of Polymer Gels and Biological Tissues: A Critical Review of Analytical Approaches in the Hertzian Regime and Beyond,” Soft Matter, 4(4), pp. 669–682 [CrossRef]
Betti, E. , 1872, IlnuovoCimento (Societaitaliana di Fisica), Italian Physical Society, Bologna, Italy.
Lord Rayleigh, 1873, “London Mathematics Society Proceedings,” The London Mathematical Society, London.
Landau, L. D. , and Lifshitz, E. M. , 1975, Theory of Elasticity, Pergamon Press, Oxford, UK, Chap. 1.
Shield, R. T. , 1967, “ Load Displacement Relations for Elastic Bodies,” Z. Angew. Math. Phys., 18(5), pp. 682–693. [CrossRef]
Israelachivili, J. N. , 1992, Intermolecular and Surface Forces, 3rd ed., Academic Press, Santa Barbara, CA, Chap. 10.
Tse, J. R. , and Engler, A. J. , 2010, “ Preparation of Hydrogel Substrates With Tuneable Mechanical Properties,” Current Protocols in Cell Biology, Wiley, Hoboken, NJ, Chap. 10.
Pelham, R. J. , and Wang, Y. , 1997, “ Cell Locomotion and Focal Adhesion Are Regulated by Substrate Flexibility,” Proc. Natl. Acad. Sci. U.S.A., 94(25), pp. 13661–13665. [CrossRef] [PubMed]
Schaus, Y. A. , Okes, P. W. , Sticker, J. , Winter, S. P. , and Gardel, M. L. , 2010, “ Preparation of Complaint Matrices for Quantifying Cellular Contraction,” JOVE, 46, p. 2173.
Hutter, J. L. , and Bechhoefer , 1993, “ Calibration of Atomic Force Microscope Tips,” Rev. Sci. Instrum., 64(7), pp. 1868–1873. [CrossRef]
Darling, E. M. , Zauscher, S. , Block, J. A. , and Guilak, F. , 2007, “ A Thin-Layer Model for Viscoelastic, Stress-Relaxation Testing of Cells Using Atomic Force Microscopy: Do Cell Properties Reflect Metastatic Potential?,” J. Biophys., 92(5), pp. 1784–1791. [CrossRef]
MathWorks, 2014, “ MATLAB and Statistics Toolbox Release 2014,” The MathWorks, Inc., Natick, MA.
Gunning, A. P. , Chambers, S. , Pin, C. , Man, A. L. , Morris, V. J. , and Nicoletti, C. , 2008, “ Mapping Specific Adhesive Interaction on Living Human Intestinal Epithelial Cells With Atomic Force Microscopy,” FASEB J., 22(7), pp. 2331–2339. [CrossRef] [PubMed]
Zhu, C. , 2000, “ Kinetics and Mechanics of Cell Adhesion,” J. Biomech., 33(1), pp. 23–33. [CrossRef] [PubMed]
Zhu, A. P. , Fang, N. , Chan-Park, M. B. , and Chan, V. , 2006, “ Adhesion Contact Dynamics of 3T3 fibroblasts on Poly (Lactide-co-Glycolide Acid) Surface Modified by Photochemical Immobilization of Biomacromolecules,” Biomaterials, 12(12), pp. 2566–2576. [CrossRef]
Mathur, A. B. , Collinsworth, A. M. , Reichert, W. M. , Kraus, W. E. , and Truskey, G. A. , 2001, “ Endothelial, Cardiac Muscle and Skeletal Muscle Exhibit Different Viscous and Elastic Properties as Determined by Atomic Force Microscopy,” J. Biomech., 34(12), pp. 1545–1553. [CrossRef] [PubMed]
Wolfram Research, 2012, “ Mathematica (Programming Language), Version 9.0,” Wolfram Research Inc., Champaign, IL.


Grahic Jump Location
Fig. 1

(a) Raw indentation data obtained from nucleus region of the cell. Contact point, maximum force (Fmax), and detachment point are denoted by a, b, and c, respectively. Indentation data are shifted to origin after separating the precontact and postdetachment data. (b) First and second column of plots shows the loading and unloading curve fitted with the present model (using Eqs. (7) and (11)) and their subsequent residuals along indentation depth. Both loading and unloading show residuals of similar magnitude (20–40 pN), except few point in the beginning of unloading process which might be due to creep at tip–sample contact.

Grahic Jump Location
Fig. 2

(a) Comparison of average elastic properties measured from unloading curves on thick gels of two different stiffnesses using Sirghi and Rossi [25] (based on infinite thickness assumption) and present contact model, where A: acrylamide and B: bis-acrylamide (n = 20 curves). (b) and (c) Comparison of the mean elastic property of MCF-7 cells extracted from loading and unloading curves for 500 pN and 1000 pN indentation force. Elastic properties evaluated from Sneddon's [20] (loading curve), Sirghi and Rossi [25] (unloading curve) contact models, and compared with present model. In the case of loading curve analysis, new contact model without adhesion term (Eq. (7)) is used in curve fitting (n = 20 cells). (n = 20 cells).

Grahic Jump Location
Fig. 3

(a) Cell height profile and indentation depth derived from AFM F–z curves taken along the indentation axis and (b) δ/h variation along the axis of indentation. (c) and (d) Elastic and adhesion property variation along the length of indentation. (e) Comparison of the effect of finite thickness correction on E and γ properties. The deviation in evaluated properties between two models at every location is normalized by dividing them with respective properties observed at nucleus region.

Grahic Jump Location
Fig. 4

A point force (P) is acting at point C on the sample surface. An observation point A which is at an in-plane distance of s from point C will displace by z in the transverse direction, where Ω is an area of the sample, P is the pressure force, and ɵ is the angular distance.

Grahic Jump Location
Fig. 5

Experimental force–indentation curves show (a) stiffening effect at thin region of sample, (b) presence of adhesion (gel sample), and (c) presence of viscosity and adhesion (cell sample)

Grahic Jump Location
Fig. 6

Contact mode image of soft gel surface shows that sample is well bonded to the substrate. Indentation data's are collected prior to imaging the gel surface.



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