Measuring nanoscale viscoelastic parameters of cells directly from AFM force-displacement curves

Yuri M Efremov,Arvind Raman,Robert L Geahlen,Shana D Hardy,Wen-Horng Wang

doi:10.1038/s41598-017-01784-3

Abstract

Force-displacement (F-Z) curves are the most commonly used Atomic Force Microscopy (AFM) mode to measure the local, nanoscale elastic properties of soft materials like living cells. Yet a theoretical framework has been lacking that allows the post-processing of F-Z data to extract their viscoelastic constitutive parameters. Here, we propose a new method to extract nanoscale viscoelastic properties of soft samples like living cells and hydrogels directly from conventional AFM F-Z experiments, thereby creating a common platform for the analysis of cell elastic and viscoelastic properties with arbitrary linear constitutive relations. The method based on the elastic-viscoelastic correspondence principle was validated using finite element (FE) simulations and by comparison with the existed AFM techniques on living cells and hydrogels. The method also allows a discrimination of which viscoelastic relaxation model, for example, standard linear solid (SLS) or power-law rheology (PLR), best suits the experimental data. The method was used to extract the viscoelastic properties of benign and cancerous cell lines (NIH 3T3 fibroblasts, NMuMG epithelial, MDA-MB-231 and MCF-7 breast cancer cells). Finally, we studied the changes in viscoelastic properties related to tumorigenesis including TGF-β induced epithelial-to-mesenchymal transition on NMuMG cells and Syk expression induced phenotype changes in MDA-MB-231 cells.

Highlights

In recent years interest has increased in the measurement of the viscoelastic properties of soft biological samples motivated by their correlation with disease, differentiation, or cellular transformation[1,2,3,4]
The method is validated with finite element (FE) simulations, with experiments performed on polyacrylamide hydrogel (PAAm) samples, and by comparison with the existed Atomic Force Microscopy (AFM) viscoelasticity measurement techniques
We show that the developed method is highly robust, does not require changes in experimental design and is compatible with findings from conventional AFM microrheology

Summary

Introduction

In recent years interest has increased in the measurement of the viscoelastic properties of soft biological samples motivated by their correlation with disease, differentiation, or cellular transformation[1,2,3,4]. The Hertz model or its modifications are applied to the approach part of the F-Z curve to extract Young’s modulus (EHertz), the elastic parameter used for characterization of the sample’s mechanical properties[18, 19]. We propose a new method to extract viscoelastic properties of soft samples like cells and hydrogels directly from standard AFM F-Z curves. This method is based on the theoretical model developed by Ting[32] for the problem of the indentation of a linear viscoelastic half-space by a rigid axisymmetric indenter for arbitrary load history. We tested applicability of two commonly used relaxation models, standard linear solid (SLS) and power-law rheology (PLR), on data collected on hydrogels and the above cell lines

Methods

Results

Conclusion