Measurements of fast fluctuations of viscoelastic properties with the quartz crystal microbalance

Abstract

The quartz crystal microbalance (QCM) was used to study the variability of acoustic properties of living cells on the sub-second time scale. A confluent cell layer of rat cardiac myocytes was grown onto the electrode of quartz crystal resonator. The cell layer performed periodic, synchronous contractions at a rate of about 1.5 Hz. In order to monitor these rather fast changes in the state of the cells, the QCM was operated in a “fast mode”, which allows sampling of the shift of the resonance frequency and energy dissipation with a rate of up to 100 Hz. The contractions were clearly reflected in periodic variations of the resonance frequency and the bandwidth. The rate of the contractions, in particular, could be easily detected in this way. Building on the rate of contraction, the setup can be used to monitor the response of the cell layer to heart stimulating drugs like isoproterenol. Depending on the concentration of isoproterenol, the beat rate was found to increase by up to a factor of two.

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1. Introduction

The quartz crystal microbalance (QCM) is widely used to monitor the thickness of films deposited on their surfaces in gaseous or liquid environments.^1–3 The capabilities of the QCM can be much extended by impedance analysis [see, for example, ref. 4]. By recording the complex admittance Y(ω) = G(ω) + iB(ω) around a resonance frequency and fitting resonance curves to the admittance spectra, one can obtain both the frequency shift and the shift in bandwidth (proportional to dissipation). The frequency shift, δf, and the shift in bandwidth, δΓ, are the changes of the resonance frequency and the resonance bandwidth obtained when loading the crystal. This procedure can be easily repeated on a number of overtones, providing an entire set of shifts in frequency and bandwidth. From the frequency shift, one infers the stress–speed ratio as⁴
where δf* is a complex frequency shift, δf is the frequency shift, δΓ is the shift of the half-band–half-width, f₀ is the fundamental frequency, is the stress–speed ratio (the load impedance), σ is the lateral stress at the crystal surface, is the lateral speed at the crystal surface, and Z_q = 8.8 × 10⁶ kg m⁻² s⁻¹ is the acoustic impedance of AT-cut quartz. For semi-infinite samples, the load Z_L is equal to the acoustic impedance Z = (G_sρ)^1/2 (G_s is the modulus and ρ the density).

Importantly, the acoustic load responds very sensitively to subtle changes in the state of the sample. The presence of a dilute polymer adsorbate, for example, can change the impedance easily by a factor of 10. The increase in the optical refractive index, for comparison, typically is in the range of a few percent. With shear waves in soft matter-environments, one usually finds large acoustic contrast. The practical challenge often is not the detection of a frequency shift, but rather its correct interpretation.

The conventional picture of acoustic reflectometry assumes a system of laterally homogeneous layers. Structured samples—like living cells, colloidal assemblies, or a tip touching the surface—cannot be quantitatively analyzed in this way. However, qualitative information can still be gathered. Recently, this method has been applied to the process of attachment and spreading of mammalian cells onto the solid electrode of the quartz sensor.^5–7 Real-time measurements of the shift in resonance frequency and energy dissipation due to changes in mass and viscoelastic properties give information about the state of the cell adhesion.⁸ In this study we show that the QCM technique can also probe fast changes of acoustic properties of the sample.

2. Experimental setup

2.1 Cell culture

We isolated cardiac myocytes from CD neonatal rats (1–2 days old). The hearts were removed under sterile conditions and placed in Hank's balanced salt solution (HBSS) (w/o Ca²⁺, Mg²⁺) on ice. Excess blood was removed and the tissue was chopped into small pieces. The enzymatic dissociation was done step by step in a solution of mild Trypsin in DNAseI solution for 15 min at 37 °C, each. The supernatant was collected in Ham's F12 medium supplemented with 30% fetal calf serum (FCS) and penicillin G sodium with streptomycin sulfate (Pen-Strep) (F12 HAM/Pen-Strep/30% FCS) in order to stop the reaction. This trypsinization step was repeated until all remaining heart tissue was dissociated. Afterwards a cell sieve (Falcon, pore size 50 µm) was used to remove non-dissociated cell agglomerations and tissue. Finally, to obtain a homogeneous population of cardiac myocytes, an enrichment protocol was used to remove contaminating fibroblasts. After 1 h of incubation many of the fibroblasts adhered to the bottom of the culture flask whereas the cardiac myocytes remained in the collected supernatant.

The enriched myocytes were directly grown onto the fibronectin-treated gold electrode surface of the QCM with a density of 1.25–5.0 10⁵ cell cm⁻². After 3–4 days in vitro the confluent layer of cardiac myocytes began to contract synchronously.

2.1 Setup

The central element of the QCM is an AT cut quartz crystal resonator (Maxtek, Santa Fe Springs, CA) with a fundamental resonance frequency of 5 MHz coated with gold electrodes on both sides (Fig. 1). The crystal is mounted in a cylindrical Teflon holder (CHT-100, Maxtek) and placed in a modified incubator (Zeiss, Germany) which provides a controlled sterile environment at 37 °C and 5% CO₂. The periodic contraction of the cell layer can be watched with a microscope.

Fig. 1 Schematic diagram of the experimental setup used for the QCM measurements on cardiac myocytes. The inlet depicts the displacement pattern. The decay length of the shear wave usually is less than the height of the cell.

2.2 Data acquisition

The frequency shift, δf, and the shift in half-band–half-width, δΓ, were determined via impedance analysis in a “fast mode” described in detail below. In principle, these measurements can be done with simple oscillation circuits, as well. For a sensor application, oscillators are certainly much cheaper than impedance analysis. Advanced oscillators circuits like the PLO10 from Maxtek even allow for the simultaneous determination of frequency shift and dissipation. Impedance analysis, generally speaking, provides more insight because one can see the entire resonance curves and many different overtones. We used an E5100 network analyzer (Agilent) in the conductance mode. In a first step, an entire resonance curve was acquired by a frequency sweep. Fitting a resonance curve to the trace of the spectrum of the electrical admittance, we determine the resonance frequency, f_res, the half-band–half-width, Γ, and the peak conductance G_max (Fig. 2). The software determines the slope of the susceptance curve (the imaginary part of the complex admittance) at the resonance frequency, dB/df, (dotted line in Fig. 3). Later on, this slope is used for conversion from shifts in susceptance, δB, to shifts in resonance frequency, δf. Also, the software calculates a conversion factor relating a decrease in peak conductance, δG_max to an increase in bandwidth, δΓ, termed “dG_max/dΓ” (see Fig. 2). After these calibration steps, a “fast mode” is initiated, during which the instrument continuously measures the conductance, G(f_fix), and the susceptance, B(f_fix), at one fixed frequency, f_fix ,where the latter is chosen as the resonance frequency in the unperturbed state. The data acquisition rate for this single-frequency measurement is 50 Hz. Using the conversion factors dB/df and dG_max/dΓ, the program translates shifts in B(t) and G(t) to shifts in frequency δf(t) and bandwidth δΓ(t). Clearly, this analysis (based on the linearization of the susceptance curve in the center of the resonance) only is correct as long as all shifts are small enough. The instrument checks whether the values of B(f_fix) are within a range indicated by the horizontal lines in Fig. 3. If this range is exceeded the software interrupts and reinitializes.

Fig. 2 Principle of the operation of the fast mode: The figure shows a typical shape of the conductance, G, and the susceptance, B, as a function of frequency. In the fast mode, the instrument tracks the complex admittance G + iB at a fixed frequency f_fix close to the center of the resonance. The frequency shift, δf, and the shift of the half-band–half-width, δΓ, are inferred from the shifts in B and G, respectively.

Fig. 3 Susceptance B as a function of frequency at the 3rd harmonic. In the calibration step, the instrument linearized the curve around the initial resonance frequency f_fix in order to find the slope (dB/df) needed for conversion. Whenever B(t) leaves the interval between B_min and B_max the software interrupts and recalibrates.

2.3 Statistical analysis

For statistical analysis a linear drift is subtracted from the raw data δf(t) and δΓ(t). The root mean square (rms) amplitudes δf_rms = <δf²>^1/2 and δΓ_rms = <δΓ²>^1/2 are calculated, where angular brackets denote an average over 256 data points corresponding to a time interval of about eight seconds. In a second step, the software calculates the power spectral densities, |P_f(ω)| and |P_Γ(ω)| via a fast Fourier transform (FFT) of these data points (Fig. 4). The beat rate r_beat is the frequency of the peak of the power spectrum. This procedure can be applied to both δf(t) and δΓ(t). The two ways of deriving r_beat always yielded the same result. Sometimes two separate beat frequencies are seen, corresponding to two unsynchronized groups of cells beating at different rates. In this case the software analyzes the stronger peak and disregards the small one.

Fig. 4 Shift of the half-band–half-width δΓ (left) as a function of time for a contracting cardiac myocyte layer (top) before and (bottom) after the addition of isoproterenol (0.01 µM). The power spectral densities calculated via a fast Fourier transform are shown on the right-hand-side. The contraction rate, r, the amplitude of the main peak peak A(r), and the ratio of the second harmonic and the main peak A(2r)/A(r) are calculated from these spectra.

The beat frequency, r_beat, is the central sensor parameter. Further information on the shape of the signal can be extracted from the overtone amplitudes in the power spectrum. We routinely determine amplitudes of the 2nd, the 3rd, and the 4th harmonic.

3. Results and discussion

Fig. 5 shows a typical example of the raw signal. This measurement had been carried out on the third overtone at 15 MHz. As the figure shows, the resonance parameters δf and δΓ vary periodically with a rate of about 1.5 Hz. Since the shifts in frequency (a) were always smaller than shifts in the bandwidth (b) we mostly base the statistical analysis on the bandwidth. The analysis based on frequency yields similar results with a lower signal-to-noise ratio. Panel c shows the control experiment. No periodic variations of either frequency or bandwidth are found after the cells have been removed.

Fig. 5 QCM measurement of a contracting cardiac myocyte layer after four days in vitro. The periodic shift of the resonance frequency δf (a) and the half-band–half-width δΓ (b) is shown as a function of time. The data acquisition has been carried out in the fast mode with a sampling rate of 30 Hz. A reference measurement (c) is shown for δΓ after the cells have been removed from the quartz surface.

Response to the addition of heart-stimulating drugs

In order to demonstrate that the instrument can easily detect variations of the beat rate in response to the presence of heart-stimulating drugs, we exposed the cell layer to isoproterenol in two steps. The raw data and their Fourier transforms are shown in Fig. 4. The outcome of the statistical analysis is displayed in Fig. 6. At t = 4 min the dose was in a first step increased from 0 to 0.01 µM. The upper and the lower part of Fig. 4 show raw data and the Fourier transform before and after this addition. The beat rate increases from 1.4 to about 2 Hz. Later in the course of the experiment (t = 23 min), the dose was increased to a level of 0.1 µM, resulting in a further increase of the beat rate to about 2.5 Hz. While the beat rate increases, the amplitude decreases at the same time. This can be interpreted as a weakening of the contraction. In fact, the contraction of the cell layer stopped shortly after the end of the experiment. The cell layer did not survive the experiment. The bottom panel shows the development of the second harmonic component of the beat pattern. The second harmonic component is strong, but does not vary systematically with dosage. The third harmonic (visible as a small peak on the upper right in Fig. 4) did not show a systematic trend with dosage either. In this experiment, the peak shape did not correlate with the addition of the drug.

Fig. 6 Parameters extracted from the statistical analysis (cf.Fig. 4) as a function of time. The data were derived from the variability of δΓ.

4. Conclusions

It was demonstrated that the QCM in the impedance analysis mode can pick up fast variations of the acoustic properties of biological cells deposited on the crystal surface. The data acquisition rate was 30 Hz. We monitored the periodic contraction of cardiac myocytes. The beat rate increased upon the addition of the heart-stimulating drug isoproterenol.

References

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Footnote

† Presented at the Biosensors and Biomaterials Workshop, Tsukuba, Japan, March 7–9, 2005.

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