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Low-Frequency Dynamics of BSA Complementarily Studied by Raman and Inelastic Neutron Spectroscopy Anna V. Frontzek, Jan Peter Embs, Laurent Paccou, Yannick Guinet, and Alain Hedoux J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.7b01395 • Publication Date (Web): 06 Apr 2017 Downloaded from http://pubs.acs.org on April 10, 2017

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The Journal of Physical Chemistry

Low-Frequency Dynamics of BSA Complementarily Studied by Raman and Inelastic Neutron Spectroscopy Anna V. Frontzek (neé Svanidze),*,1,2 Jan Peter Embs,3 Laurent Paccou,4 Yannick Guinet4 and Alain Hédoux4 1

Jülich Center for Neutron Science (JCNS), Forschungszentrum Jülich GmbH, Outstation at

MLZ, Lichtenbergstraße 1, 85747 Garching, Germany 2

A.F. Ioffe Physical Technical Institute, ul. Politekhnicheskaya 26, 194021 St. Petersburg,

Russian Federation 3

Laboratory for Neutron Scattering and Imaging, Paul Scherrer Institut, CH-5232 Villigen,

Switzerland 4

Université Lille Nord de France, F-59000 Lille, France, USTL UMET UMR 8207, F-59655

Villeneuve d’Ascq Cedex, France

ABSTRACT: The present study focuses on protein motions on the picosecond time scale, generally characterized by the overlapping of vibrational and relaxational dynamics in disordered molecular systems. Recently it has been demonstrated that a dry protein, bovine serum albumin (BSA), shows a glass-like transition located in the temperature range between 240 K and 260 K. Here, we present the results of combined low-frequency Raman and inelastic neutron scattering studies of dry BSA at conditions close to this glass-like transition. The use of both techniques allows us to perform a detailed comparison of the dynamic susceptibility and the vibrational density of states of BSA obtained at different temperatures and to calculate the light-vibration coupling coefficient C (ω ) . Moreover, we analyzed the temperature evolution of the boson peak and a peak located at ~ 80 cm-1, which has previously been identified to originate from protein dynamics. We observe that both modes show an anomalous temperature behavior in the vicinity of T g .

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INTRODUCTION Recently, the study of biopolymer dynamics became an important and a quickly developing scientific area attracting a considerable number of researchers. This interest is motivated by the strong relationship between dynamical properties of biopolymers and mechanisms of their functioning.1-3 Numerous investigations have demonstrated that proteins show a lot of similarities with amorphous systems.4-12 The deep cooling of hydrated or solvated protein powders is accompanied by a glass and the so-called dynamical transitions.4-10 Up to now there were many discussions about the nature of the dynamical transition,4-10 leading to the conclusion that it is a glass transition in the hydration shell of a protein.4-6 Interestingly, recent studies of the solvent-solute system different than biopolymers (in particular, containing a non-biological polymer, polystyrene, and toluene as a solvent) show that the dynamical transition in proteins is a manifestation of a universal feature of solvent-solute dynamical relationship.12 In general, water plays a critical role in protein dynamics facilitating their motions.4,13-15 And vice versa, the water dynamics is significantly affected by the close proximity of protein: the fast rearrangement dynamics of water forming the hydration shell of a protein exhibit a 6-7 times slowing down compared to bulk water.16,17 The dynamics of dry proteins are strongly suppressed, so much that the protein biological activity cannot be detected if the hydration level is below 0.2.13 It is commonly accepted that a dry protein undergoes a crossover from harmonic to anharmonic dynamics in the vicinity of 150-180 K due to the onset of rotational motions of methyl groups.4,7 Recently, it has been unexpectedly revealed that the dry protein, bovine serum albumin (BSA), undergoes a transition in the temperature range between 240 K and 260 K, which shows some features similar to glass transitions in disordered systems.18 This glass-like transition identifies itself by significant anomalies in the temperature behavior of relaxational dynamics and vibrational modes as observed by inelastic neutron scattering.18 However, the nature of the transition still has to be understood. The vibrational spectra of proteins include various vibrational excitations, particularly, acoustic19,20 and optical phonons,21-23 and the boson peak.19,24-30 The presence of low energy modes excess in the vibrational density of states (VDOS or G (ω ) ) of various proteins over those expected according to the predictions of the Debye model can be considered as another feature similar to disordered systems.19,31 The conclusions about the excess of vibrational modes in VDOS, also called the boson peak, for the case of proteins were made mainly based on the analysis of the shape of the dynamic structure factor S ( q , ω ) , obtained by inelastic neutron scattering,18,19,24-27 Raman spectroscopic data28 and the low-temperature behavior of the specific heat of globular proteins.32,33 It manifests itself in S ( q , ω ) and Raman spectra as a peak located 2 ACS Paragon Plus Environment

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at around 3 meV (or ~ 25 cm-1) overlapping with quasi-elastic scattering (QES).18,19,24-28 In contrast to conventional glassformers, vibrational spectra of proteins include a contribution at ~ 80 cm-1 that is visible in Raman spectra of protein solutions22,34,35 and single crystals.23,36 The origins of the boson peak as well as a vibrational band at ~ 80 cm-1 are still not unambiguously determined and remain points of intensive debate. Inelastic neutron scattering (INS) and low-frequency Raman spectroscopy (LFRS) are the most informative, complimentary methods, which allow for investigation of protein lowfrequency dynamics by exploring the VDOS19,20 and dynamic susceptibility χ '' (ω ) .37 Moreover, the combined application of these techniques gives the possibility to calculate directly the light-vibration coupling coefficient C (ω ) , which is in fact a proportionality coefficient between G (ω ) and χ '' (ω ) . The knowledge of C (ω ) could be important for the understanding of how different low-frequency vibrational bands can couple to radiation.32,38 If the coefficient C ( ω ) for some certain protein is known, its VDOS could be easily extracted from low-

frequency Raman spectra. General investigations of various glassy systems revealed that C (ω ) is often linearly proportional to ω in the region near the boson peak maximum,31 but there might be an exceptional cases like triphenyl phosphite that exhibits the power dependence slightly bigger then 1.39 Similar to the many small molecular

with the spectral dimension

glassforming systems, the coefficient C (ω ) of chicken egg-white lysozyme has been shown to be linearly dependent on ω above 20 cm-1 and below 80 cm-1.38 At lower ω some materials demonstrate the dependence C (ω ) .31,39 Moreover, according to the model of Martin and Brenig, considering a glass as a continuous disordered network, C (ω ) should exhibit a maximum near the boson peak frequency.40-43 In our study, we used both techniques – INS and LFRS, for a detailed investigation and comparison of low-frequency parts of both – VDOS and χ '' (ω ) of dry BSA. The experiments have been performed in a broad temperature range including the temperature of glass-like transition Tg as deduced in

18

. The temperature evolution of the boson peak, of the vibrational

mode located at ~ 80 cm-1 in Raman spectra of dry BSA, and of the coupling coefficient have been determined and analyzed.

MATERIAL AND METHODS Sample preparation. Bovine serum albumin (BSA) has been purchased from Sigma-Aldrich and used for neutron and light scattering experiments without further treatment. In order to 3 ACS Paragon Plus Environment


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identify the water amount in our protein sample we performed a thermogravimetrical analysis coupled to the mass-spectroscopic measurements from water. The results of our thermogravimetric analysis have shown a hydration level of 0.04. So, the studied BSA powder can be considered as being dry.13,14,44 In order to perform neutron experiments, the BSA sample was placed in a cylindrical aluminum can; the can was sealed with an Indium wire. For the Raman scattering experiments, the powder was placed into a glass capillary, which was afterwards sealed from the both ends using araldite adhesive suited for very low temperatures.

Low-frequency Raman scattering experiment. The Raman scattering data for dry BSA powder have been obtained using an experimental setup, which consists of an ArgonKrypton Coherent laser (wavelength λ=514.5 nm), a XY Dilor spectrometer and a CCD camera for data accumulation. The high-dispersive system of the Raman spectrometer is composed of a double monochromator coupled to an additional monochromator, characterized by a focal length of 800 mm. Keeping all the slits opened at ~ 150 µm allows for a high rejection rate of elastically scattered light. These conditions yield a resolution better than 1.5 cm-1 for the 514.5 nm incident laser light. The capillary filled with the BSA powder was mounted on a goniometer. The sample temperature was controlled by a regulated nitrogen-flow maintained by Cryostream Plus device (from Oxford Cryosystems). To ensure temperature stability, the sample was kept at least for 10 min. at a certain temperature before collecting the spectra. The incident laser beam was focused on the capillary containing the protein powder in the horizontal direction while the cold nitrogen flow was vertically oriented in the direction of the capillary glass. The capillary was cooled first down to 200 K and then heated gradually up to 350 K. Raman spectra were recorded in backscattering geometry. The program PeakFit v4.12 (Systat Software Inc.45) was used for spectra fitting.

Neutron scattering experiment. INS experiments have been performed at Paul Scherrer Institut, at SINQ (Switzerland) using the cold neutron time-of-flight spectrometer FOCUS. The used temperature range was from 180 K up to 340 K. Details of the INS experiment can be found elsewhere.18 The collected raw neutron data have been treated using the standard time-of-flight to energy conversion, the normalization to vanadium and a correction for the empty can signal. The DAVE package46 has been used to perform data reduction. The VDOS were determined using standard computer programs with corrections for the Debye-Waller factor.47 The data were represented in one-phonon scattering approximation, which allows considering mainly the lowfrequency part of VDOS. The neutron data were analyzed using the program packages DAVE and PeakFit v4.12.


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Raman and neutron scattering data analysis. The analysis of the low-frequency Raman spectrum of dry BSA measured at 250 K is described in Fig. 1. It can be seen that the spectrum includes overlapping contributions from QES and two vibrational modes (Fig. 1a). In order to analyze the temperature behavior of the vibrational modes,36,48 we subtracted the QES contribution from the reduced Raman intensity I r (ω ) and finally transformed the thus obtained intensity into the imaginary part of dynamic susceptibility χ '' ( ω ) using the following equations: I r (ω ) =

I (ω )

(1)

B (ω ) ω

(2)

χ ′′ (ω ) = I r (ω ) ω

B ( ω ) = n (ω ) + 1 ,

(3)

where I (ω ) is the observed Raman intensity, B (ω ) and n (ω ) are the temperature and Bose factors, respectively.37 Fig. 1b depicts the dynamic susceptibility χ '' ( ω ) obtained from the BSA Raman spectrum (Fig. 1a) using the procedure described above. To fit the Raman data in Fig. 1a we used a Lorentzian for the quasi-elastic component and lognormal distributions to reconstruct the shape of the peaks that correspond to the two lowfrequency vibrational modes.29,49 χ '' ( ω ) was fitted with two log-normal distributions (Fig. 1b). The same fitting procedure has been applied to analyze all Raman data measured at different temperatures. The Raman susceptibility χ '' ( ω ) is related to G (ω ) through the light-vibration coupling coefficient C (ω ) according to: χ '' (ω ) = ω I r (ω ) =

C (ω )

ω

G (ω ) .

(4)

Therefore, the INS and LFRS results can be compared directly if they are represented as χ '' (ω ) and G (ω ) spectra.

RESULTS AND DISCUSSIONS As it can be seen in Fig. 1a, the Raman spectrum of dry BSA contains the contributions from QES and two low-frequency vibrational modes. Let’s consider each contribution separately. In general, among the relaxational motions of proteins, the relaxation of methyl groups, fast picosecond relaxations, large scale motions, and the “main structural relaxation”, strongly affected by the hydration level and most probably comprising some parts of a protein molecule 5 ACS Paragon Plus Environment


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or certain secondary structures, have been identified.15 In the case of hydrated proteins, the water dynamics contribution can be superimposed to the frequency range where protein internal vibrations or fast motions manifest themself.16 Since the BSA powder studied here is supposed to be dry, the QES most probably arises from picosecond relaxational motions of side-chain residues in a cage formed by other residues or the protein backbone.50 The quantity of residual water in our sample is too small to form the first hydration layer. So the water molecules are most probably bound to the protein and may scarcely accomplish reorientation motions observable in the 5–70 cm-1 region. The vibrational contribution to χ '' (ω ) at ~ 32 cm-1, observed as a gentle shoulder on the low-frequency side of the broad bump, can be assigned to the boson peak (Fig. 1).28 The value of its maximum frequency is within the range of energy transfer values, where the boson peak usually manifests itself in INS spectra.24,25,28,51-53 The origin of the boson peak still remains a source of controversy.24,25,27,29,30,51-53 It is supposed to appear due to the localization of vibrational modes caused by a disorder and a defect-like structure of glassy materials.54 According to recent investigations, the boson peak in proteins originates from acoustic waves quasi-localized on the length-scales of a macromolecule and is related to the protein rigidity/elasticity.28,29 Interestingly, proteins demonstrate boson peak vibrations in both states - powder and solution, while the glass-forming systems55 and even a small peptide, Nacetyl-leucine-methylamide56 – only in liquid state that points out at the relationship between the boson peak vibrational motions and the heterogeneities at corresponding length-scales. The other band in χ '' (ω ) , centered at ~ 80 cm-1, is commonly accepted to originate from the protein vibrational dynamics,34 however, its exact nature is unclear till now. One of the possible interpretations of its origin was given by Lushnikov et al.,20,57 where a fractal approach was proposed for the description of the low-frequency dynamics of lysozyme. According to this approach, the bump at ~ 80 cm-1 might originate from vibrational modes quasi-localized on structural inhomogeneities of a protein, exhibiting the structural similarity at different lengthscales, so-called fractons.20,57 It can be reasonably expected that collective motions of structural entities of different length scales overlap with internal motions corresponding to distortions of flexible chains. In agreement to this suggestion, a broad band detected by femtosecond optical Kerr-effect spectroscopy in lysozyme solutions in a similar frequency range has been revealed to be an underdamped mode, delocalized over the entire protein.1 The mode has been demonstrated to be of biochemical significance since it shows a blue shift after binding of an inhibitor to lysozyme molecules.1 It is worth noting that this band is systematically observed 6 ACS Paragon Plus Environment

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to be shifted in Raman spectra of proteins in solutions as compared to protein powders, probably because of the coupling between solvent and protein dynamics.22,58 The temperature dependences of the boson peak maximum obtained by LFRS as well as by INS18 are depicted in Fig. 2. The details of neutron experiment and the procedure applied for S (ω ) analysis can be found in

18

. The results of both experiments

show that the temperature increase leads to a shift of the boson peak towards the elastic line. Earlier Raman spectroscopic investigations of hydrated lysozyme have demonstrated a similar tendency in the boson peak temperature behavior.59 It is important to note that the slopes of both curves in Fig. 2 become much steeper above 250 K exhibiting a characteristic point in a certain way. The neutron data exhibit the sharp step-like anomaly near 250 K, while the Raman data change more smoothly over the whole temperature range, showing a pronounced kink near 250 K. Such a discrepancy can be referred to as the lack of experimental points in the case of neutron experiment, on one hand, and bigger experimental errors in Raman data coming from the fitting procedure, on the other hand. Since a similar temperature evolution of the boson peak was observed for glass-forming systems it can be considered as a specific feature of a glass transition60 and, thus, it was concluded that the dry BSA shows a glass-like transition in the vicinity of 250 K.18 Here we prove the presence of the transition using a technique that is complementary to INS, i.e. LFRS. The use of light scattering helps to avoid such contradictory questions as the influence of hydrogen-deuterium exchange on the neutron experimental data and a determination of coherent and incoherent contributions in neutron spectra. An attentive eye could already notice such a detail as a difference in the absolute values of ω

BP

corresponding to the boson peak maximum identified by neutron and

Raman scattering (see Fig. 2), respectively. To show this clearly, we plotted the VDOS and the dynamic susceptibility χ '' (ω ) of dry BSA measured at the same temperature as G (ω ) ω 2 and χ '' (ω ) ω 2 versus ω (Fig. 3). Here, it is unambiguously seen that the

boson peak in the neutron spectrum manifests itself at a lower frequency relative to the Raman data. Such a difference can be referred to as the light-coupling coefficient C (ω ) , which is a proportionality coefficient between the VDOS and the dynamic susceptibility and shows how the vibrational modes are coupled to radiation. Additionally, we could observe that the vibrational mode located at ~ 80 cm-1 is visible only in the Raman spectrum in case the data represented as a dependence of G (ω ) ω 2 or χ '' (ω ) ω 2 on ω . However, this band manifests itself clearly if the VDOS and the dynamic susceptibility are plotted in a usual 7 ACS Paragon Plus Environment


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scales, namely, as a function of ω (see insert in Fig. 3). It is worth noting that the discrepancy between INS and LFRS data at higher frequencies might appear due to a higher resolution of Raman spectroscopy in a wider region (10-200 cm-1) that is coherent scattering method compare to INS and the possible contribution of multiple scattering to the neutron spectra at higher frequencies.48 Consequently, the χ '' (ω ) and G (ω ) spectra might exhibit systematic differences above ~ 50 cm-1. However, in spite of these differences, it has been demonstrated that the χ '' (ω ) spectra of lysozyme aqueous solution and water-disaccharide mixtures are very similar to the VDOS spectra obtained by molecular dynamics simulations in the range of 10-200 cm-1. 61 The temperature dependence of the band observed at ~ 80 cm-1 in the Raman spectra of dry BSA is shown in Fig. 4. It can be seen that the band maximum ω P D doesn’t vary with temperature up to ~250 K. However, further heating leads to a pronounced decrease in ω P D . We associate the change in the slope of d ω P D d T

also as a

characteristic of the glass-like transition in dry BSA. As it was already mentioned above, the Raman susceptibility χ '' (ω ) of amorphous systems in general31,37 and BSA powder, in particular, is related to the vibrational density of states G (ω ) through the coupling coefficient C (ω ) (see Eq. (4)). It was shown in numerous publications, that the coefficient C (ω ) depends on ω and that different frequency regions may exhibit a behavior

with different values of

.31 For example, in the case of glassy SiO2 there exist two regimes where (i) C (ω ) ~ ω 2 at ω < 20 cm − 1 and (ii) C (ω ) ~ ω at ω > 20 cm − 1 . This finding was explained by the nature of the glass structure leading to specific features in the low-frequency dynamics. Namely, the crossover was supposed to be due to disorder in the glass network, which leads to the localization of vibrations in inhomogeneities or clusters isolated by a weakening of bonds.62 Based on various investigations of glass-forming systems, it is expected in general that C (ω ) shows a dependence, which is close to be linear with ω in the region near the boson peak maximum31,62 and doesn’t exhibit the maximum predicted by Martin and Brenig theory.40 Our results make it possible to calculate the coefficient C (ω ) for dry BSA in a certain temperature interval from 200 up to 340 K in the wide range of ω . Prior to the calculation of C (ω ) , both – the VDOS and χ '' (ω ) were normalized to the integral intensity in the region from 0 to 150 cm-1. Fig. 5 shows C (ω ) obtained as a result of our 8 ACS Paragon Plus Environment

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calculations for three temperatures: 200 K, 240 K and 340 K. Presenting C (ω ) on double logarithmic scales facilitates the observation of two regimes with power exponents x1 and x 2 in the ranges of 11 cm − 1 < ω < 20 cm − 1 and 20 cm − 1 < ω < 80 cm − 1 , respectively. The value

of x 2 varies around 1.0±0.2 in the whole temperature range studied. However, the exponent x1 exhibits a quite unusual dependence on T (Fig. 6). First, heating from 200 K up to 240 K leads to a decrease of x1 from 4.2 to 2.7, then there exists a sharp, step-like anomaly – a drop of the value of x1 from 2.7 down to 1.0 in a narrow interval of 240260 K. Finally, further heating up to 340 K is accompanied by an increase of x1 up to the value of 2. It is necessary to note that the linear dependence of C (ω ) on ω in the range 20 cm − 1 < ω < 80 cm − 1 looks more or less usual. It was expected due to the similarity of

protein dynamics with the dynamics of glass-forming systems. The hen egg-white lysozyme has been shown to exhibit the linear C (ω ) dependence in the same range of ω.38 The value of x1 ≈ 2 , obtained at room temperature, looks also reasonable. Many authors, investigating glassy systems, came to the conclusion that C (ω ) ~ ω 2 at

( )

ω < 20 cm − 1 when the Debye law G ω ~ ω 2 holds. It is not clear why the value of x1

reaches such high numbers as from 2.7 to 4.2 at low temperatures. Since the Debye law is obeyed for VDOS of proteins19,20,57 including the VDOS of our BSA powder (data not shown), some other reasons rather than phonon behavior should exist. For example, the critical behavior of the system in the vicinity of the glass-like transition near 250 K might be relevant. We suppose that the step-like anomaly in the temperature dependence of x1 is a manifestation of this glass transition. One more important feature of the C (ω ) dependence is the existence of a maximum (Fig. 5). The appearance of a maximum in C ( ω ) has been previously predicted by the Martin and Brenig model considering a glass

as a continuous network with inhomogeneities.40 However, the authors supposed that the maximum might be observed at a frequency somewhere close to the boson peak frequency, which clearly is different in our case. According to our results it is located at ~ 80-100 cm-1, in the range where the band arising from protein dynamics was observed in Raman spectra. Therefore, we could suppose that the nature of the band at ~ 80 cm-1 might be similar to the nature of the boson peak in glass-forming systems, but specific for proteins and might be explained by the specificity of their structural disorder. 1,19,20,57 9 ACS Paragon Plus Environment


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We have demonstrated here that the glass-like transition in dry BSA near 250 K manifests itself as an anomalous behavior of vibrational low-frequency modes and, moreover, affects the coupling coefficient C (ω ) in the low-frequency region. The downshift of the boson peak points out that the protein elasticity increases with rising temperature much steeper above 250 K.28 Interestingly, the temperature behavior of the maximum of band located at ~ 80 cm-1 looks quite similar to the temperature behavior of the boson peak maximum. So, the transition affects both vibrational modes in a similar way. The simultaneous application of neutron and low-frequency Raman spectroscopy provided the possibility to identify the light-vibration coupling coefficient C (ω ) of dry BSA in the vicinity of Tg . It is important to note that the character of temperature evolution of C (ω ) in the low-frequency region also changes at the glass-transition (see Fig. 6). Since the coefficient C (ω ) shows how different low-frequency vibrational bands couple to radiation, apparently the character of this coupling is different in low and high temperature phases.

CONCLUSIONS We have investigated the low-frequency dynamics of dry BSA by two complimentary methods – LFRS and INS. The simultaneous use of both techniques gave us the possibility to perform a detailed comparison of low-frequency Raman and neutron spectra – in particular, to compare the temperature evolutions of the dynamic susceptibility and VDOS, and to obtain the light-vibration coupling coefficient C (ω ) at ω between 11 and 150 cm-1. The light-vibration coefficient C (ω ) calculated using the results of neutron and Raman experiments has revealed different exponential dependencies on ω : (i) C ( ω ) ~ ω x1

where

x1 ≈ 2

at very low frequencies 11 cm − 1 < ω < 20 cm − 1

at room

temperature; (ii) C (ω ) ~ ω in the frequency range 20 cm − 1 < ω < 80 cm − 1 at all temperatures (200-340 K), which is in good agreement with previous investigations of lysozyme32,38 and various glass-forming systems.31,62 Surprisingly, the pronounced maximum in C (ω ) has been found above 80 cm-1 present at all temperatures investigated. The detailed analysis of temperature changes of C (ω ) shows that in the region 11 cm − 1 < ω < 20 cm − 1 , C ( ω ) exhibits an unusual temperature evolution in contrast to higher frequencies where C ( ω ) remains close to be T-independent. The exponent x1 in the power law reaches a


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value of ~ 4.2 at 200 K, and decreases down to 2 at room temperature upon heating. Moreover, it exhibits a step-like anomaly near 250 K, the temperature of the supposed glass-like transition in dry BSA.18 Our Raman scattering data for dry BSA are in a good agreement with the data obtained by INS: the characteristic features of a glass-like transition in the dry protein are clearly observable by both techniques. In addition to the critical temperature behavior of the power exponent x1 identified by our analysis of C (ω ) in the vicinity of supposed Tg , the vibrational modes visible in Raman spectra show also anomalies near the same T. The dynamic susceptibility of dry BSA shows two vibrational contributions: a shoulder arising from the boson peak and a band at ~ 80 cm-1 corresponding to the protein dynamics. The temperature dependencies of the boson peak maximum obtained by Raman and neutron techniques look similar and exhibit anomalies near T g =250 K. The anomalous temperature behavior has been revealed for the band located at ~ 80 cm-1 as well. Moreover, the character of the temperature evolution looks similar for both vibrational modes.

AUTHOR INFORMATION Corresponding author * E-mail: [email protected] Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS Dr. Anna Frontzek (née Svanidze) thanks Université Lille Nord de France (F-59000 Lille France, USTL UMET UMR 8207 F-59655 Villeneuve d’Ascq France) for the financial support for her visit to perform the Raman scattering experiments in the scientific group of Prof. Dr. Alain Hedoux. The authors thank Dr. Ekaterina Pomjakushina and Dr. Katharina Rolfs for the performance of thermogravimetrical analysis for BSA powder, and Dr. Matthias D. Frontzek for working on the text improvement. This work is based on experiments performed at the Swiss spallation neutron source SINQ, Paul Scherrer Institute, Villigen, Switzerland.



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FIGURES Figure 1. The Raman spectrum (a) and the dynamic susceptibility χ '' (ω ) (b) of dry BSA obtained at 250 K. The final fits for both curves are shown by red lines. The blue dotted line corresponds to the Lorentzian used to describe the relaxational component; the green and blue lines were used to show the log-norm functions corresponding to vibrational modes.

Figure 2. The temperature dependences of the boson peak maximum obtained by low-frequency Raman spectroscopy ω BP (black circles) and inelastic neutron scattering

(grey circles) for

dry BSA powder.18

Figure 3. Comparison of the VDOS and the dynamic susceptibility χ '' (ω ) of dry BSA powder obtained by INS and LFRS, correspondingly. Both spectra were measured at 220 K. As it can be seen, both dependences are scaled by 1 ω 2 . The insert in Fig. 4 shows the same VDOS and χ '' (ω ) as a function of ω.

Figure 4. The maximum frequency of the vibrational mode located at ~ 80 cm-1 in low-frequency Raman spectra of dry BSA plotted as a function of temperature.

Figure 5. The frequency dependence of the light-vibration coupling coefficient C (ω ) of dry BSA calculated for temperatures: 200 K (blue squares), 240 K (cyan triangles) and 340 K (red circles). The double-logarithmic scales are used to enable the observation of regions with different power laws.

Figure 6. Temperature dependence of the power exponent x1 calculated for C (ω ) at low frequencies ω < 20 cm − 1 .



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Figure 1. The Raman spectrum (a) and the dynamic susceptibility χ''(ω) (b) of dry BSA obtained at 250 K. The final fits for both curves are shown by red lines. The blue dotted line corresponds to the Lorentzian used to describe the relaxational component; the green and blue lines were used to show the log-norm functions corresponding to vibrational modes. 99x119mm (600 x 600 DPI)

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Figure 2. The temperature dependences of the boson peak maximum obtained by low-frequency Raman spectroscopy ωBP (black circles) and inelastic neutron scattering hωBP (grey circles) for dry BSA powder18. 87x99mm (600 x 600 DPI)



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Figure 3. Comparison of the VDOS and the dynamic susceptibility χ”(ω) of dry BSA powder obtained by INS and LFRS, correspondingly. Both spectra were measured at 220 K. As it can be seen, both dependences are scaled by 1/ω2. The insert in Fig. 4 shows the same VDOS and χ”(ω) as a function of ω. 109x150mm (300 x 300 DPI)


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Figure 4. The maximum frequency of the vibrational mode located at ~ 80 cm-1 in low-frequency Raman spectra of dry BSA plotted as a function of temperature. 79x80mm (600 x 600 DPI)



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Figure 5. The frequency dependence of the light-vibration coupling coefficient C(ω) of dry BSA calculated for temperatures: 200 K (blue squares), 240 K (cyan triangles) and 340 K (red circles). The double-logarithmic scales are used to enable the observation of regions with different power laws. 69x57mm (300 x 300 DPI)


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Figure 6. Temperature dependence of the power exponent x1 calculated for C(ω) at low frequencies ω

Low-Frequency Dynamics of BSA ... - ACS Publications

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