Passive microrheology of soft materials with atomic force microscopy: A wavelet-based spectral analysis

International audienceCompared to active microrheology where a known force or modulation is periodically imposed to a soft material, passive microrheology relies on the spectral analysis of the spontaneous motion of tracers inherent or external to the material. Passive microrheology studies of soft or living materials with atomic force microscopy (AFM) cantilever tips are rather rare because, in the spectral densities, the rheological response of the materials is hardly distinguishable from other sources of random or periodic perturbations. To circumvent this difficulty, we propose here a wavelet-based decomposition of AFM cantilever tip fluctuations and we show that when applying this multi-scale method to soft polymer layers and to living myoblasts, the structural damping exponents of these soft materials can be retrieved. Local stiffness and internal friction of soft materials (passive or active such as living cells) have lately been addressed at the nanoscale thanks to the development of pico-to nano-Newton force sensing systems and of nanome-ter resolution position detection devices. 1 Atomic force mi-croscopy (AFM) is one of these methods, where a sharply tipped flexible cantilever is indented inside a material to extract its local viscoelasticity from the shift and spreading of the cantilever spectral resonance modes. 2–4 However, these estimations are limited to rather narrow frequency bands surrounding the cantilever resonance modes or their higher harmonics. Spectral decomposition of cantilever fluctuations in contact with soft living tissues in the low frequency range has more rarely been explored. The few attempts which can be found in the literature were performed with small amplitude harmonic excitations (50 nm) of the sample position driven by a piezo-translator, in the 0.1 to 100 Hz frequency range, for a small and finite number of frequencies. 5,6 Whereas passive (driven by thermal fluctuations) microrheology has been performed for the past two decades by a variety of techniques capturing micro-probe spatial fluctuations , 7 it has not been applied yet to AFM cantilever fluctuations. The limitation of AFM-based passive rheology in the low frequency range comes from the mixing of the background vibrations of the liquid chamber with the cantilever fluctuations given by the rheological response of the material which are difficult to disentangle by standard FFT-based spectral averaging methods. In this work, we show that in quasi-stationary situations, these limitations can be circumvented using a wavelet-based spectral analysis of micro-cantilever fluctuations under passive excitation. Two experimental applications to passive polymer layers and living adherent myoblast cells are reported. Based on the generalized Stokes-Einstein relation (GSER) and associated generalizing assumptions, 8 passive microrheology of soft materials enables the extraction of the frequency-dependent complex modulus GðxÞ which is common to a large class of soft materials (foams, emulsions, slur-ries, and cells). 9–11 The observed scaling laws are explained by a characteristic structural disorder and the metastability of these materials which are embodied under the name of " soft glassy materials " or structural damping model. 12 Their complex shear modulus behaves a

Fractional rheology of muscle precursor cells

The authors propose a wavelet-based decomposition of creep fluctuation signals recorded from living muscle precursor cells that revisit the traditional computation of their power spectrum from FFT-based decomposition. This decomposition offers a higher sensitivity for detecting the occurrence of fractional fluctuations and for quantitatively estimating the power-law exponent ² of this spectrum as a signature of the scale-invariant rheology of living cells. This new method has also the unprecedented advantage of providing a test of the validity of the commonly assumed 'monofractal' self-similar (as compared to 'multifractal' intermittent) nature of these fluctuations and hence accrediting the use of a single rheological exponent ± = ²/2. We report and discuss results obtained when applying this method to creep experiments performed with an AFM nanoindenter placed in contact with single myoblasts and myotubes, adherent on collagen coated coverslips, and in different culture conditions

Tracking in real time the crawling dynamics of adherent living cells with a high resolution surface plasmon microscope

We introduce a high resolution scanning surface plasmon microscope for long term imaging of living adherent mouse myoblast cells. The coupling of a high numerical aperture objective lens with a fibered heterodyne interferometer provides both enhanced sensitivity and long term stability. This microscope takes advantage of the plasmon resonance excitation and the amplification of the electromagnetic field in near -field distance to the gold coated coverslip. This plasmon enhanced evanescent wave microscopy is particularly attractive for the study of cell adhesion and motility since it can be operated without staining of the biological sample. We show that this microscope allows very long-term imaging of living samples, and that it can capture and follow the temporal deformation of C2C12 myoblast cell protusions (lamellipodia), during their migration on a flat surface