Noncontact Viscoelastic Imaging of Living Cells Using a Long-Needle Atomic Force Microscope with Dual-Frequency Modulation

Imaging of surface topography and elasticity of living cells can provide insight into the roles played by the cells’ volumetric and mechanical properties and their response to external forces in regulating the essential cellular events and functions. Here, we report a unique technique of noncontact viscoelastic imaging of live cells using atomic force microscopy (AFM) with a long-needle glass probe. Because only the probe tip is placed in a liquid medium near the cell surface, the AFM cantilever in air functions well under dual-frequency modulation, retaining its high-quality resonant modes. The probe tip interacts with the cell surface through a minute hydrodynamic flow in the nanometer-thin gap region between them without physical contact. Quantitative measurements of the cell height, volume, and Young’s modulus are conducted simultaneously. The experiment demonstrates that the long-needle AFM has a wide range of applications in the study of cell mechanics.

Figure 1

Schematic of the system. (a) Sketch of the experimental setup. The inset shows the flow geometry in the gap region between the fiber tip and cell surface. (b) A scanning electron microscope image of the actual long glass fiber of diameter $d\simeq 2.5\mu \mathrm{m}$ and length $\ell \simeq 180\mu \mathrm{m}$. The inset shows a magnified image of the fiber tip with radius $R\simeq 200\mathrm{nm}$. (c) A flowchart showing the AFM controls for simultaneous topographic and viscoelastic mapping with dual-frequency modulation (see text for more details).

Figure 2

Simultaneously measured (a) amplitude $A_1$, (b) phase ${\phi }_1$, (c) resonant frequency $f_0$, (d) driving voltage $V_0$, and (e) deflection $z$ of the AFM cantilever as a function of surface separation $D$ between the needle tip and cell surface. The measurement is made with the needle tip approaching the cell surface at a constant speed $u=100\mathrm{nm}/\mathrm{s}$. The gray dashed line in (e) illustrates the traditional elastic measurement on living cells by a forced indentation.

Figure 3

Measured response function $K^{*}(D)$ for a living Hela cell. The real part $K^{\prime }(D)$ (red circles) and imaginary part $K^{\prime \prime }(D)$ (red triangles) of $K^{*}(D)$ are obtained when a long-needle probe with tip radius $R=355\mathrm{nm}$ approaches the cell surface. The blue dashed line shows the Reynolds damping [Eq. (2)] for a rigid substrate, and the green dotted vertical line indicates the crossover distance $D_c\simeq 100\mathrm{nm}$. The black solid lines show the fits of the numerically calculated Eq. (3) to the data with the cell Young’s modulus $E=58\pm 5\mathrm{kPa}$ and viscosity $\eta =11.9\pm 2.4\mathrm{cP}$.

Figure 4

(a) Calculated $\tilde{p}(0;\alpha ,\beta )$ as a function of $\alpha$ for different values of $\beta$ (color symbols) using the numerical solution of Eq. (3). The black solid line shows the analytical solution $\tilde{p}(0;\alpha ,0)$ given in Eq. (8). (b) Scaling plot of $\tilde{p}(0;\alpha ,\beta )[1+0.12(\beta /\alpha {)}^2]$ as a function of $\alpha /(1+0.2\beta )$. The data used are the same as those in (a). The black solid line is the analytical solution $\tilde{p}(0;\alpha ,\beta )$ given in Eq. (9).

Figure 5

AFM images of a living Hela cell. (a),(b) Images of cell height $h$ and phase ${\phi }_1$ obtained under the tapping mode. (c),(d) Images of resonant frequency ${\omega }_0$ and dissipative force $F_2$ simultaneously obtained under the FM mode. (e) 3D height image converted from (a). (f) Image of Young’s modulus $E$ converted from images (a),(c),(d). The scale bar is $10\mu \mathrm{m}$ for all figures.

Figure 6

Mechanical changes during the cell division. Optical image (first row) and AFM images of 3D height $h$ (second row) and Young’s modulus $E$ (third row) of living Hela cells at four different stages of the cell division: interphase (a), mitosis (b), cytokinesis (c), and two daughter cells after division (d). (e)–(g) Histograms of the measured $E$ in (a)(iii), (b)(iii), and (c)(iii), respectively. (h) Variations of the cell volume $V$ at the four stages of the cell division. The scale bars are $10\mu \mathrm{m}$.