Resonance compensating chirp mode for mapping the rheology of live cells by high-speed atomic force microscopy

Abstract

We developed resonance compensating chirp mode (RCCM), an atomic force microscopy (AFM) technique to measure the frequency dependence of the complex shear modulus of live cells over a large bandwidth (quasi-) continuously. RCCM works by applying a continuous frequency sweep (chirp) to the z-scanner and recording the resulting cantilever deflection at high speed. From this data, the frequency-resolved complex shear modulus is extracted. To reach a high maximum frequency, we iteratively shaped the chirp signal to compensate for scanner resonances. This allowed us to measure at frequencies five times higher than the resonant frequency of the scanner. Using a high-speed AFM with small cantilevers, we measured the complex shear modulus of live fibroblast cells in a continuous range between 5 Hz and 30 kHz. We found that the modulus and the loss tangent exhibit a power-law behavior throughout this frequency range. A short chirp duration of 200 ms allowed us to map live cells and generate spatially resolved images of the power-law parameters within minutes. These maps represent a unique combination of high spatial and frequency resolution, low measurement duration, and high maximum frequency.

High-speed force spectroscopy: microsecond force measurements using ultrashort cantilevers

“…Maps of b height and c shear modulus (G 0 ) on a live fibroblast (scale bars 3 μm, 64 × 64 pixels). The G 0 map was built by analyzing the frequency dependant of the storage and loss moduli (right plot, G′, red, and G″, blue) and loss tangent ( η , gray) in a frequency range of 5 Hz–30 kHz at each pixel (inset curve) (reprinted from Schachtele et al 2018)…”

“…High frequency microrheology of living cells was recently improved. Schächtele et al (2018) developed a new resonance compensating chirp mode (RCCM) to probe the frequency dependence of the viscoelasticity of living cells (quasi-) continuously over a large frequency range (5 Hz–30 kHz) and with a resolution of 5 Hz. A continuous frequency sweep (chirp) is applied to the z-scanner and is iteratively shaped to compensate for scanner resonances.…”

Bulk rheometry at high frequencies: a review of experimental approaches

“…for the detection of malign tumor cells, which showed distinct mechanical characteristics owing to the filaments that become more tense (Rigato et al 2017;Mohammadi and Sahai 2018). In order to improve the quantification of such analyses, further developments in the field of high-frequency rheometry will be essential (Schächtele et al 2018).…”

Combined High‐Speed Atomic Force and Optical Microscopy Shows That Viscoelastic Properties of Melanoma Cancer Cells Change during the Cell Cycle

“…The spring constants of the cantilevers were calibrated using the thermal noise method. [53,54] Viscoelastic Measurement Modes: A combination of force clamp force mapping (FCFM) [35] and resonance compensating chirp mode (RCCM) [55] allowed to investigate the viscoelastic properties in both the time and frequency domain at the same position of the sample right after each other. At each pixel, the cantilever was approached to the sample just as in force mapping mode with a constant speed until a predefined trigger force F Clamp was reached and the force was then kept constant for the clamp duration Δt Clamp (0.2 s for Figure 3, 0.1 s for Figure 4) using a force feedback loop.…”