Nanorheology and Nanoindentation Revealed a Softening and an Increased Viscous Fluidity of Adherent Mammalian Cells upon Increasing the Frequency

Abstract

The nanomechanical response of a cell depends on the frequency at which the cell is probed. The components of the cell that contribute to this property and their interplay are not well understood. Here, two force microscopy methods are integrated to characterize the frequency and/or the velocity‐dependent properties of living cells. It is shown on HeLa and fibroblasts, that cells soften and fluidize upon increasing the frequency or the velocity of the deformation. This property was independent of the type and values (25 or 1000 nm) of the deformation. At low frequencies (2‐10 Hz) or velocities (1–10 µm s−1), the response is dominated by the mechanical properties of the cell surface. At higher frequencies (>10 Hz) or velocities (>10 µm s−1), the response is dominated by the hydrodynamic drag of the cytosol. Softening and fluidization does not seem to involve any structural remodeling. It reflects a redistribution of the applied stress between the solid and liquid‐like elements of the cell as the frequency or the velocity is changed. The data indicates that the quasistatic mechanical properties of a cell featuring a cytoskeleton pathology might be mimicked by the response of a non‐pathological cell which is probed at a high frequency.

Measuring the viscoelastic relaxation function of cells with a time-dependent interpretation of the Hertz-Sneddon indentation model

“…Many nanoindentation force models have been developed in the last decade to study the viscoelastic properties of soft materials with the AFM, with particular emphasis on materials exhibiting power-law relaxation [5] , [7] , [26] , [31] , [32] , [33] . In contrast, different research groups independently developed similar models departing from fractional calculus [34] and the functional method of Lee and Radok [35] .…”

“…The viscoelastic relaxation of living cells is most usually described as a single PL in the time domain [26] , [37] where is a reference value of the elasticity modulus at an arbitrary scaling time, , and β is the relaxation exponent that lies in the range , where indicates a perfectly elastic sample, and represents a Newtonian viscous fluid. Intermediate values of β hold both solid and fluid behaviors and hence are characteristic of power-law viscoelastic materials.…”

“…Measuring the mechanical properties of cells with the AFM requires careful choice of parameters like cantilever stiffness, tip geometry, applied forces and measurement speeds [24] , [25] , [26] , [27] . Tip geometry is important because it defines the contact area and ultimately the spatial resolution of the measurements [24] , [25] .…”

“…Tip geometry is important because it defines the contact area and ultimately the spatial resolution of the measurements [24] , [25] . The maximum applied forces also matter because it is well known that cells may respond non-linearly exhibiting either stress softening or stiffening [26] , [28] , and the speed of measurements is relevant because of the viscoelastic response of cells [26] , [27] . Despite all these intricacies, most body of knowledge about cell mechanics has been learned within the simple framework of the HS indentation model.…”