AFM Cell Indentation: Fluid Shell Model

Cellular mechanical properties provide insights into the state and health of cells. However, accurately measuring these properties is challenging due to the small size and low stiffness of cells. In recent years, Atomic Force Microscopy (AFM) has emerged as a promising tool for assessing the mechanical characteristics of individual cells. The evaluation of AFM measurements is complicated by the nonlinear contact between the AFM tip and the cell, which induces deformations throughout the entire cell. This leads to a nonlinear cell stiffness that varies with the depth of indentation. To bridge the gap between measured indentation data and the inherent material properties of the cell, irrespective of the experimental setup, we have introduced a theoretical model for cell deformation during indentation. Our model is built upon the Laplace equation adopted for fluid membranes. It predicts the areas of contact and the corresponding indentation forces as functions of indentation depth, aligning closely with experimental observations. Furthermore, our model takes into consideration both the size of the AFM tip and the dimensions of the cell while characterizing cell material properties through an area expansion modulus. Notably, this material parameter, derived by fitting the AFM deflection curve of DPPC liposomes, falls within the range documented in existing literature. This model holds the potential for further enhancement by factoring in adhesion energy and exploring the effects of different AFM tip shapes. Such refinements could advance our understanding of cell mechanics by accurately measuring cell membrane intrinsic material properties.