Glass Transitions in Aqueous Solutions of Protein (Bovine Serum

Oct 2, 2009 - ... García SakaiMadhusudan TyagiHugh O'NeillQiu ZhangSimone ... Yasuhito Suzuki , Martin Steinhart , Robert Graf , Hans-Jürgen Butt , ...
0 downloads 0 Views 2MB Size
Download PDF
14448

J. Phys. Chem. B 2009, 113, 14448–14456

Glass Transitions in Aqueous Solutions of Protein (Bovine Serum Albumin) Naoki Shinyashiki,*,† Wataru Yamamoto,† Ayame Yokoyama,† Takeo Yoshinari,† Shin Yagihara,† Rio Kita,† K. L. Ngai,‡ and Simone Capaccioli§ Department of Physics, Tokai UniVersity, Hiratsuka, Kanagawa 259-1292, Japan, NaVal Research Laboratory, Washington, D.C. 20375-5320, and Dipartimento di Fisica, UniVersita` di Pisa and polyLab, CNR-INFM, Largo B. PontecorVo 3, I-56127, Pisa, Italy ReceiVed: June 12, 2009; ReVised Manuscript ReceiVed: August 26, 2009

Measurements by adiabatic calorimetry of heat capacities and enthalpy relaxation rates of a 20% (w/w) aqueous solution of bovine serum albumin (BSA) by Kawai, Suzuki, and Oguni [Biophys. J. 2006, 90, 3732] have found several enthalpy relaxations at long times indicating different processes undergoing glass transitions. In a quenched sample, one enthalpy relaxation at around 110 K and another over a wide temperature range (120-190 K) were observed. In a sample annealed at 200-240 K after quenching, three separated enthalpy relaxations at 110, 135, and above 180 K were observed. Dynamics of processes probed by adiabatic calorimetric data are limited to long times on the order of 103 s. A fuller understanding of the processes can be gained by probing the dynamics over a wider time/frequency range. Toward this goal, we performed broadband dielectric measurements of BSA-water mixtures at various BSA concentrations over a wide frequency range of thirteen decades from 2 mHz to 1.8 GHz at temperatures from 80 to 270 K. Three relevant relaxation processes were detected. For relaxation times equal to 100 s, the three processes are centered approximately at 110, 135, and 200 K, in good agreement with those observed by adiabatic calorimetry. We have made the following interpretation of the molecular origins of the three processes. The fastest relaxation process having relaxation time of 100 or 1000 s at ca. 110 K is due to the secondary relaxation of uncrystallized water (UCW) in the hydration shell. The intermediate relaxation process with 100 s relaxation time at ca. 135 K is due to ice. The slowest relaxation process having relaxation time of 100 s at ca. 200 K is interpreted to originate from local chain conformation fluctuations of protein slaved by water. Experimental evidence supporting these interpretations include the change of temperature dependence of the relaxation time of the UCW at approximately TgBSA ≈ 200 K, the glass transition temperature of protein in the hydration shell, similar to that found for the secondary relaxation of water in a mixture of myoglobin in glycerol and water [Swenson et al. J. Phys.: Condens. Matter 2007, 19, 205109; Ngai et al. J. Phys. Chem. B 2008, 112, 3826]. The data all indicate in hydrated BSA or other proteins that the secondary relaxation of water and the conformation fluctuations of the protein in the hydration shell are inseparable or symbiotic processes. 1. Introduction Water is important for the functionality of biological systems. Indeed, dehydrated proteins cannot function, but a thin layer of water surrounding them fully activates the protein functionality. A solvent, often water or mixtures of water with other hydrophilic compounds (like glycerol or sugars), is present in the hydration shell surrounding the protein, but the solvent is also present outside the protein in the bulk form.1 The water in the hydration shell is an intrinsic part of the protein structure, as opposed to the bulk solvent outside. Among several interesting aspects, perhaps the most often addressed one is the role played by the solvent in determining the dynamic properties and function. Insight into motions of hydrated proteins apparently came first from the mean square displacement (MSD) of fast processes in hydrated proteins measured by the Mo¨ssbauer effect2,3 and later on by neutron scattering by many workers. Here we cite a few examples.4-6 These experiments have shown in hydrated proteins that the rate of change of the mean-square displacement with temperature increases abruptly on crossing * Correspondence author. E-mail: [email protected]. † Tokai University. ‡ Naval Research Laboratory. § Universita` di Pisa and polyLab, CNR-INFM.

a temperature that is dependent on the protein, the solvent, and its weight fraction. In the cases cited, the temperature falls in the neighborhood of 200-240 K. The change of fast dynamics of the hydrated protein in crossing this temperature can be likened to that found by neutron scattering in glass-forming substances because similar properties of the MSD were found.7,8 Similar changes in the temperature dependences of various other properties of hydrated proteins have been found (see the review by Ringe and Petsko in ref 9). Hence, the phenomenon is commonly referred to as the protein glass transition. To understand protein functions, one must first understand how water affects conformation dynamics of the protein, and the dynamics of water molecules in the hydration layer surrounding proteins as well. The experimental data from various sources all indicate that the dynamics of protein and solvent in the hydration shell are physically coupled, and the glass transition involves cooperative motion of the two components. For this reason, the motion of proteins is described as being “slaved” to that of the solvents surrounding the protein molecules,10 and it is clear from this that the glass transition temperature of the protein depends on the solvent. A collection of references and reviews addressing the phenomenon of protein glass transition can be found in ref

10.1021/jp905511w CCC: $40.75  2009 American Chemical Society Published on Web 10/02/2009

Glass Transitions in Solutions of Protein 9. It is an important phenomenon because the conformational fluctuations and correlated motions in the protein are arrested in the glassy state of the hydrated protein, and the biological function of the protein ceases. It is also of interest in the research on food science and cryopreservation. Thus, the molecular mechanism leading to the protein glass transition deserves indepth studies experimentally and theoretically, particularly the motion of the solvent and the role it plays in the dynamics over time which eventually end up with the protein glass transition. In reality, glass transition occurs at temperatures when the structural relaxation times become much longer than the laboratory observation time (typically on the order of 103 s and longer), and the system falls out of equilibrium. Therefore, the protein glass transition and the molecular dynamics from which it originates are most directly studied by calorimetry and by dielectric spectroscopy with time window that extends down to near 103 s. The measurements have been made recently by calorimetry11,12 and by dielectric relaxation.13 Broadband dielectric relaxation measurements of a solution of myoglobin in a mixture of water and glycerol13 provide rich information on the secondary relaxation of water in the hydration shell and the cooperative relaxation responsible for the slaved myoglobin glass transition.14 The property of relaxation of water in the hydrated myoglobin is similar to that found in the secondary β-relaxation of water in many aqueous mixtures including the change of temperature dependence of the relaxation time when crossing the glass transition temperature of the mixture. Furthermore, the same dynamics were found in mixtures of two van der Waals glass-formers, which are even simpler systems than aqueous mixtures because of the absence of hydrogen bonding between the two components. The experimental data of these ideal mixtures of van der Waals liquids15-19 have shown that the secondary relaxation of a component and the cooperative relaxation involving the same component are so strongly correlated in properties that they cannot be separately considered, consistent with the coupling model description of the dynamics of glassforming substances. Since the properties of hydrated proteins, aqueous mixtures, and the binary mixtures of van der Waals liquids are similar, the theoretical understanding gained in the study of the binary mixtures of van der Waals liquids has been transferred to the hydrated proteins.14 The purpose of this paper is threefold. First, we would like to see if we can find in another hydrated protein the same principal relaxation processes reported by Swenson et al. in myoglobin solvated by equal fractions of water and glycerol. The system we have chosen is 20% (w/w) aqueous solution of bovine serum albumin (BSA). Second, if the same principal relaxations are present in the hydrated BSA, it would be interesting to know if they have similar properties. The choice of this hydrated BSA system is motivated by the recently published adiabatic calorimetry data of an identical system by Kawai et al.12 They found several enthalpy relaxations at long times from different processes undergoing glass transitions. Dynamics of processes probed by adiabatic calorimetric data are limited to long times on the order of 103 s. A better understanding of the processes can be gained by extending the knowledge of their dynamics over a wider time/frequency range. Broadband dielectric relaxation measurements would considerably extend the dynamic range of the data obtained by adiabatic calorimetry. Thus the third purpose is to present broadband dielectric measurements performed on this BSA-water mixture over frequency range of twelve decades from 2 mHz to 1.8 GHz (equivalent in time from about 10-10 to 102 s) and at temperatures from 80 to 270 K. Our dielectric data at low frequencies

J. Phys. Chem. B, Vol. 113, No. 43, 2009 14449 are compared with the adiabatic calorimetry data of the same system to show that the same relaxation processes are found by both techniques. The considerable extension of the range of frequency by dielectric measurements makes is possible for us to see the change of the temperature dependence of the secondary relaxation time of water below and above the glass transition temperature of the hydrated BSA. This property seems to be general because exactly the same was seen before in the hydrated myoglobin13 and in other aqueous mixtures.20,21 It also indicates that the secondary relaxation of water in the hydration shell and the cooperative relaxation responsible for the glass transition of hydrated BSA are strongly connected and may be considered as inseparable processes. 2. Experimental Section The protein used in these experiments was bovine serum albumin (BSA) [further purified fraction V above 98% by gel electrophoresis] which was purchased from Sigma, and it was used without further purification. The appropriate amount of distilled and deionized water with an electrical resistivity higher than 18.3 MΩ · cm obtained from an ultrapure water product (Millipore, Milli-Q Lab.) was added to the BSA and shaken until the undissolved powders disappeared completely. In order to have more complete dissolution, the mixtures were kept at 277 K for 2 days before starting the dielectric measurements. Dielectric measurements were performed on the 20 wt % aqueous solution of bovine serum albumin (BSA) in the frequency range between 2 mHz and 1.8 GHz at temperatures between 80 and 270 K. We used three different instruments and a method to cover this wide frequency range: an RF impedance/material analyzer (HP 4291A) between 1 MHz and 1.8 GHz, an LCR meter (HP 4284A) between 20 Hz and 1 MHz, and an AC phase analysis (ACPA) method and digital lock-in amplifier (NF Corporation, LI5640) from 2 mHz to 100 Hz. Details of the equipment and procedures employed were reported in previously published papers.22-26 For the dielectric measurements at frequencies below 1 MHz, the sample within the electrodes was cooled from room temperature down to 80 K for 6 h and kept there for about 10 h before the first dielectric measurement was made. The temperature was then raised 5 or 10 K in 2 h and kept for 20 h during the next measurement. This procedure was repeated in subsequent measurements each with increment of temperature of 5 or 10 K. The dielectric measurements at the frequencies between 2 mHz and 1 MHz took about 10 h. For the dielectric measurements at frequencies above 1 MHz, the sample was cooled down to 210 K (which is the low limit of our temperature control for dielectric measurement at frequencies above 1 MHz). In order to achieve completion of the crystallization process, the sample was kept at 210 K overnight (ca. 12 h). Then dielectric measurements were performed and at higher temperatures for every increase of 5 K. The 5 K increase of temperature was accomplished in about 2 h, and the final temperature was kept constant for 2 h before dielectric measurement commenced. 3. Results The 20 wt % BSA-water mixture is a system composed of two components with spatial variations, i.e., protein, hydration shell, and bulk water. Naturally, the dielectric spectra are quite complicated. Fortunately, the various relaxations have widely different relaxation times at the same temperature or have comparable relaxation times at significantly different temperatures. Thus, starting at low temperatures, we can see first the appearance of the fastest relaxation process in the isothermal

14450

J. Phys. Chem. B, Vol. 113, No. 43, 2009

Shinyashiki et al.

Figure 1. (a). Frequency dependencies of real and imaginary parts of dielectric functions for 20 wt % BSA-water mixture at various temperatures at frequencies between 2 mHz and 1 MHz. The dielectric functions were shown at temperatures from 80 to 100 K with steps of 10 K and temperatures from 100 to 160 K with steps of 5 K. (b) Frequency dependencies of real and imaginary parts of dielectric functions for 20 wt % BSA-water mixture at various temperatures at frequencies between 2 mHz and 1 MHz. The dielectric functions were shown at temperatures from 165 to 270 K with steps of 5 K. (c) Frequency dependencies of real and imaginary parts of dielectric functions for 20 wt % BSA-water mixture at various temperatures at frequencies between 40 Hz and 1.8 GHz. The dielectric functions were shown at temperatures from 210 to 270 K with steps of 5 K. These real and imaginary parts were measured by an impedance analyzer (4294A Agilent Technology) and impedance material analyzer (4192 Hewlett-Packard). These dielectric functions are displayed in order to avoid the displays of the dielectric functions being mixed and complicated.

dielectric relaxation spectra, and its characteristics including relaxation time, frequency dispersion, and dielectric strength can be gleaned. On further increase of temperature, the slower relaxation processes appear sequentially in the spectra and are identified. Shown in Figure 1a are the frequency, f, dependencies of the real part, ε′(f), and the imaginary part, ε′′(f), of the dielectric susceptibility measured at frequencies between 2 mHz and 1 MHz from 80 to 160 K. The data were obtained in steps of 10 K from 80 to 100 K and with steps of 5 K from 100 to 160 K.

At 80 and 90 K, ε′(f) and ε′′(f) are small, and over many decades of frequency from 1 to 106 Hz, no relaxation process can be detected. There are small changes of ε′(f) and ε′′(f) with frequency, and this feature reminds us of the nearly constant loss (NCL) found in many glassformers, which can be interpreted as the frequency and temperature regime when all molecules are mutually caged and no rotational or translational motion can occur. The NCL is caused by anharmonicity of the intermolecular potential defining the cages, as well as fluctuation of the cages with time.27 At 100 K, the loss peak of a relaxation

Glass Transitions in Solutions of Protein

J. Phys. Chem. B, Vol. 113, No. 43, 2009 14451

process appears from the low frequency side of ε′′(f). The peak shifts to higher frequency with increasing temperature from 100 up to 130 K. This is the fastest relaxation process (I). Its loss peak is highly asymmetric and extremely broad on the low frequency side to suggest that it is composed of more than one process. On further increase to 140 and up to 160 K, a slower relaxation (II) appears on the low frequency side of the faster relaxation, and both move to higher frequencies with increasing temperature (see Figure 1a). Figure 1b shows ε′(f) and ε′′(f) at frequencies from 2 mHz to 1 MHz and temperatures from 165 to 270 K in steps of 5 K. At 165 K and about 30 K above it, the two relaxations (I and II) can be seen from the two steps in ε′(f) and the two corresponding loss peaks in ε′′(f). However, the shift of the loss peak frequency of the slower process II with increasing temperature is larger than that of process I, and process I can no longer be resolved at temperatures above ca. 200 K. A new feature at frequencies above 100 kHz shows up in ε′′(f) as a bulge at temperatures above190 K indicating yet another process faster than the previously resolved process I (see Figure 1b). This bulge is easily visualized in Figure 1c where the data of ε′′(f) obtained up to 1 GHz at 210 K and up to 270 K are presented. The bulge seen at 210 K changes shape and becomes a shoulder or barely resolved loss peak at higher temperatures as shown in Figure 1c. Direct current (dc) conductivity having ε′′(f) ∝ f κ with κ ≈ -1 appears at 180 K and above with the consequence that the loss peak of process II cannot be resolved at temperatures higher than 260 K. Concurrently, starting at 190 K and higher temperatures up to the highest measurement temperature of 270 K, the slowest major relaxation (III) makes its presence as a shoulder in ε′(f) (see Figure 1b and c). This process cannot be seen in the dielectric loss ε′′(f) because of the overwhelming contribution of dc conductivity. The continued rise of ε′(f) with decreasing frequency above the shoulder of process III to values higher than 106 comes from electrode polarization (EP). Data of ε′(f) and ε′′(f) at selected temperatures of 110, 140, 190, 220, and 250 K are shown in Figure 2 for the sake of clarity and ease in identifying all the processes. Three major processes, I, II, and III, can be identified, processes I and II from the loss peaks of ε′(f) and III from the step in ε′(f) to be followed by the large electrode polarization. In this work, we model the contribution to the complex permittivity from any relaxation process, p, by an empirical Cole-Cole function

T) ) ε*(ω, p

∆εp(T) 1 + (iωτp(T))βp(T)

(1)

Here ∆εp(T), τp(T), and βp(T) are the dielectric strength, relaxation time, and fractional exponent of process p, and ω ) 2πf is the angular frequency. The dc conductivity contribution is represented by σ(T)/jωε0, where σ is the dc conductivity and ε0 the permittivity of free space. For process I, we have already seen from its anomalously broadening on the low frequency side and the appearance of the bulge on its high frequency side in Figure 1a-c that process I is composed of more than one relaxation. We found that three or four processes modeled by the Cole-Cole functions are needed to fit the isothermal ε′(f) and ε′′(f) of process I for all temperatures. The presence of process Ia is amply clear in the data at 110 and 140 K shown in Figure 2. At temperatures below 145 K, there is a plateau at the low frequency side of the loss peak of process Ia. To fit this plateau, we introduce process Ib.

Figure 2. Real and imaginary parts of dielectric functions for 20 wt % BSA-water mixture at various temperatures. The plots were obtained experimentally. The curves were obtained by the fitting procedures. The dark blue, light blue, blue, dark green, green, red, black dashed lines are the processes Ia, Ib, Ic, IIa, IIb, III, and electrode polarization, respectively. The solid lines are the sum of all the processes. The term ε∞ obtained by the fitting procedure was added to the each curve in the real part of the dielectric function.

At 135 and 140 K, the ε′′(f) data on the higher frequency side of the loss peak of process IIa exceeds the Cole-Cole fit. To fit this excess wing, we need to assume another process IIb as shown for the data at 140 K in Figure 2. Although we need the process Ib and IIb to fit the data in between the process Ia and IIa by this procedure, there are no clear loss peaks to substantiate that they are absolutely necessary. The possibility remains that the data are due to broad relaxation time distributions and/or an excess wing of processes Ia and IIa, each of which cannot be described by the Cole-Cole empirical relaxation functions. For example, process IIb may be incorporated into process IIa with the former as the excess wing of the latter. On the higher frequency side of the process Ia at frequencies above 100 kHz, we have seen in Figure 1b that there is yet another process. This additional relaxation which we called process Ic can be seen clearly at frequencies above 10 MHz in Figure 1c. At temperatures below 185 K, the loss peak of process Ia can be seen clearly, but it cannot be distinguish from the loss peak of the process IIa above 200 K. At the same time, above 190 K, the loss peaks of process Ic becomes well resolved and are located at frequencies above 1 MHz. The disappearance of process Ia and the emergence of process Ic at temperatures around 200 K can be seen in Figure 1b. Process Ic seems to be present at temperatures below 190 K although there is no loss peak, and we can only see it through the change of the slope of the high frequency flank of process Ia. The strength of process Ic at temperatures below 190 K is small. After having discussed all the possible processes necessary for fitting the isothermal ε′(f) and ε′′(f) data with each process modeled by a Cole-Cole function including the electrode polarization (EP), fits to the data were made by the sum of their contributions given by

ε*(ω, T) ) ε∞ +

∆ε (T)

σ ∑ 1 + (iωτp (T))β (T) + iωε 0 p

p

p

(2)

14452

J. Phys. Chem. B, Vol. 113, No. 43, 2009

Figure 3. Plots of relaxation times, τ, relaxation strengths, ∆ε, and Cole-Cole shape parameters, β, for 20 wt % BSA-water mixture against reciprocal temperatures of processes Ia (solid circles), Ib (open circles), Ic (solid and open diamonds), IIa (solid triangles), IIb (open triangles), III (solid squares). The open symbols of the processes Ib (open circles), IIb (open triangles), and Ic (open diamonds) indicate that their loss peaks are not observed definitely (see text).

where p runs over the processes Ia, Ib, Ic, IIa, IIb, III, and EP. The fits to the experimental data of ε′(f) and ε′′(f) at the five representative temperatures are shown in Figure 2. The parameters, τp(T), ∆εp(T), and β p(T), of each relaxation process p determined by the fits are presented as a function of temperature in Figure 3. 4. Discussions Figure 4 duplicates the results of the temperature dependences of τp(T) of the various processes of 20% (w/w) aqueous solution of BSA given already in Figure 3, but for comparison, we include the relaxation time of pure ice, τice(T), obtained by us and Johari et al.,28 and the data of the 40% (w/w) aqueous solution. It can be seen in Figure 4 that τp(T) vaues of processes p ) IIa and IIb straddle τice(T) and the three have similar activation energies in both the 20 and 40% solutions. This observation leads to the conclusion that processes IIa and IIb originate from crystallized bulk water in the aqueous solutions of BSA. Kawai et al.12 found in their 20% (w/w) aqueous solution of BSA a broad enthalpy relaxation by adiabatic calorimetry with a relaxation time of 103 s centered at about 135 K in a sample after it was annealed at temperatures in the range of 200-240 K. Incidentally, τIIa of process IIa as well as τice are near this enthalpy relaxation time at 135 K (see Table I). This coincidence suggests that processes IIa and IIb may be identified with the enthalpy relaxation at 135 K. The relaxation times, τIa and τIb, of processes Ia and Ib are comparable, have almost the same activation energies, and hence can be considered to originate from same molecular mechanism. Moreover, their relaxation times also are comparable to that of the secondary (or Johari-Goldstein) relaxation of water found in the glassy states of various aqueous mixtures20,21 and in the glass state of myoglobin solvated by an equal fraction of water and glycerol.13,14 The similarities suggest that processes Ia and

Shinyashiki et al.

Figure 4. Plots of relaxation times, τ, for 20 wt % BSA-water mixture against reciprocal temperatures of processes Ia (solid circles), Ib (open circles), Ic (solid and open diamonds), IIa (solid triangles), IIb (open triangles), and III (solid squares). The open symbols of the processes IIb (open triangles), Ib (open circles), and Ic (open diamonds) indicate that their loss peaks are not observed definitely (see text). The plots of the relaxation times of process Ia (open circles with cross), IIa (open triangles with cross), and III (open squares with cross) are obtained for 40 wt % BSA-water mixtures. Crosses and asterisks denote the plots of pure ice by our measurement and that quoted from ref 28, respectively. The magenta solid curve represents the relaxation time τc of reorientational motion of heavy water (D2O) near the surface of myoglobin in D2O-hydrated myoglobin (0.35 g/g) determined by deuteron NMR from ref 5. Enthalpy relaxations with a relaxation time of 103 s originating from different processes found by Kawai et al.12 are indicated by the thick line bounded on both sides by circles with a cross in the broad range from 170 to 220 K, a double circle at 135 K, and a circle with a plus at 110 K. The magenta straight dashed line represents the relaxation time τHN obtained for the β-fluctuations in the hydration shell of myoglobin embedded in solid polyvinyl alcohol reported in ref 51.

Ib are also the secondary relaxation of uncrystallized water (UCW) in the hydration water. The difference in various environments of water in the hydration layers may explain the broad frequency dispersion of the observed secondary relaxation of water, which requires two Cole-Cole processes Ia and Ib to fit it. On extrapolating the Arrhenius T-dependence of τIa and τIb of the 20 and 40 wt % solutions of BSA to lower temperatures, the relaxation time of 102 s is reached by τIa and τIb within the range from 110 to 95 K. These relaxation processes can be identified with that found by enthalpy relaxation obtained by adiabatic calorimetry12 in the same system. This is because the enthalpy relaxation time of 103 s occurs in a neighborhood of 110 K, which is comparable to that found for our dielectric relaxation times τIa and τIb. Thus, our dielectric identification of the secondary relaxation of water in the hydrated BSA is substantiated by the same from adiabatic calorimetry by Kawai et al.12 and vice versa (see Table I). This interpretation is supported by adiabatic calorimetry measurements of water confined in the pores of silica gel with average diameter of 1.1 nm.29 The study reported the presence of a faster and a slower process. The relaxation times of the faster process of confined water is 103 s at T ) 115 K, comparable to what we found for τIa and τIb. As mentioned in the previous section, process Ic seems to be related to process Ia. Here we give further discussion of the characteristics of these two processes to support that they are indeed the same process. This needs to be done because in the relaxation map (Figure 3 or 4) their relaxation times τIa and τIc presented in two nonoverlapping temperature regions could give an impression that these are distinctly different processes. As discussed below, this is a false impression originating from unavoided complications and uncertainties in data analysis caused by contribution to ε* from the processes of the crystallized water overlapping that from process 1a. Let us first

Glass Transitions in Solutions of Protein

J. Phys. Chem. B, Vol. 113, No. 43, 2009 14453

TABLE I: Temperatures at which the Dielectric Relaxation Times are 100 and 1000 s and the Enthalpy Relaxations Were Observed by Adiabatic Calorimetry12 temperatures at which the relaxation time is 100 and 1000 s relaxation processes

BSA concentration (wt %)

Tτ)100s (K)

Tτ)1000s (K)

III III IIa IIb IIa pureicea Ib Ia Ia

20 40 20 20 40 0 20 20 40

202 195 139 122 130 129 101 92 107

192 187 131 115 123 124 93 85 100

a

temperatures at which the enthalpy relaxation observed by calorimetry (K) 170-220 135

110

Reference 28.

consider the temperatures dependences of their dielectric strengths ∆εIa and ∆εIc obtained from our data analysis shown in Figure 3. It shows starting from 100 K, ∆εIa increases with increasing temperature which is normal for secondary relaxation. However, when approaching the temperature TgBSA (≈ 200 K and indicated by the red dashed line), the trend is reversed past 160 K and ∆εIa decreases with temperature. This temperature dependence of ∆εIa on approaching TgBSA is anomalous for a secondary relaxation and is a first indication of the large uncertainty of τIa determined in the temperature range from 160 to 200 K where τII and τIIb of crystallized water comes close to τIa (see Figures 3 and 4). In reality, ∆εIa continues to increase with temperature. The increase of ∆εIc, with increasing temperature for T > TgBSA as well as T < TgBSA is typical for a secondary relaxation. However, when T falls below TgBSA, its decrease to small values comparable to that of ∆εIa is due to the large uncertainty that cannot be avoided in analyzing data in this region. Ignoring the data of ∆εIa and ∆εIc in this region, one can rationalize from the magnitudes that ∆εIc for T > TgBSA is a continuation of ∆εIa for T < 160 K. From these correlations between processes Ia and Ic in their relaxation times and dielectric strengths, we conclude that the process Ia and Ic originated from the same molecular motions detected through the same dipole moments. One is replaced by the other when crossing TgBSA. The apparent mismatch of τIa and τIc in the neighborhood of TgBSA is an artifact resulting from the procedure used to fit the dielectric spectra and the assumption that they are two separately different relaxations in the first place, i.e. eq 2. The similarities of process Ib to relaxation of ice are also evident. At temperatures higher than 200 K, τIb is much smaller than τice. However, at temperatures below 200 K, the slope of τIb in Figure 4 mimics that of τice we observed. In fact, τice obtained by our measurement agrees well at temperatures above 170 K with that published by Johari and Whalley.28 However, their difference becomes larger with decreasing temperature below 170 K. At lower temperature, it is plausible that τice can change by small differences in impurities or thermal history. The same reason may justify that process Ib below 200 K is also due to ice with its structure modified by the presence of protein in the mixture. More study is necessary to make absolutely clear the origin of process Ib below 200 K. Interpreted this way as a single process and the secondary relaxation of water, the stronger T-dependence of its relaxation time for T > TgBSA than the Arrhenius T-dependence for T < TgBSA is to be noted. Such change of the T-dependence of the secondary relaxation of water in 20 and 40 wt % aqueous

solutions of BSA has been found in many aqueous mixtures,20,21 myoglobin solvated by an equal fraction of water and glycerol,13,14 and even in the secondary relaxation of the faster component of binary van der Waals liquids.15-19 In the other systems, the change of T-dependence occurs at the glass transition temperature of the other component of the mixture. We shall see that the same holds for our present system after identifying the molecular mechanism of process III in the following paragraph, and explanation given before in the other systems applies here. Process III is the slowest among processes originating from molecular motions in the aqueous solutions of BSA. Its relaxation times τIII are shown in Figures 3 and 4. Compared with τIc and τII, τIII has much stronger T-dependence that appears to have the Vogel-Fulcher-Tammann-Hesse form, typically shown by structural R-relaxation of glass-forming liquids. As can be seen in Figure 4, τIII reaches 100 s at TgBSA ≈ 200 K and 103 s at about 192 K. This means that this process is related to the enthalpy relaxation with relaxation time of 103 s seen in the region from 180 to 220 K by Kawai et al.12 (see Table I). Thus, process III is responsible for the glass transition at TgBSA of the hydrated BSA as seen by dielectric relaxation. The glass transition is driven by the cooperative motion of BSA and the water in the hydration shell. The dielectric strength of the process III shown in Figure 3 is too large for it to be due solely to the local chain motion of protein. Fluctuations of counterions, interfacial polarization in heterogeneous partially crystallized systems, and/or the effect of an internal electric field can also contribute to process III. This anomaly warrants further investigation in the future. Notwithstanding the fact that the strength is too large, the temperature at which τIII attains 100 s agrees well with the glass transition temperature of protein observed by calorimetric measurements.12 This agreement suggests that process III bears some relationship to the molecular motion responsible for the glass transition of protein. The relation of processes Ia and Ic combined (secondary relaxation of water in the hydration shell) to process III in hydrated BSA resembles that found in myoglobin solvated by water/glycerol mixtures,13,14 as well as in many aqueous mixtures,20,21 in the dynamics of a component in binary mixtures of van der Waals glass-forming liquids17,30-32 and in neat glass-formers.33-36 The commonality is the change of the T-dependence of the secondary relaxation time from Arrhenius dependence at temperatures below Tg (τIa and TgBSA in the present case) to a stronger T-dependence above Tg (τIc and TgBSA in the present case). This indicates that the secondary relaxation of water in the hydration shell and the structural relaxation of the hydrated BSA are connected to each other as inseparable

14454

J. Phys. Chem. B, Vol. 113, No. 43, 2009

Shinyashiki et al.

processes. There is a large amount of published works in ordinary glassforming substances that show the universal presence of a secondary relaxation that mimics the properties of and bears strong and inseparable relation to the primary structural relaxation responsible for glass transition. To distinguish secondary relaxations having fundamental importance in glass transitions from other trivial ones, they have been called Johari-Goldstein (JG) β-relaxations.15-20,30-39 Their strong connection is best illustrated by the R- and Johari-Goldstein (JG) β-relaxations of a component in binary mixtures of van der Waals liquids.17 As an example, the ratio of the R- and JG β-relaxation times, τR/τJG, of a component was found to be invariant to different combinations of temperature T and pressure P that maintain τR constant while the density varies over a sizable range. Another example is the observation of the connection directly by nuclear magnetic resonance spin-lattice relaxation weighted stimulated-echo spectroscopy.37,38 Other connections can be found in the following review: ref 39. Many of these connections have been explained or rationalized by the coupling model (CM).40,41 According to the CM, the structural R-relaxation is the end product of the build-up of many-molecule relaxation with increasing time starting from the primitive relaxation, which is identifiable with the JG β-relaxation by the approximate relation, τJG ≈ τ0.40,41 Naturally from CM, the R relaxation is connected to the primitive relaxation or the JG β-relaxation. In fact, the connection between τR and τJG is given by the relation

τR ) [tc-nτ0]1/(1-n) ≈ [tc-nτJG]1/(1-n)

(3)

Here tc is a constant approximately equal to 2 ps for molecular substances, and coupling parameter n is the same quantity appearing in the stretched exponential (Kohlrausch) correlation function of the R-relaxation when written as

φ(t) ) exp[-(t/τR)1-n]

(4)

A measure of the many-molecule involvement or degree of cooperativity in the R-relaxation is given by n. An alternative interpretation of eq 3 is that τR is governed by τJG through the coupling parameter n. When specialized to the hydrated protein problem, this is translated as that the motion of the hydrated protein and its relaxation time τR (τIII in the present case) is governed or slaved by τJG of the solvent (τIa and τIc, of water in the present case) surrounding the protein molecules. Moreover, glass transition temperature determined by τR of the protein depends crucially on the solvent because in eq 3 both τJG and n depend on the solvent. This is our interpretation of a slaved glass transition by the solvent, a term often used to describe the glass transition of solvated proteins in the literature.42 The literature on dynamics of hydrated proteins and other biomolecules is vast. Many published studies show evidence that the dynamics of protein and solvent are physically coupled. The observed glass transition arises from the cooperative motion between the protein molecules and the bound water molecules in the hydration shell. References of these works consistent with our interpretations given here can be found in the review by Ringe and Petsko.9 Here, we cite just a few: refs 11 and 43-45. The τIc of water in the hydration shell determined by our dielectric measurements can be compared with the relaxation time, τc, of reorientational motion of D2O near the surface of myoglobin in D2O-hydrated myoglobin (0.35 g/g) determined

by deuteron NMR.46 The method probes the reorientational relaxation of the O-D vector, and τc obtained from about 200 to 300 K has been fitted by the super-Arrhenius T-dependence, τc(T) ) (0.96)exp[460/(T - 167)] ps, given in ref 5 and is shown in Figure 4 by the solid magenta line. Fair agreement between τc from NMR and τIc from dielectric measurements can be seen. According to our interpretation like in other aqueous mixtures and ordinary glass formers and mixtures,20,47 τIc from dielectric as well as τc from NMR is the JG relaxation time of water, which is not undergoing glass transition at 200 K itself but is the precursor of the glass transition of the hydrated protein near 200 K. In fact, the relaxation time of hydration water reaches 103 s at the much lower temperature range from 87-110 K depending on the method of measurement, dielectric relaxation, or calorimetry (see Figure 4). Our interpretation of the dynamics of hydration water differs from that offered in ref 46, where the super-Arrhenius T-dependence of τc is considered as evidence that hydration water turns into a glassy state near 200 K. In this connection, we also mention a NMR study of hydrated BSA (BSA/H2O 32 wt %),48 which found significant change of the proton second moment of the hydration water at 170-180 K. The finding was interpreted as due to water forming a disordered solid at the protein interface below ∼170 K, which reduces the local motions in both the main-chain and the sidechain of the protein.48 The change of dynamics occurring near 200 K observed as a change of slope of some quantity appears to be ubiquitous in hydrated proteins. This includes the classic example of the rapid increase of the mean-square displacement (MSD) of hydrated protein motion past 200 K seen by Mo¨ssbauer effect.2-5 The effect often referred to as “dynamic transition” is often interpreted as a kinetic glass transition of the solvent coupled with the protein motions. The MSD data from neutron scattering experiments are obtained at very short times typically of the order of tens to hundreds of picoseconds, depending on the spectrometer used. Mo¨ssbauer spectroscopy monitors the displacements of the heme iron inserted in the protein at longer times on the order of hundreds of nanoseconds. In the elastic neutron scattering experiments, only processes which are fast enough to be resolved by the spectrometer contribute and are observed as the MSD. When these processes are slowed down on cooling, they no longer contribute to neutron scattering and the MSD shows an abrupt change at some temperature. Using τc(T) of hydration water from deuteron NMR and assuming neutron instrument resolution-limited displacements parametrized by an equation provided in ref 5, Doster was able to calculate the MSD, finding that it is in nearly perfect agreement with neutron backscattering data (see Figure 7 in ref 5). This he used to support the conclusion that the dynamical transition at 240 K is created by the crossing of two characteristic times: the IN13 instrumental resolution time of 50 ps and a strongly temperature dependent reorientational rate of protein-adsorbed water. Let us recall as already shown in Figure 4 that τc(T) from deuteron NMR are in fair agreement with τIc, from dielectric measurements, which has been identified as the relaxation time of the JG relaxation of water. Therefore, in the context of our interpretation of dynamics of hydrated protein, Doster’s conclusion means specifically that the JG relaxation of hydration water is responsible for the dynamical transition at 240 K seen by neutron scattering. A different interpretation of the rapid increase in the conformational MSD was recently proposed by Frauenfelder and co-workers.42,49-51 These authors showed that there is no “dynamical transition” in proteins near 200 K. According their

Glass Transitions in Solutions of Protein studies, the rapid increase in the mean-square displacement with temperature in many neutron scattering experiments can be quantitatively predicted by the β-fluctuations in the hydration shell. In their energy landscape model of hydrated proteins with hierarchical tiers, the β-fluctuations in the hydration shell is the lowest tier, whose relaxation time has Arrhenius temperature behavior. It is important to point out that their β-fluctuations are different from the JG β-relaxation of water in the hydration shell proposed by some of us.14 Actually, in the latest dielectric relaxation study by Chen et al.51 of hydrated myoglobin embedded in solid polyvinyl alcohol from 40 Hz to 110 MHz, they emphasize that the β-fluctuations in the hydration shell are different from the JG relaxations in glassformers. Their isothermal dielectric loss functions ε′′(ω) of the β-fluctuations measured from 40 Hz to 110 MHz at 235 K and up to 295 K are fitted to the Havriliak-Negami (HN) functions. The HN relaxation times, τHN, have the Arrhenius T-dependence given by τHN/s ) 10-20.5 exp[(79.2 kJ/mol)/RT]. The HN times are about four decades longer than τW, the JG relaxation time of water in the hydration shell of BSA reported here, as well as of myoglobin.13 The relaxation time τHN of the β-fluctuations reported51 turns out to be not much shorter than the structural relaxation time of the hydrated BSA and myoglobin shown in Figure 4 and this suggests that they may be the same process. Nevertheless, Frauenfelder and co-workers are able to explain the rapid increase in the mean-square displacement measured by neutron scattering5 with a time resolution log(τn/s) ) -log(ωn/s-1) ) -10 in the temperature range from 235 to 295 K by calculating the part of the dielectric loss spectrum at angular frequencies higher than ωn ) 1010 radians/s. This was performed by extrapolating at very high frequencies the HN fits. The extrapolation by the HN function to such a wide frequency range could involve large uncertainties. For instance, any fast process that can occur at shorter time than the βfluctuations could show up in the spectrum, so perturbing the power law behavior of the high frequency flank of the Havriliak-Negami function and making the extrapolation unreliable. On the other hand, based on our own result (or that of Swenson et al.13), the JG relaxation time of water τw at 200 K is still about 5 decades longer than τn ) 10-10 s and cannot contribute to the MSD. However, at shorter time than JG relaxation time or τW in this case, there appears the caged dynamics exemplified as the nearly constant loss (NCL) in the susceptibility spectra of glassforming substances in general (see ref 27 for more details). This phenomenon can be observed in the frequency range used in this present dielectric study only at very low temperature, when the JG process becomes slow and moved outside the experimental frequency window. The NCL shows up as nearly flat dielectirc loss evident in Figure 1 at cryogenic temperatures. According to this interpretation, the MSD of hydration water of proteins measured by neutron scattering (after subtracting vibration and methyl group dynamics) is contributed by the NCL below 200 K and in some region above it. To explain the change in temperature dependence of the MSD observed by neutron scattering in hydrated proteins, we invoke the same phenomenon observed in MSD of ordinary glassformers when crossing Tg. Whether observed by neutron scattering as MSD or as NCL in the susceptibility spectrum by dynamic light scattering at frequencies above 1 GHz, the intensity changes from a weak T-dependence below Tg to a stronger one above Tg. This is found in many glassformers,7,8,52,53 and references therein and ref 27. Similar changes in relaxation strength of the JG relaxation across Tg also found experimentally in general for many glassformers, and this has been explained

J. Phys. Chem. B, Vol. 113, No. 43, 2009 14455 by the close relation between the JG relaxation and the structural relaxation (see ref 27 and references therein.). This property of the relaxation strength of the JG relaxation in turn gives rise to the similar change in T-dependence of the NCL and the corresponding MSD obtained by neutron scattering, as shown in ref 54. When T is increased and τW approaches closer to τn ) 10-10 s, the JG of hydration water starts to contribute to the MSD. This JG contribution may explain the rapid rise of the MSD of Doster and Settles46 when T exceeds 230 or 240 K because τW ≈ τn ) 10-10 s at T ) 250 K (see Figure 2). 5. Conclusion The broadband dielectric relaxation data of 20 and 40 wt % BSA-water mixture presented in this paper were obtained over the frequency range from 2 mHz to 1.8 GHz and temperature range from 80 to 270 K. Our dielectric data have considerably extended the adiabatic calorimetry data which only probe relaxation processes through enthalpy relaxation when their relaxation times are on the order of thousands of seconds. Three major relaxation processes are found, and their characteristics including relaxation times, frequency dispersion, and dielectric strength have been determined. The fastest process has relaxation times comparable to the relaxation of water in many aqueous mixtures which had previously been identified as the JohariGoldstein β-relaxation of the water in these mixtures. Hence, this fastest relaxation in hydrated BSA is interpreted in the same way as the JG β-relaxation of water in the hydration shell of BSA. Its dielectric relaxation time at 110 K is comparable to that found by adiabatic calorimetry. The intermediate relaxation process having relaxation times nearly the same as pure ice is interpreted as due to crystallized bulk water. The slowest process has the characteristics of structural R-relaxation of ordinary glass-formers and is responsible for the glass transition observed by adiabatic calorimetry as enthalpy relaxation at 103 s in the range from 180 to 220 K. This process is due to cooperative motion of water physically coupled to the BSA. An outstanding feature of the dielectric data is the change of the temperature dependence of the JG β-relaxation time of water in the hydration shell of BSA when crossing the glass transition temperature TgBSA. This property, also found in aqueous mixtures, mixtures of van der Waals glass-formers, and even in a variety of neat glass-formers, indicates that the local structural dynamics of protein and water in the hydration shell are coupled, and the glass transition of solvated protein is governed or “slaved” by the JG β-relaxation of the solvent. Consequently, the glass transition temperature of the solvated protein depends on the solvent as observed by others. Acknowledgment. This research was supported at Tokai UniversitybyaGrant-in-AidforScientificResearch(C)(19540429), at NRL by the Office of Naval Research, and at the Universita’ di Pisa by MIUR-FIRB 2003 D.D.2186 grant RBNE03R78E. References and Notes (1) Gregory, R. B., Ed. Protein-solVent interactions; Marcel Dekker: New York, 1995. (2) Parak, F.; Formanek, H. Acta Crystallogr. A 1971, 27, 573. (3) Parak, F.; Knapp, E. W.; Kucheida, D. J. Mol. Biol. 1982, 161, 177. (4) Doster, W.; Cusak, S.; Petry, W. Nature 1989, 337, 754. (5) Doster, W. Eur. Biophys. J. 2008, 37, 591. (6) Zanotti, J.-M.; Gibrat, G.; Bellissent-Funel, M.-C. Phys. Chem. Chem. Phys. 2008, 10, 4865. (7) Buchenau, U.; Zorn, R. Europhys. Lett. 1992, 18, 523. (8) Ngai, K. L. J. Non-Cryst. Solids 2000, 275, 7. (9) Ringe, D.; Petsko, G. A. Biophys. Chem. 2003, 105, 667.

14456

J. Phys. Chem. B, Vol. 113, No. 43, 2009

(10) Beece, D.; Eisenstein, L.; Frauenfelder, H.; Good, M.; Marden, M. C.; Reinisch, L.; Reynolds, A. H.; Sorensen, L. B. J. Am. Chem. Soc. 1980, 19, 5147. (11) Miyazaki, Y.; Matsuo, T.; Suga, H. J. Phys. Chem. B 2000, 104, 8044. (12) Kawai, K.; Suzuki, T.; Oguni, M. Biophys. J. 2006, 90, 3732. (13) Swenson, J.; Jansson, H.; Hedstrom, J.; Bergman, R. J. Phys.: Condens. Matter 2007, 19, 205109. (14) Ngai, K. L.; Capaccioli, S.; Shinyashiki, N. J. Phys. Chem. B 2008, 112, 3826. (15) Capaccioli, S.; Ngai, K. L. J. Phys. Chem. B 2005, 109, 9727. (16) Capaccioli, S.; Kessairi, K.; Prevosto, D.; Lucchesi, M.; Ngai, K. L. J. Non-Cryst. Solids 2006, 352, 4643. (17) Capaccioli, S.; Kessairi, K.; Prevosto, D.; Lucchesi, M.; Rolla, P. J. Phys.: Condens. Matter 2007, 19, 205133. (18) Mierzwa, M.; Pawlus, S.; Paluch, M.; Kaminska, E.; Ngai, K. L. J. Chem. Phys. 2008, 128, 044512. (19) Kessairi, K.; Capaccioli, S.; Prevosto, D.; Lucchesi, M.; Rolla, P. A. J. Chem. Phys. 2007, 127, 174502. (20) Capaccioli, S.; Ngai, K. L.; Shinyashiki, N. J. Phys. Chem. B 2007, 111, 8197. (21) Shinyashiki, N.; Sudo, S.; Yagihara, S.; Spanoudaki, A.; Kyritsis, A.; Pissis, P. J. Phys.: Condens. Matter 2007, 19, 205113. (22) Sudo, S.; Shinyashiki, N.; Yagihara, S. J. Mol. Liq. 2001, 90, 113. (23) Sudo, S.; Shimomura, M.; Shinyashiki, N.; Yagihara, S. J. NonCryst. Solids 2002, 307-310–356. (24) Sudo, S.; Shimomura, M.; Saito, T.; Kashiwagi, T.; Shinyashiki, N.; Yagihara, S. J. Non-Cryst. Solids 2002, 305, 197. (25) Sudo, S.; Shimomura, M.; Tsubotani, S.; Shinyashiki, N.; Yagihara, S. J. Chem. Phys. 2004, 121, 7332. (26) Sudo, S.; Shimomura, M.; Kanari, K.; Shinyashiki, N.; Yagihara, S. J. Chem. Phys. 2006, 124, 044901. (27) Capaccioli, S.; Shain Thayyil, M.; Ngai, K. L. J. Phys. Chem. B 2008, 112, 16035. (28) Johari, G. P.; Whalley, E. J. Chem. Phys. 1981, 75, 1333. (29) Oguni, M.; Maruyama, S.; Wakabayashi, K.; Nagoe, A. Chem. Asian J. 2007, 2, 514. (30) Blochowicz, T.; Ro¨ssler, E. A. Phys. ReV. Lett. 2004, 92, 225701. (31) Kessairi, K.; Capaccioli, S.; Prevosto, D.; Sharifi, S.; Rolla, P. J. Non-Cryst. Solids 2007, 353, 4273. (32) Capaccioli, S.; Prevosto, D.; Lucchesi, M.; Rolla, P. A.; Casalini, R.; Ngai, K. L. J. Non-Cryst. Solids 2005, 351, 2643. (33) Paluch, M.; Roland, C. M.; Pawlus, S.; Zioło, J.; Ngai, K. L. Phys. ReV. Lett. 2003, 91, 115701.

Shinyashiki et al. (34) Sanz, A.; Nogales, A.; Ezquerra, T. A.; Lotti, N.; Finelli, L. Phys. ReV. E 2004, 70, 021502. (35) Capaccioli, S.; Prevosto, D.; Kessairi, K.; Lucchesi, M.; Rolla, P. J. Non-Cryst. Solids 2007, 353, 3984. (36) Bra´s, A. R.; Noronha, J. P.; Antunes, A. M. M.; Cardoso, M. M.; Scho¨nhals, A.; Affouard, F.; Dionı´sio, M.; Correia, N. T. J. Phys. Chem. B 2008, 112, 11087. (37) Bo¨hmer, R.; Diezemann, G.; Geil, B.; Hinze, G.; Nowaczyk, A.; Winterlich, M. Phys. ReV. Lett. 2006, 67, 135701. (38) Nowaczyk, A.; Geil, B.; Hinze, G.; Bo¨hmer, R. Phys. ReV. E 2006, 74, 041505. (39) Ngai K. L.; Casalini, R.; Capaccioli, S.; Paluch, M.; Roland, C. M. AdVances in Chemical Physics Part B Fractals, Diffusion and Relaxation in Disordered Complex Systems; Kalmykov, Y. P., Coffey, W. T., Rice, S. A., Eds.; Wiley: New York, 2006; Chapter 10, p 497, Vol. 133. (40) Ngai, K. L. J. Chem. Phys. 1998, 109, 6982. (41) Ngai, K. L. J. Phys.: Condens. Matter 2003, 15, S1107. (42) Fenimore, P. W.; Frauenfelder, H.; McMahon, B. H.; Young, R. D. Proc. Natl. Acad. Sci. 2004, 101, 14408. (43) Teeter, M. M.; Yamano, A.; Stec, B.; Mohanty, U. Proc. Natl. Acad. Sci. U.S.A. 2001, 98, 11242. (44) Tarek, M.; Tobias, D. J. Phys. ReV. Lett. 2002, 88, 138101. (45) Tarek, M.; Tobias, D. J. Eur. Biophys. J 2008, 37, 701. (46) Doster, W.; Settles, M. Biochim. Biophys. Acta 2005, 1749, 173. (47) Ngai, K. L.; Capaccioli, S.; Shinyashiki, N. UniVersal Secondary Relaxation of Water in Aqueous Mixtures, in Nano-Confinement, and in Hydrated Proteins. AIP Conference Proceedings. 5th International Workshop on Complex Systems, Melville, New York, Sept 25-28, 2007; American Institute of Physics: 2008; Vol. 982, p 14. (48) Goddard, Y. A.; Korb, J.-P.; Bryant, R. G. Biophys. J. 2006, 91, 3841. (49) Fenimore, P. W.; Frauenfelder, H.; McMahon, B. H.; Young, R. D. Physica A 2005, 351, 1. (50) Chen, G.; Fenimore, P. W.; Frauenfelder, H.; Mezei, F.; Swenson, J.; Young, R. D. Philos. Mag. 2008, 88, 3877. (51) Frauenfelder, H.; Chen, G.; Berendzen, J.; Fenimore, P. W.; Jansson, H.; McMahon, B. H.; Stroe, I. R.; Swenson, J.; Young, R. D. Proc. Natl. Acad. Sci. USA 2009, 106, 5129. (52) Magazu`, S.; Maisano, G.; Migliardo, F.; Mondelli, C. Biophys. J. 2004, 86, 3241. (53) Ngai, K. L.; Habasaki, J.; Leon, C.; Rivera, A. Z. Phys. Chem. 2005, 219, 47. (54) Ngai, K. L. Philos. Mag. 2004, 84, 1341.

JP905511W