Improvement of Contact Models by Finite Element Analysis for the Evaluation of Yeast Mechanical Properties

In this work, we extended our previous studies on the limitations of classical contact models from polymers to a biological system. We used yeast as a model system to investigate how contact evolution during indentation affects the accuracy of AFM-based determination of Young's modulus. We proposed a practical correction framework for the classical Hertz and Sneddon flat-punch models to improve the extraction of mechanical properties from experimental data. Force-indentation curves were measured using a spherical (SPHERE) probe with a 2 μm radius and a flat (FLAT) probe with a 4 μm radius of plateau. The experimental results were analyzed using both corrected and uncorrected contact models, while a finite element analysis (FEA) model was used to determine the contact radius-indentation dependence. It showed that Young's modulus estimated from AFM indentation using classical formulations is probe-dependent because the contact radius is inadequately described. By incorporating the FEA-derived effective contact radius into Hertz and Sneddon contact models, the same Young's modulus was obtained for yeast with both probes and compared to reference values with other techniques. These findings establish contact evolution as a governing factor in AFM-based cell mechanics and provide a practical route toward robust, probe-independent, and more accurate determination of mechanical properties for living cells.