Protein dynamics from X-ray crystallography: anisotropic, global motion in diffuse scattering patterns

Understanding X-ray crystallographic diffuse scattering is likely to improve our comprehension of equilibrium collective protein dynamics. Here, using molecular dynamics (MD) simulation, a detailed analysis is performed of the origins of diffuse scattering in crystalline Staphylococcal nuclease, for which the complete diffuse scattering pattern has been determined experimentally. The hydrogen-atom contribution and the scattering range over which the scattering can be considered to be a sum of solvent and protein scattering are determined. Two models of correlated protein motion are investigated by calculating the model-derived diffuse scattering and comparing with the scattering calculated directly from MD trajectories. In one model, previously used in diffuse scattering interpretation, the atomic displacement correlations decay isotropically with increasing separation. Model correlation lengths are obtained by refining the model scattering against the simulation-derived scattering pattern, and are found to be significantly different from those correlation lengths derived directly from the MD trajectories. Furthermore, the convergence between the model-derived and MD-derived scattering is poor. The second model, in which the displacement correlations are calculated from the principal components of the MD trajectories, is capable of fully reproducing the MD-derived diffuse scattering if the approximately 50% lowest-frequency modes are included. However, a small number ( approximately 10) of lowest-frequency and largest-amplitude modes dominates the diffuse scattering and thus the correlated protein motions. A detailed analysis of the principal components is performed. In particular, the effective free energy profile associated with each principle mode is analyzed and the eigenfrequency and damping coefficient computed using a model of Brownian dynamics. Those collective modes with effective frequencies below approximately 0.5 THz, including those that determine the diffuse scattering, are overdamped.     

Protein conformations explored by difference high-angle solution X-ray scattering: oxidation state and temperature dependent changes in cytochrome C

We demonstrate the use of high-angle X-ray scattering to explore protein conformational states in solution by resolving oxidation state- and temperature-dependent changes in the conformation of horse heart cytochrome c. Several detailed models exist for oxidation-dependent changes in mitochondrial class I c cytochromes determined by X-ray crystallography and solution NMR techniques. These models differ in the magnitude and locations of structural change. Our scattering measurements show that high-angle X-ray scattering can discriminate between these models, and that the experimental scattering data for horse cytochrome c can be best reconciled with selected NMR models for the same protein. These results demonstrate the ability to use high-angle X-ray scattering to resolve conformational states of proteins in solution, and to relate these measurements to detailed structural models. Furthermore, temperature-dependent changes are found in the high angle scattering patterns for horse cytochrome c, illustrating the sensitivity of these measurements to dynamic aspects of protein structure. These results demonstrate the ability to use difference high angle scattering as a quantitative monitor of reaction-linked changes in protein conformation and structural dynamics. Synchrotron-based high-angle scattering holds promise as a widely applicable, high throughput technique for exploring conformational states linked to physiological protein function, for resolving configurational differences between protein structures in solution and crystalline states, and for bridging the gap between solution NMR and crystallographic structure techniques.     

The low-temperature heat capacity of solid proteins.

Several harmonic models of protein fluctuations are used to calculate the heat capacity. They get the spectral density of conformational modes from inelastic neutron scattering, normal mode calculations, or macroscopic elasticity (Debye model). It is assumed that the low-frequency spectral density depends only weakly on temperature and protein species. The Debye model predicts temperatures below which modes are primarily in their ground states: 10 and 80 K for the lattice and conformational modes, respectively. The models differ most below 100 K. The mode calculations yield the most accurate predictions, though all three models are within twofold of the data. The heat capacity has the power law form aTb for T less than 30 K. The experimental b's of proteins are 1.6-1.8, and the theoretical, 1.1-1.3. One possible explanation for the discrepancy is the occurrence of transitions between discrete conformations. All of the models approach the measured data in the range 100-200 K. They are very similar above 200 K, where the heat capacity includes significant contributions from bond stretching and bending. This masks the possible anharmonic behavior of the conformational modes. Hydration substantially increases the heat capacity above 200 K. This effect seems to be a consequence of conformational transitions that have higher energy than the ones seen with low hydration. The analysis also predicts that denaturation with constant hydration produces a negligible increase of heat capacity. The larger increment in solution arises from the different hydration of the folded and unfolded states, and is responsible for the existence of cold denaturation. This phenomenon is thus predicted not to occur when the hydration is constant.     

Reweighting of molecular simulations with explicit-solvent SAXS restraints elucidates ion-dependent RNA ensembles

Small-angle X-ray scattering (SAXS) experiments are increasingly used to probe RNA structure. A number of forward models that relate measured SAXS intensities and structural features, and that are suitable to model either explicit-solvent effects or solute dynamics, have been proposed in the past years. Here, we introduce an approach that integrates atomistic molecular dynamics simulations and SAXS experiments to reconstruct RNA structural ensembles while simultaneously accounting for both RNA conformational dynamics and explicit-solvent effects. Our protocol exploits SAXS pure-solute forward models and enhanced sampling methods to sample an heterogenous ensemble of structures, with no information towards the experiments provided on-the-fly. The generated structural ensemble is then reweighted through the maximum entropy principle so as to match reference SAXS experimental data at multiple ionic conditions. Importantly, accurate explicit-solvent forward models are used at this reweighting stage. We apply this framework to the GTPase-associated center, a relevant RNA molecule involved in protein translation, in order to elucidate its ion-dependent conformational ensembles. We show that (a) both solvent and dynamics are crucial to reproduce experimental SAXS data and (b) the resulting dynamical ensembles contain an ion-dependent fraction of extended structures.     

How good are comparative models in the understanding of protein dynamics?

The 3D structure of a protein is essential to understand protein dynamics. If experimentally determined structure is unavailable, comparative models could be used to infer dynamics. However, the effectiveness of comparative models, compared to experimental structures, in inferring dynamics is not clear. To address this, we compared dynamics features of ~800 comparative models with their crystal structures using normal mode analysis. Average similarity in magnitude, direction, and correlation of residue motions is >0.8 (where value 1 is identical) indicating that the dynamics of models and crystal structures are highly similar. Accuracy of 3D structure and dynamics is significantly higher for models built on multiple and/or high sequence identity templates (>40%). Three-dimensional (3D) structure and residue fluctuations of models are closer to that of crystal structures than to templates (TM score 0.9 vs 0.7 and square inner product 0.92 vs 0.88). Furthermore, long-range molecular dynamics simulations on comparative models of RNase 1 and Angiogenin showed significant differences in the conformational sampling of conserved active-site residues that characterize differences in their activity levels. Similar analyses on two EGFR kinase variant models highlight the effect of mutations on the functional state-specific αC helix motions and these results corroborate with the previous experimental observations. Thus, our study adds confidence to the use of comparative models in understanding protein dynamics.     

Inelastic neutron scattering analysis of picosecond internal protein dynamics. Comparison of harmonic theory with experiment

The experimental inelastic neutron scattering spectrum of a protein, the bovine pancreatic trypsin inhibitor (BPTI), in a powder sample is presented together with the generalized density of states, G(omega), as a function of the frequency, omega, derived from the scattering data. The experimental results are compared with calculations from two different normal mode analyses of BPTI. One of these, based on an improved model, gives a calculated spectrum and density of states in general agreement with those obtained experimentally; the other, based on an earlier model, shows considerable disagreement. The important improvements in the newer normal mode analysis are the explicit treatment of all atoms (non-polar as well as polar hydrogens are included) and a modified truncation scheme for the long-range electrostatic interactions. The fact that the inelastic neutron scattering measurements can distinguish between the two theoretical models makes clear their utility for the analysis of protein dynamics.     

Analytical ultracentrifugation combined with X-ray and neutron scattering: Experiment and modelling

Analytical ultracentrifugation and solution scattering provide different multi-parameter structural and compositional information on proteins. The joint application of the two methods supplements high resolution structural studies by crystallography and NMR. We summarise the procedures required to obtain equivalent ultracentrifugation and X-ray and neutron scattering data. The constrained modelling of ultracentrifugation and scattering data is important to confirm the experimental data analysis and yields families of best-fit molecular models for comparison with crystallography and NMR structures. This modelling of ultracentrifugation and scattering data is described in terms of starting models, their conformational randomisation in trial-and-error fits, and the identification of the final best-fit models. Seven applications of these methods are described to illustrate the current state-of-the-art. These include the determination of antibody solution structures (the human IgG4 subclass, and oligomeric forms of human IgA and its secretory component), the solution structures of the complement proteins of innate immunity (Factor H and C3/C3u) and their interactions with macromolecular ligands (C-reactive protein), and anionic polysaccharides (heparin). Complementary features of joint ultracentrifugation and scattering experiments facilitate an improved understanding of crystal structures (illustrated for C3/C3u, C-reactive protein and heparin). If a large protein or its complex cannot be crystallised, the joint ultracentrifugation-scattering approach provides a means to obtain an overall macromolecular structure.     

On the interpretation and prediction of X-ray scattering profiles of biomolecules in solution

If solution scattering curves can be accurately predicted from structural models, measurements can provide useful tests of predictions of secondary and tertiary structure. We have developed a computational technique for the prediction and interpretation of x-ray scattering profiles of biomolecules in solution. The method employs a Monte Carlo procedure for the generation of length distribution functions and provides predictions to moderate resolution (～5 Å). In addition to facilitating the assignment and interpretation of features in a solution scattering profile, the method also allows the elucidation of the role of protein motion in shaping the final scattering curve. The effect of protein motion on a scattering profile is investigated by generating scattering curves from several consecutive 0.147 ps atomic coordinate frames from a molecular dynamics simulation of the motion of bovine pancreatic trypsin inhibitor (BPTI) [McCammon, J. A. & Karplus, M. (1980) Annu. Rev. Phys. Chem. 31 , 29–45]. The theoretical approach is applied to chicken egg white lysozyme and BPTI, and the overall features in the resulting theoretical scattering profiles match well with the experimental solution scattering curves recorded on film. It is apparent from this study that the scattering profile prediction technique in conjunction with other experimental methods may have value in testing ideas of conformational change based on crystallographic studies; investigations of this type would include a comparison of predicted scattering curves generated from a variety of crystallographic models with an actual scattering profile of the biomolecule in solution.     

Evolutionary Conserved Positions Define Protein Conformational Diversity

Conformational diversity of the native state plays a central role in modulating protein function. The selection paradigm sustains that different ligands shift the conformational equilibrium through their binding to highest-affinity conformers. Intramolecular vibrational dynamics associated to each conformation should guarantee conformational transitions, which due to its importance, could possibly be associated with evolutionary conserved traits. Normal mode analysis, based on a coarse-grained model of the protein, can provide the required information to explore these features. Herein, we present a novel procedure to identify key positions sustaining the conformational diversity associated to ligand binding. The method is applied to an adequate refined dataset of 188 paired protein structures in their bound and unbound forms. Firstly, normal modes most involved in the conformational change are selected according to their corresponding overlap with structural distortions introduced by ligand binding. The subspace defined by these modes is used to analyze the effect of simulated point mutations on preserving the conformational diversity of the protein. We find a negative correlation between the effects of mutations on these normal mode subspaces associated to ligand-binding and position-specific evolutionary conservations obtained from multiple sequence-structure alignments. Positions whose mutations are found to alter the most these subspaces are defined as key positions, that is, dynamically important residues that mediate the ligand-binding conformational change. These positions are shown to be evolutionary conserved, mostly buried aliphatic residues localized in regular structural regions of the protein like β-sheets and α-helix.     

The ternary 5-S RNA complex of proteins L 18 and L 25. A small-angle X-ray scattering titration study.

The 5-S RNA (A) and the proteins L 18 (B) and L25 (C) from Escherichia coli ribosomes form a ternary complex of the type ABC with a stepwise stability constant, log K111 approximately equal to 6.5. This is indicated from X-ray scattering titrations recorded at 21 degrees C in ribosomal reconstitutional buffer. When the ternary ABC complex forms there is only a limited change in the scattering curve compared to that of 5-S RNA, indicating that 5-S RNA does not undergo a major conformational change during the complex formation. The increase in the radius of gyration from 3.61 nm (5-S RNA) to 3.95 nm (ABC complex) as well as the experimental scattering curve can be explained by models where it is assumed that the elongated L 18 and L25 models are quite far from the electron density centre and where the protein molecules interact mainly with the minor arms of the supposed Y-shaped 5-S RNA molecule.     

Performance-based selection of likelihood models for phylogeny estimation

Phylogenetic estimation has largely come to rely on explicitly model-based methods. This approach requires that a model be chosen and that that choice be justified. To date, justification has largely been accomplished through use of likelihood-ratio tests (LRTs) to assess the relative fit of a nested series of reversible models. While this approach certainly represents an important advance over arbitrary model selection, the best fit of a series of models may not always provide the most reliable phylogenetic estimates for finite real data sets, where all available models are surely incorrect. Here, we develop a novel approach to model selection, which is based on the Bayesian information criterion, but incorporates relative branch-length error as a performance measure in a decision theory (DT) framework. This DT method includes a penalty for overfitting, is applicable prior to running extensive analyses, and simultaneously compares all models being considered and thus does not rely on a series of pairwise comparisons of models to traverse model space. We evaluate this method by examining four real data sets and by using those data sets to define simulation conditions. In the real data sets, the DT method selects the same or simpler models than conventional LRTs. In order to lend generality to the simulations, codon-based models (with parameters estimated from the real data sets) were used to generate simulated data sets, which are therefore more complex than any of the models we evaluate. On average, the DT method selects models that are simpler than those chosen by conventional LRTs. Nevertheless, these simpler models provide estimates of branch lengths that are more accurate both in terms of relative error and absolute error than those derived using the more complex (yet still wrong) models chosen by conventional LRTs. This method is available in a program called DT-ModSel.     

Addition of missing loops and domains to protein models by x-ray solution scattering

Inherent flexibility and conformational heterogeneity in proteins can often result in the absence of loops and even entire domains in structures determined by x-ray crystallographic or NMR methods. X-ray solution scattering offers the possibility of obtaining complementary information regarding the structures of these disordered protein regions. Methods are presented for adding missing loops or domains by fixing a known structure and building the unknown regions to fit the experimental scattering data obtained from the entire particle. Simulated annealing was used to minimize a scoring function containing the discrepancy between the experimental and calculated patterns and the relevant penalty terms. In low-resolution models where interface location between known and unknown parts is not available, a gas of dummy residues represents the missing domain. In high-resolution models where the interface is known, loops or domains are represented as interconnected chains (or ensembles of residues with spring forces between the C(alpha) atoms), attached to known position(s) in the available structure. Native-like folds of missing fragments can be obtained by imposing residue-specific constraints. After validation in simulated examples, the methods have been applied to add missing loops or domains to several proteins where partial structures were available.     

X-ray scattering study of hagfish protease inhibitor, a protein structurally related to complement and alpha 2-macroglobulin.

A protease inhibitor from hagfish blood plasma, homologous to human alpha 2-macroglobulin, has been studied in solution using small-angle X-ray scattering; the radius of gyration, R, was found to be 7.0 nm, the molecular weight 340,000 +/- 20,000, and the largest distance within the molecule, Dmax, 22 nm. When the inhibitor reacts with chymotrypsin, its 1:1 chymotrypsin complex is found to be more compact than the native molecule, R = 6.1 nm. A very similar conformational change is observed after the protein is reacted with methylamine. The data are consistent with models consisting of two equal elliptic cylinders with the same size as the one used as a model for the complement proteins C3 and C4 [cf. Osterberg et al. (1989) Eur. J. Biochem. 183, 507-511]. In the model for the native protein, these cylinders are arranged in an extended form, and in the one for the methylamine derivative (or chymotrypsin complex), they are closer together so that the projection of their elliptic surfaces forms an angle of about 70 degrees. These models for the hagfish protease inhibitor were expanded to models for the twice as large human alpha 2-macroglobulin using symmetry operations, and the resulting alpha 2-macroglobulin models were found to agree with those emerged from earlier studies involving electron microscopy and X-ray scattering methods.     

Conformational Flexibility of Ubiquitin-Modified and SUMO-Modified PCNA Shown by Full-Ensemble Hybrid Methods

Ubiquitin-modified proliferating cell nuclear antigen (PCNA) and small ubiquitin-like modifier (SUMO)-modified PCNA regulate DNA damage tolerance pathways. X-ray crystal structures of these proteins suggested that they do not have much conformational flexibility because the modifiers have preferred binding sites on the surface of PCNA. By contrast, small-angle X-ray scattering analyses of these proteins suggested that they have different degrees of conformational flexibility, with SUMO-modified PCNA being more flexible. These conclusions were based on minimal-ensemble hybrid approaches, which produce unrealistic models by representing flexible proteins with only a few static structures. To overcome the limitations of minimal-ensemble hybrid approaches and to determine the degree of conformational flexibility of ubiquitin-modified PCNA and SUMO-modified PCNA, we utilized a novel full-ensemble hybrid approach. We carried out molecular simulations and small-angle X-ray scattering analyses of both proteins and obtained outstanding agreement between the full ensembles generated by the simulations and the experimental data. We found that both proteins have a high degree of conformational flexibility. The modifiers occupy many positions around the back and side of the PCNA ring. Moreover, we found no preferred ubiquitin-binding or SUMO-binding sites on PCNA. This conformational flexibility likely facilitates the recognition of downstream effector proteins and the formation of PCNA tool belts.     

Validating Solution Ensembles from Molecular Dynamics Simulation by Wide-Angle X-ray Scattering Data

Wide-angle x-ray scattering (WAXS) experiments of biomolecules in solution have become increasingly popular because of technical advances in light sources and detectors. However, the structural interpretation of WAXS profiles is problematic, partly because accurate calculations of WAXS profiles from structural models have remained challenging. In this work, we present the calculation of WAXS profiles from explicit-solvent molecular dynamics (MD) simulations of five different proteins. Using only a single fitting parameter that accounts for experimental uncertainties because of the buffer subtraction and dark currents, we find excellent agreement to experimental profiles both at small and wide angles. Because explicit solvation eliminates free parameters associated with the solvation layer or the excluded solvent, which would require fitting to experimental data, we minimize the risk of overfitting. We further find that the influence from water models and protein force fields on calculated profiles are insignificant up to q ≈ 15 nm^?1. Using a series of simulations that allow increasing flexibility of the proteins, we show that incorporating thermal fluctuations into the calculations significantly improves agreement with experimental data, demonstrating the importance of protein dynamics in the interpretation of WAXS profiles. In addition, free MD simulations up to one microsecond suggest that the calculated profiles are highly sensitive with respect to minor conformational rearrangements of proteins, such as an increased flexibility of a loop or an increase of the radius of gyration by  <  1%. The present study suggests that quantitative comparison between MD simulations and experimental WAXS profiles emerges as an accurate tool to validate solution ensembles of biomolecules.     

An improved structural characterisation of reduced French bean plastocyanin based on NMR data and local-elevation molecular dynamics simulation

Deriving structural information about a protein from NMR experimental data is still a non-trivial challenge to computational biochemistry. This is because of the low ratio of the number of independent observables to the number of molecular degrees of freedom, the approximations involved in the different relationships between particular observable quantities and molecular conformation, and the averaged character of the experimental data. For example, protein (3)J-coupling data are seldom used for structure refinement because of the multiple-valuedness and limited accuracy of the Karplus relationship linking a (3)J-coupling to a torsional angle. Moreover, sampling of the large conformational space is still problematic. Using the 99-residue protein plastocyanin as an example we investigated whether use of a thermodynamically calibrated force field, inclusion of solvent degrees of freedom, and application of adaptive local-elevation sampling that accounts for conformational averaging produces a more realistic representation of the ensemble of protein conformations than standard single-structure refinement in a non-explicit solvent using restraints that do not account for averaging and are partly based on non-observed data. Yielding better agreement with observed experimental data, the protein conformational ensemble is less restricted than when using standard single-structure refinement techniques, which are likely to yield a picture of the protein which is too rigid.