Spatio – Temporal Features of Protein Specific Motions. The Influence of Hydration

The angular dependencies of inelastic intensities of Rayleigh scatteringof Moessbauer radiation were measured for lysozyme and myoglobin (fordifferent degrees of hydration: from h = 0.05 till h = 0.7). The treating ofthe data at h > 0.05 approves the existence of segmental motions(-helices for myoglobin, -helices and -sheets forlysozyme) as well as of individual motions. Further hydration increase themean-square displacements for both types of intraglobular motions for theseproteins, while the motions of the globule as a whole remain nearlythe same as for h = 0.05. Results of the study of the radial distributionfunction deduced by Fourier – transform from the diffuse x-raymeasurements together with RSMR data allow to conclude that the waterduring hydration of proteins competes with the intramolecular hydrogenbonds, loosens the protein and increases the internal dynamics. At the sametime water arranges the ordering of macromolecule from `glassy' state ath 0.02 to the native state at h = 0.4–0.7. Differentarchitecture of proteins leads to the different structural dynamics as in thecase of lysozyme and myoglobin.     

Study of the dynamics of human serum albumin by coherent Rayleigh dispersion of Mossbauer radiation]

The measurements of angle dependencies of total and elastic Rayleigh scattering of Mossbauer radiation intensities have been performed for human serum albumin (HSA) with hydration degrees h = 0.13 and h = 0.4. The extended model was developed for calculating the inelastic intensity of Rayleigh scattering. Original data for HSA and published data on met-Mb were fitted within the frame of this model. The best agreement with experiment was obtained when two types of intraglobular motions were taken into account: individual motions of small side-chain groups and cooperative (mechanical) motions of segments (most probable alpha-helices). Long-range correlated motions are essential at low hydration degree. The possibilities of application of the coherent version of RSMS technique are described.     

A study of protein structure changes during hydration by diffuse X-ray scattering. I. The intensity and the shape of "10-angstrom" maximum

The angle dependencies of diffuse x-ray scattering intensities were studied in a wide range of angles from 3 to 80 degrees for water-soluble and membrane proteins with a different structural organization: alpha-helical protein myoglobin, alpha-helical protein serum albumen, alpha + beta protein lysozyme, and transmembrane proteins of photosynthetic reaction centers (RC) from purple bacteria Rhodobacter sphaeroides, and Blastochlorii (Rhodopseudomonas) viridis containing cytocrome c, situated out side the membrane, and for H and L+M subunits of membrane protein of reaction center from Rb. sphaeroides for various hydration degrees. The hydration/dehydration process was studied for water-soluble proteins (within hydration range from h = 0.05 to h = 1). The hydration/dehydration process appears to be reversible. All water-soluble proteins show a 10 angstroms peak, and proteins of reaction center do not show this peak. A quantitative comparable study of the behaviour for of the 10 angstroms peak different proteins the degree of lysozyme hydration increases from h = 0.05 to h = 0.45, the protein structure slightly changes (most probably the motifoffolding), the structure of myoglobin in solution is slightly different from the structure in crystal. By taking into account the changes in the shape and intensity of the 10 angstroms peak only, it is impossible to make the conclusion about structural changes in other proteins studied. A correlation between the structural changes observed and dynamic and functional properties of proteins is discussed.     

Water-coupled low-frequency modes of myoglobin and lysozyme observed by inelastic neutron scattering.

Conformational changes of proteins often involve the relative motion of rigid structural domains. Normal mode analysis and molecular dynamics simulations of small globular proteins predict delocalized vibrations with frequencies below 20 cm(-1), which may be overdamped in solution due to solvent friction. In search of these modes, we have studied deuterium-exchanged myoglobin and lysozyme using inelastic neutron scattering in the low-frequency range at full and low hydration to modify the degree of damping. At room temperature, the hydrated samples exhibit a more pronounced quasielastic spectrum due to diffusive motions than the dehydrated samples. The analysis of the corresponding lineshapes suggests that water modifies mainly the amplitude, but not the characteristic time of fast protein motions. At low temperatures, in contrast, the dehydrated samples exhibit larger motional amplitudes than the hydrated ones. The excess scattering, culminating at 16 cm(-1), is suggested to reflect water-coupled librations of polar side chains that are depressed in the hydrated system by strong intermolecular hydrogen bonding. Both myoglobin and lysozyme exhibit ultra-low-frequency modes below 10 cm(-1) in the dry state, possibly related to the breathing modes predicted by harmonic analysis.     

Influence of hydration on the dynamics of lysozyme

Quasielastic neutron and light-scattering techniques along with molecular dynamics simulations were employed to study the influence of hydration on the internal dynamics of lysozyme. We identified three major relaxation processes that contribute to the observed dynamics in the picosecond to nanosecond time range: 1), fluctuations of methyl groups; 2), fast picosecond relaxation; and 3), a slow relaxation process. A low-temperature onset of anharmonicity at T approximately 100 K is ascribed to methyl-group dynamics that is not sensitive to hydration level. The increase of hydration level seems to first increase the fast relaxation process and then activate the slow relaxation process at h approximately 0.2. The quasielastic scattering intensity associated with the slow process increases sharply with an increase of hydration to above h approximately 0.2. Activation of the slow process is responsible for the dynamical transition at T approximately 200 K. The dependence of the slow process on hydration correlates with the hydration dependence of the enzymatic activity of lysozyme, whereas the dependence of the fast process seems to correlate with the hydration dependence of hydrogen exchange of lysozyme.     

A molecular dynamics analysis of protein structural elements

The relation between protein secondary structure and internal motions was examined by using molecular dynamics to calculate positional fluctuations of individual helix, beta-sheet, and loop structural elements in free and substrate-bound hen egg-white lysozyme. The time development of the fluctuations revealed a general correspondence between structure and dynamics; the fluctuations of the helices and beta-sheets converged within the 101 psec period of the simulation and were lower than average in magnitude, while the fluctuations of the loop regions were not converged and were mostly larger than average in magnitude. Notable exceptions to this pattern occurred in the substrate-bound simulation. A loop region (residues 101-107) of the active site cleft had significantly reduced motion due to interactions with the substrate. Moreover, part of a loop and a 3(10) helix (residues of 67-88) not in contact with the substrate showed a marked increase in fluctuations. That these differences in dynamics of free and substrate-bound lysozyme did not result simply from sampling errors was established by an analysis of the variations in the fluctuations of the two halves of the 101 psec simulation of free lysozyme. Concerted transitions of four to five mainchain phi and psi angles between dihedral wells were shown to be responsible for large coordinate shifts in the loops. These transitions displaced six or fewer residues and took place either abruptly, in 1 psec or less, or with a diffusive character over 5-10 psec. Displacements of rigid secondary structures involved longer timescale motions in bound lysozyme; a 0.5 A rms change in the position of a helix occurred over the 55 psec simulation period. This helix reorientation within the protein appears to be a response to substrate binding. There was little correlation between the solvent accessible surface area and the dynamics of the different structural elements.     

Dynamics of tRNA at Different Levels of Hydration

The influence of hydration on the nanosecond timescale dynamics of tRNA is investigated using neutron scattering spectroscopy. Unlike protein dynamics, the dynamics of tRNA is not affected by methyl group rotation. This allows for a simpler analysis of the influence of hydration on the conformational motions in RNA. We find that hydration affects the dynamics of tRNA significantly more than that of lysozyme. Both the characteristic length scale and the timescale of the conformational motions in tRNA depend strongly on hydration. Even the characteristic temperature of the so-called “dynamical transition” appears to be hydration-dependent in tRNA. The amplitude of the conformational motions in fully hydrated tRNA is almost twice as large as in hydrated lysozyme. We ascribe these differences to a more open and flexible structure of hydrated RNA, and to a larger fraction and different nature of hydrophilic sites. The latter leads to a higher density of water that makes the biomolecule more flexible. All-atom molecular-dynamics simulations are used to show that the extent of hydration is greater in tRNA than in lysozyme. We propose that water acts as a “lubricant” in facilitating enhanced motion in solvated RNA molecules.     

Coupling of protein and environment fluctuations

We review the concepts of protein dynamics developed over the last 35years and extend applications of the unified model of protein dynamics to heat flow and spatial fluctuations in hydrated myoglobin (Mb) powders. Differential scanning calorimetry (DSC) and incoherent neutron scattering (INS) data on hydration Mb powders are explained by the temperature-dependence of the hydration-shell β(h) process measured by dielectric relaxation spectroscopy (DRS). The unified model explains the temperature dependence of DSC and INS data as a kinetic effect due to a fixed experimental time window and a broad distribution of hydration-shell β(h) fluctuation rates. We review the slaving of large scale protein motions to the bulk solvent α process, and the metastability of Mb molecules in glass forming bulk solvent at low temperatures. This article is part of a Special Issue entitled: "Protein Dynamics: Experimental and Computational Approaches".     

Generalized correlation for biomolecular dynamics

Correlated motions in biomolecules are often essential for their function, e.g., allosteric signal transduction or mechanical/thermodynamic energy transport. Because correlated motions in biomolecules remain difficult to access experimentally, molecular dynamics (MD) simulations are particular useful for their analysis. The established method to quantify correlations from MD simulations via calculation of the covariance matrix, however, is restricted to linear correlations and therefore misses part of the correlations in the atomic fluctuations. Herein, we propose a general statistical mechanics approach to detect and quantify any correlated motion from MD trajectories. This generalized correlation measure is contrasted with correlations obtained from covariance matrices for the B1 domain of protein G and T4 lysozyme. The new method successfully quantifies correlations and provides a valuable global overview over the functionally relevant collective motions of lysozyme. In particular, correlated motions of helix 1 together with the two main lobes of lysozyme are detected, which are not seen by the conventional covariance matrix. Overall, the established method misses more than 50% of the correlation. This failure is attributed to both, an interfering and unnecessary dependence on mutual orientations of the atomic fluctuations and, to a lesser extent, attributed to nonlinear correlations. Our generalized correlation measure overcomes these problems and, moreover, allows for an improved understanding of the conformational dynamics by separating linear and nonlinear contributions of the correlation.     

Dielectric behavior of water in biological solutions: studies on myoglobin, human low-density lipoprotein, and polyvinylpyrrolidone

The dielectric behavior of the aqueous solutions of three widely differing macromolecules has been investigated: myoglobin, polyvinylpyrrolidone (PVP), and human serum low-density lipoprotein (LDL). It was not possible to interpret unambiguously the dielectric properties of the PVP solution in terms of water structure. The best interpretation of the dielectric data on the myoglobin and LDL solutions was that, in both cases, the macromolecule attracts a layer of water of hydration one or two water molecules in width. For LDL, this corresponds to a hydration factor of only 0.05 g/g, whereas for myoglobin the figure is nearer 0.6 g/g. With myoglobin, part of the water of hydration exhibits its dispersion at frequencies of a few GHz, and the rest disperses at lower frequencies, perhaps as low as 10-12 MHz. The approximate constancy of the width of the hydration shell for two molecules as dissimilar in size as LDL and myoglobin confirms that the proportion of water existing as water of hydration in a biological solution depends critically on the size of the macromolecules as well as on their concentration.     

Influence of water clustering on the dynamics of hydration water at the surface of a lysozyme

Dynamics of hydration water at the surface of a lysozyme molecule is studied by computer simulations at various hydration levels in relation with water clustering and percolation transition. Increase of the translational mobility of water molecules at the surface of a rigid lysozyme molecule upon hydration is governed by the water-water interactions. Lysozyme dynamics strongly affect translational motions of water and this dynamic coupling is maximal at hydration levels, corresponding to the formation of a spanning water network. Anomalous diffusion of hydration water does not depend on hydration level up to monolayer coverage and reflects spatial disorder. Rotational dynamics of water molecules show stretched exponential decay at low hydrations. With increasing hydration, we observe appearance of weakly bound water molecules with bulklike rotational dynamics, whose fraction achieves 20-25% at the percolation threshold.     

Structure and internal mobility of proteins: a molecular dynamics study of hen egg white lysozyme

The structure and internal motions of the protein hen egg white lysozyme are studied by analysis of simulation and experimental data. A molecular dynamics simulation and an energy minimization of the protein in vacuum have been made and the results compared with high-resolution structures and temperature factors of hen egg white lysozyme in two different crystal forms and of the homologous protein human lysozyme. The structures obtained from molecular dynamics and energy minimization have root-mean-square deviations for backbone atoms of 2.3 Å and 1.1–1.3 Å, respectively, relative to the crystal structures; the different crystal structures have root-mean-square deviations of 0.73–0.81 Å for the backbone atoms. In comparing the backbone dihedral angles, the difference between the dynamics and the crystal structure on which it is based is the same as that between any two crystal structures. The internal fluctuations of atomic positions calculated from the molecular dynamics trajectory agree well with the temperature factors from the three structures. Simulation and crystal results both show that there are large motions for residues involved in exposed turns of the backbone chain, relatively smaller motions for residues involved in the middle of helices or β-sheet structures, and relatively small motions of residues near disulfide bridges. Also, both the simulation and crystal data show that side-chain atoms have larger fluctuations than main-chain atoms. Moreover, the regions that have large deviations among the x-ray crystal structures, which indicates flexibility, are found to have large fluctuations in the simulation.     

A model for water motion in crystals of lysozyme based on an incoherent quasielastic neutron-scattering study

This paper reports an incoherent quasielastic neutron scattering study of the single particle, diffusive motions of water molecules surrounding a globular protein, the hen egg-white lysozyme. For the first time such an analysis has been done on protein crystals. It can thus be directly related and compared with a recent structural study of the same sample. The measurement temperature ranged from 100 to 300 K, but focus was on the room temperature analysis. The very good agreement between the structural and dynamical studies suggested a model for the dynamics of water in triclinic crystals of lysozyme in the time range approximately 330 ps and at 300 K. Herein, the dynamics of all water molecules is affected by the presence of the protein, and the water molecules can be divided into two populations. The first mainly corresponds to the first hydration shell, in which water molecules reorient themselves fivefold to 10-fold slower than in bulk solvent, and diffuse by jumps from hydration site to hydration site. The long-range diffusion coefficient is five to sixfold less than for bulk solvent. The second group corresponds to water molecules further away from the surface of the protein, in a second incomplete hydration layer, confined between hydrated macromolecules. Within the time scale probed they undergo a translational diffusion with a self-diffusion coefficient reduced approximately 50-fold compared with bulk solvent. As protein crystals have a highly crowded arrangement close to the packing of macromolecules in cells, our conclusion can be discussed with respect to solvent behavior in intracellular media: as the mobility is highest next to the surface, it suggests that under some crowding conditions, a two-dimensional motion for the transport of metabolites can be dominant.     

Thermal fluctuations of DNA enclosed by glycerol–water glassy matrices: an elastic neutron scattering investigation

Through elastic neutron scattering measurements, we investigated the thermal fluctuations of DNA enclosed by glycerol–water glassy matrices, at different levels of hydration, over the wide temperature range from 20 to 300 K. For all the samples, the extracted hydrogen mean square displacements (MSD) show a purely vibrational harmonic trend at very low temperatures, and a first onset of anharmonic dynamics above ∼100 K. Such onset is consistent with the activation of DNA methyl group rotational motions. Then, at a certain temperature T _d, the MSD show a second onset of anharmonicity, which corresponds to the DNA dynamical transition. The T _d values vary as a function of the hydration degree of the environment. The crucial role of the solvent mobility to activate the DNA thermal fluctuations is proposed, together with a preferential hydration effect of the DNA phosphate groups. Finally, a comparison between the average mobility of homologous samples of DNA and the lysozyme protein is considered. Advanced neutron scattering and complementary techniques to study biological systems. Contributions from the meetings, “Neutrons in Biology”, STFC Rutherford Appleton Laboratory, Didcot, UK, 11–13 July and “Proteins At Work 2007”, Perugia, Italy, 28–30 May 2007.     

THz time scale structural rearrangements and binding modes in lysozyme-ligand interactions

Predicting the conformational changes in proteins that are relevant for substrate binding is an ongoing challenge in the aim of elucidating the functional states of proteins. The motions that are induced by protein-ligand interactions are governed by the protein global modes. Our measurements indicate that the detected changes in the global backbone motion of the enzyme upon binding reflect a shift from the large-scale collective dominant mode in the unbound state towards a functional twisting deformation that assists in closing the binding cleft. Correlated motion in lysozyme has been implicated in enzyme function in previous studies, but detailed characterization of the internal fluctuations that enable the protein to explore the ensemble of conformations that ultimately foster large-scale conformational change is yet unknown. For this reason, we use THz spectroscopy to investigate the picosecond time scale binding modes and collective structural rearrangements that take place in hen egg white lysozyme (HEWL) when bound by the inhibitor (NAG) ₃. These protein thermal motions correspond to fluctuations that have a role in both selecting and sampling from the available protein intrinsic conformations that communicate function. Hence, investigation of these fast, collective modes may provide knowledge about the mechanism leading to the preferred binding process in HEWL-(NAG) ₃. Specifically, in this work we find that the picosecond time scale hydrogen-bonding rearrangements taking place in the protein hydration shell with binding modify the packing density within the hydrophobic core on a local level. These localized, intramolecular contact variations within the protein core appear to facilitate the large cooperative movements within the interfacial region separating the α- and β- domain that mediate binding. The THz time-scale fluctuations identified in the protein-ligand system may also reveal a molecular mechanism for substrate recognition.     

Dynamics of Protein and its Hydration Water: Neutron Scattering Studies on Fully Deuterated GFP

We present a detailed analysis of the picosecond-to-nanosecond motions of green fluorescent protein (GFP) and its hydration water using neutron scattering spectroscopy and hydrogen/deuterium contrast. The analysis reveals that hydration water suppresses protein motions at lower temperatures (<∼200 K), and facilitates protein dynamics at high temperatures. Experimental data demonstrate that the hydration water is harmonic at temperatures <∼180–190 K and is not affected by the proteins’ methyl group rotations. The dynamics of the hydration water exhibits changes at ∼180–190 K that we ascribe to the glass transition in the hydrated protein. Our results confirm significant differences in the dynamics of protein and its hydration water at high temperatures: on the picosecond-to-nanosecond timescale, the hydration water exhibits diffusive dynamics, while the protein motions are localized to <∼3 Å. The diffusion of the GFP hydration water is similar to the behavior of hydration water previously observed for other proteins. Comparison with other globular proteins (e.g., lysozyme) reveals that on the timescale of 1 ns and at equivalent hydration level, GFP dynamics (mean-square displacements and quasielastic intensity) are of much smaller amplitude. Moreover, the suppression of the protein dynamics by the hydration water at low temperatures appears to be stronger in GFP than in other globular proteins. We ascribe this observation to the barrellike structure of GFP.     

Fluctuations and correlations in crystalline protein dynamics: a simulation analysis of staphylococcal nuclease

Understanding collective motions in protein crystals is likely to furnish insight into functional protein dynamics and will improve models for refinement against diffraction data. Here, four 10 ns molecular dynamics simulations of crystalline Staphylococcal nuclease are reported and analyzed in terms of fluctuations and correlations in atomic motion. The simulation-derived fluctuations strongly correlate with, but are slightly higher than, the values derived from the experimental B-factors. Approximately 70% of the atomic fluctuations are due to internal protein motion. For 65% of the protein atoms the internal fluctuations converge on the nanosecond timescale. Convergence is much slower for the elements of the interatomic displacement correlation matrix--of these, >80% converge within 1 ns for interatomic distances less, approximately <6 A, but only 10% for separations approximately =12 A. Those collective motions that converged on the nanosecond timescale involve mostly correlations within the beta-barrel or between alpha-helices of the protein. The R-factor with the experimental x-ray diffuse scattering for the crystal, which is determined by the displacement variance-covariance matrix, decreases to 8% after 10 ns simulation. Both the number of converged correlation matrix elements and the R-factor depend logarithmically on time, consistent with a model in which the number of energy minima sampled depends exponentially on the maximum energy barrier crossed. The logarithmic dependence is also extrapolated to predict a convergence time for the whole variance-covariance matrix of approximately 1 micros.     

Dynamics of well-folded and natively disordered proteins in solution: a time-of-flight neutron scattering study

Casein proteins belong to the class of natively disordered proteins. The existence of disordered biologically active proteins questions the assumption that a well-folded structure is required for function. A hypothesis generally put forward is that the unstructured nature of these proteins results from the functional need of a higher flexibility. This interplay between structure and dynamics was investigated in a series of time-of-flight neutron scattering experiments, performed on casein proteins, as well as on three well-folded proteins with distinct secondary structures, namely, myoglobin (alpha), lysozyme (alpha/beta) and concanavalin A (beta). To illustrate the subtraction of the solvent contribution from the scattering spectra, we used the dynamic susceptibility spectra emphasizing the high frequency part of the spectrum, where the solvent dominates. The quality of the procedure is checked by comparing the corrected spectra to those of the dry and hydrated protein with negligible solvent contamination. Results of spectra analysis reveal differences in motional amplitudes of well-folded proteins, where beta-sheet structures appear to be more rigid than a cluster of alpha-helices. The disordered caseins display the largest conformational displacements. Moreover their global diffusion rates deviate from the expected dependence, suggesting further large-scale conformational motions.     

Reaction Trajectory Revealed by a Joint Analysis of Protein Data Bank

Structural motions along a reaction pathway hold the secret about how a biological macromolecule functions. If each static structure were considered as a snapshot of the protein molecule in action, a large collection of structures would constitute a multidimensional conformational space of an enormous size. Here I present a joint analysis of hundreds of known structures of human hemoglobin in the Protein Data Bank. By applying singular value decomposition to distance matrices of these structures, I demonstrate that this large collection of structural snapshots, derived under a wide range of experimental conditions, arrange orderly along a reaction pathway. The structural motions along this extensive trajectory, including several helical transformations, arrive at a reverse engineered mechanism of the cooperative machinery (Ren, companion article), and shed light on pathological properties of the abnormal homotetrameric hemoglobins from α-thalassemia. This method of meta-analysis provides a general approach to structural dynamics based on static protein structures in this post genomics era.     

A molecular dynamics simulation of bacteriophage T4 lysozyme.

An analysis of a 400 ps molecular dynamics simulation of the 164 amino acid enzyme T4 lysozyme is presented. The simulation was carried out with all hydrogen atoms modeled explicitly, the inclusion of all 152 crystallographic waters and at a temperature of 300 K. Temporal analysis of the trajectory versus energy, hydrogen bond stability, r.m.s. deviation from the starting crystal structure and radius of gyration, demonstrates that the simulation was both stable and representative of the average experimental structure. Average structural properties were calculated from the enzyme trajectory and compared with the crystal structure. The mean value of the C alpha displacements of the average simulated structure from the X-ray structure was 1.1 +/- 0.1 A; differences of the backbone phi and psi angles between the average simulated structure and the crystal structure were also examined. Thermal-B factors were calculated from the simulation for heavy and backbone atoms and both were in good agreement with experimental values. Relationships between protein secondary structure elements and internal motions were studied by examining the positional fluctuations of individual helix, sheet and turn structures. The structural integrity in the secondary structure units was preserved throughout the simulation; however, the A helix did show some unusually high atomic fluctuations. The largest backbone atom r.m.s. fluctuations were found in non-secondary structure regions; similar results were observed for r.m.s. fluctuations of non-secondary structure phi and psi angles. In general, the calculated values of r.m.s. fluctuations were quite small for the secondary structure elements. In contrast, surface loops and turns exhibited much larger values, being able to sample larger regions of conformational space. The C alpha difference distance matrix and super-positioning analyses comparing the X-ray structure with the average dynamics structure suggest that a 'hinge-bending' motion occurs between the N- and C-terminal domains.