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J. Phys. Chem. B 2008, 112, 3522-3528
Hydration-Dependent Protein Dynamics Revealed by Molecular Dynamics Simulation of Crystalline Staphylococcal Nuclease Yasumasa Joti,†,‡ Hiroshi Nakagawa,§ Mikio Kataoka,§,| and Akio Kitao*,†,‡ Institute of Molecular and Cellular Biosciences, UniVersity of Tokyo, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan, Japan Science and Technology Agency, Core Research for EVolutional Science and Technology, 1-1-1 Yayoi, Bunkyo-ku, Tokyo 113-0032, Japan, Neutron Biophysics Group, Neutron Biology Research Center, Quantum Beam Science Directorate, Japan Atomic Energy Agency, Tokai, Ibaraki 319-1195, Japan, and Graduate School of Materials Science, Nara Institute of Science and Technology, 8916-5 Takayama, Ikoma, Nara 630-0192, Japan ReceiVed: October 16, 2007; In Final Form: December 28, 2007
Molecular dynamics simulations of crystalline Staphylococcal nuclease in full and minimal hydration states were performed to study hydration effects on protein dynamics at temperatures ranging from 100 to 300 K. In a full hydration state (hydration ratio in weight, h ) 0.49), gaps are fully filled with water molecules, whereas only crystal waters are included in a minimal hydration state (h ) 0.09). The inflection of the atomic mean-square fluctuation of protein as a function of temperature, known as the glass-like transition, is observed at ∼220 K in both cases, which is more significant in the full hydration state. By examining the temperature dependence of residual fluctuation, we found that the increase of fluctuations in the loop and terminal regions, which are exposed to water, is much greater than that in other regions in the full hydration state, but the mobilities of the corresponding regions are relatively restricted in the minimal hydration state by intermolecular contact. The atomic mean-square fluctuation of water molecules in the full hydration state at 300 K is 1 order of magnitude greater than that in the minimal hydration state. Above the transition temperature, most water molecules in the full hydration state behave like bulk water and act as a lubricant for protein dynamics. In contrast, water molecules in the minimal hydration state tend to form more hydrogen bonds with the protein, restricting the fluctuation of these water molecules to the level of the protein. Thus, intermolecular interaction and solvent mobility are important to understand the glass-like transition in proteins.
1. Introduction Proteins are molecular machines that require flexibility for their function. Perturbations on proteins (e.g., ligand binding) lead to structural changes. Experiments have shown that fluctuations in equilibrium correlate with the conformational change upon perturbation.1 Thus, characterization of protein fluctuations in equilibrium states should provide valuable information on protein function. By measuring the response of a protein system to temperature change, we can extract useful information to understand characteristics of the system. After the pioneering work by Frauenfelder et al.,2 temperature dependence of the atomic meansquare fluctuation 〈∆r2〉 has been investigated using a variety of experimental techniques, such as X-ray crystallography,2-4 Mo¨ssbauer spectroscopy,5,6 and incoherent neutron scattering.7-12 Similar to the glass transition in glassy materials, a “dynamical” or “glass-like” transition is observed as an increase in atomic fluctuations at temperatures greater than ∼200 K. The physical mechanism of the glass-like transition in proteins is understood as follows. Below the transition temperature, a protein molecule is trapped in one conformational substate and undergoes nearly harmonic motions within a local potential energy minimum. * Corresponding author. Tel.: +81-3-5841-2297. Fax: +81-3-58412297. E-mail:
[email protected]. † University of Tokyo. ‡ Japan Science and Technology Agency. § Japan Atomic Energy Agency. | Nara Institute of Science and Technology.
Above the transition temperature, anharmonic motions are enhanced, due to the onset of jumping among different substrates, which confers a diffusive character to the conformational dynamics. Such diffusive anharmonic motions are crucial to the function of bacteriorhodopsin in a purple membrane8 and crystalline ribonuclease A.3 Collective motions are often inferred to be important for protein function,13 and a small number of anharmonic collective motions dominate the total fluctuations.14,15 Protein fluctuations also depend on solvent properties. The glass-like transition shifts to higher temperatures when solvent water molecules are mixed with glycerol and a portion of the water molecules gradually exchange with glycerol.7 Moreover, the glass-like transition in proteins is strongly suppressed in dry protein,8 indicating that solvent molecules are involved with the activation of diffusive anharmonic motions. Recent neutron scattering experiments have shown that the glass-like transition in hen egg-white lysozymes is only observed at a hydration level h greater than 0.2 g D2O/g protein.10 Our neutron scattering experiment of Staphylococcal nuclease (SNase) also showed the hydration-dependent transition of 〈∆r2〉 at ∼240 K.12 The hydrated SNase did not contain any cosolvent in this experiment. Bulk water would be frozen below 273 K in the absence of cosolvent. However, the behavior of water confined by biological macromolecules at cryogenic temperature was suggested to be different from that of bulk water.16 To capture the physical nature of the glass-like transition in proteins, the temperature dependence of solvent properties should be investigated as along
10.1021/jp710039p CCC: $40.75 © 2008 American Chemical Society Published on Web 02/23/2008
MD Simulation of Crystalline Staphylococcal Nuclease
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with that of protein dynamics because protein and solvent dynamics are significantly coupled to each other. Molecular dynamics (MD) simulate the detailed dynamic features of proteins as well as solvents from femtosecond to microsecond timescales and have been used for studying the temperature dependence of protein dynamics.10,17-22 Application of MD to myoglobin molecules partially solvated by water molecules at hydration level h ) 0.39 g H2O/g protein shows a glass-like transition similar to experimental data.17 The glasslike transition temperature of isolated bovine pancreatic trypsin inhibitor (BPTI) protein is less (∼120 K) than that produced by experiments.19 Solvent mobility, or the translational dynamics of water, is the dominant factor in determining protein fluctuations.18,21,22 Tarek et al. claimed that simulation of the cluster system consisting of a protein surrounded by a finite water shell with free boundaries is not appropriate for the study of proteinwater dynamics.23,24 They concluded that simulation results with the crystal and pseudo-powder models are comparable with inelastic neutron scattering spectra. Powder samples are commonly used in neutron experiments.7-12 Molecular interaction between proteins should be considered as well as that between protein and solvent to interpret the results of neutron scattering experiments. The difference in temperature dependence of 〈∆r2〉 between full and minimal hydration states can be understood from this point of view. For this study, we performed MD simulations of crystalline SNase in the minimal hydration state (MHS: h ) 0.09) as well as in the full hydration state (FHS: h ) 0.49) at six temperatures ranging from 100 to 300 K. MHS contained only crystal water molecules and counterions as a solvent, which mimics a “dry” state realized in experiments, assuming these water molecules adhere to the protein even after lyophilization. The system in FHS is designed to mimic fully solvated “wet” protein in microcrystals, by filling the gaps in the crystal with water and counterions. We show our simulations can reproduce qualitatively the temperature dependence of the atomic mean-square fluctuation of the experimental results. This is followed by a discussion of the difference in protein dynamics between FHS and MHS, focusing on protein-protein and protein-water interactions. Finally, we show the difference in the dynamic properties of water molecules between FHS and MHS. 2. Methods Elastic Incoherent Structure Factor (EISF) and MeanSquare Fluctuation. The quantity of interest in the elastic incoherent neutron scattering experiment is the elastic incoherent structure factor (EISF), S(Q,0), where Q is the momentum transfer. Theoretically, the EISF is given as25
S(Q,0) )
2 |〈e-iQ‚∆r 〉|2 ∑a binc,a a
(1)
where binc,a is the incoherent atomic scattering length of the ath atom and ∆ra is the displacement of the ath atom from its average position. The angle bracket indicates an ensemble average. Using the cumulant expansion and taking spherical average on the sphere |Q| ) Q, eq 1 can be rewritten as
S(Q,0) )
2 e-(1/3)〈∆r ∑a binc,a
2〉Q2+O(Q4)
a
(2)
From eq 2, the natural logarithm of S(Q,0) at small Q region can be expanded as
ln S(Q,0) ) -
1
2 〈∆ra2〉 ∑a binc,a
3
∑a
Q2 + O(Q4)
(3)
2 binc,a
Thus, atomic mean-square fluctuation, 〈∆r2〉, can be estimated from the slope of the regression line of ln S(Q,0) as a function of Q2 by neutron scattering experiments. The estimated 〈∆r2〉 is the weighted-average of 〈∆ra2〉 using atomic scattering length as
〈∆r2〉 )
2 〈∆ r2a) ∑a binc,a
∑a
(4) 2 binc,a
The square of the proton atomic scattering length is 635.9 fm2, which is much larger than that of deuterium (16.3 fm2). If deuterated water is employed as a solvent as in typical neutron scattering experiments of proteins, the protons in protein are the main contributors to 〈∆r2〉. In addition, the frequency resolution function of the instrument affects the estimated 〈∆r2〉 in the experiments.26,27 Here, we present idealized results without adopting the frequency resolution function to investigate the physical nature of the solvent effects. MD Simulations. Typically a powder sample is employed to measure S(Q,0) of protein. Here, we assumed a powder state as an ensemble of microcrystals and performed a molecular dynamics simulation of crystalline SNase in water using the program AMBER9 PMEMD.28 The minimal and full hydration systems were prepared as follows. The crystal structure of SNase (PDB code: 1STN) was used as the initial structure of the simulation. The simulated system was constructed to mimic the crystal unit cell, having a space group symmetry of P41. Missing residues 1-5 and 142-149 in 1STN were modeled on the basis of the NMR structures of SNase (PDB code: 1JOR). Both the minimal and the full hydration systems contained four protein models in the simulated box. To construct the former, crystal water molecules were placed in the original positions in PDB as D2O. This system consists of 4 protein molecules (596 residues, 9580 atoms), 332 D2O molecules, and 32 chloride ions. The full hydration system was created by filling out the empty space of the initial coordinates of the minimal hydration system with additional 1500 D2O molecules. Exchangeable protons in the two systems were replaced by deuterium as expected in ordinary neutron scattering experiments. The hydration levels of the minimal and full hydration systems, h, were 0.09 and 0.49 g D2O/g protein, respectively. The periodic boundary condition was imposed, and the particle mesh Ewald method29 was used. The real space Ewald sum was smoothly switched to 0 at 10 Å. The AMBER ff99 force field30 and TIP3P water model31 were employed. The TIP3P model has been widely used to investigate the dynamical properties of solvated proteins at cryogenic temperatures and to obtain the corresponding neutron scattering data.10,17-22 The molecular weight of hydrogen atoms in water molecules was modified to 2.014 to model deuterated water. The system was weakly coupled to a heat bath using the method by Berendsen et al.32 with a relaxation time of 1.0 ps to maintain a constant temperature. This method also was used to maintain a pressure constant at 1 bar with a relaxation time of 1.0 ps. Hydrogen atoms were constrained using SHAKE,33 and MD was con-
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Figure 1. Temperature dependence of 〈∆r2〉 averaged over all protein atoms calculated at six temperatures ranging from 100 to 300 K: the results in FHS (O) and MHS (4).
Figure 3. (a,b) Inter- (upper triangle) and intra- (lower triangle) molecular contact regions of SNase, defined by the condition CR-CR distance
