Mechanics of Biological Systems and Materials, Volume 6

to obtain the cantilever stiffness (~0.05 N/m), subsequent measurements are set to trigger on cantilever deflection. Approach velocity of the AFM cantilever during indentation is set at 500 nm/s and kept constant. Because cells can exhibit frequency dependence as explored in Sect. 24.3.2, we limit the indentation depth and set the same approach velocity so that the same probing frequency is maintained for all cells regardless of stiffness. All measurements were conducted in recording buffer solution. 24.2.4 Approach Velocity Modulation Following Caporizzo et al. [7], who pioneered the Variable Indentation-rate Viscoelastic Analysis (VIVA) method, the apparent elastic modulus is measured on the same cell, in the same location, with varying approach velocity. By varying the approach velocity while maintaining the same indentation depth, the corresponding probing frequency is therefore varied by, f ¼V=δ; ð24:1Þ where f is the frequency (s 1), Vis the approach velocity (m/s), and δ is the indentation depth (m). Six approach velocities were chosen: 0.1, 0.2, 0.5, 1, 2, and 5 (μm/s). At each approach velocity, 3–5 force indentation curves were recorded, and the frequency was calculated from Eq. (24.1) and ranged 0.3–24 s 1. The elastic modulus at each approach velocity was extracted using the force curve analysis discussed in Sect. 24.2.5. The geometric mean of the elastic modulus values was calculated for each approach velocity. The calculated frequencies were averaged at each approach velocity. This procedure gives rise to an apparent elastic modulus over a range of frequencies in order to identify the viscoelastic properties of living cells. 24.2.5 Force Curve Analysis Stiffness measurements were acquired on multiple cultured substrates for a given test condition and were repeated. One perinuclear location on each cell was indented for elasticity measurements. Five successive measurements were taken and the moduli values from the Hertz model were averaged with good agreement (Fig. 24.1c). The trigger point was set to cantilever deflection indicated in Fig. 24.1b, which ranged 5–20 nm. The amount of resulting indentation within the cell will depend on the stiffness of the cell; therefore the cantilever deflection trigger set point was varied to maintain similar indentation depths for all cell lines. The average indentation depth across all measurements was 360 200 nm. The number of cells tested in each condition ranged from 33 to 49, an overall average of 36 cells per condition, resulting in 542 total number of cells tested. Fig. 24.1 (a) Side view schematic of an AFM cantilever over a cell, highlighting the substrate effects from measurements taken in the cell periphery. (b) Five successive force curve measurements taken on a fibroblast cell with Hertz model fit in black, approach curve inred, retraction curve in blue. Using Eqs. (24.2) and (24.3), average modulus value for the five curves is 1.97 0.07 kPa. (c) Image from the inverted optical microscope (Nikon oil-immersion 100 objective) of a human dermal fibroblast cell underneath the AFM cantilever with colloid positioned perinuclear (outlines of cell and nucleus, and colloid for visualization). Adapted from [17] 24 Cytoskeletal Perturbing Drugs and Their Effect on Cell Elasticity 171

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