Analyzing Whole-Cell Viscoelastic Properties with Atomic Force Microscopy

Jean-Pierre Rabbah, Department of Biomedical Engineering, Columbia University, New York, NY 10027 Kunal Bose, Department of Biomedical Engineering, Columbia University, New York, NY 10027 Evren U Azeloglu, Department of Biomedical Engineering, Columbia University, New York, NY 10027 Gerard A Ateshian, Department of Mechanical Engineering, Columbia University, New York, NY 10027 Kevin D Costa, Department of Biomedical Engineering, Columbia University, New York, NY 10027

Abstract Determining the mechanical response of whole cells to obtain their elastic and viscoleastic properties is critical for providing details on stresses and strains induced on the cell. This, in turn is utilized to determine the distribution and transmission of forces to the cytoskeletal and sub-cellular components. Ultimately, to develop and validate multi-scale models to study the mechanisms of mechanotransduction, a reliable characterization of whole cell mechanical properties is fundamental. For this purpose, we developed a novel protocol using a modified atomic force microscopy (AFM) technique based on unconfined compression. Custom AFM probes with hemispherical polystyrene tips provided a flat rigid surface to rapidly compress and hold a spherical cell for 60 sec, which was repeated in three successive cycles to capture any changes in viscoelastic response resulting from active cytoskeletal reorganization. We studied two types of cells, neonatal rat cardiac fibroblasts (NRCF) and bovine chondrocytes (BC), which both naturally reside in mechanically demanding physiological environments. Analysis of the cell deformation was based on Hertzian contact mechanics, with the elastic modulus replaced by the relaxation function of a linear viscoelastic model. Two models were studied, a 3-parameter standard linear solid (SLS) and a more complex 4-parameter inverse power law solid (PLS). The material parameters of each model were optimized to fit the experimental force data using the measured deformation transient. Monte Carlo simulation was used to determine parameter variability, the results of which indicated that the parameter determining the power of the time dependence in the PLS model should be constrained. Comparing root-mean-squared errors from the model fits showed that the PLS model, rather than the more commonly used SLS model, more accurately described the experimental response of both BC cells (PLS: 0.19 ± 0.05 nN, SLS: 0.30 ± 0.09 nN, p = 0.0016, n = 12) and NRCF cells (PLS: 0.16 ± 0.04 nN, SLS: 0.36 ± 0.06 nN, p < 0.0001, n = 12), providing an excellent fit to the data. Accordingly, the instantaneous and equilibrium elastic moduli, Go and G∞ respectively, and the apparent viscosity,η, were determined for the PLS model. The values were significantly greater for BC (Go = 1.43 ± 0.59 kPa, G∞ = 0.79 ± 0.41 kPa, η = 3.54 ± 3.05 kPa·s) than for NRCF (Go= 1.02 ± 0.32 kPa, G∞ = 0.39 ± 0.22 kPa, η = 0.88 ± 0.46 kPa·s). Fluorescence microscopy revealed inherent structural differences in the cell types that may contribute to the observed differences in material properties. In particular, the relative areas of nucleus and tubulin were greater in BC than in NRCF, consistent with data that indicate nuclei are stiffer than cytoplasm and microtubules increase cell viscosity. In conclusion, the PLS model describes the viscoelastic response of BC and NRCF cells to unconfined compression with AFM, providing a promising new technique for quantifying the bulk cell mechanical properties that govern the mechanotransduction process.

Full Text: PDF