Thermal diffuse X-ray scattering and its contribution to understanding protein dynamics

X-ray Scattering Studies of Protein Structural Dynamics

X-ray scattering is uniquely suited to the study of disordered systems and thus has the potential to provide insight into dynamic processes where diffraction methods fail. In particular, while X-ray crystallography has been a staple of structural biology for more than half a century and will continue to remain so, a major limitation of this technique has been the lack of dynamic information. Solution X-ray scattering has become an invaluable tool in structural and mechanistic studies of biological macromolecules where large conformational changes are involved. Such systems include allosteric enzymes that play key roles in directing metabolic fluxes of biochemical pathways, as well as large, assembly-line type enzymes that synthesize secondary metabolites with pharmaceutical applications. Furthermore, crystallography has the potential to provide information on protein dynamics via the diffuse scattering patterns that are overlaid with Bragg diffraction. Historically, these patterns have been very difficult to interpret, but recent advances in X-ray detection have led to a renewed interest in diffuse scattering analysis as a way to probe correlated motions. Here, we will review X-ray scattering theory and highlight recent advances in scattering-based investigations of protein solutions and crystals, with a particular focus on complex enzymes.

Acoustic vibrations contribute to the diffuse scatter produced by ribosome crystals

The diffuse scattering pattern produced by frozen crystals of the 70S ribosome from Thermus thermophilus is as highly structured as it would be if it resulted entirely from domain-scale motions within these particles. However, the qualitative properties of the scattering pattern suggest that acoustic displacements of the crystal lattice make a major contribution to it.

Predicting X-ray diffuse scattering from translation-libration-screw structural ensembles

Identifying the intramolecular motions of proteins and nucleic acids is a major challenge in macromolecular X-ray crystallography. Because Bragg diffraction describes the average positional distribution of crystalline atoms with imperfect precision, the resulting electron density can be compatible with multiple models of motion. Diffuse X-ray scattering can reduce this degeneracy by reporting on correlated atomic displacements. Although recent technological advances are increasing the potential to accurately measure diffuse scattering, computational modeling and validation tools are still needed to quantify the agreement between experimental data and different parameterizations of crystalline disorder. A new tool, phenix.diffuse, addresses this need by employing Guinier's equation to calculate diffuse scattering from Protein Data Bank (PDB)-formatted structural ensembles. As an example case, phenix.diffuse is applied to translation-libration-screw (TLS) refinement, which models rigid-body displacement for segments of the macromolecule. To enable the calculation of diffuse scattering from TLS-refined structures, phenix.tls_as_xyz builds multi-model PDB files that sample the underlying T, L and S tensors. In the glycerophosphodiesterase GpdQ, alternative TLS-group partitioning and different motional correlations between groups yield markedly dissimilar diffuse scattering maps with distinct implications for molecular mechanism and allostery. These methods demonstrate how, in principle, X-ray diffuse scattering could extend macromolecular structural refinement, validation and analysis.

On the relationship between diffraction patterns and motions in macromolecular crystals

The quality of many macromolecular crystal structures published recently has been enhanced through the use of new methods for treating the effects of molecular motion and disorder on diffraction patterns, among them a technique called translation, libration, screw-axis (TLS) parameterization. TLS parameterization rationalizes those effects in terms of domain-scale, rigid-body motions and, interestingly, the models for molecular motion that emerge when macromolecular diffraction data are analyzed this way often make sense biochemically. Here it is pointed out that all such models should be treated with caution until it is shown that they are consistent with the diffuse scatter produced by the crystals that provided the diffraction data from which they derive.

Concordance of Residual Dipolar Couplings, Backbone Order Parameters and Crystallographic B-factors for a Small α/β Protein: A Unified Picture of High Probability, Fast Atomic Motions in Proteins

Using ensemble refinement of the third immunoglobulin binding domain (GB3) of streptococcal protein G (a small alpha/beta protein of 56 residues), we demonstrate that backbone (N-H, N-C', Calpha-Halpha, Calpha-C') residual dipolar coupling data in five independent alignment media, generalized order parameters from 15N relaxation data, and B-factors from a high-resolution (1.1A), room temperature crystal structure are entirely consistent with one another within experimental error. The optimal ensemble size representation is between four and eight, as assessed by complete cross-validation of the residual dipolar couplings. Thus, in the case of GB3, all three observables reflect the same low-amplitude anisotropic motions arising from fluctuations in backbone phi/psi torsion angles in the picosecond to nanosecond regime in both solution and crystalline environments, yielding a unified picture of fast, high-probability atomic motions in proteins. An understanding of these motions is crucial for understanding the impact of protein dynamics on protein function, since they provide part of the driving force for triggered conformational changes that occur, for example, upon ligand binding, signal transduction and enzyme catalysis.

Molecular dynamics simulations of a double unit cell in a protein crystal: volume relaxation at constant pressure and correlation of motions between the two unit cells

Eight molecular dynamics simulations of a double crystal unit cell of ubiquitin were performed to investigate the effects of simulating at constant pressure and of simulating two unit cells compared to a single unit cell. To examine the influence of different simulation conditions, the constant-pressure and constant-volume simulations were each performed with and without counterions and using two different treatments of the long-range electrostatic interactions (lattice-sum and reaction-field methods). The constant-pressure simulations were analyzed in terms of unit cell deformation and accompanying protein deformations. Energetic and structural properties of the proteins in the simulations of the double unit cell were compared to the results of previously reported one-unit-cell simulations. Correlation between the two unit cells was also investigated based on relative translational and rotational movements of the proteins and on dipole fluctuations. The box in the constant-pressure simulations is found to deform slowly to reach convergence only after 5-10 ns. This deformation does not result from a distortion in the structure of the proteins but rather from changes in protein packing within the unit cell. The results of the double-unit-cell simulations are closely similar to the results of the single-unit-cell simulations, and little motional correlation is found between the two unit cells.

Dynamics of the substrate binding pocket in the presence of an inhibitor covalently attached to a fungal lipase

To gain insight into the mobility of the occupied ligand-binding pocket of the Rhizomucor miehei lipase we have conducted a rigorous molecular dynamics analysis. The covalently attached inhibitor, ethylhexylphosphonate, was employed as a mimic of the putative tetrahedral intermediate in the esterolytic reaction. Our results show that in this lipase, ligand recognition is influenced by the flexibility of the binding pocket, a feature that is common to many other enzymes. Several regions around the active site were found to move significantly to adapt to the inhibitor. These motions are correlated to the flexibility of the inhibitor. In particular, the hexyl chain of the inhibitor shows considerable mobility, and adjacent residues in the binding cleft accommodate to this flexibility. Pronounced fluctuations in the binding pocket induced by the flexibility of the inhibitor are observed in the hinge region F79-S82, the active site loop region W88-V95 and the protein regions P209-F215/H257-Y260. The flexibility in the regions F79-S82 and H257-Y260, where the shorter ethyl chain is located, indicates that additional space in this binding cleft region is available for accommodating a larger moiety. Fluctuations in the region W88-V95 and P209-F215 are due to the relatively short flexible hexyl carbon chain. This part of the binding pocket could be stiffened by the presence of a longer carbon chain. Though the inhibitor is covalently attached through the phosphonate moiety, interaction of the remainder of the molecule and the enzyme are determined by hydrophobic interactions, where the Van der Waals energies are approximately 25% lower than the electrostatic contributions.

Conformational disorder of proteins assessed by real-space molecular dynamics refinement

Motion is critical to the function of many proteins, but much more difficult to study than structure. Due to lack of easy alternatives, although there are inherent limitations, there have been several prior attempts to extract some information from the Bragg scattering in conventional diffraction patterns. Bragg diffraction reflects only a small proportion of a protein's motion and disorder, so fitted values likely underestimate reality. However, this work shows that the fitted estimates should be even smaller, because current methods of refinement over-fit the Bragg diffraction, leading to a component of the disorder that is not based on any experimental data, and could be characterized as a guess. Real-space refinement is less susceptible than other methods, but its application depends on the availability of very accurate experimental phases. A future challenge will be the collection of such data without resort to cryo-techniques, so that a physiologically relevant understanding can be achieved.

Motions of calmodulin characterized using both Bragg and diffuse X-ray scattering

BACKGROUND

Calmodulin is a calcium-activated regulatory protein which can bind to many different targets. The protein resembles a highly flexible dumbbell, and bends in the middle as it binds. This and other motions must be understood to formulate a realistic model of calmodulin function.

RESULTS

Using the Bragg reflections from X-ray crystallography, a multiple-conformer refinement of a calmodulin-peptide complex shows anisotropic displacements, with high variations of dihedral angles in several nonhelical domains: the flexible linker; three of the four calcium-binding sites (including both of the N-terminal sites); and a turn connecting the C-terminal EF-hand calcium-binding domains. Three-dimensional maps of the large scale diffuse X-ray scattering data show isotropic liquid-like motions with an unusually small correlation length. Three-dimensional maps of the small scale diffuse streaks show highly coupled, anisotropic motions along the head-to-tail molecular packing direction in the unit cell. There is also weak coupling perpendicular to the head-to-tail packing direction, particularly across a cavity occupied by the disordered linker domain of the molecule.

CONCLUSIONS

Together, the Bragg and diffuse scattering present a self-consistent description of the motions in the flexible linker of calmodulin. The other mobile regions of the protein are also of great interest. In particular, the high variations in the calcium-binding sites are likely to influence how strongly they bind ions. This is especially important in the N-terminal sites, which regulate the activity of the molecule.

Highly constrained multiple-copy refinement of protein crystal structures

In the course of refining atomic protein structures, one often encounters difficulty with molecules that are unusually flexible or otherwise disordered. We approach the problem by combining two relatively recent developments: simultaneous refinement of multiple protein conformations and highly constrained refinement. A constrained Langevin dynamics refinement is tested on two proteins: neurotrophin-3 and glutamine synthetase. The method produces closer agreement between the calculated and observed scattering amplitudes than standard, single-copy, Gaussian atomic displacement parameter refinement. This is accomplished without significantly increasing the number of fitting parameters in the model. These results suggest that loop motion in proteins within a crystal lattice can be extensive and that it is poorly modeled by isotropic Gaussian distributions for each atom.

Conformational substates in enzyme mechanism: the 120 K structure of alpha-lytic protease at 1.5 A resolution

Insight into the dynamic properties of alpha-lytic protease (alpha LP) has been obtained through the use of low-temperature X-ray crystallography and multiple-conformation refinement. Previous studies of alpha LP have shown that the residues around the active site are able to move significantly to accommodate substrates of different sizes. Here we show a link between the ability to accommodate ligands and the dynamics of the binding pocket. Although the structure of alpha LP at 120 K has B-factors with a uniformly low value of 4.8 A2 for the main chain, four regions stand out as having significantly higher B-factors. Because thermal motion should be suppressed at cryogenic temperatures, the high B-factors are interpreted as the result of trapped conformational substates. The active site residues that are perturbed during accommodation of different substrates are precisely those showing conformational substates, implying that substrate binding selects a subset of conformations from the ensemble of accessible states. To better characterize the precise nature of these substates, a protein model consisting of 16 structures has been refined and evaluated. The model reveals a number of features that could not be well-described by conventional B-factors: for example, 40% of the main-chain residue conformations are distributed asymmetrically or in discrete clusters. Furthermore, these data demonstrate an unexpected correlation between motions on either side of the binding pocket that we suggest is a consequence of "dynamic close packing." These results provide strong evidence for the role of protein dynamics in substrate binding and are consistent with the results of dynamic studies of ligand binding in myoglobin and ribonuclease A.

NMR evidence for slow collective motions in cyanometmyoglobin

Residual dipolar couplings observed in NMR spectra at very high magnetic fields have been measured to a high degree of accuracy for the paramagnetic protein cyanometmyoglobin. Deviations of these measurements from predictions based on available crystallographic and solution structures are largely systematic and well correlated within a given helix of this highly alpha-helical protein. These observations can be explained by invoking collective motion and small displacements of representative helices from their reported average positions in the solid state. Thus, the measurements appear to be capable of providing important insights into slower, collective protein motions, which are likely to be important for function, and which have been difficult to study using established experimental techniques.