Influence of cell spreading and contractility on stiffness measurements using AFM†

Atomic Force Microscopy (AFM) is widely used for measuring mechanical properties of cells, and to understand how cells respond to their mechanical environments. A standard method for obtaining cell stiffness from experimental force–indentation curves is based on the simplified Hertz theory developed for studying the indentation of a semi-infinite elastic body by a spherical punch, assumptions that do not hold for biological cells. The modified Hertz theory developed by Dimitriadis et al., which takes the finite sample height into account, is widely used by experimentalists for greater accuracy. However, neither of these two models account for the finite lateral spread of the cells and cellular contractility. In this paper, we address the influence of cell geometry, cell pre-stress, and nuclear properties on cell stiffness measurements by modeling indentation of a cell of prescribed geometry with a spherical AFM probe using the finite element method. Using parametric studies, we develop scaling relationships between the effective stiffness probed by AFM and the bulk cell stiffness, taking cell and tip geometry into account. Taken together, our results demonstrate the need to take cell geometry into account while estimating the cell stiffness and provide simple expressions for doing so.