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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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.

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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).

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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.

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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.

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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)

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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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