Automated analysis of AFM indentation curves

When estimating the stiffness of cells using AFM, we need to indent the cells at points that can be uniquely defined. This is paramount because when comparing the stiffness of cells, we need to measure at similar points on each cell. We describe a technique to obtain cell stiffness at the apex of the nucleus.

Cells were first imaged (Fig. 1a) in the contact mode using a small contact force. The approximate position of the nucleus was identified from the topography image. Multiple force-displacement curves (typically 4 × 4 grid) on a small region (typically 5 μm × 5 μm) above the nucleus was obtained. Each of these curves were analyzed to obtain the apparent modulus of elasticity of the cell and the point of contact between the cantilever tip and the cell (Fig. 1b). The highest point among the contact points is chosen as the apex of the nucleus and the corresponding modulus is chosen as the elastic modulus of the cell (Fig. 1c).

Figure 1: Measuring the stiffness of the cell using AFM: (a) Topography of a cell obtained by contact imaging. The 4x4 grid on top of the nucleus is also shown (b) Typical f-d curve (dotted blue curve), after base correction (solid black curve) and the Hertzian contact model fit (bold red curve). The red marker shows the point of contact. (c) The contact points at each grid point represented as a surface. The highest contact point is chosen as the top of the nucleus.

For obtaining the elastic modulus and the point of contact from the f-d curves, we have used the Hertzian contact model. First, the approach region of the f-d curve when the cantilever is not in contact with the cell is identified and the force in this region is corrected to zero . In this region, the f-d curve is linear and almost flat (blue curve in Fig. 1b). A straight line is fit to this region and this line is subtracted from the f – d curve to correct for the baseline force (black curve in Fig. 1b). The elastic modulus and contact point is now obtained from the baseline-corrected f-d curve by fitting a Hertzian contact model for the region slightly away from the point of contact (typically between 0.4 – 1 nN). The highest point among the points of contact is chosen as the apex of the nucleus and the elastic modulus corresponding to that point is the apparent modulus of elasticity of the cell.

The algorithm was coded in MATLAB. Using this routine a large number of AFM indentation curves could be conveniently analysed. Codes are available on request.

Details are available in the supplementary information of our pre-print.