Asymptotic approach to analyze the mechanical properties of biological cells

Abstract

The Hertz model assuming a small indentation over the infinite hemisphere has been most widely applied to calculate elastic moduli of biological cells from data obtained by atomic force microscopy (AFM)-based indentation experiments. Previously reported experiments were mostly performed with a low stress to satisfy the Hertz assumption. In spite of its importance, mechanical heterogeneity observed in the high stress regime is often ignored due to the violation of the Hertz assumption. In this study, we have performed the hyperbolic fit modified from the Hertz model considering the asymptotic behaviors of layered structures in order to corroborate this issue. We demonstrate that our asymptotic approach confirmed the self-consistent elastic behavior of the cell cortex regardless of the applied stress regime. In addition, we have determined the elastic moduli of cellular regions beyond the cell cortex, where previous AFM indentation experiments could not easily access. We conclude that our asymptotic approach using hyperbolic fits provides a new empirically analytic mean to quantify the mechanical properties of biological cells including the high stress regime.