Table 4.

Using Atomic Force Microscopy to determine cell stiffness, with emphasis on methods to detect mechanical effects of IFs

1. AFM cantilever calibration. Before each experiment, the cantilever is moved down onto a rigid surface such as the bottom of the glass or plastic plate while measuring the bending of the cantilever, as assessed by the laser beam deflected from its surface and the vertical displacement of the base of the cantilever as determined by the piezoelectric device. Since the rigid surface cannot be deformed by the relatively soft AFM cantilevers used for cells, any difference between the vertical displacement of the cantilever tip and base is due to deflection of the cantilever. The measured deflection is calibrated by taking the slope of the cantilever deflection vs. piezo displacement curve. The spring constant of the cantilever is then determined by measuring its resonance frequency in liquid, as discussed in detail elsewhere (Levy & Maaloum, 2002).

2. Culture cells on standard glass or plastic dishes or on substrates of adjustable stiffness. The substrates need to be rigidly held in a container that is large enough in diameter and deep enough to allow the AFM column (often call the head) which holds the cantilever, to be immersed into medium above the cell. Typically the width of the dish is >20 mm and the depth of liquid above the cell is several mm. The piezoelectric devices that move the AFM probe vertically have limited range, so the depth of liquid cannot be much larger than mm.

3. Identifying the point of contact between AFM probe and cell surface. Usually, the probe is moved near the cell surface using the microscope stage and imaging the focal plain of the AFM probe relative to that of the cell's apical surface. Once near enough to allow the piezoelectric drive to span the remaining distance, (generally several microns) the final movements are made by the AFM software and hardware. The probe can be moved slowly until the deflection of the laser beam indicates that the cantilever is beginning to bend, presumably because it has touched the tip of the cell. Other methods based on changes in resonance can also determine the point at which contact is made.

4. Indentation of the cell surface. As the AFM tip descends farther into the cell or gel, the cantilever will become increasingly bent (unless something breaks or slips) and the result is a force-extension curve where force is calculated from the measured bending of the cantilever, and extension from the vertical displacement of the AFM tip.

5. Force-displacement measurements. The force-displacement data derived from the initial indentation into the sample are generally limited to a few hundred nms, over a time on the order of a second, depending on the shape of the probe, the material properties of interest, and the capabilities of the instrument hardware and software. Indentation is usually followed immediately by retraction. Perfect superposition of the indentation and retraction curves is expected for a purely elastic material to which the probe does not adhere. In reality, there is usually a difference between the indentation and retraction curves. The area between the curves is a measure of energy dissipated during the deformation, and often termed the plasticity index, but it is not simply related to a material constant such as a viscosity. This quantity is particularly dependent on the depth to which cells are indented and changes as a result of differences in IF expression.

6. Calculation of elastic modulus. Quantifying the cell stiffness requires calculating an elastic modulus (usually the Young's modulus, a material property) from the force-extension curve (an experimental system-specific set of values). Conversion of force-indentation curves to absolute values of stiffness is perhaps the most challenging aspect of AFM measurements and the one most likely to lead to errors. Generally, a formula like that derived by Hertz is used to calculate elastic moduli from force measurements by accounting for the size and shape of the AFM probe and making assumptions about the nature of the sample's surface. For a spherical or hemi-spherical shape AFM tip, the Hertz relation is:

$f=k^{*}d=\frac{4}{3}\frac{E{R}^{1/2}{\delta }^{3/2}}{(1-{\nu }^2)}$

where f is the force applied to the cell, k is the spring constant of the cantilever, d is the deflection of the cantilever, E is the Young’s modulus of the cell or other sample, R is the radius of the bead, δ is the indentation into the cell and ν is the Poisson’s ratio of the cell (a value related to the extent to which the sample maintains constant volume when deformed and often assumed to be near 0.5 for full volume conservation). For different geometries of the AFM tip the form of the Hertz relation varies, as detailed in several recent reports (Guz, Dokukin, Kalaparthi, & Sokolov, 2014; Melzak & Toca-Herrera, 2015; Thomas, Burnham, Camesano, & Wen, 2013).

7. IF-specific AFM methods and results. Detecting the mechanical effects of changes in IF expression by AFM depends on the way the cell is deformed. For example, loss of keratin leads to softening detected by small amplitude deformation of the cell surface, but often loss of vimentin does not. However, when cells are repeatedly deformed or deformed to greater depths, loss of vimentin becomes evident by changes in elastic modulus or plasticity index.