Preparation of Extracellular Matrix Protein Fibers for Brillouin Spectroscopy

Brillouin spectroscopy is an emerging technique in the biomedical field. It probes the mechanical properties of a sample through the interaction of visible light with thermally induced acoustic waves or phonons propagating at a speed of a few km/sec. Information on the elasticity and structure of the material is obtained in a nondestructive contactless manner, hence opening the way to in vivo applications and potential diagnosis of pathology. This work describes the application of Brillouin spectroscopy to the study of biomechanics in elastin and trypsin-digested type I collagen fibers of the extracellular matrix. Fibrous proteins of the extracellular matrix are the building blocks of biological tissues and investigating their mechanical and physical behavior is key to establishing structure-function relationships in normal tissues and the changes which occur in disease. The procedures of sample preparation followed by measurement of Brillouin spectra using a reflective substrate are presented together with details of the optical system and methods of spectral data analysis.


Introduction
The Brillouin light scattering (BLS) effect was discovered by Léon Brillouin in 1922. 1 It consists of the inelastic scattering of visible light by thermally activated acoustic phonons in a material. In solid state physics, acoustic phonons are coherent vibrations of all atoms in a lattice. A one-dimensional chain of two alternating types of atoms in a lattice is a simple model illustrating the difference between acoustic phonons, revealed by BLS, and optical phonons, probed by IR absorption and Raman scattering (Figure 1). Acoustic phonons are in-phase movements of atoms in the chain with a displacement along the direction of propagation (longitudinal acoustic phonons) or perpendicular to the propagation direction (transverse acoustic phonons), whilst optical phonons are out-of-phase movements of the atoms producing an oscillating electrical dipole moment (longitudinal or transverse modes).
BLS spectroscopy has been used in analytical science since the 1920s; however, only since the 1980s have high contrast measurements been possible through the use of the tandem multipass Fabry-Perot spectrometer. Since then, an increasing number of advances in BLS for analytical applications in condensed matter (where the photon-phonon interaction is exploited) 2-4 and magnetic materials (through the photonmagnon interaction) 5 has been brought about. Seminal works on biomedical applications [6][7][8] have paved the route to the development of various approaches, including the one applied here and the one described previously 9 using a reflective substrate in a platelet-like configuration to achieve the full description of the elasticity tensor of a sample.
In the present work, we apply BLS spectroscopy to the fundamental constituents of the extracellular matrix in connective tissues, the fibrous proteins elastin and type I-collagen. Type I collagen is a rigid, triple helical molecule which assembles laterally and longitudinally with extensive cross linking to form essentially rigid fibers in tissues such as tendons. Networks of collagen often co-exist with networks of elastin, a protein which, unusually, generates long range elasticity through a combination of entropy and hydrophobic interactions with its environment and is essential to the functions of tissues such as lung and skin. Both fibers are modeled using a hexagonal crystal model in the current research. 9 In part 1, we describe the protocol to extract the fibers from animal tissues and to prepare the sample for the spectroscopic measurements. In part 2, the procedure for setting up the Brillouin apparatus and acquiring spectra from the fibers is presented. Part 3 gives details of data analysis applied to the Brillouin spectra to extract the relevant mechanical information contained therein. Then, representative results are presented and discussed.
Copyright © 2016 Creative Commons Attribution 3.0 License September 2016 | 115 | e54648 | Page 3 of 10 4. Place a thin glass coverslip over the fiber and seal the chamber by passing a heated soldering iron gently over the glass surface to melt the parafilm beneath the glass. Careful: Avoid damaging the fiber by not bringing the soldering tip too close or heating the substrate excessively. 5. Place the sealed chamber on a flat surface under a small weight and leave it for around 12 hr to achieve a good contact between the sample and silicon substrate while avoiding damage to the specimen. 6. Remove the weight and secure the chamber in place on the substrate, using screws.  Careful: The laser output power may be too high and produce a burn in the sample. Make sure that it is set sufficiently high to give a good sensitivity but not too high to avoid damage to the sample. Here we used a power of ca. 76 mW on the sample. This was sufficient to get a good sensitivity without burning the sample, also considering that this is thin and in contact with a substrate that helps dissipating the heat generated by laser illumination. 3. Position the sample at a 45° angle (Φ) to the incident laser beam using a Vernier scale. Achieve optimal positioning by running a measurement and maximizing the intensity of the peaks in the spectrum (see below).

Setting up the Brillouin Experiment and Acquiring Fiber Spectra
2. Setting up the spectrometer 1. Open the software for acquisition and manipulation of the data and set up the acquisition of a Brillouin spectrum of the sample 12 . The procedure described here applies to the multipass tandem interferometer (Figure SI-1A). 2. Align the two Fabry-Perot (FP) interferometers independently changing the voltages applied to the piezo by the control unit. For this pre-alignment procedure, observe the light reflected by each FP. When the intensity reflected by the two FPs tends to zero, the correct alignment is reached. 3. Calibrate the spectrum: the accessible frequency range, or free spectral range (FSR), is dependent on the distance between the two mirrors of the first FP cavity, L, through FSR = c/2L, where c is the speed of light and L is measured by a dial-gauge. 4. Synchronize the scans of the two FP interferometers and switch the optical system to the tandem multipass configuration. A feedback control of the transmitted laser light intensity will automatically maintain the alignment of the two FPs during the measurement.

Measurement of Brillouin Spectra
Careful: The Brillouin spectrum is highly dependent on the temperature and hydration of the sample and so careful control of these parameters is key to obtaining reproducible spectra. 1. Start the acquisition of a Brillouin spectrum of the sample and run it until a good signal-to-noise ratio is achieved. This may take several minutes depending on the scattering cross section, concentration and thickness of the sample. NOTE: There is not a rule of thumb for the signal-to-noise ratio but the spectral quality is checked by the experimentalist based on the specific sample analyzed. There is a trade-off between spectral quality and duration of the measurement, therefore the experimental parameters need to be selected according to the specific application. 2. For the measurement of a dry specimen, take successive spectra -for each of them, following step 2.3.1 -until no changes in the position of the peaks is observed. This is achieved when the sample is at equilibrium with the room atmosphere and no further drying will affect the spectrum. 3. Select the light polarization (VV or VH; V stands for vertical and H for horizontal direction of the light polarization relative to the scattering plane) and acquire spectra at each angle to fiber axis (θ ; Figure SI-1) by rotating the sample in plane by hand. 4. Save the Brillouin spectra to file for subsequent processing.

Analysis of Brillouin Spectra
NOTE: Fit analysis of Brillouin peaks can be performed using various functions. A damped harmonic oscillator (DHO) function 4,13 was selected as this is a valid model for peaks originating from damped acoustic modes in viscoelastic media.

Fit analysis of Brillouin peaks
1. Select the spectral range for the peak of interest in the Brillouin spectrum. 2. Enable a baseline in the fit if the spectral background is much higher than zero. NOTE: The baseline can vary between spectra. Ensure that the correction is applied in a systematic and reproducible manner. 3. Apply a detailed least squares fitting using a DHO function 4,13 to the Brillouin peak of interest iteratively until convergence is achieved and the best fitting curve is obtained. Then, save the fit results to file. 4. Obtain average values from the fit parameters of the two peaks of each Brillouin doublet. 5. Calculate the acoustic wave velocity from the peak frequency (using the expression below). 6. Plot the fit results through graphs, e.g., acoustic wave velocity vs. angle to fiber axis, θ , and apply relevant models (e.g., for acoustically anisotropic systems Figure 2 shows BLS spectra of dry and hydrated trypsin-digested collagen fibers obtained with VV polarization at 0.2 GHz resolution, with a 30 GHz free spectral range and approximately 10 min collection time per spectrum. Each spectrum corresponds to a specific angle of rotation, θ (Figure SI-1C). In dry collagen fiber at θ = 0°, longitudinal modes give rise to a bulk peak at (18.92 ± 0.02) GHz whilst the PS mode is at (9.85 ± 0.03) GHz (Figure 2A). The PS peak shifts to lower frequencies as θ goes from 0° (phonon probing the axial orientation of the fiber) to 90°( phonon probing the radial orientation), whereas the bulk peak only slightly red-shifts upon changing θ in the same range (phonon probing a quasi-radial direction throughout the rotation). In wet collagen fiber, the two peaks due to longitudinal phonons are essentially unchanged throughout the experiment, with the bulk peak at ca. 10.5 GHz and the PS peak at 4.9 GHz (Figure 2B). This indicates an 80 to 100% reduction in peak frequency (relative to the data of 18.92 and 9.85 GHz, respectively), and hence of stiffness of the material, due to hydration. Note that the bulk and PS modes of hydrated collagen lie close in frequency to the modes of pure water, suggesting that its elastic constants are a combination of the water and fiber contributions, with a dominant role played by water. Figure 3 shows a spectrum of dry trypsin-digested collagen fiber measured at θ = 30° with VH polarization; a leakage of the VV polarization enables the PS and bulk peaks to still be observed. Transverse modes account for a peak at (4.1 ± 0.2) GHz (θ = 0°) which slightly blueshifts as θ changes from 0° to 90°. Fit results for both the transverse and PS peaks are also shown. Peak parameters were extracted and acoustic wave velocities were derived as V L = vλ/√2, where v is the frequency of the mode obtained by curve-fit analysis of the peaks and λ is the excitation wavelength, 532 nm. Note that in this geometry, knowledge of the refractive index of the material is not required to obtain the acoustic mode velocity (owing to the scattering geometry, q s = 2k i sin(Φ); Figure SI-1b,c), hence making this approach especially advantageous.  Table 1).
The longitudinal and transverse acoustic wave velocities are given by 9 , (A1) where ρ is the density of the material, and c 11 , c 33 , c 44 and c 13 are four of the five elastic constants that characterize systems with a hexagonal symmetry. The fifth constant, c 12 , can be derived from the approximate relation c 12 ~ c 11 -2c 44 . 7 Coefficients are similar to those previously obtained from unpurified collagen fibers. 9 A noticeable difference occurs for the coefficient c 13 that is reflected into similar values of the elastic moduli E ǁ and E (approximately 7.2 and 7.7 GPa) for the purified collagen. Figure 5 is a plot of the longitudinal acoustic wave velocity of wet collagen versus θ . In this case, no periodic change in frequency is observed, giving a constant velocity within the error. Figure 6 shows the spectra of dry and hydrated elastin fibers measured at θ = 0°. Transverse modes were not detected for these samples. In dry elastin, the bulk peak occurs at 16.8 GHz whilst the PS mode at 8.2 GHz 9 (13 and 20% lower than the corresponding peaks of dry collagen). Wet elastin fibers present a bulk peak at (12.30 ± 0.01) GHz (37% lower in frequency than the bulk peak of dry elastin). The PS mode of wet elastin is not apparent in the spectrum because of the intense tail of the elastic peak at those frequencies.
On the other hand, the peak at ca. 7.5 GHz is attributed to the bulk water. Figure 7 shows the dependence of acoustic wave velocity in dry elastin fiber on θ. From these data, the elasticity tensor components (and mechanical moduli) were obtained ( Table 1). 9 As in wet collagen, there is evidence of isotropy in the mechanical modulus of hydrated elastin fibers. These results indicate how Brillouin spectroscopy can give relevant information on stiffness, composition and structural aspects of a material.  Brillouin spectra of trypsin-purified type I collagen fibers from rat tail tendon. Spectra of (A) dry fiber and (B) hydrated fiber from VV measurements at different angle to fiber axis θ, in degrees. A spectrum of pure distilled water is also shown. Spectra were normalized to the intensity (height) of the bulk peak. Labels B and PS denote peaks related to bulk and parallel-to-surface modes, respectively. Error bars indicate the standard error (square root of number of counts). Please click here to view a larger version of this figure.