Mark J. van der Woerd

Biophysical analysis and small-angle X-ray scattering-derived structures of MeCP2–nucleosome complexes

MeCP2 is a highly abundant chromatin architectural protein with key roles in post-natal brain development in humans. Mutations in MeCP2 are associated with Rett syndrome, the main cause of mental retardation in girls. Structural information on the intrinsically disordered MeCP2 protein is restricted to the methyl-CpG binding domain; however, at least four regions capable of DNA and chromatin binding are distributed over its entire length. Here we use small angle X-ray scattering (SAXS) and other solution-state approaches to investigate the interaction of MeCP2 and a truncated, disease-causing version of MeCP2 with nucleosomes. We demonstrate that MeCP2 forms defined complexes with nucleosomes, in which all four histones are present. MeCP2 retains an extended conformation when binding nucleosomes without extra-nucleosomal DNA. In contrast, nucleosomes with extra-nucleosomal DNA engage additional DNA binding sites in MeCP2, resulting in a rather compact higher-order complex. We present ab initio envelope reconstructions of nucleosomes and their complexes with MeCP2 from SAXS data. SAXS studies also revealed unexpected sequence-dependent conformational variability in the nucleosomes themselves.

Non-invasive measurement of X-ray beam heating on a surrogate crystal sample

Cryocooling is a technique routinely used to mitigate the effects of secondary radiation damage on macromolecules during X-ray data collection. Energy from the X-ray beam absorbed by the sample raises the temperature of the sample. How large is the temperature increase and does this reduce the effectiveness of cryocooling? Sample heating by the X-ray beam has been measured non-invasively for the first time by means of thermal imaging. Specifically, the temperature rise of 1 mm and 2 mm glass spheres (sample surrogates) exposed to an intense synchrotron X-ray beam and cooled in a laminar flow of nitrogen gas is experimentally measured. For the typical sample sizes, photon energies, fluxes, flux densities and exposure times used for macromolecular crystallographic data collection at third-generation synchrotron radiation sources and with the sample accurately centered in the cryostream, the heating by the X-ray beam is only a few degrees. This is not sufficient to raise the sample above the amorphous-ice/crystalline-ice transition temperature and, if the cryostream cools the sample to 100 K, not even enough to significantly enhance radiation damage from secondary effects.

Extracting trends from two decades of microgravity macromolecular crystallization history.

Since the 1980s hundreds of macromolecular crystal growth experiments have been performed in the reduced acceleration environment of an orbiting spacecraft. Significant enhancements in structural knowledge have resulted from X-ray diffraction of the crystals grown. Similarly, many samples have shown no improvement or degradation in comparison to those grown on the ground. A complex series of interrelated factors affect these experiments and by building a comprehensive archive of the results it was aimed to identify factors that result in success and those that result in failure. Specifically, it was found that dedicated microgravity missions increase the chance of success when compared with those where crystallization took place as a parasitic aspect of the mission. It was also found that the chance of success could not be predicted based on any discernible property of the macromolecule available to us.

Finding a cold needle in a warm haystack: infrared imaging applied to locating cryocooled crystals in loops

The use of infrared imaging to locate crystals mounted in cryoloops and cryopreserved in a nitrogen gas stream at 100 K is demonstrated. In the home laboratory, crystals are clearly seen in the infrared images with light transmitting through the sample while irradiating the crystal from behind, and with illumination from a direction perpendicular to the direction of view. The crystals transmit and reflect infrared radiation at different levels to the surrounding mother liquor and loop. Because of differences in contrast between crystals and their surrounding mother liquor, it is possible to identify the crystal position. At the synchrotron, with robotically mounted crystals, the small depth of field of the lens required the recording of multiple images at different focal points. Image processing techniques were then used to construct a clear image of the crystal. The resulting infrared images and intensity profiles show that infrared imaging can be a powerful complement to visual imaging in locating crystals in cryocooled loops.

Neutron structure of the cyclic glucose-bound xylose isomerase E186Q mutant.

Ketol-isomerases catalyze the reversible isomerization between aldoses and ketoses. D-Xylose isomerase carries out the first reaction in the catabolism of D-xylose, but is also able to convert D-glucose to D-fructose. The first step of the reaction is an enzyme-catalyzed ring opening of the cyclic substrate. The active-site amino-acid acid/base pair involved in ring opening has long been investigated and several models have been proposed. Here, the structure of the xylose isomerase E186Q mutant with cyclic glucose bound at the active site, refined against joint X-ray and neutron diffraction data, is reported. Detailed analysis of the hydrogen-bond networks at the active site of the enzyme suggests that His54, which is doubly protonated, is poised to protonate the glucose O5 position, while Lys289, which is neutral, promotes deprotonation of the glucose O1H hydroxyl group via an activated water molecule. The structure also reveals an extended hydrogen-bonding network that connects the conserved residues Lys289 and Lys183 through three structurally conserved water molecules and residue 186, which is a glutamic acid to glutamine mutation.

Optimizing crystal volume for neutron diffraction: D-xylose isomerase

Neutron diffraction is uniquely sensitive to hydrogen positions and protonation state. In that context structural information from neutron data is complementary to that provided through X-ray diffraction. However, there are practical obstacles to overcome in fully exploiting the potential of neutron diffraction, i.e. low flux and weak scattering. Several approaches are available to overcome these obstacles and we have investigated the simplest: increasing the diffracting volume of the crystals. Volume is a quantifiable metric that is well suited for experimental design and optimization techniques. By using response surface methods we have optimized the xylose isomerase crystal volume, enabling neutron diffraction while we determined the crystallization parameters with a minimum of experiments. Our results suggest a systematic means of enabling neutron diffraction studies for a larger number of samples that require information on hydrogen position and/or protonation state.

Autocovariance Structures for Radial Averages in Small‐Angle X‐Ray Scattering Experiments

Small-angle X-ray scattering (SAXS) is a technique for obtaining low-resolution structural information about biological macromolecules, by exposing a dilute solution to a high-intensity X-ray beam and capturing the resulting scattering pattern on a two-dimensional detector. The two-dimensional pattern is reduced to a one-dimensional curve through radial averaging; that is, by averaging across annuli on the detector plane. Subsequent analysis of structure relies on these one-dimensional data. This paper reviews the technique of SAXS and investigates autocorrelation structure in the detector plane and in the radial averages. Across a range of experimental conditions and molecular types, spatial autocorrelation in the detector plane is present and is well-described by a stationary kernel convolution model. The corresponding autocorrelation structure for the radial averages is non-stationary. Implications of the autocorrelation structure for inference about macromolecular structure are discussed.

Laplace Variational Approximation for Semiparametric Regression in the Presence of Heteroscedastic Errors

Variational approximations provide fast, deterministic alternatives to Markov chain Monte Carlo for Bayesian inference on the parameters of complex, hierarchical models. Variational approximations are often limited in practicality in the absence of conjugate posterior distributions. Recent work has focused on the application of variational methods to models with only partial conjugacy, such as in semiparametric regression with heteroscedastic errors. Here, both the mean and log variance functions are modeled as smooth functions of covariates. For this problem, we derive a mean field variational approximation with an embedded Laplace approximation to account for the nonconjugate structure. Empirical results with simulated and real data show that our approximate method has significant computational advantages over traditional Markov chain Monte Carlo; in this case, a delayed rejection adaptive Metropolis algorithm. The variational approximation is much faster and eliminates the need for tuning parameter selection, achieves good fits for both the mean and log variance functions, and reasonably reflects the posterior uncertainty. We apply the methods to log-intensity data from a small angle X-ray scattering experiment, in which properly accounting for the smooth heteroscedasticity leads to significant improvements in posterior inference for key physical characteristics of an organic molecule.

Minimum Mean Squared Error Estimation of the Radius of Gyration in Small-Angle X-Ray Scattering Experiments

ABSTRACT Small-angle X-ray scattering (SAXS) is a technique that yields low-resolution structural information of biological macromolecules by exposing a large ensemble of molecules in solution to a powerful X-ray beam. The beam interacts with the molecules and the intensity of the scattered beam is recorded on a detector plate. The radius of gyration for a molecule, which is a measure of the spread of its mass, can be estimated from the lowest scattering angles of SAXS data. This estimation method requires specification of a window of scattering angles. Under a local polynomial model with autoregressive errors, we develop methodology and supporting asymptotic theory for selection of an optimal window, minimum mean square error estimation of the radius of gyration, and estimation of its variance. Simulation studies confirm the quality of our asymptotic approximations and the superior performance of the proposed methodology relative to the accepted standard. Our semi-automated methodology makes it feasible to estimate the radius of gyration many times, from replicated SAXS data under various experimental conditions, in an objective and reproducible manner. This in turn allows for secondary analyses of the dataset of estimates, as we demonstrate with a split–split plot analysis for 357 SAXS intensity curves. Supplementary materials for this article are available online.