Quantification of the Microrheology of Living Cells Using Multi-Frequency Magnetic Force Modulation Atomic Force Microscopy

The multi-frequency force modulation (MFFM) atomic force microscope (AFM) offers the advantage of ensuring a consistent cell state at each measurement frequency. However, the commonly used piezo-driven AFM suffers from a limited high end of measurement frequency range, while the dynamics of cellular structures such as cytoskeleton filaments is expected to emerge at high-frequency microrheology measurements (>10 kHz). In this article, we have developed a multi-frequency magnetic force modulation AFM to measure the viscoelastic mechanical properties of living cells over a broad frequency range. The tip of the AFM probe is composed of a ferromagnetic sphere whose magnetization direction is along the long axis of the cantilever to provide sufficient driving force. Further, the vibration amplitude of the cantilever is much smaller than the depth of the indentation, which simplifies the contact mechanics model used. To account for the effects of the inertial and hydrodynamic forces on the cantilever dynamics, a calibration method for eliminating the distortion of the frequency sweeping curves is proposed to obtain the resonance frequency and
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factor of the AFM probe in a liquid environment. The practicality of the AFM technique is demonstrated by characterizing microrheology of living cells at multiple frequencies with different indentation depth over the range of 40 Hz to 12 kHz. This technique has significant potential of becoming a multidimensional mechanical phenotyping characterization tool for studying the viscoelastic mechanics of cellular structures.