AFM-based spherical indentation of a brush-coated soft material: modeling the bottom effect

It is a common practice in the atomic force microscopy (AFM)-based studies of living cells to differentiate them by values of the elastic (Young's) modulus, which is supposed to be an effective characteristic of the mechanical properties of a cell as a heterogeneous matter. The elastic response of a cell to AFM indentation is known to be affected by a relative distance from an AFM probe to a solid support on to which the cell is cultured. Besides this so-called bottom effect, AFM measurements may carry significant information regarding the effect of molecular brushes covering living cells. Here, we develop a mathematical model for determining the intrinsic effective Young's modulus of a single brush-coated cell from the force-indentation curve with the bottom effect taken into account. The mathematical model is illustrated with the example of AFM data on testing of an eukaryotic cell taken from the literature.