Measuring The Viscoelastic Mechanical Properties Of Cells Based On Atomic Force Microscopy

The mechanical properties of cells play essential roles in the biological and physiological processes such as cell migration,cell division,cell differentiation,cell adhesion as well as cellular uptake of nanoparticles.It is suggested from a series of relevant research that the cell mechanical properties can be treated as important indicators in the field of pathological analysis and biomedical engineering.Therefore,the accurate measurement of the cell mechanical properties is of great interest to advancing our fundamental biological understandings as well as many practical applications such as detection,diagnosis,and treatment of diseases.However,based on the traditional elastic model,the studies of measuring the cell mechanical properties show that the measured Young's modulus of the same cell line was quite different in different researches and are influenced by the experimental environment and loading mode.Therefore,how to detect the cell mechanical properties in an accurate way is urgently required.Indeed,cells are soft viscoelastic materials showing both solid-like elasticity and fluid-like viscous properties.In this way,extensive efforts have been conducted to address the mechanical properties of cells by using a variety of linear viscoelastic models.However,the associated constitutive equations of cells obtained from these experiments are still difficult to unify,and often need a large number of viscoelastic parameters to fit the measured data in their own experiments.In addition,the measured results on cell mechanical properties show significant dependent on loading conditions.On the other hand,before choosing a mechanical model to describe cell mechanical properties,the linear and nonlinear cell deformation should be identified in advance.Here,this paper integrates the atomic force microscope indentation experiments and continuum mechanics theory to systematically investigate the cell mechanical viscoelastic properties,such as constitutive relationship,creep,relaxation,tip size-dependent mechanical properties as follows:(1)Creep and relaxation are the important characters of all viscoelastic materials.This work measured the mechanical properties of normal hepatic(L02),hepatic cancer(Hep G2),hepatic stellate(LX2),normal gastric(GES-1)and gastric cancer(AGS,NCI-N87,SGC7901 and HGC-27)cell lines by creep and relaxation loading respectively.For the linear viscoelastic cell lines,this work calculated their trajectories of creep compliance and relaxation modulus based on the indentation theory of linear viscoelastic body.For the nonlinear viscoelastic cell lines,this work calculated their normalized relaxation modulus by the dimensionless law of contact between rigid indenter and generalized viscoelastic body.Both linear viscoelastic cell lines and nonlinear viscoelastic cell lines,this work listed their viscoelastic parameters extracted by our experimental data.This work provides a reference experimental method for determining the linear and nonlinear viscoelastic properties of cells by creep and relaxation experiments,and gives executable suggestions for establishing a convenient viscoelastic parameters system of cells.(2)According to the convolution relationship between creep compliance and relaxation modulus in linear viscoelastic theory,this work first proposed a method of verifying whether the cell line is a nonlinear viscoelastic material though independent creep and relaxation measurement.By using this method to verify the above human cell lines,it is found that human gastric normal cell line GES-1,human gastric cancer cell lines SGC7901 and HGC-27 have obvious nonlinear viscoelastic properties.This work provides an important basis for the selection of theoretical constitutive models about quantitative measurement of cell mechanical properties,and points out the deficiency of using linear viscoelastic theory to analyze cell mechanical properties in previous experimental studies.(3)In order to avoid the deviation of cell mechanical properties caused by measurement method,this work also studied the influences of loading mode,loading force and the tip geometry of probes on the measurement of cellular viscoelastic mechanical properties.For the loading mode,the viscoelastic properties of human breast cancer cell line MCF-7 was measured by relaxation loading and constant loading at different speeds,respectively.Based on the analysis of viscoelastic theory and contact mechanics,it is pointed out that the loading mode does not influence the measured viscoelastic properties of cells.For the loading force,this work measured human normal hepatic cell line L02 by using the same indenter with varies loading force;For the tip geometry of probes,this work also indented L02 cells with the nanotube tip.The experimental data indicate the cells have multi-scale nano-mechanical structures,and both loading force and indenter geometry will influence the measured mechanical properties of cells.However,these influences can be eliminated by using probes with a large contact area and low loading force during the measurement of the overall cell mechanical properties.This work provides an important reference for establishing an effective measuring method of cell viscoelastic properties.(4)This work proposed an experimental method to measure the cell viscoelastic properties by eliminating bottom effect.Based on this method,this work measured the viscoelastic properties in different region of L02 cells.The measuring results indicate the intrinsic connection between the distribution law of viscoelastic properties and cell morphology.This work provides a reference data support for solving mechanical problems in the field of cell biology and pathological analysis.