Coarse-grained elastic network modelling: A fast and stable numerical tool to characterize mesenchymal stem cells subjected to AFM nanoindentation measurements

The knowledge of the mechanical properties is the starting point to study the mechanobiology of mesenchymal stem cells and to understand the relationships linking biophysical stimuli to the cellular differentiation process. In experimental biology, Atomic Force Microscopy (AFM) is a common technique for measuring these mechanical properties. In this paper we present an alternative approach for extracting common mechanical parameters, such as the Young's modulus of cell components, starting from AFM nanoindentation measurements conducted on human mesenchymal stem cells. In a virtual environment, a geometrical model of a stem cell was converted in a highly deformable Coarse-Grained Elastic Network Model (CG-ENM) to reproduce the real AFM experiment and retrieve the related force-indentation curve. An ad-hoc optimization algorithm perturbed the local stiffness values of the springs, subdivided in several functional regions, until the computed force-indentation curve replicated the experimental one. After this curve matching, the extraction of global Young's moduli was performed for different stem cell samples. The algorithm was capable to distinguish the material properties of different subcellular components such as the cell cortex and the cytoskeleton. The numerical results predicted with the elastic network model were then compared to those obtained from hertzian contact theory and Finite Element Method (FEM) for the same case studies, showing an optimal agreement and a highly reduced computational cost. The proposed simulation flow seems to be an accurate, fast and stable method for understanding the mechanical behavior of soft biological materials, even for subcellular levels of detail. Moreover, the elastic network modelling allows shortening the computational times to approximately 33% of the time required by a traditional FEM simulation performed using elements with size comparable to that of springs.