Effect of Temperature, Pressure, and Cosolvents on Structural and

Jan 3, 2008 - It is now generally agreed that the hydration water and solvational properties play a crucial role in determining the dynamics and hence...
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J. Phys. Chem. B 2008, 112, 997-1006

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Effect of Temperature, Pressure, and Cosolvents on Structural and Dynamic Properties of the Hydration Shell of SNase: A Molecular Dynamics Computer Simulation Study Nikolai Smolin† and Roland Winter* Physical Chemistry and Biophysical Chemistry, Department of Chemistry, UniVersity of Dortmund, Otto-Hahn-Str. 6, D-44227 Dortmund, Germany ReceiVed: August 10, 2007; In Final Form: October 17, 2007

It is now generally agreed that the hydration water and solvational properties play a crucial role in determining the dynamics and hence the functionality of proteins. We present molecular dynamics computer simulation studies on staphylococcal nuclease (SNase) at various temperatures and pressures as well as in different cosolvent solutions containing various concentrations of urea and glycerol. The aim is to provide a molecular level understanding of how different types of cosolvents (chaotropic and kosmotropic) as well as temperature and high hydrostatic pressure modify the structure and dynamics of the hydration water. Taken together, these three intrinsic thermodynamic variables, temperature, pressure, and chemical potential (or activity) of the solvent, are able to influence the stability and function of the protein by protein-solvent dynamic coupling in different ways. A detailed analysis of the structural and dynamical properties of the water and cosolvents at the protein surface (density profile, coordination numbers, hydrogen-bond distribution, average H-bond lifetimes (water-protein and water-water), and average residence time of water in the hydration shell) was carried out, and differences in the structural and dynamical properties of the hydration water in the presence of the different cosolvents and at temperatures between 300 and 400 K and pressures up to 5000 bar are discussed. Furthermore, the results obtained help understand various thermodynamic properties measured for the protein.

1. Introduction It is well-known that water plays a key role in governing the structure, stability, dynamics, and functionality of proteins.1-5 The properties of water molecules present in the first hydration layers of a protein are of most importance due to the structural and dynamical coupling that exist between these water molecules and the protein surface. Microscopic information about such coupling is necessary to understand the role played by water during biological processes, such as protein-substrate binding, protein folding and unfolding, as well as protein aggregation and amyloid formation.6-9 In recent years, several studies have been reported on aqueous protein solution with particular emphasis on exploring the structural and dynamical properties of water present in the first hydration layer.1-18 Femtosecond resolved fluorescence spectroscopy revealed a bimodal distribution of solvation time scales.3,10 While the initial component within a few picoseconds is attributed to fast librational and reorientational motions of the hydration layer water molecules, the second component observed in the time scale of tens of picoseconds is attributed to the coupled slower dynamics of water molecules hydrating the protein surface. Quasi-elastic neutron-scattering techniques have shown that the relaxation dynamics of the hydration layer of water is non-exponential in nature and that the water translational dynamics exhibits a non-Arrhenius behavior over a wide range of temperatures.15 Attempts have also been made * To whom correspondence should be addressed. Phone: +49 231 755 3900. Fax: +49 231 755 3901. E-mail address: roland.winter@ uni-dortmund.de. † Current address: Department of Bioengineering, University of Washington, Seattle, WA 98195-5061.

to study the dynamics of proteins and hydration water at different time scales using other experimental techniques such as dielectric and nuclear magnetic relaxation measurements.16-18 In recent years, also computer simulations have developed into one of the most powerful theoretical techniques capable of studying the complex structural and dynamic phenomena at the protein-solvent interface on the atomic level. This is due to the accessibility of the time scale associated with such dynamics by MD simulations. Several simulation studies have been reported on the structure and dynamics of water at the surface of proteins and their correlation with the dynamics of the proteins themselves.5,19-34 Proteins in nature are generally not solvated by pure water, and intracellular solutions are crowded with many types of proteins, nucleic acids, metabolites, osmolytes, salts, and other molecules. Cosolvents in aqueous solution can have profound effects on the protein’s stability, structure, and function.35-47 The use of such solutions to stabilize or destabilize proteins, depending on the type of cosolvent, is commonplace. The presence of the cosolvents generally alters protein equilibria and reaction kinetics by perturbing the chemical potential of the protein system by associating either more strongly or more weakly with the protein than water. Furthermore, irrespective of whether cosolvents directly bind to or are rejected by the protein surface, they are expected to induce significant changes in the quantity of interfacial water and its associated physical properties. In general, protein hydration, as well as its packing and dynamics, also changes in the course of protein un- and refolding, aggregation, and binding events. The use of osmolytes such as glycerol has gained much importance, primarily because of their ability to stabilize the folded protein through a mechanism that may not involve direct

10.1021/jp076440v CCC: $40.75 © 2008 American Chemical Society Published on Web 01/03/2008

998 J. Phys. Chem. B, Vol. 112, No. 3, 2008 contact but rather alter the hydration shell around the protein. The presence of the glycerol is also important for a number of organisms for its cryoprotective properties. It has been proposed that the driving force for stabilizing the protein conformation is a nonspecific solvation effect in which the preferential exclusion of solvents from the protein surface arises from enhanced solvent ordering (structure makers).35,42,45 Recently,43 it was also shown that an increase in glycerol concentration leads to a distortion of the percolation of the hydrogen-bonded water network and prevents crystallization of the water (i.e., reduces the water available to form extracellular ice). In contrast, when denaturating cosolvents such as urea bind to proteins, water-protein and water-cosolvent interactions are replaced by relatively stronger cosolvent-protein interactions with a concomitant release of water molecules into the bulk phase. Furthermore, these cosolvents tend to reduce the solvent ordering.44 In this work, our focus was to compare the effects of a chaotropic (urea) and a kosmotropic (glycerol) agent as well as temperature and pressure on the hydration shell of a wellcharacterized monomeric protein, staphylococcal nuclease (SNase), to reveal the different static and dynamic properties in the hydration shell upon applying these various perturbation parameters.

Smolin and Winter TABLE 1: Average Number of Water-Water Hydrogen Bonds Per Water Molecule, NHB, in the Bulk, within a Hydration Shell of 4.5 Å Thickness, and Near Protein Nonpolar Atoms at Different Temperatures and Pressures bulk 300 K, 1 bar 360 K, 1 bar 400 K, 1 bar 300 K, 2 kbar 300 K, 5 kbar

hydration shell

nonpolar atoms

NHB

NHB

NHB

3.64 3.37 3.16 3.79 3.95

3.00 2.75 2.56 3.15 3.30

3.38 3.08 2.84 3.52 3.67

TABLE 2: Average Coordination Number of Water in the Bulk, within a Hydration Shell of 4.5 Å Thickness, and Near the Protein Nonpolar Atoms, NW, at Different Temperatures and Pressures bulk 300 K, 1 bar 360 K, 1 bar 400 K, 1 bar 300 K, 2 kbar 300 K, 5 kbar

hydration shell

nonpolar atoms

NW

NW

NW

5.18 4.93 4.70 5.81 6.56

4.33 4.07 3.87 4.79 5.36

4.57 4.30 4.05 5.02 5.60

surface, we omitted internal (structural) water molecules from our analysis.

2. Methods A series of molecular dynamics (MD) simulations was performed on SNase in water at constant temperature and ambient pressure, namely, at 300, 360, and 400 K. Furthermore, MD simulation runs at 300 K and at high pressure were carried out at 2000 and 5000 bar, respectively. Under these conditions, in the MD simulation, the protein does not unfold. Details of the simulation method at ambient conditions can be found in our previous paper.23 Briefly, the structure of SNase was constructed using the crystallographic heavy atom coordinates from the Protein Data Bank.48,49 The MD simulations were performed using AMBER 6.050 and the all-atom force field by Cornell et al.51 All protein atoms were explicitly included in the simulations, and the TIP3P water model was used.52 An integration time step of 2 fs was used, the Lennard-Jones interactions were calculated using a cutoff of 10 Å, and the particle mesh Ewald (PME)53 was used for the calculation of electrostatic interactions. In the simulations of SNase in the presence of cosolvents, published OPLS parameters for urea54 and for glycerol55 were used. First, equilibrated boxes with different concentrations of urea and glycerol were prepared. The urea and glycerol systems were constructed by randomly replacing water molecules with urea or glycerol, respectively. Next, the protocol for solvation and equilibration of the protein as for the pure water simulations was repeated. Finally, four urea simulations were performed, UR1, UR2, UR3, and UR4, with urea mole fractions of 0.029, 0.066, 0.115, and 0.184, respectively. Three glycerol simulations were performed, GL1, GL2, and GL3, with glycerol mole fractions of 0.013, 0.043, and 0.061, respectively. The simulations were continued for 7-14 ns. For the analysis, the trajectories from the last 2 ns were used. For the analysis of hydrogen bonds, the following geometric criterion was used: the proton-donor to heavy-atom acceptor distance must be less than 2.5 Å, and the hydrogen-bond angle (D-H-A) must be greater than 120°. These criteria are compatible with those reported in the literature.56-59 Since we want to focus on the structural and dynamical properties of the hydration water that interacts with the protein

3. Results 3.1. Structural Properties of the Hydration Water of SNase. To analyze the properties of the hydration water of SNase, a distance of 4.5 Å is an optimal choice for the width of the first hydration shell, which does not change drastically with increasing temperature or pressure.23,26,60,61 The average number of water-water H-bonds per water molecule (NHB) and the average coordination number of water (NW) as a function of distance from the nearest heavy atoms of the protein are first discussed. Table 1 displays the average number of water-water hydrogen bonds per water molecule, NHB, in the bulk, within the hydration shell of SNase, and near the nonpolar surface atoms of SNase at the different p and T conditions chosen. As expected, the average number of hydrogen bonds in bulk water decreases with increasing temperature, from 3.64 at 300 K to 3.16 at 400 K. On the contrary, a pressure increase up to 5 kbar leads to an ∼9% increase (NHB ) 3.95) of the average number of hydrogen bonds in bulk water. A similar trend is observed for the hydration water of the protein (Table 1): The average number of water-water hydrogen bonds per water molecule within the hydration shell of 4.5 Å is smaller and decreases with increasing temperature, from 3.00 at T ) 300 K to 2.56 at T ) 400 K. Conversely, NHB increases with increasing pressure to 3.30 at p ) 5 kbar for T ) 300 K. Hence, the relative temperature and pressure induced changes for bulk and hydration water hydrogen bond formation follow similar trends. The same holds true for the average numbers of water-water hydrogen bonds of the water molecules that are located near the hydrophobic surface atoms of the protein, which take on intermediate NHB values (Table 1). The average coordination numbers NW of water in the bulk, within the 4.5 Å hydration shell thickness of SNase, and near the nonpolar atoms of SNase at different p and T conditions are assembled in Table 2. A temperature increase from 300 to 400 K leads to a ∼12% decrease of the average coordination number of water (from 4.33 to 3.87 Å), and NW increases from 4.33 Å at 1 bar to 5.36 Å at 5 kbar (∼21% increase) for T ) 300 K. The corresponding average coordination number of water

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in the bulk decreases by a similar amount with increasing temperature, from 5.18 Å at T ) 300 K to 4.70 Å at 400 K, and increases similarly as strong with increasing pressure, from 5.18 Å at 300 K and 1 bar to 6.56 Å at 300 K and p ) 5 kbar, respectively. The average coordination number for water in the bulk at 300 K and 1 bar is in agreement with previous computer simulations and experimental data.52 Again, the NW values near the nonpolar atoms of the protein take on intermediate values. 3.2. Dynamic Properties of the Hydration Water of SNase. To determine the role of the water dynamics in the stability of the protein, we have also analyzed the temperature-, pressure-, and cosolvent dependencies of the protein-water and hydration shell H-bond dynamics. In particular, water molecules form hydrogen bonds with carbonyl and N-H groups of the backbone and with several polypeptide side chains. The breaking and forming of these hydrogen bonds was suggested to be a prerequisite for the occurrence of stochastic large amplitude motions of the macromolecule.19 To distinguish the fast formation and break up of hydrogen bonds due to water rotation/ libration and the slower relaxation of the protein-water hydrogen bond network due to diffusion of water molecules between sites on the protein surface and/or exchange with bulk water, we used two measures of the hydrogen bond lifetime, following a recent analysis of fast and slow hydrogen-bond dynamics in supercooled water and in molecular dynamics simulations of crystals and dehydrated powders.28,31 The fast hydrogen-bond lifetime, τHB, is defined as the average time that a given hydrogen bond remains intact. The slower hydrogen bond (network) relaxation time is defined in terms of the decay of the H-bond correlation function

c(t) )

〈h(0)h(t)〉 〈h〉

(1)

where h(t) is a hydrogen-bond population operator, which is equal to 1 if a given donor-acceptor (D-A) pair is hydrogen bonded at time t and 0 otherwise, and the angular brackets mean an average over all D-A pairs and starting times. Hence, the H-bond correlation function is the probability that the hydrogen bond is intact at time t, given it was intact at time zero (independent of possible breaking in the interim time). Therefore, beyond an initial transient period, the decay of c(t) is not determined by fast hydrogen-bond breaking by water rotation/ libration but rather by the rearrangement of the hydrogen bond network. The characteristic hydrogen bond network relaxation time, τR,HBN, is defined as the time at which c(t) decays to 1/e, i.e., where c(τR,HBN) ) e-1.28 In a similar way, we define the relaxation time of the hydration shell, τR,HS (in that case, the function h(t) describes the entry and escape of the water molecules from the protein’s hydration shell). To obtain information about the fast dynamics of the hydration water of the protein, first the average lifetimes of water-water hydrogen bonds, τHB, were calculated. The results are given in Table 3. Moreover, an analysis of different types of water-water hydrogen bonds was performed. The average lifetime of the hydrogen bonds τHB between two water molecules was calculated (i) when both molecules are located within the protein hydration shell and (ii) when one water molecule is within the hydration shell and another one located out of the hydration shell. Additionally, for comparison, the average lifetime of the water-water hydrogen bonds in bulk water was calculated for the same p and T conditions. τHB in the bulk water region decreases with increasing temperature and also, but less markedly, by pressure (Table 3). A similar trend for the lifetime of the water-water hydrogen bonds was observed

TABLE 3: Average H-Bond Lifetimes, τHB, of the Hydrogen Bonds of Water-Protein and Water-Water in the Hydration Shell, of Water-Water in the Bulk, and of Hydration Water-Bulk Water, and Mean Residence Times, τRes, of Water Molecules in the Hydration Shell of 4.5 Å Thickness of SNase, at Different p and T Conditions τHB/ps water-water

300 K, 1 bar 360 K, 1 bar 400 K, 1 bar 300 K, 2 kbar 300 K, 5 kbar

bulkbulk

shellshell

shellbulk

proteinwater

τRes/ps

0.88 0.64 0.54 0.82 0.76

0.72 0.55 0.47 0.74 0.75

0.47 0.39 0.36 0.47 0.47

1.89 1.39 1.16 1.74 1.67

2.67 2.28 2.07 3.06 3.49

TABLE 4: Properties of the Hydration Shell of SNase at Different Cosolvent Conditions at T ) 300 Ka hydration shell (4.5 Å) Water UR1 UR2 UR3 UR4 GL1 GL2 GL3

NW

NC

NWHB

NCHB

3.91 3.96 3.69 3.34 2.95 4.02 3.70 3.47

0.38 0.71 1.04 1.39 0.24 0.47 0.63

2.61 2.76 2.55 2.30 2.07 2.81 2.60 2.47

0.26 0.48 0.70 0.93 0.16 0.31 0.43

a NW and NC are the average coordination numbers of water and cosolvent molecules around H2O within the hydration shell of SNase. NWHB and WCHB are the average number of water-water and watercosolvent hydrogen bonds within the hydration shell of the protein, respectively.

TABLE 5: Protein-Water Hydrogen Bond Network Relaxation Time, τR,HBN, and the Relaxation Time of the Hydration Shell, τR,HS, of SNase at Different p and T Conditions 300 K, 1 bar 360 K, 1 bar 400 K, 1 bar 300 K, 2 kbar 300 K, 5 kbar

τR,HBN/ps

τR,HS/ps

35.4 14.8 8.7 36.4 48.8

66.8 30.4 19.8 78.8 99.8

by Stanley and co-workers for liquid water using molecular dynamics simulations.29 The average lifetime of the waterwater hydrogen bonds, when both water molecules are located within the hydration shell of the SNase, decreases with increasing temperature but, interestingly, slightly increases or remains essentially constant upon pressurization up to 5 kbar. The average residence time of water in the 4.5-Å hydration shell of SNase, τRes, decreases with increasing temperature, from 2.67 ps at T ) 300 K to 2.07 ps at 400 K, but increases with increasing pressure, from 2.67 ps at ambient pressure to 3.49 ps at p ) 5 kbar for T ) 300 K. As can also be inferred from Table 3, the protein-water hydration bond lifetimes are a factor of about two larger than the bulk water-water τHB values. Similar to the temperature and pressure dependence of τHB of bulk water, the proteinwater average H-bond lifetimes decrease with increasing temperature and decrease less markedly by pressure. In Table 5, we present data on the protein-water hydrogen bond network relaxation time, τR,HBN, and the relaxation time of the hydration shell, τR,HS, of SNase at different p and T conditions. τR,HBN is 35.4 ps at T ) 300 K and decreases to 8.7 ps at 400 K. The H-bond network relaxation time τR,HBN thus

1000 J. Phys. Chem. B, Vol. 112, No. 3, 2008 decreases drastically with increasing temperature, at a rate of -0.267 ps/°C, but increases significantly with increasing pressure (ca. 2.68 ps/kbar), indicating a decreasing stability of the hydrogen-bond network at the protein interface with increasing temperature and decreasing pressure. A similar scenario holds for the relaxation time of the hydration shell; the τR,HS values are a factor of about two larger, however. 3.3. Structural Properties of the Solvation Shell of SNaseCosolvent Solutions. Table 4 exhibits structural properties of the water within the hydration shell (of 4.5 Å thickness) of SNase in two cosolvent mixtures (urea, glycerol), namely, the average coordination number of the water (NW) and cosolvent (NC) molecules in the first coordination shell of the water molecules as well as the average number of the water-water (NWHB) and water-cosolvent (NCHB) hydrogen bonds, respectively. As expected, upon addition of increasing amounts of the chaotropic agent urea, the average coordination number of the water molecules in the first coordination shell decreases drastically, and the number of cosolvent molecules increases concomitantly. For example, NW decreases from 3.91 in the pure water hydration shell to 2.95 for 18.4 mol % urea (UR4), and NWHB from 2.61 to 2.07, respectively. With a decreasing number of water-water hydrogen bonds, the number of watercosolvent hydrogen bonds increases concomitantly. Interestingly, addition of the osmolyte glycerol has a similar effect, i.e., the glycerol molecules do not seem to be excluded largely from the hydration shell as one would expect from a simple preferential hydration model as often discussed for such type of osmolyte. However, their preferential binding coefficients ΓXP ) (∂mX/∂mP)µX32 are different. ΓXP yields information regarding the interaction between a protein and the components of the mixed solvent and the excess number of cosolvent molecules in the domain of the protein. In other words, ΓXP diminishes (ΓXP > 0) or increases (ΓXP < 0) the respective concentration in the bulk solvent upon adding of the protein to the solution, i.e., ΓXP > 0 for preferential binding, and ΓXP < 0 for preferential exclusion of the cosolvent (mX,P is the molality of cosolvent X and protein P, respectively). Clearly, the term “preferential exclusion of cosolvent” does not mean that there are no cosolvent molecules in the local domain; it rather indicates that the number ratio of cosolvent and water molecules at the protein interface differs from that of the bulk value. Generally, a change in the numbers of water and cosolvent molecules in the “protein phase” results from the interaction with the protein (either direct or indirect). Possible interaction mechanisms are: (i) association of cosolvent molecules with the protein, eventually in competition with water; (ii) inaccessibitity of the protein to the cosolvent molecule due to steric reasons; and (iii) solvent reorganization. The actual mechanism responsible for the protein’s stability depends on the physical and chemical nature of the cosolvent as well, i.e., on its size, charge, polarity, flexibility, H-bonding capacity, etc., but also on the charge and surface topology of the protein. As an example, for a protein solution containing glycerol or sucrose, negative values of ΓXP are found, meaning that the proteins are preferentially hydrated or that glycerol and sucrose are preferentially excluded from the local domain of the protein. If the cosolvent molecule is significantly larger than the water molecules, the cosolvent is excluded from a certain volume shell around the protein for pure geometrical reasons already, i.e., ΓXP < 0. Conversely, for cosolvents such as urea, which carries -NH2 groups and forms only weak hydrogen bonds with water, preferentially binding to the protein occurs, thus leading to a destabilization of the native state if the cosolvent concentration

Smolin and Winter

Figure 1. The orientational probability distribution P(cos θ) of the water dipole moment (µ) as a function of distance (d) from nearest protein heavy atoms. θ is the angle between the water dipole vector and the surface normal that points to the water phase (T ) 300 K, p ) 1 bar).

is high enough (typically ∼6 M). On the other hand, it may not only be the preferential binding but also the change in the water structure that favors the solvation of exposed amino acid residues. Often, the two mechanisms act in combination, particularly at high cosolvent concentrations. The ΓXP values can be determined theoretically from the partial pair correlation functions and the bulk density values.32 For example, results from MD simulations on RNase T1 yielded values of ΓXP ) 5.2 for 1.1 M urea and ΓXP ) -1.6 for 1.07 M glycerol. Similar results have been obtained for other proteins as well as using the Kirkwood-Buff theory for calculation of preferential binding parameters.34 To estimate the preferential binding coefficient, we used the method suggested by Baynes and Trout.32 ΓXP was calculated as described by Baynes and Trout,32 using a cutoff of 8 Å as the boundary between the local and bulk domain. Our analysis reveals ΓXP values of 3.8 ( 1.1, 5.7 ( 1.6, 7.3 ( 2.1, and 10.1 ( 2.6 for the UR1 (2.9 mol %), UR2 (6.6 mol %), UR3 (11.5 mol %), and UR4 (18.4 mol %) urea solutions, respectively. In the simulations with glycerol as cosolvent, we found that ΓXP ) -0.7 ( 1.0, -1.9 ( 0.9, and -2.5 ( 1.1 for the GL1 (1.3 mol %), GL2 (4.3 mol %), and GL3 (6.1 mol %) glycerol solutions. Figure 1 compares the orientational probability distribution P(cos θ) of the water dipole moment at different distances from nearest protein heavy atoms at ambient conditions. θ is the angle between the water dipole vector and the surface normal that points to the water phase. The two peaks correspond to water molecules which bind to the protein surface. The left peak at θ ) 130° (cos θ ≈ -0.64) and the right peak at about 40° (cos θ ≈ 0.77) correspond to the protein-water hydrogen bonds when atoms from the protein act as acceptor or as donor of hydrogen bonds, respectively. The distribution becomes broader at distances that correspond to the location of water near hydrophobic protein atoms (d ≈ 3.7 Å). Figure 2 shows the average orientational probability distribution of the water dipole moment within the protein’s hydration shell as a function of the shell thickness. When the thickness of the hydration shell is small (3.5 Å), two pronounced peaks of the distribution are observed. With increasing shell thickness (4.5 Å), the average orientational probability distribution becomes broader due to an increasing number of water molecules that locate near the protein’s nonpolar atoms. The average orientational probability distribution of the water dipole moment within the hydration shell of 4.5 Å near SNase at different p and T conditions are shown in Figure 3. The distribution function becomes slightly broader, and both peaks decrease with increasing temperature, indicating a temperature-

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Figure 2. The orientational probability distribution P(cos θ) of the water dipole moment as a function of the thickness of the hydration shell of SNase.

Figure 4. The orientational probability distribution P(cos θ) of the water dipole moment in the hydration shell of SNase of 4.5 Å thickness near nonpolar protein atoms, only. Upper figure: at p ) 1 bar and T ) 300, 360, and 400 K. Lower figure: T ) 300 K and p ) 1 bar, 2 kbar, and 5 kbar.

Figure 3. The orientational probability distribution P(cos θ) of the water dipole moment within the hydration shell of SNase of 4.5 Å thickness. Upper figure: p ) 1 bar and T ) 300, 360, and 400 K. Lower figure: T ) 300 K and p ) 1 bar, 2 kbar, and 5 kbar.

induced weakening of the water-protein interactions and smearing out of the orientational structure of the hydration shell. With increasing pressure, the left peak at θ ) 130° (cos θ ≈ -0.64) slightly decreases. The right peak increases slightly and shifts to θ values of about 75°, which corresponds to an average orientation of water molecules almost parallel to the protein surface. This could be due to a pressure-induced increase of the relative population of water molecules near hydrophobic atoms of the protein. Figure 4 depicts the orientation of the average dipole moment within the hydration shell of SNase near the nonpolar protein atoms as a function of temperature and pressure, respectively. The peak of the distribution function corresponds to those water molecules with almost parallel orientations close to the protein surface (θ ≈ 75°). With increasing temperature, the height of the maximum of the distribution decreases and broadens slightly, demonstrating a weakening of the hydration of the hydrophobic atoms at the protein surface. No significant changes are observed in the orientational distribution of the water molecules near the hydrophobic protein atoms upon pressurization up to 5 kbar. According to Figure 3, only the number of waters near the hydrophobic atoms of the protein increases upon pressurization. In fact, pressure increase has been shown to decrease hydro-

phobic interactions leading to water penetration into hydrophobic pockets.62-65 The density profiles of water, urea, and glycerol (normalized to the bulk water and bulk cosolvent densities, respectively) were computed for different cosolvent concentrations and are shown in Figures 5 and 6. For computing the density profiles, each cosolvent molecule was treated as a point at its center of mass. As can be seen from Figure 5, the presence of the cosolvents urea and glycerol significantly changes the shape of the water density profile in the region of the second peak, which corresponds to water molecules which are largely located near hydrophobic atoms of the SNase. Whereas the first peak in the water density profile remains essential unchanged upon addition of the cosolvents, the height of the second peak strongly decreases with increasing cosolvent concentration, and water is markedly depleted in the distance range from about 3 to 6 or 7 Å. This effect is more pronounced in the case of glycerol for comparable concentrations. The perturbation of the water density profile compared to the bulk behavior extends to about 6 Å for bulk water and the water/urea mixtures. In the case of the glycerol solution, probably due to the larger size of the glycerol molecule and/or an increase in the perturbed solvation shell, such perturbation is observed even up to 7 Å. Beyond the regions of total exclusion from the protein surface (d < 0.6 Å for water, d < 1 Å for glycerol and urea), well pronounced first-coordination shells of the cosolvents are seen (Figure 6). The peaks of the first-coordination shells of the cosolvents appear at about 3.8 Å for urea and ∼4.5 Å for the larger glycerol molecules, respectively. The sizes of the water, urea, and glycerol molecule are about 3, 4.5, and 6.5 Å, respectively. With increasing cosolvent concentration, the peaks become broader and shift slightly to larger distances, d. Clearly, the urea molecules are more narrowly localized at the protein

1002 J. Phys. Chem. B, Vol. 112, No. 3, 2008

Figure 5. MD results of the local density profile of water, F(d), near the surface of SNase in water and urea (upper panel) and glycerol (lower panel) solutions as a function of distance (d) from nearest protein heavy atoms, normalized by the density of water in the bulk region, Fbulk.

Figure 6. Local density profile, F(d), of urea and glycerol near the surface of SNase in water and urea (upper panel) and glycerol (lower panel) solutions as a function of the distance (d) from nearest protein heavy atoms, normalized by the density of the cosolvent in the bulk region.

interface. Significantly smaller and broader second-coordination shell peaks are also visible for the urea solvating SNase. At

Smolin and Winter distances larger than 7 Å from the protein, the solvation shells of the two cosolvents cannot be discerned anymore, and the local densities of water, urea, and glycerol reach their bulk values (F/Fbulk ) 1). These results are in good agreement with previous molecular dynamics simulations of RNase A in urea and glycerol solutions.32 Because of local packing effects, the peaks of the first-coordination shells are high even at low cosolvent concentrations. Still, the concentration of glycerol in the protein’s vicinity is lower as in the bulk as reflected in the ΓXP < 0 values. Conversely, ΓXP > 0 for the cosolvent urea. These findings are in good agreement with results from other groups.32,66-70 As discussed above, such different behavior is largely caused by differences in the strength of interaction of the protein with the cosolvent compared to the strength of interactions of the protein and cosolvent with water, respectively, but also due to simple geometrical considerations. To understand the structural properties of the cosolvents near the SNase surface in more detail, the local density profiles of the urea and glycerol atoms near the protein surface were determined for one particular cosolvent concentration. Both the total density profiles of the cosolvent atoms as well as the density profiles of various cosolvent atoms near the polar and nonpolar atoms of the SNase are shown. Figure 7 shows such profiles for the UR1 (left panels) and GL1 (right panels) solutions, respectively. The total density profiles of the cosolvent atoms are shown in Figure 7a. For further evaluation of the urea and glycerol density profiles around different types of protein atoms, the density profiles around polar and nonpolar atoms of SNase were calculated (parts b and c of Figure 7, respectively). The left-hand panel of Figure 7a shows pronounced peaks of the hydrogen and oxygen atoms of urea near the protein surface. Those peaks correspond to the urea molecules that form H-bonds with the polar atoms of the SNase as revealed by comparison with Figure 7b (left-hand panel). A similar result is observed for the glycerol solution (parts a and b of Figure 7, right-hand panels). Besides, orientations of the urea and glycerol molecules near the nonpolar atoms of SNase are found to be almost parallel to the surface of the SNase (data not shown). Variations in the local density profiles with distance for each cosolvent appear up to about 7 Å, corresponding to about two hydration shells of water (the thickness of one water shell is about 3 Å) around the protein. Glycerol is not excluded from close contact with the protein, though the average distance, due to the larger size, is displaced by about 0.5-1 Å to larger d values. These results are in agreement with previous molecular dynamics simulations of proteins in glycerol solutions.32 Figure 8 shows the average orientational probability distribution of the water dipole moment within the protein hydration shell for different cosolvent solutions. With increasing urea concentration (Figure 8, upper panel), the average orientational probability distribution function increases near the hydrophilic protein atoms and decreases near hydrophobic atoms, probably due to exchange of loosely bound interfacial water molecules by urea. On the contrary, the average orientational probability distribution of the water dipole moment is rather insensitive to the addition of low concentrations of glycerol (Figure 8, lower panel). 3.4. Dynamical Properties of the Solvation Shell of SNaseCosolvent Solutions. Water hydrogen-bond lifetimes have also been determined to gain insight into the dynamical properties of interfacial water in the first, or successive, hydration shell of protein atoms exposed to the cosolvent solutions.

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Figure 7. Local density profile, F(d), of urea and glycerol atoms (C, H, N, O) near the surface of SNase in UR1 (left panel) and GL1 (right panel) solutions as a function of distance d from nearest protein heavy atoms. (a) The total density profiles of the cosolvent atoms. (b) The density profile of cosolvent atoms near the polar and (c) near the nonpolar atoms of the SNase.

Table 6 depicts the information about the fast water molecules’ dynamics in the hydration shell of SNase for different cosolvent solutions. With increasing cosolvent concentration, the average H-bond lifetime τHB generally increases slightly. Compared to the urea solution at a similar concentration (UR2, 6.6 mol % urea), the τHB values in the glycerol solutions (GL3, 6.1 mol % glycerol) are slightly larger. Also the average lifetimes of H-bonds to the protein surface increases with increasing cosolvent concentration, again more pronounced for the glycerol solution (∼6% for 6.1 mol % glycerol (GL3)). The effect of glycerol on the increase of the H-bond lifetime is largest for the water-protein surface interaction, i.e., the addition of glycerol leads to a stronger protein-water coupling. The mean residence times of the water molecules in the hydration shell increase slightly for both cosolvent solutions, only (∼2%). In Table 7, the protein-water hydrogen bond network relaxation time, τR,HBN, and the relaxation time of the hydration shell, τR,HS, of SNase are given for the various cosolvent concentrations. Addition of both cosolvents leads to a marked increase of the H-bond network relaxation time τR,HBN at the protein interface. The increase is much more pronounced for glycerol than for urea: τR,HBN ) 35.4 ps in H2O, τR,HBN ) 47.8 ps in 6.6 mol % urea, and τR,HBN ) 82.4 ps in the 6.1 mol % glycerol solution. The τR,HS values are affected in a similar way. Hence, the increase of both cosolvents also leads to a marked increase of the H-bond network stability at the protein surface,

which is significantly more pronounced for the kosmotropic agent glycerol. 4. Discussion and Summary The hydration water around proteins exhibits structural and dynamical properties markedly deviating from those of the bulk, and the peculiar features of the hydration water in the proximity of the protein surface play a significant role in regulating the protein dynamics and hence functionality. Furthermore, they are important for understanding the mechanisms of protein unfolding and denaturation by temperature and pressure and the destabilisation/stabilization by cosolvents. In this work, we performed MD simulations on a monomeric protein, SNase, to study the various effects of temperature, pressure, chaotropic (urea), and kosmotropic (glycerol) cosolvents on the solvation properties of the protein. The results also help understanding various thermodynamic properties measured for the protein, which are known to be largely determined by their solvational properties.45,60,65,71 We first analyzed the structural properties of the hydration water of SNase. Variations in the pair correlation function with distance for water and each cosolvent are evident up to about 6-7 Å, or two solvation layers, away from the protein. The average number of hydrogen bonds per water molecule, NHB, within the hydration shell of 4.5 Å is smaller compared to bulk water and decreases with increasing temperature, from 3.00 at

1004 J. Phys. Chem. B, Vol. 112, No. 3, 2008

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Figure 8. The orientational probability distribution P(cos θ) of the water dipole moment within the hydration shell of SNase of 4.5 Å thickness. Upper panel: p ) 1 bar and T ) 300 in urea solutions. Lower panel: T ) 300 K and p ) 1 bar in glycerol solutions.

TABLE 6: Average Lifetime, τHB, of the Hydrogen Bonds of Water-Protein and Water-Water in the Hydration Shell, of Water-Water in the Bulk, and of Hydration Water-Bulk Water in Different Solvent Environments, and Residence Time, τRes, of Water Molecules in the Hydration Shell of 4.5 Å Thickness of SNase in Water and Water-Urea/Glycerol Solutions (1 bar, 300 K) τHB/ps water-water bulk-bulk shell-shell shell-bulk protein-water τRes/ps Water UR1 UR2 UR3 GL1 GL2 GL3

0.88 0.89 0.90 0.91 0.88 0.93 0.95

0.72 0.73 0.72 0.74 0.72 0.73 0.76

0.47 0.47 0.48 0.49 0.47 0.49 0.50

1.89 1.90 1.94 1.95 1.97 2.02 2.01

2.67 2.61 2.69 2.76 2.52 2.70 2.74

TABLE 7: Protein-Water Hydrogen Bond Network Relaxation Time, τR,HBN, and the Relaxation Time of The Hydration Shell, τR,HS, of SNase in Different Cosolvent Environments (1 bar, 300 K) water UR1 UR2 UR3 GL1 GL2 GL3

τR,HBN/ps

τR,HS/ps

35.4 41.3 47.8 60.0 42.0 59.4 82.4

66.8 70.2 76.6 100.0 80.0 87.6 101.8

T ) 300 K to 2.56 at T ) 400 K. Conversely, NHB increases with increasing pressure (NHB ) 3.30 at 5 kbar and 300 K). A similar trend is found for the average coordination number of water within the first hydration shell. It decreases with temperature (12% from 300 to 400 K) and increases with pressure up to 5 kbar at 300 K by ∼21%. The corresponding NW-values of bulk water exhibit similar temperature and pressure depend-

ences, have higher absolute values, however. The orientational distribution function of the water with respect to the normal of the protein interface was also calculated for the different temperature and pressure conditions. With increasing pressure, an increased orientation of water molecules almost parallel to the protein surface is found, which is probably due to a pressureinduced increase of the relative population of water molecules near hydrophobic atoms of the protein. Also for two cosolvent mixtures, urea and glycerol, the average coordination numbers of the water (NW) and cosolvent (NC) molecules in the first coordination shell of the water molecules as well as the average number of the water-water (NWHB) and water-cosolvent (NCHB) hydrogen bonds were determined. As expected, upon addition of increasing amounts of the chaotropic agent urea, NW in the first coordination shell decreases drastically, and the number of cosolvent molecules increases concomitantly. For example, NW decreases from 3.91 in the pure water hydration shell to 2.95 for 18.4 mol % urea and NWHB from 2.61 to 2.07, respectively. Interestingly, addition of the osmolyte glycerol at a similar concentration has a similar effect, i.e., the glycerol molecules do not seem to be excluded largely from the hydration shell as one would expect from a simple preferential hydration model as often discussed for osmolytes. However, the preferential binding coefficients ΓXP are of opposite signs. The preferential binding coefficient of glycerol is negative, whereas that of urea is positive. Hence, though glycerol is not totally excluded from close contact with the protein, it is less likely than urea to be found in such a position. Whereas the first peak in the water density profile remains essentially unchanged upon addition of the cosolvents, the height of the second peak strongly decreases with increasing cosolvent concentration, and water is markedly depleted in the distance range from about 3 to 6 or 7 Å. Clearly, the urea molecules are more narrowly localized at the protein interface. The perturbation of the water density profile compared to the bulk behavior extends to about 6 Å for bulk water and the water/urea mixtures. In the case of the glycerol solution, probably due to the larger size of the glycerol molecule and/or an increase in the perturbed solvation shell, such perturbation is observed even up to 7 Å. This might lead to the observed increase of the apparent expansion coefficient R of the protein, which is largely determined by its solvational properties, as observed in recent pressure-perturbation calorimetric studies.61,71 Further, we determined the water dynamics at the protein interface and distinguished between a fast formation and break up of hydrogen bonds due to water rotation/libration and a slower relaxation of the protein-water hydrogen bond network due to diffusion of water molecules between sites on the protein surface. The average lifetime of water-water hydrogen bonds, τHB, in the bulk water region decreases with increasing temperature and also, but less markedly, by pressure. When water molecules are located within the hydration shell of the SNase, τHB also decreases with increasing temperature but remains essentially constant upon pressurization up to 5 kbar. The average residence time of water in the 4.5-Å hydration shell of SNase, τRes, decreases with increasing temperature, but increases with increasing pressure (from 2.67 ps at ambient pressure to 3.49 ps at p ) 5 kbar for T ) 300 K). The protein-water hydration bond lifetimes are a factor of about two larger than the bulk water-water τHB values. Similar to the temperature and pressure dependence of τHB of bulk water, the proteinwater average H-bond lifetimes decrease with increasing temperature and, less markedly, by pressure.

Properties of the Hydration Shell of SNase According to Tarek and Tobias,31 the slow relaxation of the protein-water hydrogen-bond network is responsible for most of the protein structural relaxation above the dynamic transition temperature (occurring at ∼200 K). The protein-water hydrogen bonds are generally stronger and hence have longer lifetimes. These biologically important coupled water-protein fluctuations occur on tens of picoseconds, and the addition of cosolvents leads to a restructuring of the protein-water hydrogen bond network of the protein. The protein-water hydrogen bond network relaxation time, τR,HBN, and the relaxation time of the hydration shell, τR,HS, of SNase have also been determined at the different p and T conditions. τR,HBN is 35.4 ps at T ) 300 K and decreases to 8.7 ps at 400 K. (Please note that during the simulation runs at these temperatures and pressures, SNase did not unfold. In fact, it was shown in previous work that SNase unfolds at 500 K within 12 ns in molecular dynamics runs, only.60) Conversely, τR,HBN significantly increases with increasing pressure, and a similar scenario holds for the relaxation time of the hydration shell, with τR,HS values being a factor of about two larger. With increasing cosolvent concentration of both agents, the average H-bond lifetime τHB in the hydration shell and to the protein surface increase. The effect is more pronounced for the glycerol solution at comparable concentrations, i.e., the addition of glycerol leads to the strongest protein-water coupling, which seems to be reflected in measured thermodynamic properties of the protein, such as the increased R values of proteins in osmolytes such as glycerol, sorbitol, and sucrose.61,71-73 Addition of both cosolvents leads to a marked increase of the H-bond network relaxation time τR,HBN at the protein interface as well. Again, the increase is much more pronounced for glycerol than for urea (for example, τR,HBN is 35.4 ps in H2O, 47.8 ps in 6.6 mol % urea, and 82.4 ps in 6.1 mol % glycerol solutions). The τR,HS values are affected in a similar way. Hence, addition of glycerol leads to the strongest increase of the H-bond network stability. Acknowledgment. Financial support from the DFG (FOR 436), the country NRW, and the European Union (Europa¨ischer Fonds fu¨r regionale Entwicklung) is gratefully acknowledged. References and Notes (1) Pal, S. K.; Zewail, A. H. Chem. ReV. 2004, 104, 2099. (2) Gregory, R. B., Ed. Protein-SolVent Interaction; Marcel Dekker: New York, 1995. (3) Bagchi, B. Chem. ReV. 2005, 105, 3197. (4) Rossky, P. J.; Karplus, M. J. Am. Chem. Soc. 1979, 101, 1913. (5) Bandyopadhyay, S.; Chakraborty, S.; Balasubramanian, S.; Pal, S.; Bagchi, B. J. Phys. Chem. B 2004, 108, 12608. (6) Grudzielanek, S.; Jansen, R.; Winter, R. J. Mol. Biol. 2005, 351, 879. (7) Javid, N.; Vogtt, K.; Krywka, C.; Tolan, M.; Winter, R. Phys. ReV. Lett. 2007, 99, 028101. (8) Javid, N.; Vogtt, K.; Krywka, C.; Tolan, M.; Winter, R. Chem. Phys. Chem. 2007, 8, 679. (9) Dzwolak, W.; Grudzielanek, S.; Smirnovas, V.; Ravindra, R.; Nicolini, C.; Jansen, R.; Loksztejn, A.; Porowski, S.; Winter, R. Biochemistry 2005, 44, 8948. (10) Qiu, W.; Kao, Y.-T.; Zhang, L.; Yang, Y.; Wang, L.; Stites, W. E.; Zhong, D.; Zewail, A. H. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 13979. (11) Cheng, Y. K.; Rossky, P. J. Nature 1998, 392, 696. (12) Li, T.; Hassanali, A. A.; Kao, Y-T.; Zhong, D.; Singer, S. J. J. Am. Chem. Soc. 2007, 129, 3376. (13) Sahu, K.; Mondal, S. K.; Ghosh, S.; Roy, D.; Sen, P.; Bhattacharyya, K. J. Phys. Chem. B 2006, 110, 1056. (14) Nilsson, L.; Halle, B. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 13867. (15) Russo, D.; Murarka, R. K.; Copley, J. R. D.; Head-Gordon, T. J. Phys. Chem. B 2005, 109, 12966.

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