Computation of adherent cell elasticity for critical cell-bead geometry in magnetic twisting experiments

Quantification of the cell elastic modulus is a central issue of micromanipulation techniques used to analyze the mechanical properties of living adherent cells. In magnetic twisting cytometry (MTC), magnetic beads of radius R, linked to the cell cytoskeleton through transmembrane receptors, are twisted. The relationships between imposed external torque and measured resulting bead rotation or translation only provide values of the apparent cell stiffness. Thus, specific correcting coefficients have to be considered in order to derive the cell elastic modulus. This issue has been highlighted in previous studies, but general relationships forhandling such corrections are still lacking while they could help to understand and reduce the large dispersion of the reported values of cell elastic modulus. This work establishes generalized abacuses of the correcting coefficients from which the Young's modulus of a cell probed by MTC can be derived. Based on a 3D finite element analysis of an hyperelastic (neo-Hookean) cell, we show that the dimensionless ratio h(u)/2R, where h(u) is the cell height below the bead, is an essential parameter for quantification of the cell elasticity. This result could partly explain the still intriguing question of the large variation of measured elastic moduli with probe size.