The Dynamics of Hydrated Proteins Are the Same as Those of Highly Asymmetric Mixtures of Two Glass-Formers.

Customarily, the studies of dynamics of hydrated proteins are focused on the fast hydration water ν-relaxation, the slow structural α-relaxation responsible for a single glass transition, and the protein dynamic transition (PDT). Guided by the analogy with the dynamics of highly asymmetric mixtures of molecular glass-formers, we explore the possibility that the dynamics of hydrated proteins are richer than presently known. By providing neutron scattering, dielectric relaxation, calorimetry, and deuteron NMR data in two hydrated globular proteins, myoglobin and BSA, and the fibrous elastin, we show the presence of two structural α-relaxations, α1 and α2, and the hydration water ν-relaxation, all coupled together with interconnecting properties. There are two glass transition temperatures T g α1and T g α2 corresponding to vitrification of the α1 and α2 processes. Relaxation time τα2(T) of the α2-relaxation changes its Arrhenius temperature dependence to super-Arrhenius on crossing T g α1 from below. The ν-relaxation responds to the two vitrifications by changing the T-dependence of its relaxation time τν(T) on crossing consecutively T g α2 and T g α1. It generates the PDT at T d where τν(T d) matches about five times the experimental instrument timescale τexp, provided that T d > T g α1. This condition is satisfied by the hydrated globular proteins considered in this paper, and the ν-relaxation is in the liquid state with τν(T) having the super-Arrhenius temperature dependence. However, if T d < T g α1, the ν-relaxation fails to generate the PDT because it is in the glassy state and τν(T) has Arrhenius T-dependence, as in the case of hydrated elastin. Overall, the dynamics of hydrated proteins are the same as the dynamics of highly asymmetric mixtures of glass-formers. The results from this study have expanded the knowledge of the dynamic processes and their properties in hydrated proteins, and impact on research in this area is expected.

Introduction

The emphasis in the studies of dynamics of hydrated protein has been on two processes, namely, the structural α-relaxation and the secondary β-relaxation of hydration water, analogous to those of glass-formers. Their relaxation times τα(T) and τβ(T) were determined by dielectric relaxation,[1−7] nuclear magnetic resonance,[8−11] and neutron scattering spectroscopy.[1,12−19] The phenomenon that attracted most interest is the protein dynamical transition (PDT), first observed in Mössbauer spectroscopy[20] and in neutron scattering[12−23] by a change in temperature dependence of the mean-squared displacements (MSD) at temperature Td, which depends on the experimental timescale. The PDT is believed to be essential for biological activity of the protein. If not masked by the methyl group contribution, another change in T-dependence of the MSD occurs at Tg below Td, independent of the experimental timescale,[9,10,13,15,16,21−23] analogous to that found by neutron scattering in glass-formers of different kinds.[24,25]

The crossover of the MSD at Tg was explained in terms of the caged molecular dynamics and the associated nearly constant loss changing intensity at Tg,[25−27] as proffered by the coupling model.[27] The PDT at Td was explained by the β-relaxation of hydration water of the Johari-Goldstein (JG) kind[10,28] entering the experimental time window.[9,10,16,23] It is not due to the α-relaxation as proposed in ref (15), simply because its relaxation time τα(T) at T = Td is orders of magnitude too long for it to be involved.[10]

Advances were made in characterizing the α-relaxation and the hydration water β-relaxation and understanding their roles in the changes in MSD observed at Tg and at Td of the PDT. Notwithstanding, the question that remains is whether there are still some features of the dynamics not yet been explored, and if found, the new features may deepen the current level of knowledge of the dynamic processes in hydrated proteins. Our exploration is motivated by the new findings in recent experimental studies[29−33] and theoretical interpretations[33−36] of the dynamics of highly asymmetric mixtures (HAM) of two glass-formers A and B with glass transition temperature TgA of A much higher than TgB of B and particularly at low concentration of the fast component B. The dynamics of HAM are composed of three processes, α1, α2, and JG β.[34−37] The α1 and α2 are cooperative relaxations that give rise to glass transition at temperatures Tgα1 and Tgα2, respectively, and can be observed by calorimetry. The slower α1 is dominated by the slower component A with participation of the component B, and its relaxation times τα1(T) has Vogel–Fulcher–Tammann (VFT) temperature dependence, leading to the higher Tgα1. The α2 is contributed by the component B in the presence of the slower A component with relaxation times τα2(T) shorter than τα1(T). At temperatures above Tgα1, τα2(T) also has a VFT dependence. However, at temperatures below Tgα1, τα2(T) changes to assume an Arrhenius dependence because the B molecules are confined by the immobile A molecules. The confinement by the frozen matrix of component A causes localization of the α2-relaxation at temperatures below Tgα1 to make it in some way like a secondary relaxation. Despite τα2(T) being Arrhenius below Tgα1, the α2-relaxation will subsequently become vitrified at Tgα2. Both Tgα1 and Tgα2 increase monotonically with a decrease in the concentration of the faster component cB, although a different interpretation was also reported.[31−33] At lower cB, the difference (Tgα1 – Tgα2) is larger and τα2(T) becomes more separated from τα1(T), making the former easier to determine.[36,37] The JG β-relaxation involves the more local motions of the B molecules coupled to the A molecules at temperatures below Tgα1 and Tgα2.[37] This β-relaxation has properties indicating that it is strongly connected to each of the two α-relaxations and thus it is of the JG kind.[27,28] For example, its relaxation time τβ(T) changes temperature dependence from Arrhenius below Tgα2 to a stronger Arrhenius dependence above Tgα2 and exhibits another change on crossing Tg to assume a super-Arrhenius T-dependence above Tgα1. This double change in temperature dependence is easier to observe in HAM at lower concentration of the fast component cB.[34−37] An example of HAM showing all the properties described above is 50% methyl-tetrahydrofuran (MTHF) in polystyrene with a high molecular weight of 60,000 g/mol.[30] The relaxation times τα1(T), τα2(T), and τβ(T) and their properties of this example are summarized in Figure S1 in the Supporting Information.

Since the Tg of dry proteins is much higher than the Tg of water,[4] it is reasonable to consider hydrated proteins as HAM and to expect similar dynamics. This hypothesis is supported by a close correlation between solvent and protein dynamics based on experimental and simulation evidence,[38−41] like the coupling between components A and B found in the α1-, α2-, and JG β-relaxations in HAM,[29−37] and also in peptide solutions.[42,43]

In this paper, we verify by experiments the anticipated analogy of the dynamics in hydrated proteins with those in HAM. The α1 process is predetermined by the protein but facilitated by the coupling with the hydration water. Its τα1(T) has Vogel–Fulcher–Tammann (VFT) dependence above Tgα1. The α2 process is contributed mainly by the hydrated water coupled to protein. The T-dependence of its τα2(T) changes from VFT dependence at temperatures above Tgα1 to Arrhenius below Tgα1, which continues with temperature falling until the α2-relaxation is vitrified at Tgα2. The JG β process originates from the hydration water, and for this reason, it is also called the ν-relaxation.[2,4,5] Below Tgα2, its τβ(T) or equivalent τν(T) has an Arrhenius dependence in response to confinement by the frozen α1 and α2 processes combined. By increasing temperature to cross Tgα2, τν(T) assumes a stronger Arrhenius dependence due to devitirification of the α2 process. A further increase in temperature and after crossing Tgα1, the α1 process is also devitrified. Consequently, τν(T) has its temperature dependence changed to super-Arrhenius or VFT-like, in response to the equilibrium liquid state of the hydrated protein above Tgα1. The VFT-like dependence of τν(T) continues with increasing temperature until τν(T) matches the timescale of either the Mössbauer or the neutron scattering spectrometer, giving rise to the PDT. Thus, if verified, the dynamics of hydrated proteins are richer than presently known and the additional properties of the α1, α2, and ν processes that we found enhance the current knowledge and impact theoretical interpretation.

Results and Discussion

Neutron Scattering Measurements of Hydrated Myoglobin

As mentioned before, in HAM, the observation of the three processes, α1, α2, and JG β, their properties, and inter-relationship is best brought out at lower concentrations of the faster component because τα1(T), τα2(T), and τβ(T) become more widely separated. Many neutron scattering and dielectric relaxation studies of hydrated proteins in the past were performed at higher hydration levels h, and this explains why together the three processes and their properties were not made known. Therefore, we made neutron scattering measurements of hydrated myoglobin at h = 0.30 and dielectric relaxation at slightly lower h = 0.28 in order to better resolve the three processes in the spectra. Elastic intensities S(q,Δt) of dry H-MYO and H-MYO in D2O at h = 0.3 were obtained by measurements using neutron scattering spectrometers HFBS at NIST and DNA at J-PARC with two resolutions of 1 and 13 μeV, respectively. Details are given in the Experimental Section. S(q,Δt) were normalized to data measured at ∼10 K and summed over values of q ranging from 0.45 to 1.75 Å–1. The MSD ⟨x2(T)⟩ corresponding to S(q,Δt) are shown in Figure , while the latter is given in Figure S2 of the Supporting Information. The first change in T-dependence of ⟨x2(Δt)⟩ is independent of the spectrometer resolution, and it originates from the response of caged dynamics to vitrification of the α1-relaxation at Tgα1 ≈ 198 K.[9,10,16,23] This result is a microscopic and reliable determination of Tgα1 by neutron scattering since the method had been proven in various kinds of glass-formers as shown in a review[24] and especially in several hydrated proteins presented in refs (9, 16, 13). However, the anticipated change in the elastic intensity at a lower Tgα2 ≈ 178 K (see Figure later) was not resolved. This is rationalized first by the weaker relaxation strength of the α2-relaxation and second by myoglobin being probed in H-MYO/D2O instead of water, while the α2-relaxation is predominately contributed by water. The secondary change in T-dependence of ⟨x2(Δt)⟩ is the PDT at Td ≈ 250–255 K and Td ≈ 275 K, respectively, for 1 and 13 μeV energy resolutions.

Figure 1

Mean-squared atomic displacements, derived from elastic intensity S(q,Δt) using Gaussian approximation in the q range from 0.45 to 0.9 Å–1, of dry H-MYO and H-MYO in D2O at h = 0.3. (a) 1 μeV energy resolution. (b) 13 μeV energy resolution.

Figure 2

Selected isothermal spectra for hydrated myoglobin (h = 0.28). The dielectric loss ε″(f) spectra measured directly at nine temperatures are each represented by closed squares. On the other hand, the open circles represent the spectra of dε′(f)/dlog f derived by performing the derivative of the real part ε′(f) with respect to log f at three temperatures, 243, 223, and 203 K, as examples. Continuous lines are fits by superposition of Cole–Cole functions and conductivity σ contributions. All four processes σ, α1, α2, and ν are revealed in the spectra of ε″(f) and dε′(f)/dlog f combined. Dashed lines are from the fits by power laws B(T)f–λ dependence of ε″(f) with λ small to the high frequency data at several lower temperatures. The slope at high frequency for 183 K is −0.18 and for 203 K is −0.28.

Differential scanning calorimetry (DSC) is a conventional method to detect glass transition and glass transition temperature. The technique was applied to hydrated biomolecules, and the results of the studies before 1994 were reviewed by Sartor et al.[44] According to the review,[44] the DSC measurements of myoglobin crystals and hydrated powders in 1986 by Doster et al.[45] had an increase in heat capacity observed at ∼220 K and was attributed to glass–liquid transition of water. This temperature of ∼220 K is much higher than the onset temperature of the glass transition of 162–170 K for vitrified and freezable water in hydrated methemoglobin (MetHb) in the 1992 study by Sartor et al.[46] The sharp glass transitions in myoglobin crystals observed in calorimetry by Miyazaki et al.[47] with Tg values at 188 and 216 K are in conflict with those by Doster et al.[45] Although the DSC Tg of hydrated myoglobin powder (0.4 g/g) was reported in Figure of the 2010 paper of Doster[14] to be ∼170 K. The 1994 paper by Sartor et al.[44] not only addressed the discrepancy between the DSC T values but also resolved the discrepancy by their own DSC studies of hydrated lysozyme, hemoglobin, and myoglobin powders to show that their heat capacity slowly increases with increasing temperature, without showing an abrupt increase characteristic of glass–liquid transition. Their study further showed that annealing from ∼150 K up to the denaturation temperature has a substantial calorimetric effect, which may be confused with glass transition. The results led them to suggest that the DSC glass transition in hydrated hemoglobin, myoglobin, and lysozyme occurs over a broad temperature range that extends from ∼150 K up to the denaturation temperature, and no single glass transition temperature from DSC can be assigned to the three hydrated proteins.[44] Bearing in mind the problem of DSC data revealed by Sartor et al., we nevertheless made our own DSC measurements on the same hydrated sample H-MYO in D2O at h = 0.30 studied by neutron scattering. The DSC measurement was carried out by cooling the sample directly to ∼100 K and then heating back to 300 K at a rate of 5 K/min. The results during heating were recorded and presented in Figure S3 of the Supporting Information without any annealing. A small endothermic hump observed at ∼200 K in our sample seems to indicate Tgα1 ≈ 204 K, but it could result from the unfreezing of the fastest portion of the broad distribution of relaxation time of the structural dynamics in the hydrated proteins, as suggested by Sartor et al.[44] Despite the uncertainty of DSC data, we still have a reliable determination of Tgα1 ≈ 198 K from neutron scattering. As we shall see, this value of Tgα1 is supported by dielectric relaxation data to be presented next.

Figure 4

TSDC data of BSA with h = 0.40 and 0.60 shown in the upper panel are taken from ref (51) but previously unpublished. The two arrows indicate the values of Tgα1 and Tgα2 from TSDC and indicate that the α2 process undergoes a glass transition of around 170 K. The various relaxation times are from ref (5) and replotted against reciprocal temperature in the lower panel. There are changes in T-dependence of τν(T) at Tgα1 and Tgα2. The two parallel lines indicate the lower bounds of τν(T) found empirically.5,10 For details, see text.

Dielectric Spectra of Hydrated Myoglobin

The isothermal dielectric loss ε″(f) spectra of hydrated myoglobin H-MYO at h = 0.28 over 11 decades of frequencies from 103 to 263 K are shown in Figure together with the derivative dε′(f)dlog f of the real part ε′(f) with respect to log f. The latter enables all three processes, α1-, α2-, and ν- or JG β-relaxation, to be resolved in the high temperature range from 203 to 263 K. The source of the H-MYO sample in the dielectric study was the same as that in the neutron scattering study. Dielectric measurements were made on both the heating and cooling paths of the sample, and the same results were obtained. The possibility of the α1 process might be a polarization process of Maxwell–Wagner type due to enhanced conductivity of the sample. An effective criterion is the comparison of the values of ε′ and ε″ at the frequency of the loss peak. In the case where ε′ = ε′′, there is strong indication that the loss peak is of Maxwell–Wagner type. It was found otherwise, and therefore, the α1 process is correlated with the segmental-like mobility of the hydrated protein. Further support comes from the fact that its timescale and temperature dependence to be shown in Figure are consistent with the calorimetric glass transition at 204 K of the H-MYO hydrated at 0.30 (see Figure S3 in the Supporting Information). Regarding the rather high strength of the α1 process, as has been already reported for many hydrated proteins,[2,4−6,10] it may be attributed to counterions, strong internal electric fields, or interfacial polarization processes. Recording similar dielectric responses during cooling and heating supports further that the α1 process is related/triggered by the segmental mobility of the hydrated macromolecules and that it is not related with a rather random polarization process due to charge accumulations at interfaces.

Figure 3

Red closed circles, open circles, and inverted triangles are τα1(T), τα2(T), and τν(T) of hydrated myoglobin (h = 0.28) determined from the fits to our dielectric spectra in Figure . The black closed squares, open squares, and plus signs are τα1(T), τα2(T), and τν(T), respectively, of hydrated myoglobin (h = 0.34) taken from ref (6) and (h = 0.40) taken from ref (3) and replotted in this new figure. The legends of the other symbols are given in the figure. The T-dependence of τν(T) changes at two temperatures, which are near Tgα1 and Tgα2 where τα1(Tgα1) and τα2(Tgα2) are equal to 103 s. A change in T-dependence of τα2(T) occurs near Tgα1. The large gray triangle stands for τα2(195 K) ≈ T1(195 K) ≈ 0.02 s (see text).

Starting at 183 K and temperatures below, appearing in the ε″(f) loss spectra is the nearly constant loss (NCL) of caged molecules dynamics with the characteristic power law B(T)f–λ dependence of ε″(f) with λ small. The loss data at 163 K indicate that the NCL is terminated by the onset of the ν-relaxation, a property found in all glass-formers.[25,27,48,49]

After performing the fits to the data in Figure by superposition of Cole–Cole functions and conductivity σ contributions, the dielectric relaxation times τα1(T), τα2(T), and τν(T) were determined. The results presented in Figure exhibit clearly the change in T-dependence of τα2(T) from VFT to Arrhenius on crossing Tgα1 ≈ 200 K. The Arrhenius dependence of τα2(T) determines Tgα2 ≈ 176 K. The T-dependence of τν(T) changes its temperature dependence from Arrhenius with an activation energy of about 40.2 kJ/mol below Tgα2 to another Arrhenius-like dependence with an activation energy of about 51.8 kJ/mol above Tgα2. On a further increase in temperature, the second Arrhenius-like dependence is changed to a VFT-like dependence at temperatures above Tgα1.

In Figure , the arrow indicates the temperature at which τν(T) = 5 ns (dotted horizonatal line), which is five times the neutron experimental timescale τexp = 1 ns. The latter is commonly used to compare with the temperature Td at the onset of the rise of the MSD defining the PDT in Figure a.[9,15,50] It can be seen from Figure that Td is about 250 K, in good agreement with a value of 250–255 K determined by the MSD in Figure , assuming that the change in Td with the increase in h from 0.28 to 0.30 is not large and within the accuracy of determining h. The α2 was observed dielectrically before in hydrated lysozyme and myoglobin by others,[1,3,6] but the various interpretations given are different from this paper. In contrast to the other works, our dielectric data of hydrated myoglobin data at h = 0.28 are more complete in showing not only all three processes at the same time but also their individual and inter-related properties as well as the two glass transition temperatures Tgα2 and Tgα1, and verifying the dielctric τν(T) determines the PDT temperature Td determined by neutron scattering (see Figure a) by the criterion τν(T) equal to five times the experimental instrument timescale (see Figure ).

Our conclusion that α2 is the structural relaxation of water component is furthermore supported by the 2H NMR study of H-MYO/D2O (h = 0.35),[8] which reported that 2H spin–lattice relaxation is exponential above ∼195 K but nonexponential below (see Figure S4 in the Supporting Information). This observation means that the D2O subsystem becomes nonergodic on the experimental timescale T1(195 K) = 0.02 s upon cooling through this temperature. In Figure , we find τα2(195 K) ≈ T1(195K), while α2 is faster and slower than T1 at higher and lower temperatures, respectively. These findings show that α2 is the ergodicity-restoring process of the D2O subsystem and, hence, it can be identified with its structural relaxation.

Dielectric and TSDC Data of Hydrated Bovine Serum Albumin

In order to support the experimental findings in hydrated myoglobin, we search for similar data of other hydrated proteins. A case is the dielectric study by Panagopoulou et al.[5,51] on hydrated bovine serum albumin (BSA) at h = 0.28 and 0.40. They found a water (W) relaxation slower than the ν-relaxation and faster than the α1-relaxation with Tgα1 = 185 K from DSC. We identified the W process with the α2-relaxation. Its relaxation times τα2(T) are shown together with τα1(T) of the α1-relaxation, τν(T) of the ν-relaxation, and τice(T) of ice in the lower panel of Figure .

By using a combination of DSC and thermally stimulated depolarization currents (TSDC) techniques,[4] they found two Tg values from the TSDC thermograms in hydrated BSA with h > 0.30. The upper panel of Figure shows the TSDC thermograms versus inverse temperature for h = 0.40 and 0.60 taken from ref (51), which was not published before. The TSDC values of Tgα1 and Tgα2 for h = 0.40 are indicated in the figure together with the corresponding TSDC relaxation time τα1(Tgα1) = 103 s = τα2(Tgα2). Interestingly, one can observe in Figure for BSA at h = 0.40 that τα2(T) changes from VFT dependence above Tgα1 to Arrhenius dependence below Tgα1. Also, τν(T) changes from the low-temperature Arrhenius dependence to a stronger temperature dependence on crossing a temperature close to Tgα2 = 170 K and another change to VFT-like dependence after crossing Tgα1. The two crossovers of τν(T) at Tgα2 and Tgα1in hydrated BSA are analogous to those found in hydrated myoglobin (see Figure ). On closer examination of the data of τν(T) for h = 0.60, it seems that there are two similar changes in T-dependence at temperatures slightly lower than Tgα2 and Tgα1 of hydrated BSA at h = 0.40, which are reasonable since the two temperatures are expected to be lower at a higher hydration level.

Neutron Scattering Data of Hydrated Elastin

We consider also the neutron scattering data of the fibrous protein elastin having a very high value of Tg = 464 K when dry. In hydrated elastin at h = 0.224, Tgα1 is 320 K,[19,52,53] much higher than that of hydrated globular proteins, and hence ideal to resolve the α2-relaxation. Indeed, in neutron scattering experiments,[19] the changes in T-dependence of the MSD were observed at two temperatures, Tgα2 = 195 K and Tgα1 = 320 K, as shown in Figure for hydrated elastin at h = 0.23. Found by a dielectric study of hydrated elastin at h = 0.23[53] and 0.25[54] are the α2 and ν processes, and their τα2(T) and τν(T) are plotted versus reciprocal temperature in the inset of Figure . Shown also are the 2H NMR data for h = 0.25[11] and the thermal stimulated current (TSC) data at h = 0.50.[52]

Figure 5

MSD of dry elastin, ELA-H2O, and ELA-D2O at h = 0.20. The lines indicate approximately linear behaviors in various temperature ranges. The arrows mark crossover temperatures T1 ≈ 125 K, Tgα2 ≈ 195 K, and Tgα1 ≈ 320 K. The inset shows dielectric (green diamonds, h = 0.23; red circles, h = 0.25) and 2H NMR relaxation times τα2(T) and τν(T). The two plus signs indicate τα2(T) and τν(T) at h = 0.50 from TSC.

Like hydrated myoglobin and BSA, τν(T) changes from one Arrhenius dependence to another Arrhenius dependence on crossing Tgα2 ≈ 193 K, which is consistent with Tgα2 ≈ 195 K determined independently from neutron scattering MSD data in Figure . One can see from the inset that the ν-relaxation remains in the vitrified state of α1, while τν(T) has decreased to ps and still Tgα1has not been reached. By contrast, in hydrated globular proteins, the ν-relaxation is in the liquid state when τν(Td) matches 5τexp of either Mössbauer or neutron scattering spectroscopy, i.e., Td is above Tgα1, and τν(T) has VFT dependence (see deuteron NMR data in Figure ). On the other hand, in hydrated elastin, the Td satisfying the rule τν(Td) = 5τexp is far below Tgα1 (see the broken line at 5 ns in the inset of Figure ), and thus, the ν-relaxation is confined in the glassy matrix and τν(T) has Arrhenius T-dependence. This difference in the property of the ν-relaxation at temperature where τν(T) = 5τexp between hydrated globular proteins and hydrated elastin is important. It is the reason why the protein dynamic transition (PDT) was observed in hydrated globular protein but not in hydrated elastin.[19] Since the dynamics of hydrated collagen are similar to those of hydrated elastin as shown by dielectric data in ref (10), we predict that the PDT cannot be observed by neutron scattering as well.

Dielectric and Neutron Scattering Data of Ribonuclease A

It is worthwhile to briefly mention the dielectric relaxation[10] and neutron scattering data[10,55] of the globular protein ribonuclease A (RNase A) at hydration level h = 0.4. Like hydrated lysozyme and myoglobin, the dynamics of RNase A were shown[10] to have all the α1, α2, and ν processes, the nearly constant loss of caged molecules, and most of their properties. The protein dynamic transition was observed by neutron scattering, and it conforms to the rule τν(Td) = 5τexp verified in the other hydrated globular proteins. The dielectric spectra are shown in Figures S5 and S6 of the Supporting Information. Hence, the data of hydrated RNase throw another support of the generality of the dynamics of hydrated proteins proffered in this paper.

Summary and Conclusions

In summary, we have provided neutron scattering, dielectric relaxation, and deuteron NMR data in three hydrated globular proteins, myoglobin, BSA, and RNase, and the fibrous elastin to show the presence of three relaxations, α1, α2, and ν, with properties that are inter-related, analogous to the α1-, α2-, and JG β-relaxations in highly asymmetric mixtures of two molecular glass-formers. There are two glass transition temperatures Tgα1and Tgα2 corresponding, respectively, to vitrification of the α1 and α2 processes. The α2-relaxation responds to vitrification of α1-relaxation by changing the T-dependence of its relaxation time τα2(T) on crossing Tgα1. The ν-relaxation responds to the two vitrifications of α1- and α2-relaxations by changing the T-dependence of its relaxation time τν(T) on crossing Tgα1 and Tgα2. The ν-relaxation generates the protein dynamic transition (PDT) at Td where τν(Td) matches approximately five times the experimental instrument timescale τexp, provided that Td > Tgα1. The ν-relaxation is in the liquid state and τν(T) has VFT-like temperature dependence. The ν-relaxation of the hydrated globular proteins considered in this paper satisfies the condition Td > Tgα1, and the PDT is generated and detected. On the other hand, if Td < Tgα1, the ν-relaxation is confined within the glassy state and τν(T) has Arrhenius temperature dependence. This contrasting condition Td < Tgα1 of the ν-relaxation prevails in hydrated elastin, which renders the ν-relaxation ineffective in generating the PDT, and explains why PDT was not found by neutron scattering before in the case of hydrated elastin. Thus, the dynamics of hydrated proteins are exactly the same as those of highly asymmetric mixtures of glass-formers and are richer and diversified than presently known. The advances made by this study should have impact on future research efforts in the dynamics of hydrated proteins and applications.

Materials and Methods

Sample Preparation

Myoglobin (MYO) from equine skeletal muscle was purchased from Sigma-Aldrich (Shanghai, China). In order to exclude the effect of ions, the protein was dialyzed. It was then dissolved in D2O to allow full deuterium exchange of all exchangeable hydrogen atoms and then lyophilized for 12 h to obtain the dry sample. The lyophilized MYO is then suspended on top of liquid D2O in a desiccator to absorb D2O till the desired hydration level (h, gram D2O/gram protein). The deuterium oxidized (D2O, 99.9 atom % D) was purchased from Sigma-Aldrich (Shanghai, China). The hydration levels of protein samples were controlled by measuring the sample weights before and after water adsorption. The h of the dry sample is 0.02, while it is 0.3 for the hydrated one, which corresponds to a case that roughly a single layer of water molecules covers the protein surface.[56,57] The accuracy of h is controlled within 10% error, e.g., h = 0.3 ± 0.03 gram water/gram protein. All samples were sealed tightly in the aluminum cans in a nitrogen atmosphere for subsequent neutron scattering experiments.

Experimental Section

Elastic Incoherent Neutron Scattering

The elastic scattering intensity S(q,Δt) is normalized to the lowest temperature (∼10 K) and is approximately the value of the intermediate scattering function when decaying to the instrument resolution time (Δt).[58] All the S(q,Δt) data were obtained in the temperature range from ∼10 to 300 K during heating with a heating rate of 1.0 K/min by using the HFBS at NIST and DNA at J-PARC. The energy resolutions of HFBS and DNA are 1 μeV and 13 μeV, corresponding to the resolution times of ∼1 ns[59] and ∼80 ps,[60] respectively. The results from instruments with the two different resolutions were summed over the same q from 0.45 to 1.75 Å–1.

The mean-squared atomic displacements ⟨x2(t)⟩ were obtained with the Gaussian approximation of .[61] The values of q used in the Gaussian approximation range from 0.45 to 0.9 Å–1.

Broadband Dielectric Spectroscopy

Dielectric relaxation data of hydrated myoglobin H-MYO with h = 0.28 gram water/gram protein were obtained in the frequency range from 10 mHz to 3 GHz, by the combination of dielectric response analysis (Novocontrol Dielectric Analyzer) and coaxial reflectometry (Agilent Network Analyzer 8753ES). Myoglobin powder was hydrated, compacted, and transferred in a sealed capacitor cell by using the same procedures used for hydrated biomolecules in refs (6, 10). Temperature was varied over a wide range, spanning from the deep glassy state to ambient temperature, following isothermal steps after a suitable equilibration time. Real and imaginary parts of the spectra have been simultaneously fitted with a superposition of Havriliak–Negami and Cole–Cole relaxation functions. The derivative of the real part was used to resolve the α1 and α2 processes by suppressing the conductivity contribution, as done before in ref (6). The characteristic relaxation times reported in Figure correspond to the maximum of the loss function of each process, i.e., the most probable time in the distribution of relaxation times at each temperature for each of the three relaxation process α, α2, and ν.