Estimation of Cell Young’s Modulus of Adherent Cells Probed by Optical and Magnetic Tweezers: Influence of Cell Thickness and Bead Immersion

Abstract

A precise characterization of cell elastic properties is crucial for understanding the mechanisms by which cells sense mechanical stimuli and how these factors alter cellular functions. Optical and magnetic tweezers are micromanipulation techniques which are widely used for quantifying the stiffness of adherent cells from their response to an external force applied on a bead partially embedded within the cell cortex. However, the relationships between imposed external force and resulting bead translation or rotation obtained from these experimental techniques only characterize the apparent cell stiffness. Indeed, the value of the estimated apparent cell stiffness integrates the effect of different geometrical parameters, the most important being the bead embedding angle 2gamma, bead radius R, and cell height h. In this paper, a three-dimensional finite element analysis was used to compute the cell mechanical response to applied force in tweezer experiments and to explicit the correcting functions which have to be used in order to infer the intrinsic cell Young's modulus from the apparent elasticity modulus. Our analysis, performed for an extensive set of values of gamma, h, and R, shows that the most relevant parameters for computing the correcting functions are the embedding half angle gamma and the ratio h(u)/2R, where h(u) is the under bead cell thickness. This paper provides original analytical expressions of these correcting functions as well as the critical values of the cell thickness below which corrections of the apparent modulus are necessary to get an accurate value of cell Young's modulus. Moreover, considering these results and taking benefit of previous results obtained on the estimation of cell Young's modulus of adherent cells probed by magnetic twisting cytometry (MTC) (Ohayon, J., and Tracqui, P., 2005, Ann. Biomed. Eng., 33, pp. 131-141), we were able to clarify and to solve the still unexplained discrepancies reported between estimations of elasticity modulus performed on the same cell type and probed with MTC and optical tweezers (OT). More generally, this study may strengthen the applicability of optical and magnetic tweezers techniques by insuring a more precise estimation of the intrinsic cell Young's modulus (CYM).

Comparative study on the differential mechanical properties of human liver cancer and normal cells

“…Nonetheless, these results demonstrated the feasibility of similar data to be used for the purpose of increasing the accuracy of cancer diagnosis. Because the tip geometry and indentation depth dependence on elasticity could lead to unavoidable discrepancies in terms of the cell properties or incorrect diagnostic evaluations, especially for spherical tips (Mathur et al 2001;Costa 2003;Kamgoué et al 2007;Unnikrishnan et al 2007), conical tips are considered to be more suitable.…”

“…The HertzÁSneddon (HS) model has been most widely and conveniently used to estimate the elastic moduli of cells for the forceÁdisplacement curves obtained from AFM measurements (Cross et al 2007). However, the elastic modulus estimated using the HS model depends on the tip geometry and indentation depth (Mathur et al 2001;Costa 2003;Kamgoué et al 2007; Unnikrishnan et al 2007). To improve the diagnostic significance of the measured elasticity, tip geometry and indentation depths need to be optimized so that the measured values are reproducible and reliable.…”

Characterization of cellular elastic modulus using structure based double layer model

“…However, the HS model is based on overly simplified assumptions of cells being linear, homogeneous, isotropic, and axisymmetric [19], which limits the validity of the solution to certain cell types and measurement conditions. For better representation of cells in a more generalized form, the model should reflect the intracellular inhomogeneity, at least to some extent, and the geometric factors related to cell morphologies as well as actual experimental conditions, including indentation depth and its relative magnitude to the sample thickness to rule out the undesired effects from the underlying substrates [20,21].…”

Influence of power-law rheology on cell injury during microbubble flows

“…Based on this evidence, we hypothesize that accurate computational models of EpC deformation may require the use of a power-law rheology constitutive model with parameter values drawn from experimental microrheology studies. Until recently, computational models of cell mechanics, particularly for bead-based microrheology techniques such as magnetic twisting cytometry (MTC), were carried out using linear elastic (Mijailovich 2002), hyperelastic (Kamgoué et al 2007;Ohayon et al 2004), or Maxwell fluid (Kaazempur Mofrad et al 2003;Karcher et al 2003) material models. In one recent study, developed a computational model of MTC that defined the test material's frequency-dependent storage and loss moduli according to a power-law formulation:…”