Puzzle of Protein Dynamical Transition - The Journal of Physical

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Puzzle of Protein Dynamical Transition Salvatore Magazu,* Federica Migliardo, and Antonio Benedetto Dipartimento di Fisica, Universita di Messina, Viale Ferdinando Stagno D'Alcontres n 31, P.O. Box 55, Vill. S. Agata 98166 Messina, Italy ABSTRACT: Despite recent extensive efforts, the nature of the dynamics of biological macromolecules still remains unclear. In particular, contradicting models have been proposed for explaining the temperature behavior of the mean square displacement, MSD, and of the system relaxation time, τ. To solve this puzzle, different neutron scattering experiments with different instrumental energy resolutions were performed on dry and hydrated lysozyme. The obtained results show that the so called dynamical transition: (i) is a finite instrumental energy resolution effect, and more specifically, it appears when the characteristic system relaxation time intersects the resolution time, (ii) it does not imply any transition in the dynamical properties of the systems, (iii) it is not due to the fragile-to-strong dynamical crossover (FSC) in the temperature behavior of the system relaxation time, differently to what S. H. Chen et al. proposed [Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 9012]. Furthermore, the obtained results confirm the change in the τ-temperature dependence at T = 220 K of S. H. Chen et al., and show that it is not due to finite instrumental energy resolution effects and it is not connected to numerical errors in the data analysis protocol, differently to what W. Doster et al. proposed [Phys. Rev. Lett. 2010, 104, 098101].

I. INTRODUCTION During the past few years, considerable efforts have been addressed, through experimental, theoretical, and computational studies, to clarifying the microscopic nature of the dynamics of biological macromolecules. One of the phenomena which has been largely debated, even if not fully clarified, is the so-called dynamical transition in protein systems which, in the literature, is referred to as a sharp rise in the Mean Square Displacement (MSD) of hydrated proteins with respect to dry proteins, usually registered in the temperature range T = 200240 K.16 In neutron scattering, MSD is deduced from the measured elastic scattering law SR(Q, ω = 0, Δω). Interest in dynamical transition has been stimulated by the fact that the measurable biochemical activity of proteins usually appears around the same temperature range,2,710 but several exceptions exist;1113 for example, in a recent contribution, Mamontov et al.13 highlight that dynamical transition is also present in denatured hydrated proteins, and then it may not be a good physical observable for describing the protein function process. Since dynamical transition is absent in dehydrated proteins, it has been related to the dynamics of the hydration shell or at least coupled to it. In contrast to bulk water, protein-hydration water can be supercooled to a glass transition at Tg = 175 K.1416 Near Tg, translational degrees of freedom arrest; this induces discontinuities in the specific heat and in the thermal expansion coefficient of the hydration water. Because of the dynamic nature of glass transition, freezing of microscopic degrees of freedom can be observed far above Tg. The basic understanding of the mechanism underlying dynamical transition remains controversial, and various models have r 2011 American Chemical Society

been proposed. Such a transition had been ascribed to a sudden change in an effective elasticity of the protein,3 to motions of specific side groups,7 to a specific fragile-to-strong crossover in dynamics of hydration water,17 to resolution effects due to a relaxation process that enters the experimentally accessible frequency window,18 and to the microscopic manifestation of the glass transition in the hydration shell.19 More specifically, performing different quasi-elastic neutron scattering (QENS) experiments on both D2O and H2O hydrated lysozyme (with h = 0.3, i.e., 0.3 g of water/g of protein), S. H. Chen et al. in ref 17 evaluate the temperature behavior of the mean characteristic relaxation time of hydration water in lysozyme; this shows a cusp-like crossover from an Arrhenius to a non-Arrhenius behavior at a temperature value of T = 220 K (see Figure 1), which the authors associate with the kink in the extracted MSD temperature behavior, i.e., with the so-called dynamical transition, that occurs, following the authors, at the same temperature value. Furthermore, in other studies, with reference to confined water, the authors also show that a dynamical fragile-to-strong crossover (FSC), i.e., the transition from an Arrhenius to a non-Arrhenius behavior in the mean characteristic relaxation time, takes place at T = 224 K at ambient pressure for confined water in silica nanopores,2022 at T = 222 K in DNA,23 and at T = 220 K in RNA.24 On the other hand, investigating the same system as S.H. Chen et al.17 (with h = 0.4) by both dielectric spectroscopy and QENS Received: December 1, 2010 Revised: May 8, 2011 Published: May 25, 2011 7736

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Figure 1. Temperature behavior of relaxation times in hydrated lysozyme. Relaxation process of hydration water (blue points) obtained with the QENS technique by S.H. Chen et al.17 and main relaxation process (green points) and fast relaxation process (green dashed line) obtained with the dielectric spectroscopy technique by A.P. Sokolov et al.18 The red points correspond to the relaxation times extracted by the dynamical transition kink in the temperature behavior of the measured MSDs obtained from different EINS experiments in which different instrumental energy resolution values were used.

techniques, A.P. Sokolov et al. in refs 18, 25, and 26 find two relaxation processes instead of one (see Figure 1). The authors show that at T = 220 K (i) no sign of the FSC in the main characteristic relaxation time occurs and (ii) a secondary fast relaxation process appears and remains for lower temperature values; the latter process was related by the authors to hydration water relaxation. More specifically, the mean characteristic relaxation time of S. H. Chen et al.,17 related to hydration water relaxation, coincides with both the protein main relaxation time of A. P. Sokolov et al.18,25,26 for temperature values higher than T = 220 K and their secondary fast hydration water relaxation time for lower temperature values. Furthermore, J. Swenson et al. in refs 27 and 28 show that in confined water the cooperative R relaxation vanishes at about T = 200 K implying that, above this, a merging of the R and β relaxations takes places. For all these reasons, A. P. Sokolov et al.18,25,26 conclude that the FSC registered by S. H. Chen et al.17 is apparent due to the fact that QENS probes structural relaxation at higher temperatures and a secondary relaxation at lower temperatures. Finally, performing different QENS experiments on perdeuterated phycocyanin, hydrated in H2O, W. Doster et al. in ref 19 highlight that the use of a different (improved) analysis protocol with respect to the analysis protocol used by S. H. Chen et al. in ref 17 allows them to rule out the postulated FSC at T = 220 K. In other words, the authors show that the FSC of Chen et al.17 is due to numerical errors in the data analysis protocol. The presence of the FSC in protein hydration water at T = 220 K was also ruled out in ref 29 in which M. Vogel showed that water performs thermally activated jumps at T < 200 K. In the present paper, we report the results of different neutron scattering experiments performed with different instrumental energy resolutions to solve the puzzling question related to both dynamical transition and FSC, registered in the MSD and in the

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system characteristic relaxation time temperature behaviors, respectively. We will show that: (i) dynamical transition is due to finite instrumental energy resolution; more specifically, (ii) it appears when the characteristic system relaxation time intersects the resolution time; (iii) it is not necessarily connected to any transition in the dynamical properties of the systems; and consequently (iv) it is not due to FSC in the temperature behavior of the system relaxation time. Furthermore, we will show that (v) the FSC at T = 220 K in the temperature dependence of the characteristic relaxation time of hydrated water in lysozyme is due neither to the finite energy resolution effects nor to numerical errors in data analysis protocol and that (vi) the protein relaxation process found by A. P. Sokolov et al.18,25,26 and the hydration water relaxation process found by S. H. Chen et al.17 can be related to proteinwater coupled dynamics. More precisely, the main aim of the present work is to discuss and clarify how the measured elastic scattering law and the extracted MSD depend on the instrumental energy resolution used (with regard to this, several contributions are reported in the literature3032). We will show, both from the theoretical and experimental points of view, that protein dynamical transition does not require necessarily any discontinuous change in the temperature behavior of the system relaxation time, and hence, it is not necessarily connected to a real transition of the system dynamics. We will show that a kink in MSD temperature behavior appears when the relaxation time of a system process intersects the instrumental resolution characteristic time. Furthermore, the temperature behavior of the characteristic relaxation time for hydrated lysozyme will be evaluated from different neutron spectra obtained at different finite instrumental energy resolutions: at T = 220 K a change from Arrhenius to super-Arrhenius behavior is registered and is related to protein water coupled motions.

II. EXPERIMENTAL SECTION Elastic Incoherent Neutron Scattering (EINS) data were collected on lysozyme samples by using the IN13, the IN10, and the IN4 spectrometers at the Institut Laue-Langevin (ILL) Grenoble, France. These spectrometers worked at three different instrumental energy resolutions: 8 μeV for IN13, 1 μeV for IN10, and 200 μeV for IN4. The experimental setup for IN13 was: incident wavelength 2.23 Å; Q-range 0.284.27 Å1; elastic energy resolution (FWHM) 8 μeV, corresponding to a characteristic time of about 274 ps. The experimental setup for IN10 was: incident wavelength 6.27 Å; Q-range 0.302.00 Å1; elastic energy resolution (FWHM) 1 μeV, corresponding to a characteristic time of about 2192 ps. The experimental setup for IN4 was: incident wavelength 3.60 Å; Q-range 0.34.5 Å1; elastic energy resolution (FWHM) 200 μeV, corresponding to a characteristic time of 11 ps. The characteristic resolution time τRES was evaluated considering a normalized Gaussian behavior for the resolution function in ω-space in which the linewidth of the function is Δω. More specifically, it results that HWHM = 1.17Δω and τRES = 1.66/HWHM, in which the half weight at half-maximum (HWHM) is the elastic energy resolution of the spectrometer. Finally, to transform the microelectronvolts into picoseconds, we adopt the common relationship E = pω. Thus, scattering particles which move in a time scale much slower than the characteristic time corresponding to the energy resolution are seen as elastic scatterers, whereas a decrease of the 7737

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elastic intensity is observed for scattering particles which move faster. This implies that a scattering particle, which moves in a time scale between the resolution time of IN13 and IN10, contributes as an elastic process in the IN13 spectra and as a nonelastic process in the IN10 spectra. Measurements were performed for 12 h in the 20320 K temperature range on dry and D2O hydrated lysozyme by IN10, IN13, and IN4 spectrometers and on lysozyme/H2O/sucrose powder by IN10. More specifically, lysozyme in D2O at a hydration value of h = 0.4 and lysozyme in sucrose/H2O at a hydration value of h = 0.4, h = (g of water þ disaccharide)/ (g of protein), have been used. It is believed that 0.4 g of water per g of lysozyme is sufficient to cover the protein surface with a single layer of water molecules and to fully activate protein functionality.3335 Empty cell contribution was subtracted, and spectra were normalized to the vanadium standard. This data treatment was performed with the Lamp code relative to the three spectrometers used; other programs and specific new codes were used for data analysis. More specifically, the SDF procedure6,3644 was used for MSD evaluation. With regard to the lysozyme/H2O/sucrose sample, the incoherent contribution is of 92% and, more specifically, is related for 61% to protein, for 30% to water, and for 9% to sucrose. This implies that the incoherent contribution of the protein is predominant in the scattering data, which give information on protein hydrogen motions. This conclusion is also supported by the fact that the dynamics of protein and the dynamics of solvent are strongly coupled, as highlighted in ref 45. This implies that the comparison between lysozyme/D2O and lysozyme/H2O/ sucrose gives information about the effects of the disaccharide on protein dynamics.

III. DISCUSSION III.I. Resolution Effects in Elastic Incoherent Neutron Scattering. It is well-known that the scattering law S(Q,ω)

and the intermediate scattering function I(Q,t) are connected by a time Fourier transform46,47 Z ¥ 1 SðQ , ωÞ ¼ pffiffiffiffiffiffi IðQ , tÞeiωt dt ð1Þ 2π ¥ In the ω-space, due to the finite energy instrumental resolution Δω, the experimentally accessible quantity is the measured scattering law SR(Q,ω,Δω) that corresponds to the convolution of the scattering law with the instrumental resolution function R(ω,Δω)46,47 SR ðQ , ω; ΔωÞ ¼ SðQ , ωÞ X Rðω; ΔωÞ Z þ¥ ¼ SðQ , ω ω0 ÞRðω0 ; ΔωÞdω0 ¥

Figure 2. Instrumental energy resolution effects in EINS. Comparison between I(t;τ) at a fixed τ value (black lines), R(t;τRES) for different τRES values (continuous red lines), and the related SR(Q,ω = 0,Δω) (areas in blue). These latter, obtained considering eq 4, represent the measured quantities of an EINS experiment on a system with a characteristic time τ in which the instrumental resolution time used is τRES. (a) Case in which the resolution time is longer than the system characteristic time; no resolution effect is present: the elastic measured scattering law and the elastic scattering law are coincident. (b) Case in which the resolution time becomes slightly smaller but still longer than τ: in this case the measured elastic scattering intensity is slightly smaller than the elastic scattering law (here the specific IN10 resolution function has been used). (c) Case in which the resolution time becomes much smaller than the system characteristic time τ. The resolution effect becomes relevant: the measured elastic scattering law strongly differs from the elastic scattering law (here the specific IN13 resolution function has been used).

instrumental resolution function.46,47 Z ¥ SR ðQ , ω ¼ 0; ΔωÞ ¼ IðQ , tÞRðtÞdt ¥

ð2Þ

that, taking into account the Fourier transform convolution theorem, yields Z ¥ SR ðQ , ω; ΔωÞ ¼ IðQ , tÞRðtÞeiωt dt ð3Þ ¥

To evaluate the resolution effects in the EINS experiments, eq 3 has to be considered for ω = 0, as reported in eq 4: in the case of elastic contribution it corresponds to a time integral of the intermediate scattering function weighted in time by the

ð4Þ

In the ideal case in which the resolution function is a Dirac’s delta in the ω-space, one obtains that the elastic measured scattering law is the scattering law evaluated at ω = 0,46,47 as can be seen considering eq 1. Figure 2 shows the comparison between (i) the normalized time behavior of an intermediate scattering function I(t;τ) (black line) at a fixed τ value (τ = 1.5 103 ps), (ii) resolution functions R(t;τRES) (red lines) taken at three different τRES values (τ = 105 ps for simulating the ideal case, 2192 and 274 ps which correspond to the characteristic times of the energy resolution spectrometers IN10 and IN13, respectively), and (iii) measured intermediate scattering functions (blue lines) 7738


The Journal of Physical Chemistry B together with the associated measured elastic scattering laws SR(ω=0, Δω) (areas in blue) obtained by eq 4. More specifically, in Figure 2a it is shown how, due to the fact that τ , τRES, there is no effect of the resolution function on the measured elastic scattering law, i.e., SR(Q,ω = 0,Δω) = S(Q,ω = 0); in such a case, the blue area which represents the SR(Q,ω = 0,Δω) coincides with the area under the intermediate scattering function, i.e., with S(ω = 0). In Figure 2b, the case of the IN10 spectrometer is considered; it is shown how, in the measured elastic scattering law, the resolution function gives rise to a weighted value of the given intermediate scattering function; in this case the measured elastic scattering law SR(ω = 0,Δω) (blue area) is very close to the area under the intermediate scattering function, and the effects of the finite resolution are quite small. In Figure 2c the case of the IN13 spectrometer is taken into account; it clearly emerges that the resolution function originates the exclusion of a portion of the given intermediate scattering function (from the gray dashed line to longer times); in this case the measured elastic scattering law SR(ω = 0, Δω) (blue area) is much less than the area under the intermediate scattering function. Two general situations can occur. The first concerns the case in which the resolution time is longer than the system relaxation time, i.e., τRES > τ, as shown in Figure 2, a and b; under this circumstance the resolution effects are relatively small. In fact, the measured elastic scattering laws (blue areas) are very close to the areas of the intermediate scattering functions. The second case occurs when the resolution time is shorter than the system relaxation time, i.e., τRES < τ, as shown in Figure 2c; under this circumstance, the resolution effects become important: the measured elastic scattering law (blue area) is close to the area of the resolution function instead of the area of the intermediate scattering function. To better understand what quantitatively happens, in Figure 3a the measured elastic scattering law SR(ω = 0,Δω) as a function of the instrumental resolution time is shown. Starting from the same intermediate scattering function used for the case reported in Figure 2 (τ = 1.5 103 ps), the measured elastic scattering law SR(ω = 0,Δω) was evaluated as a function of the resolution time according to eq 4; the blue areas of Figure 2 have been calculated, and their behavior as a function of the instrumental resolution is shown. As can be seen, when τRES > τ the resolution effects are negligible (the upper green point and the black line in Figure 3a are close together); however, when τRES < τ the resolution effects become important (the lower green point and the black line in Figure 3a are far apart), and the measured elastic scattering law becomes equal to the resolution function (red line in Figure 3a). Let us now consider the comparison between measured elastic scattering functions associated with different characteristic system relaxation times. In Figure 3b, the measured elastic scattering laws as a function of the resolution time, obtained from intermediate scattering functions with two different characteristic system relaxation times, are reported. More specifically, the same simulation of Figure 2 and Figure 3a, i.e., τ = 1.5 103 ps, (blue line) is compared with another simulation obtained for τ = 125 ps (red line). The results obtained previously are confirmed: when τRES > τ the resolution effects are negligible (see the two green points labeled IN10 and the upper green point labeled IN13 in Figure 3b); on the other hand, when τRES < τ the resolution effects become important (see the lower green point in Figure 3b). It must be noted that the two characteristic relaxation times used for the two simulations are shorter than the IN10 resolution

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Figure 3. Measured elastic scattering law, SR(Q,ω = 0,Δω), as a function of the resolution time, τRES, for a system with fixed τ values. (a) Starting from the same intermediate scattering function used for the cases reported in Figure 2 (for which the system relaxation time is τ = 1.5 103 ps), the SR(ω = 0,Δω) has been evaluated as a function of τRES according to eq 4; in particular, the blue areas of Figure 2 have been calculated as a function of the instrumental resolution time, and the result is reported (blue line); the vertical blue dashed line indicates the system characteristic time. The two cases of Figure 2 are considered (green points), and two regimes are found: when τRES > τ the resolution effects are negligible (case of Figure 2b); when τRES < τ, the resolution effects become important (case of Figure 2c) and the distance between the measured scattering law and the scattering law (horizontal black line) increases. (b) Comparison of measured scattering laws for two different system relaxation time values, τ = 1.5 103 ps (blue line) and τ = 125 ps (red line). The two characteristic relaxation times are shorter than the IN10 resolution time, while the IN13 resolution time lies between the two characteristic system relaxation times. In this case, the two conditions, i.e., τRES > τ and τRES < τ, are explored: when τRES > τ (see the IN13 green point on the red curve) the variation of SR with respect to S is small, but when τRES < τ (see the IN13 green point on the blue curve) the latter variation is very strong. The change from one condition to the other one occurs when the characteristic system relaxation time intersects the resolution time.

time (the condition τRES > τ is valid for the two simulations with reference to the IN10 spectrometer), but considering the IN13 spectrometer, the situation is different. The IN13 resolution time is between the two characteristic system relaxation times used, and the two conditions, i.e., τRES > τ and τRES < τ, are both explored. In the resolution time range in which τRES > τ (see the IN13 green point on the red line in Figure 3b), the variation of SR with respect to S is small (the SR can be consider constant), whereas in the range in which τRES < τ (see the IN13 green point on the blue line in Figure 3b) the latter variation is very strong. The change from one condition to the other one occurs when the 7739



Figure 4. Intermediate scattering functions as a function of time of hydrated lysozyme at different temperature values (data taken from Figure 1), together with the resolution functions of IN13 and IN10 spectrometers. The intermediate scattering function crosses the resolution function of IN10 at about T = 220 K and of IN13 at about T = 240 K.

characteristic system relaxation time intersects the resolution time (starting from the red dashed line to the blue dashed line and considering IN13 resolution value in Figure 3b). Let us consider that the comparison between the measured elastic scattering functions for different characteristic system times simulates a real case when different EINS experiments at different temperature values are performed: it is well-known that the characteristic system relaxation time is a function of temperature (e.g., Arrhenius and non-Arrhenius behaviors). Furthermore, in a complementary way, by increasing temperature, the system relaxation time is gradually expected to decrease, giving rise to changes in the intermediate scattering function. In particular, in Figure 4, starting from the data collected by S. H. Chen et al.17 and by A. P. Sokolov et al.18 and reported in Figure 1, the behavior of the main intermediate scattering function of hydrated lysozyme, taken at different temperature values, is reported together with the resolution function of IN10 and IN13 (black dashed lines). As can be seen, by increasing the temperature the intermediate scattering function crosses the IN10 resolution function, at first, at about T = 220 K and then the IN13 resolution function at about T = 240 K (it also crosses the IN4 resolution function at about T = 300 K). Therefore, with regard to our lysozyme/D2O sample, if a discontinuity is found in the scattering law (and, consequently, in its derivate observables such as MSD) measured with IN10, IN13, and IN4 at a temperature value of T = 220, 240, and 300 K, respectively, it must be connected to a merely resolution effect due to the fact that the system characteristic relaxation time intersects the instrumental resolution time, and it must be clear that it is not connected to any transition in system dynamics. III.II. Resolution Effects and Protein Dynamical Transition. The previous representation of the relationship between the intermediate scattering function, which describes system properties, and the measured elastic scattering law, which is a mix of system properties and instrumental features (see eq 4), highlights the connection between the system relaxation time and the instrumental resolution time. As a rule, two situations characterized by two distinct behaviors can occur. The first one deals with the case in which the resolution time is longer than the system

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relaxation time, i.e., τRES > τ (see Figure 2a and Figure 2b); under this circumstance the resolution effects are quite small. The second one refers to the case in which the resolution time is shorter than the system relaxation time, i.e., τRES < τ (see Figure 2c); under this circumstance the resolution effects are important. In agreement with these results, the temperature behavior of the measured elastic scattering law must show a variation at the temperature value when the system relaxation time intersects the resolution time, and consequently, the extracted MSD temperature behavior must present a kink at the same temperature value. The meaning of this kink is that, at such a temperature value, the system relaxation time intersects the characteristic time of the instrumental energy resolution used. The possibility of the presence of this kink in the temperature behavior of the measured MSD leads to two considerations. The first one is that (i) the dynamical transition registered in hydrated proteins16 may be coincident with this kink. The second one is that (ii) the temperature behavior of the system relaxation time can be extracted from different measured MSD temperature behaviors, obtained on the same system with different EINS measurements by varying the instrumental energy resolution used, i.e., (τRES, Tkink). This latter will be treated in the next paragraph. With regard to the first consideration, in Figure 5, a and b, the temperature behaviors of the measured MSDs of dry and D2O hydrated lysozymes, obtained from IN10 and IN13 data, are, respectively, shown; the so-called dynamical transition is at T = 220 K in the case of IN10 and at T = 240 K in the case of IN13. Moreover, at T = 240 K no transition is observed in the measured MSD obtained by IN10. Furthermore, the only dynamical transition kink is also at T = 300 K in the case of IN4 (data not shown) and at T = 200 K in the case of HFBS,17,18 a higherenergy resolution spectrometer with FWHM of 0.85 μeV at NIST. This implies that resolution effects corrupt the temperature value at which the dynamical transition kink registered by IN4, IN13, and IN10 in the measured MSDs occurs. This result allows us to conclude that dynamical transition is not due to the FSC in the system dynamics, as S. H. Chen et al. propose in ref 17. Moreover, the relaxation time of the studied system intersects the resolution time of IN4, IN13, IN10, and HFBS spectrometers at T = 300, 240, 220, and 200 K, respectively (see Figure 1), i.e., exactly at the dynamical transition temperatures. This implies that the dynamical transition is (i) a mere resolution effect (ii) due to the circumstance that the system relaxation time intersects the resolution time. These conclusions on the nature of dynamical transition are also confirmed by taking into account both (i) the effects on the dynamical behavior of the hydrated lysozyme due to the presence of disaccharides and (ii) several experimental data on hydrated protein systems, studied as a function of the hydration level h. With regard to the first point, since the presence of disaccharides shifts the system relaxation time toward higher values,48 it intercepts the resolution time at a higher temperature value; in other words, the system relaxation time enters the resolution energy windows at a higher temperature, and following our conclusions, the dynamical transition should occur also at a higher temperature. In Figure 5c, the temperature behavior of the measured MSDs of lysozyme/sucrose/H2O and dry lysozyme is shown. As can be seen, the dynamical transition present in the hydrated lysozyme at a temperature value of T = 220 K (see Figure 3a) is shifted to the higher temperature value of T = 255 K, in agreement with our analysis. 7740



Figure 5. Measured MSDs of dry and hydrated lysozyme obtained using two different instrumental energy resolution values. Comparison between the measured MSD temperature behavior of dry (blue) and D2O hydrated (green) lysozyme, obtained from data collected by both (a) IN10 and (b) IN13 spectrometers. (c) Comparison between the measured MSDs obtained for sucrose H2O hydrated lysozyme (red) and dry lysozyme (blue) by the IN10 spectrometer. The two hydrated samples show a kink, the so-called dynamical transition, at a temperature of about (a) T = 220 K and (b) T = 240 K; the presence of disaccharide inhibits the dynamical transition and shifts it to the temperature of T = 255 K.

Finally, concerning the second point, in the work of Janson et al.49 it has been shown that the increment of hydration level in hydrated proteins leads to a decrement of the characteristic system relaxation time; i.e., the presence of a higher number of water molecules increases the velocity of the dynamic process. If our conclusions are correct, the same system investigated with a given instrumental energy resolution at higher hydration levels should have a lower dynamical transition temperature value. Furthermore, above the dynamical transition temperature (Td), the slope of the temperature behavior of the measured MSD (dMSD) should increase when hydration level increases. In symbols: if our results about the nature of the dynamical transition are corrected, if h1 > h2 then (i) Td1 < Td2 and (ii) dMSD1 > dMSD2. Several authors have studied the effect of change hydration level in proteins, e.g., G. Schir o et al.50 and E. Cornicchi et al.51 In agreement with our results, it clearly emerged that above the dynamical transition temperature the slope of the MSD as a function of temperature increases when hydration level increases. Furthermore, in ref 51 the dynamical transition temperature for the hydrated lysozyme sample is plotted as a function of the hydration level (Figure 5, ref 51). As can be seen, the dynamical

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transition temperature decreases when the hydration level increases. This behavior is also in agreement with our results, which clarify why it occurs: the presence of a higher number of water molecules decreases the characteristic system relaxation time49 which intersects the instrumental energy resolution time at lower temperature values. More specifically, the dynamical transition temperature as a function of hydration level of E. Cornicchi et al.,51 i.e., Td(h), has been obtained by evaluating the occupancy probability ratio as a function of temperature which quantifies the ability of mobile protein protons to jump from the ground to the excited state (see Figure 3 of ref 51), and as reported by the authors, it is in agreement with the ones obtained from the temperature behavior of both the elastic intensity (Figure 1 of ref 51) and the dynamical transition kink in MSD (Figure 6 of ref 51); this latter is the common procedure to define system transitions. Furthermore, the Td(h) behavior of E. Cornicchi et al.51 is also in agreement with (i) the one obtained for glucosewater matrices with elastic neutron scattering by M. Di Bari et al.;52 (ii) the critical temperature behavior as a function of hydration level obtained from H NMR measurements by I. J. Van den Dries et al.;53 and (iii) the glass transition temperature behavior of glucosewater systems determined through differential scanning calorimetry by J. L. Green et al.54 and through dielectric relaxation technique by T. R. Noel et al.55 Finally, the decrement of the dynamical transition temperature when the hydration level increases is evident in ref 52 directly on the MSD as a function of temperature. In this case the connection between the decrease of the dynamical transition temperature and the increase of the slope of the MSD can be clearly observed, in agreement with the hypothesis presented in the present contribution. In summary, the formulated hypothesis on the nature of dynamical transition is supported (i) first, by experimental data on lysozyme systems (Figure 5 a and b); (ii) second, by experimental data concerning the effects of disaccharides on the protein dynamics (Figure 5 c); and (iii) finally by experimental data50,51 on protein hydrated systems studied as a function of the hydration level h. III.III. Resolution Effects and Dynamical Crossover in the System Relaxation Time. Let us now deal with the second consideration expressed at the beginning of the previous paragraph. The temperature behavior of the system relaxation time can be extracted from different measured MSD temperature behaviors, obtained on the same system with different EINS measurements, as a function of temperature, by varying the instrumental energy resolution used. It has been clarified that the obtained dynamical transition temperatures (Td) are the temperature values at which the system relaxation time intersects the resolution time, i.e., τ = τRES. In Figure 1 these points (τRES, Td) obtained by IN10 (2192 ps, 220 K), by IN13 (274 ps, 240 K), by IN4 (11 ps, 300 K), and by HFBS (2740 ps, 200 K) on D2O hydrated lysozyme are reported together with (i) the point obtained by HFBS on H2O hydrated lysozyme (2740 ps, 200 K), (ii) the main relaxation process and the fast relaxation process obtained by A.P. Sokolov et al.18 on hydrated lysozyme and associated to protein relaxation and hydration water relaxation, respectively, and (iii) the mean characteristic relaxation time obtained by S. H. Chen et al.17 on hydrated lysozyme and associated to hydration water relaxation. Our system relaxation time coincides in the whole temperature range with the system relaxation time of S. H. Chen et al.17 (see 7741


The Journal of Physical Chemistry B Figure 1). This implies that the FSC registered at T = 220 K by S. H. Chen et al. in ref 17 is a confirmed result in the framework of neutron scattering techniques, and therefore, it is due neither to the energy resolution effects nor to numerical errors in data analysis protocol, differently to what W. Doster et al. proposed in ref 19. However, contrarily to what reported by S. H. Chen et al.,17 it should be noticed that below T = 220 K the protein dynamics and the water dynamics are also partially coupled and the system relaxation time is related not only to water dynamics but also to the water/protein system. Experimental evidence of this fact can be found in the circumstance that the lowest temperature points (τRES = 2740 ps, T = 200 K) of D2O hydrated lysozyme and of H2O hydrated lysozyme are coincident with each other and with the faster relaxation process of A. P. Sokolov et al.18 (see Figure 1). From the comparison between our relaxation time and those of A. P. Sokolov et al.,18 we can conclude that neutron scattering experiments allow us to clearly see the faster process that, in the case of our study, coincides with the β relaxation of protein water coupled dynamics, for temperature values lower than T = 220 K, and coincides with the merging of the R and β relaxations, at higher temperature values. Finally, the comparison shown in Figure 1 allows us to shed light on the attribution of the relaxation process found by Chen et al.17 and by A. P. Sokolov et al.:18 it is possible to show that all the relaxation processes can be ascribed to proteinwater coupled motions. The temperature behavior of the characteristic system relaxation time obtained by Chen et al.17 for the water contribution in hydrated lysozyme is superimposable to our data obtained for protein contribution in hydrated lysozyme. Furthermore, both the behaviors are in agreement with the main dielectric process and to the fast dielectric process of A.P. Sokolov et al.18 that have now been attributed to proteinwater coupled motions.

IV. CONCLUSIONS In the present paper, we have reported the results of different neutron scattering experiments performed on dry and hydrated lysozyme with different instrumental energy resolutions to solve the puzzling question related to both dynamical transition and dynamical fragile-to-strong crossover, registered in the MSD and in the system characteristic relaxation time temperature behaviors, respectively. We have shown that: (i) dynamical transition is due to finite instrumental energy resolution; more specifically, (ii) it appears when the characteristic system relaxation time intersects the resolution time; (iii) it does not imply any transition in the dynamical properties of the systems; and consequently (iv) it is not due to the FSC in the temperature behavior of the system relaxation time. More in general, we have shown, both from the theoretical and experimental point of view, that the protein dynamical transition does not necessarily require any discontinuous change in the temperature behavior of the system relaxation time and hence is not necessarily connected to a real transition of the system dynamics. We have also shown that a kink in MSD temperature behavior appears when the relaxation time of a system process crosses the instrumental resolution characteristic time. Furthermore, the temperature behavior of the relaxation time has been evaluated from different neutron spectra obtained on D2O hydrated lysozymes at different finite instrumental energy resolutions. As a result, we have shown that (v) at T = 220 K a change from Arrhenius to non-Arrhenius behavior has been registered in the temperature dependence of the characteristic

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relaxation time of hydrated water in lysozyme and is due neither to the finite energy resolution effects nor to numerical errors in data analysis protocol and that (vi) the hydration water relaxation process found by S. H. Chen et al.17 and the protein relaxation process found by A. P. Sokolov et al.18 can be ascribed to proteinwater coupled dynamics.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. Tel.: þ39 0906765025. Fax: þ39 090395004.

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Puzzle of Protein Dynamical Transition - The Journal of Physical

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