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Nov 16, 2016 - ... Transition in Proteins: Insights from Translational Self-Diffusivity ... Our studies reveal a common temperature profile/dependence...
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Role of Hydration Layer in Dynamical Transition in Proteins: Insights from Translational Self-Diffusivity Prithwish K. Nandi and Niall J. English* School of Chemical and Bioprocess Engineering, University College Dublin, Belfield, Dublin 4, Ireland S Supporting Information *

ABSTRACT: Elucidation of the role of hydration water underpinning dynamical crossover in proteins has proven challenging. Indeed, many contradictory findings in the literature seek to establish either causal or correlative links between water and protein behavior. Here, via molecular dynamics, we compute the temperature dependence of mean-square displacement and translational self-diffusivities for both hen egg white lysozyme and its hydration layer from 190 to 300 K. We find that the protein’s mobility increases sharply at ∼230 K, indicating dynamical onset; concerted motion with hydration-water molecules is evident up to ∼285 K, confirming dynamical correlation between them. Exploring underlying mechanisms of such concerted motion, we scrutinize the water−protein hydrogen-bonding network as a function of temperature, noting sharp deviation from linearity of the hydrogen bond number’s profile with temperature originating near the protein dynamical transition. Our studies reveal a common temperature profile/dependence of self-diffusivity values of the protein, hydration water, and the bulk solvent, originating from a common dependence on the bulk solvent viscosity, ηS. The key mechanistic role adopted by the protein− water hydrogen bond network in relation to the onset of proteins’ dynamical transition is also discussed. 240 K vis-à-vis its dry form.15−20 Studies of such dynamical transition are important, given that experimentally measured biochemical activities have also been established in the same temperature range.21−23 In particular, although not a general rule, Mamontov et al.24 showed that in specific cases denatured hydrated proteins also exhibit such dynamical transition. Studies have also been made to understand the dynamics of bound water molecules to protein surface. Using neutronscattering experiments, Settles and Doster25 showed that the dynamics of water molecules in the hydration layer of myoglobin are significantly retarded by interactions with the protein surface. From a sublinear increase in squared displacements, they conjectured that water molecules’ displacement events spread inhomogeneously with time, resulting in anomalous diffusion extending between vibrational and hydrodynamic time scales. Many open questions remain as to the nature of these transitions, such as if these are an inherent property of the protein or, rather, an intrinsic property of the hydration layer per se or if some interplay and coupling between protein and water is to the fore. Indeed, controversies abound as to rationalizing dynamical transition in proteins and the role therein of the hydration shell. Lee et al.21 reported that hydration shell has no significant role in dynamical transitions, while Doster et al.26 studied dynamical

I. INTRODUCTION The effects of solvents on proteins are of fundamental importance, in that they serve to regulate and control stability and folding,1,2 diffusion,3 and enzyme catalysis including transition-state stabilization,4 as well as a suite of other processes, such as charge-transfer reactions, ion-channel and membrane conductance,5 and binding6,7 and electrostatic interactions.3 Naturally, water is the most important solvent for proteins, with a thin water layer, known as the hydration layer, proving essential to activate a protein’s full panoply of biological activity,8 otherwise absent in its completely anhydrous variant. Proteins, quite correctly, are often viewed as a single complex entity in conjunction with their hydration layer; such an enlightened perspective underpins their immense biological importance. The dynamics of a protein and its surrounding hydration layer has been studied extensively by experimental, theoretical, and computational means in recent decades. A detailed and illuminating account of protein glass transition in connection with the liquid−glass transition of associated hydration water is given in recent reviews by Doster.9,10 At low temperatures, a hydrated protein behaves like glasses:11,12 as temperature is increased, large picosecond time scale anharmonic thermal motions begin to dominate, and a dynamical transition is often seen. This can be viewed as a transition from a low-diffusive state to a relatively more diffusive one.13,14 Experimentally measured mean-square displacement (MSD) of hydrated proteins confirms such dynamical transition between 200 and © XXXX American Chemical Society

Received: July 4, 2016 Revised: October 14, 2016

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of the protein−water hydrogen-bond network with temperature, establishing the “breakdown” in their collective number as the causal mechanism underpinning the loss of protein− water concerted motion.

transitions in myoglobin via inelastic neutron scattering and found that structural relaxation (α-process) causes additional mobility during the transition’s onset. Another prescription22,27,28 describes that the large-scale motion and shape changes of a protein is controlled by the fluctuation and viscosity of the bulk solvent, whereas the internal ligand motions are driven by the fluctuations in the hydration shell. Similarly, marked alterations in proteins’ de facto elasticity,17 together with particular side moieties’ mobility,21 finite instrumental energy-resolution effects,20 and the onset of glass transition in the hydration shell are also ascribed to such dynamical transition in proteins.29 Suppression of dynamical transitions30,31 and biological activity8 is seen in proteins when the level of hydration is considerably reduced below monolayer thickness. Work by Chen et al.32 showed a fragile-to-strong dynamical crossover in hydration water of protein, and this has also been observed from molecular dynamics (MD) simulation by Kumar et al.33 Importantly, a two-step scenario of protein dynamical transition has also been developed by Doster.34 In addition to the anharmonic onset of the mean-square displacements arising from slow collective relaxation (α-process), a second dynamic transition has also been identified, known as the β-process, which originates from fast hydrogen-bond fluctuations near the glass temperature, Tg, leading to a change in molecular elasticity and thermal expansion.34 Intriguingly, and more universally, such dynamical crossover in hydration water has also been reported in inorganic powder samples of a hydroxylated cerium oxide sample by Mamontov et al.35 Given the ubiquity of hydration water, understanding mechanistically its nature and influence on dynamical crossover is of fundamental importance. Wong et al.36 suggested, via MD simulation, that protein’s glass transitions are driven by the surrounding water. Subsequently, Tarek and Tobias,13 using MD, revealed the importance of protein−water hydrogen bond dynamics in influencing the anharmonic and diffusive motions responsible for protein structural relaxation. They distinguished between slow and fast dynamics of hydrogen bonds, concluding that slow relaxation of the protein’s hydrogen-bond network is responsible for additional movement above the dynamicaltransition temperature. Alternatively, Becker et al.37 have suggested that dynamical transition is merely an artifact associated with limited observation time scales accessible, in both experiment and MD simulations. An insightful recent study by Schiro et al.,38 combining neutron scattering and MD, conjectured that the translational mobility of hydration-shell water molecules is responsible for large-amplitude motions in proteins. Here, we present results, obtained rigorously from MD simulation between 190 and 300 K, of the temperature dependence of the translational self-diffusivity (DT) of a prototypical and well-studied protein−hen egg white lysozyme (HEWL), together with its surrounding hydration layer. This is a directly observable quantity that provides a direct one-to-one comparison between the dynamics of the protein and hydration layer, allowing establishment of possible correlation between them, and affording insight into potential causative action of one on the other. Importantly, we also provide the distribution of self-diffusivities of individual water molecules in the hydration shell to illustrate the rich tapestry of different molecular behaviors across the full gamut of “cleft”-bound immobile water molecules to more mobile and weakly bound water32 (vide inf ra). Crucially, we elucidate the changing nature

II. METHODS All MD simulations were performed using GROMACS version 5.0.139 MD simulation package with the OPLS40,41 and SPC/ E42 potential models for HEWL and water, respectively. The SPC/E water model was chosen due to the compatibility of SPC-type models with OPLS potentials and also because of its substantially superior estimation of self-diffusivity43 and freezing point44 for water vis-à-vis the SPC model. The selfdiffusivity values for bulk water as obtained from different water models are given in Table S1 (Supporting Information). SPC/E and TIP5P models produce the best match with available experimental data at 298 K. In the literature, studies exist where different water models have been used to study proteinhydration dynamics. For example, Schiro et al.38 used the SPC/ E model recently to study hydration dynamics. Previously, Tarek and Tobias45 made a detailed comparison of MD results obtained using SPC/E and TIP3P models with neutronscattering experiments to study the dynamics of proteinhydration water. Their conclusion was that the SPC/E model leads to much better agreement with experiment than the results obtained using the TIP3P model: this was clearly demonstrated by the density of states and the dynamical susceptibility, where both the change in water dynamics from bulk in the presence of protein environment and its temperature dependence are reproduced accurately over a broad frequency range. Moreover, Kumar et al.33 used the TIP5P model to investigate the relationship between dynamic transitions between biomolecules and the dynamical and thermodynamic properties of hydration water. They reported a “protein glass transition” for lysozyme at ∼242 ± 10 K and a similar temperature dependence in self-diffusivity of TIP5P hydration water. HEWL is a small globular protein with molecular mass 14 320 Da and triclinic wild-type, namely 2LZT,46 crystal structure with an overall charge (−8e). Eight Cl− ions were added to the solution to make the net charge of the solution to be zero. The simulation system consists of the HEWL protein and SPC/E water molecules placed inside a cubic box which is periodic in all directions. Each simulation run was carried out at constant temperature and constant pressure. Temperature control was imposed using the Nosé− Hoover thermostat,47 and a pressure of 1 atm was maintained throughout the entire simulation using a Parinello−Rahman barostat.48 Holonomic constraints were handled by the LINCS 49 method. The smooth particle mesh Ewald (SPME)50 method was used to handle long-range electrostatic interactions. System energy minimization was conducted using the steepest-descent algorithm. Here, we emphasize the temperature dependence of the translational self-diffusion properties of both the protein and the hydration layer. Since protein self-diffusion is at least one order lesser than bulk water, an accurate calculation and comparison of diffusion between them demands a reasonably long simulation time. A systematic study was done for a range of temperatures varying from 190 to 310 K in steps of 10 K. For each simulation, the system was equilibrated for a total time of 20 ns, and once the system is thermally stabilized, a production run of at least 20 ns was performed for each temperature. Although, as mentioned previously, Becker et al., in 2004, have B

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The Journal of Physical Chemistry B suggested that dynamical transition may be an artifact associated with limited observation time scales accessible,37 MD simulations can now sample 10−100 times longer routinely than was typical over a decade ago, and we feel that the production runs of at least 20 ns offer reasonable lengths for adequate sampling to gauge the properties of the putative dynamical crossover, elusive though it may well be. The translational self-diffusion coefficient was estimated from the MSD in long time limit using the following Einstein relationship:51 DT = lim t →∞

1 ⟨|r(t ) − r(0)|2 ⟩ 6t

(1)

Here, DT is the diffusion coefficient, and r(t) and r(0) are the position of the center of mass of a water molecule, or a protein non-hydrogen atoms, at times t and t = 0, respectively. The angular bracket represents the time ensemble average over both molecules and time origins. For calculating self-diffusion coefficients, the slope of the MSD curve was determined using the widely known linear-regression technique, and the correlation coefficient (r) was determined for each case, to ascertain the goodness of fit. For identifying hydrogen bonds between the protein atoms and the water molecules at each snapshot over the entire simulation time, the geometric criteria as described by Durrant et al.52 were adopted. Only oxygen, nitrogen, fluorine, or sulfur atoms were considered as the heavy-atom participants in forming hydrogen bonds. The distance between the donor and the acceptor heavy atoms must be less than 3.5 Å, and the angle between hydrogen atom, the donor heavy atom, and the acceptor heavy atom must be less than 30°.

Figure 1. Density distribution of water molecules around the HEWL surface is shown here for a wide range of temperatures varying from 190 to 310 K. The existence of two distinct hydration layers around the HEWL surface is very much evident. As temperature increases, the spatial extent and the peak density of the first solvation layer decreases. In addition, the height of the first minimum and the first maximum also changes with temperature, indicating swapping of water molecules between the first hydration layer and the region corresponding to the first minimum.

weakened substantially, and water−water interactions dominate in this layer. Thus, water molecules in the second layerno longer in direct contact with the protein surfacehave higher mobility relative to those in the first one, with properties approaching those of the bulk. Therefore, to identify the true hydration layer, we followed a more rigorous “filtration” process based on the residence times of those molecules in the first solvation layer to eradicate the effects of “bulk-like” water molecules from subsequent calculations of translational diffusivities. Dynamics of HEWL and the First Hydration Layer. As mentioned previously, it is believed that the hydration layer plays an important role in activating the biofunctionality of a biomolecule. Large thermal motion of protein molecules is often conjectured to be correlated with the mobility of the water molecules present in the hydration layer.38 Diffusivity is a quantitative measure of a particle’s thermal motion. Here, we present a rigorous computation of translational diffusivities for both the protein and the associated hydration layer using the Einstein relationship (cf. Methods). As mentioned above, for computing MSDs and diffusivity of the hydration layer, a rigorous filtration process was followed throughout independent subsections of the entire trajectories (20−40 ns). The centers of mass of water molecules were tracked, and those of them that remained in the first hydration layer for at least 90% of each subsection of 0.2 ns in duration were utilized to compute the MSDs of hydration layer. The 0.2 ns sampling length of each interval is necessary to compute a sufficiently long MSD with a converged slope, but yet was found to be adequate to ensure a reasonable number of water molecules retained in the solvation layer for at least 90% of the interval, to define a reliable MSD (particularly at higher temperatures). The MSDs could then be averaged over all subsections, which is at least 100 in present case. When applied to HEWL, only the coordinates of all non-hydrogen atoms were taken into account for computing MSD and DT (cf. Methods). MSD plots of HEWL and the hydration layer are

III. RESULTS AND DISCUSSION Identification of the Hydration Layer. The main focus of this work is to explore the dynamical correlation between HEWL and its hydration layer, if any. In MD simulations, the water molecules surrounding a protein have three broadly distinct categories:32 those confined in deep clefts of the folded protein known as “bound water”, whereas those interacting directly with the exposed-surface protein atoms constitute the hydration layerknown also as “surface water”. The third category is “bulk water”in this case, water molecules not directly in contact with the protein surface, but which exchange continuously with the surface water. To identify the hydration layer around HEWL, we computed the density distribution (Figure 1) of the water molecules’ centers of masses from the protein surface. Proteins, of course, do not have a regular shape. Normalizing the density distribution requires accurate estimation of the hydration shells’ complex-shaped volumes around the protein. Using state-of-the-art Voronoi-cell analysis,53 we computed the “Voronoi” volumes associated with each molecule in the hydration layer, thus estimating the hydration shell’s total volume. The resultant density distribution is shown in Figure 1 for 190−310 K. Two distinct water layers around the protein surface are very much evident. As temperature increases, the spatial extent and the height of the first hydration layer decrease, whereas the height of the first minimum increases, indicating swapping of water molecules between the first hydration layer and the region corresponding to the first minimum. Water molecules interact with the polar ionic groups at the protein surfacethe nature of such interaction is Coulombic. This charge−dipole interaction falls of as r‑4:54 in the second hydration layer, this interaction is C

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Figure 2. Probability distribution of translational diffusion constants of each individual water molecules residing in the hydration layer at (a) T = 190 K, (b) T = 240 K, and (c) T = 300 K. Each of these distributions shows a non-Gaussian-type distribution, highlighting a heterogeneity in translational mobility. Plots are normalized such that the area under the curve represents the total number of water molecules present in the hydration layer. The number of hydration-layer water molecules drops significantly with temperature, in terms of persistent presence over at least 90−95% of sampling time windows.

ions, and the experimental hydrodynamic data are usually corrected by the viscosity data of water at 298 K, adding further errors in those estimations.55 (ii) The mobility (as defined by translational diffusivity) of bulk water and the hydration layer differs by almost 1 order of magnitude, indicating striking difference of dynamical features between themhydration water being viewed as a relatively confined layer of surface water. (iii) The magnitude of DT for the hydration layer is of the same order of magnitude as compared to the protein. (iv) The temperature variation of DT of hydration-layer water molecules follows an almost identical trend to HEWLan indication of dynamical correlation between the two. (v) The Arrhenius temperature dependence is nonlinear, suggesting a behavior of a supercooled liquid in the vicinity of a glass transition. (vi) The most striking feature is that at 280 K both the protein and the hydration layer have almost identical diffusivities, indicating a “resonance” in amplitude of thermal motion. In order to understand the nonlinear relationship between self-diffusivities and temperature, the data were fitted with the phenomenological Vogel−Fulcher−Tammann (VFT) law56 and are presented in Figure 3b. The data fit well with the VFT law for the higher temperature régime above ∼230 K, with our resultant estimate of the dynamical-crossover temperature being ∼230 K, while deviations from the VFT behavior are noticeable as temperature is lowered. The dynamic crossover in HEWL is also evident from the MSD versus temperature plot (cf. Figure S3), where data in between 190 and 220 K visibly lie on a straight line and there is an onset of mobility at 220 K. In contrast, for the hydration layer, such a definitive dynamical crossover is absent: rather, a nonlinear increase of DT with temperature is evident. The so-called VFT-defined glass transition temperature (T0) for HEWL and the hydration water is 130 ± 30 and 147 ± 22 K, respectively. In order to characterize deviations from VFT behavior for temperatures below 230 K, the data were fitted with an Arrhenius relation for HEWLwith reasonable results (cf. Figure 3b). However, in the case of the hydration layer, such an Arrhenius dependence of DT for temperature from 190 to 230 K is absent. These results suggest that although one might consider the fragile-tostrong (FSC) liquid−liquid phase transition to be present for HEWL, its associated hydration-shell water molecules do not evince any such transition, as seen experimentally by Chen et al.32 for hydration water on lysozyme and by Kumar et al.33 for the same system using molecular- dynamics simulations. Neutron-scattering studies with different instrumental energy resolutions as reported by Magazu et al.20 also show that the

shown in Figure S1 (Supporting Information). For HEWL, MSD plots are shown for temperatures ranging from 190 to 310 K; for the hydration layer, it is shown from 190 to 300 K only. MSD plots for the hydration layer for temperatures from 300 K and above suffer from lesser statistical averaging as the number of water molecules satisfying the above-mentioned stringent residence time criterion are very less and thus introduce uncertainties in the computed MSD and subsequent DT values. In Figure S2 (Supporting Information), we have compared the MSD data for the hydration water with the experimentally obtained data for the hydration water in myoglobin, as reported by Settles and Doster,25 using neutron-scattering techniques, and a reasonably good agreement is observed. On a 15 ps time scale (cf. Figure S2), displacements for the hydration water in the current study and the experimentally reported data25 follow a power law with exponents of ∼0.5 and 0.4, respectively. We also computed squared displacements, and resultant diffusivities, of each individual molecule in the hydration shell. Statistical distributions of translational diffusivities of these individual water molecules, shown in Figure 2, reveal a non-Gaussian shape, indicating the existence of molecules with widely (and wildly) different translational mobilitya dynamically heterogeneous situation with a clear bias to the mobility represented by the distribution’s mode value. It is important to note that the plots in Figure 2 are normalized such that the area under the curve represents the total number of water molecules present in the hydration layer. The number of hydration-layer water molecules drops significantly with temperature, in terms of persistent presence over at least 90−95% of sampling time windows. The values of self-diffusivities for various temperatures are plotted in Figure 3a; in the inset, we have shown the same in semilogarithmic scale, so as to make the variation in the lower temperature régime readily evident. In order to validate our MD-obtained translational diffusivities, those of HEWL from various experiments and hydrodynamic calculations were also included. The MD data of DT for HEWL, as available from literature, are also included. To differentiate the dynamics of bulk water and the hydration layer, literature experimental diffusivities for bulk water are also specified. At a first glance, several important observations can be made, as follows: (i) There is a reasonable agreement between current MD data of DT for HEWL with the available experimental, hydrodynamic and MD data, though the current DT values are slightly underestimated. It is to be noted that accurate calculations of experimental DT are strongly affected by presence of counterD

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hydration layer. The solid lines represent the fit with the phenomenological Vogel−Fulcher−Tammann (VFT) law, and the dotted line represents the Arrhenius fit. Although, for HEWL, one can argue that a fragile-to-strong liquid−liquid transition can be imagined, for the hydration layer, any such f ragile-to-strong crossover is visibly absent. (c) Translational self-diffusivity of the protein (HEWL), the hydration layer, and DP as obtained from the self-diffusivity of the bulk part of the water fraction using eq 4. It is evident from this plot that both protein diffusion and the diffusion of the hydration-water layer exhibit a parallel temperature dependence with bulk water, albeit on a logarithmic scale.

experimentally observed dynamical transition in lysozyme at ∼220 K (with our ∼230 K estimate from Figure 3a in good accord) is not due to the FSC dynamical crossover. In previous insightful work by Lichtenegger et al.,57 the role of viscoelastic relaxation of the solvent on heme-group displacements of myoglobin was discussed from Mössbauer studies. In fact, the role of viscosity near protein surface is described as an essential parameter to couple dynamics of the solvent and protein functional motions.9,10,57 In a glass-forming system, the relaxation time associated with α-process is linked to the shear viscosity by the Maxwell relation: τα = G·η. The “global” protein diffusion coefficient of protein in solution, according to hydrodynamic theory, follows from the Stokes− Einstein relation on a very basic level:

DP =

kT 6πηSRH

(2)

where RH is the hydrodynamic radius of the protein including the hydration shell and ηS denotes the viscosity of the solvent, which in the present case is the bulk water. A second Stokes− Einstein relation applies to the solvent and its self-diffusion coefficient:

DS =

kT 6πηSR S

(3)

where RS reflects the molecular radius of the solvent molecule. Combing the above two equations leads to DP(T ) = DS(T )R S/RH

(4)

Thus, one might expect that both diffusion coefficients should exhibit the same temperature dependence due to a coupling to the solvent viscosity, ηS. Here, as mentioned clearly in the Methods section, the diffusion coefficient of protein is calculated from eq 1, where the time-resolved mean-square displacement at each temperature is obtained by averaging over the translational displacement of each and every heavy atom of the protein structure, rather than from the translational mobility of the center of mass of the entire protein, as done for a “rigid and continuum” object. Therefore, protein diffusion, in the present context, is based on average effects of local atomic motions manifesting themselves in the self-diffusivity value, rather than a more global protein diffusion. We have also computed diffusion coefficients of bulk water, denoted as DS, consisting of water molecules which are not part of the hydration water. We notice that the magnitude of self-diffusivity of bulk part of the water is almost 1 order of magnitude higher than the hydration water: DP ∼ Dhyd ≪ DS. Indeed, this is quite expected, since bulk water, ipso facto, is not confined near the protein surface like hydration water and is free to diffuse. In

Figure 3. (a) Comparison of temperature dependence of translational diffusion coefficients of HEWL and those of water molecules in the first solvation layer at various temperatures. Experimental and other MD data as available from literature is also included in the plot, which shows a reasonable agreement with the current MD data. Translational diffusion coefficient data of bulk water are also included to highlight the difference of its in dynamical character from the hydration layer. The purple-colored dotted line is a guide to eye to emphasize the onset of a dynamical transition which can be seen to occur in HEWL at about 230 K. The most striking feature is the concerted dynamical motion between the protein and the hydration layer; especially, at ∼280 K, their diffusivities are effectively identical. (b) Temperature dependence of translational diffusion constants of HEWL and E

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The Journal of Physical Chemistry B Figure 3c, we have compared the self-diffusivity of the protein, its accompanying hydration layer, and DP as obtained from the self-diffusivity of the bulk part of the water fraction using eq 4. The hydrodynamic radius of solvent water molecule (RS) and the hydrodynamic radius of the protein (RH) is taken as 1.37 Å58 and 19.32 Å,59 respectively. Interestingly, it is quite evident from this plot that both protein diffusion and the diffusion of the hydration layer waters exhibit a parallel temperature dependence with bulk water, albeit on a logarithmic scale (cf. Figure 3c). It is quite compelling to consider this common temperature dependence of DP and Dhyd to originate from a common dependence on the bulk viscosity, ηS, which is generated by the bulk phase. Because of the almost identical self-diffusivity of the protein and the associated water molecules in the hydration layer, it is difficult to avoid the conclusion that the hydration water phase moves “together” with the protein, relatively close to a “no-slip” condition in hydrodynamics. Of course, some attached water molecules do escape to the bulk phase transiently and are replaced by other water molecules from the bulk: this rationalizes slightly larger self-diffusivity of the water molecules in the hydration layer. We can make a hypothesis here that the water molecules coming from the “bulk phase” to the hydration layer through this “exchange process” actually carries the signature of the “temperature dependence of bulk viscosity” and incorporates to the protein atoms in contact. At this point, the natural question arises of how hydrationlayer water molecules “communicate” with the protein residues. The interaction is indeed polar in natureit is the protein− water hydrogen bond network that plays the crucial role. Tarek and Tobias,13 from molecular-dynamics simulations, showed that for complete structural relaxation of protein, relaxation of protein−water hydrogen-bond network, via translational displacement of the solvent molecules, is essential. Restructuring of the protein−water hydrogen-bond network is also assigned to such dynamic transition by Arcangeli et al.60 In another study, fast hydrogen-bond fluctuations have been assigned as a precursor of the slow α-relaxation process in protein by Doster.18 A more recent study by Schiro et al.38 on intrinsically disordered human protein tau and globular maltose binding protein, using neutron scattering and MD, generalized the correlation between translational diffusivity of the hydration layer with large-amplitude motion of proteins at dynamicalcrossover temperatures. Using MD, they showed that the intermittent hydrogen-bond relaxation time representing the translational diffusion of water molecules at the protein surface exhibits a sharp increase at around the dynamical crossover temperature, in contrast to continuous hydrogen-bond relaxation times due to water rotational/librational motion. In view of these findings, and in order to explore mechanisms of dynamical crossover of HEWL at ∼230 K from our VFT fit to MD-based DT results (cf. Figure 3b), we computed the hydrogen-bond network existing between the protein and the hydration layer following criteria mentioned in the Methods section. The number of protein−water hydrogen bonds (NHB) exhibits a nonlinear dependence on system temperature, as seen in Figure 4. The solid line represents a third-order polynomial fit to the data. The plot shows a sharp decrease of NHB starting from 230 K, which coincides with the dynamicalcrossover temperature we observed in HEWL (cf. onset of departure from VFT behavior below 230 K in Figure 3b). We have also pointed out that at another temperature, ∼285 K, the two “asymptotes” meet. One can notice readily, from Figure 3a,

Figure 4. Number of hydrogen bonds between protein (HEWL) and water molecules residing in the hydration layer. Hydrogen bonds are identified by adopting the geometric criteria described by Durrant et al.52 A nonlinear dependence on temperature is seen, which can be fitted with a third-order polynomial. A sharp decrease in the number of bonds emanates from T ∼ 230 K, the so-called dynamical-transition temperature of the protein. This indicates that the hydrogen-bond network between the hydration layer and protein plays a key role in deciding the dynamic crossover in protein and the concerted motion between the two (see main text for further discussion). For temperatures above 310 K, so as to evaluate the hydrogen-bond network, we ran simulations up to 390 K for a shorter period (5 ns) as compared to the longer runs used for evaluating MSD and diffusivity below 310 K.

that at ∼280 K both HEWL and the hydration layer have almost identical translational self-diffusivities. Mechanistically, the key feature underlying the observed “concerted” motion between the protein and the hydration layer is the protein− water hydrogen-bond network and its persistence, which allows coupling of motion between hydration-layer water molecules and surface protein residues; this dynamic coupling is evidenced clearly by the almost-identical trend in their DT values in Figure 3a and overlap at 280 K. Given the observed sharp decline in the number of hydrogen bonds in Figure 4 at ∼285 K, following the onset of decline at the dynamicalcrossover temperature (∼230 K), a plausible hypothetical mechanism in this “breakdown” above ∼285 K is that the amplitude of larger-scale protein thermal motion becomes greater, and anharmonic, in this temperature region, either breaking down key stabilizing hydrogen bonds with water or accelerating their persistence kinetics,61 and the motion of the hydration-layer water molecules and protein become more independent. Indeed, the dramatic change in trend of both water and protein DT values above ∼280 K “resonant kink” in Figure 3a underscores this qualitative change and marked acceleration in water self-diffusivity with fewer and less strong protein−water hydrogen bonds to regulate and confine their motion. In this way, we establish prima facie causal evidence of the key mechanical role of protein−water hydrogen bonds in regulating protein−water concerted motion and how these changes over the ∼230 to ∼280 K region (cf. Figure 4) lie at the heart of rationalizing the dynamical-crossover temperature (∼230 K, consistent with Figure 3b) and “resonance then breakdown” (∼280−285 K, cf. Figure 3a). In terms of ambient-temperature conditions (∼300 K), we note that the number of protein−water hydrogen bonds at 310 K decreases by an amount of ∼16% as compared to the F

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The Journal of Physical Chemistry B corresponding value at 190 K. Therefore, the majority of hydrogen bonds remain intact in the ambient/biological temperature range; motional coupling between the protein and its hydration layer in the higher-temperature range (>285 K) slowly decreases but is by no means lost. However, one would expect that the lifetime of the existing hydrogen bonds at 300−310 K would generally be shorter compared to lowtemperature cases.61 This has the implication that at 300−310 K, larger-amplitude motion (as characterized by the marked increase in self-diffusivity above ∼285 K in Figure 3a) is facilitated by slightly fewer hydrogen bonds (around 16% less vis-à-vis 190 K), but with a key controlling factor being in their shorter lifetimes in regulating and facilitating greater water exchange between the hydration layer and bulk, as well as allowing greater diffusivity and mobility of proteins. As mentioned with acuity by Doster,9 protein and water are dynamically very much different. Whereas water molecules tend to exhibit short-range order and long-range diffusion, macromolecules like protein have long-range order and short-range diffusion. Therefore, a protein molecule surrounded by the cage of nearest-neighbor water molecules can only diffuse when the associated neighbors also move, thus resembling a collective phenomenon involved in a continuous search for an escape path, rather than making discrete jumps over energy barriers. Near the glass-transition point, this cage becomes a trap and the time scale of cage disintegration diverges. Our studies indicate that the dynamic onset in protein associated with the translational diffusion of hydration water, which also implies that the α-process of structural relaxation in liquids couples with water-dependent protein structural motion, as previously discussed by Doster.10 In any event, the more local measure of self-diffusivity of the protein studied from eq 1 for all protein heavy atoms, in contrast to a more global center-of-mass definition for the protein,66,67 means that any coupling of protein diffusion with the hydration layer is less evident, although any strong correlation would not be expected for global diffusion of the protein either.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected], Tel +353 1 7161646 (N.J.E.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors acknowledge useful discussions with Antonio Benedetto and thank Science Foundation Ireland for funding under Grant SFI 15/ERC-I3142. The authors also thank the anonymous referees for their help in improving the manuscript substantially.

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REFERENCES

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IV. CONCLUSIONS This key novelty of this study lies in resolving the mechanistic details of the elusive nature of self-diffusivity behavior in proteins and their accompanying hydration-layer water molecules and the key role in protein−water hydrogen bonding in controlling this. By computing the MSD temperature dependences and translational self-diffusivities for HEWL and hydration-layer molecules, we confirm a dynamical crossover at ∼230 K. Our studies reveal a common temperature profile/ dependence of self-diffusivity values of protein, hydration water, and the bulk solvent, originating from a common dependence on the bulk solvent viscosity, ηS, which is generated by the bulk phase. The hydration layer was also seen to exhibit a concerted dynamical mobility with the proteinhighlighting coupled motion between the two. We also show that associating such dynamical transition in protein to a fragile-to-strong liquid− liquid transition in the associated hydration layer seems inappropriate but establish causal evidence of protein−water hydrogen-bond network in controlling concerted motion.

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Plots of mean-square displacement as a function of temperature for both the protein and hydration-layer water molecules (PDF)

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