Error estimates in atom coordinates and B factors in macromolecular crystallography.

The overall diffraction precision index (DPI) of a biological macromolecule crystal structure was first described by Cruickshank in 1999. This topical review proceeds from this point and describes the subsequent elaboration of the index to individual atom coordinates. Additional developments were introduced by the availability of a webserver, which provides a transformed PDB entry with individual atom coordinate errors derived from applying the DPI method using the parameters provided by the authors and then subsequently added to the PDB file. This webserver has been extensively used and harnessed in describing non-covalent distance error estimates as well as assessing the significance, or otherwise, of atom movements in a variety of studies. The standard uncertainties on a biological macromolecule's atomic displacement parameters (the 'B factors') has been an entirely different challenge but is obviously important since the crystallographic community has developed the habit of quoting B factors to a false precision in papers. This can convey a false certainty in the dynamics of a structure. A method involving parallelisation of workflows for diffraction image data processing does however offer estimates of the precision of B factors.

X-ray-driven chemistry and conformational heterogeneity in atomic resolution crystal structures of bacterial dihydrofolate reductases.

Dihydrofolate reductase (DHFR) catalyzes the NADPH-dependent reduction of dihydrofolate to tetrahydrofolate. Bacterial DHFRs are targets of several important antibiotics as well as model enzymes for the role of protein conformational dynamics in enzyme catalysis. We collected 0.93 Å resolution X-ray diffraction data from both Bacillus subtilis (Bs) and E. coli (Ec) DHFRs bound to folate and NADP+. These oxidized ternary complexes should not be able to perform chemistry, however electron density maps suggest hydride transfer is occurring in both enzymes. Comparison of low- and high-dose EcDHFR datasets show that X-rays drive partial production of tetrahydrofolate. Hydride transfer causes the nicotinamide moiety of NADP+ to move towards the folate as well as correlated shifts in nearby residues. Higher radiation dose also changes the conformational heterogeneity of Met20 in EcDHFR, supporting a solvent gating role during catalysis. BsDHFR has a different pattern of conformational heterogeneity and an unexpected disulfide bond, illustrating important differences between bacterial DHFRs. This work demonstrates that X-rays can drive hydride transfer similar to the native DHFR reaction and that X-ray photoreduction can be used to interrogate catalytically relevant enzyme dynamics in favorable cases.

Crystal Structures Reveal Hidden Domain Mechanics in Protein Kinase A (PKA).

Cyclic-AMP-dependent protein kinase A (PKA) is a critical enzyme involved in various signaling pathways that plays a crucial role in regulating cellular processes including metabolism, gene transcription, cell proliferation, and differentiation. In this study, the mechanisms of allostery in PKA were investigated by analyzing the vast repertoire of crystal structures available in the RCSB database. From existing structures of murine and human PKA, we elucidated the conformational ensembles and protein dynamics that are altered in a ligand-dependent manner. Distance metrics to analyze conformations of the G-loop were proposed to delineate different states of PKA and were compared to existing structural metrics. Furthermore, ligand-dependent flexibility was investigated through normalized B'-factors to better understand the inherent dynamics in PKA. The presented study provides a contemporary approach to traditional methods in engaging the use of crystal structures for understanding protein dynamics. Importantly, our studies provide a deeper understanding into the conformational ensemble of PKA as the enzyme progresses through its catalytic cycle. These studies provide insights into kinase regulation that can be applied to both PKA individually and protein kinases as a class.

Dependence of crystallographic atomic displacement parameters on temperature (25-150†K) for complexes of horse liver alcohol dehydrogenase.

Enzymes catalyze reactions by binding and orienting substrates with dynamic interactions. Horse liver alcohol dehydrogenase catalyzes hydrogen transfer with quantum-mechanical tunneling that involves fast motions in the active site. The structures and B factors of ternary complexes of the enzyme with NAD+ and 2,3,4,5,6-pentafluorobenzyl alcohol or NAD+ and 2,2,2-trifluoroethanol were determined to 1.1-1.3 Šresolution below the `glassy transition' in order to extract information about the temperature-dependent harmonic motions, which are reflected in the crystallographic B factors. The refinement statistics and structures are essentially the same for each structure at all temperatures. The B factors were corrected for a small amount of radiation decay. The overall B factors for the complexes are similar (13-16 Å2) over the range 25-100 K, but increase somewhat at 150 K. Applying TLS refinement to remove the contribution of pseudo-rigid-body displacements of coenzyme binding and catalytic domains provided residual B factors of 7-10 Å2 for the overall complexes and of 5-10 Å2 for C4N of NAD+ and the methylene carbon of the alcohols. These residual B factors have a very small dependence on temperature and include local harmonic motions and apparently contributions from other sources. Structures at 100 K show complexes that are poised for hydrogen transfer, which involves atomic displacements of ∼0.3 Šand is compatible with the motions estimated from the residual B factors and molecular-dynamics simulations. At 298 K local conformational changes are also involved in catalysis, as enzymes with substitutions of amino acids in the substrate-binding site have similar positions of NAD+ and pentafluorobenzyl alcohol and similar residual B factors, but differ by tenfold in the rate constants for hydride transfer.

Room-temperature serial synchrotron crystallography of Drosophila cryptochrome.

Fixed-target serial crystallography allows the high-throughput collection of diffraction data from small crystals at room temperature. This methodology is particularly useful for difficult samples that have sensitivity to radiation damage or intolerance to cryoprotection measures; fixed-target methods also have the added benefit of low sample consumption. Here, this method is applied to the structure determination of the circadian photoreceptor cryptochrome (CRY), previous structures of which have been determined at cryogenic temperature. In determining the structure, several data-filtering strategies were tested for combining observations from the hundreds of crystals that contributed to the final data set. Removing data sets based on the average correlation coefficient among equivalent reflection intensities between a given data set and all others was most effective at improving the data quality and maintaining overall completeness. CRYs are light sensors that undergo conformational photoactivation. Comparisons between the cryogenic and room-temperature CRY structures reveal regions of enhanced mobility at room temperature in loops that have functional importance within the CRY family of proteins. The B factors of the room-temperature structure correlate well with those predicted from molecular-dynamics simulations.

B-factor accuracy in protein crystal structures.

The accuracy of B factors in protein crystal structures has been determined by comparing the same atoms in numerous, independent crystal structures of Gallus gallus lysozyme. Both B-factor absolute differences and normal probability plots indicate that the estimated B-factor errors are quite large, close to 9 Å2 in ambient-temperature structures and to 6 Å2 in low-temperature structures, and surprisingly are comparable to values estimated two decades ago. It is well known that B factors are not due to local movements only but reflect several, additional factors from crystal defects, large-scale disorder, diffraction data quality etc. It therefore remains essential to normalize B factors when comparing different crystal structures, although it has clearly been shown that they provide useful information about protein dynamics. Improved, quantitative analyses of raw B factors require novel experimental and computational tools that are able to disaggregate local movements from other features and properties that affect B factors.

Parameterizing elastic network models to capture the dynamics of proteins.

Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

Improving the thermostability of a GH11 xylanase by directed evolution and rational design guided by B-factor analysis.

Operational stability under high temperature is required for enzyme application in industrial processes. Error-prone PCR and B-factor analysis were employed to enhance the thermostability of a xylanase from GH family 11 in this study. Based on the top 10 mutants screened from the random mutation libraries, mutant Xyn371 was derived from the optimal mutant Xyn370 by integrating the beneficial residues identified in the other 9 screened mutants. Subsequently, a best-saturation mutant Xyn372 originated from Xyn371 was selected with a 60-min half-life at 70 °C (0.5-min half-life for the wild-type enzyme). According to the site-saturated mutagenesis of 10 residues with higher B-factors in Xyn372, mutants Xyn375 and Xyn376 were screened; their half-lives at 70 °C were 410 and 360 min, respectively. The substituted residues located in the "palm" region of the N-terminus and the newly generated hydrogen bonds in the mutants might contribute to improved thermostability. The significantly improved thermostability of mutants will pave the way for applications in different industrial areas.

Impact of protein dynamics on secondary structure prediction.

Protein 3D structures support their biological functions. As the number of protein structures is negligible in regards to the number of available protein sequences, prediction methodologies relying only on protein sequences are essential tools. In this field, protein secondary structure prediction (PSSPs) is a mature area, and is considered to have reached a plateau. Nonetheless, proteins are highly dynamical macromolecules, a property that could impact the PSSP methods. Indeed, in a previous study, the stability of local protein conformations was evaluated demonstrating that some regions easily changed to another type of secondary structure. The protein sequences of this dataset were used by PSSPs and their results compared to molecular dynamics to investigate their potential impact on the quality of the secondary structure prediction. Interestingly, a direct link is observed between the quality of the prediction and the stability of the assignment to the secondary structure state. The more stable a local protein conformation is, the better the prediction will be. The secondary structure assignment not taken from the crystallized structures but from the conformations observed during the dynamics slightly increase the quality of the secondary structure prediction. These results show that evaluation of PSSPs can be done differently, but also that the notion of dynamics can be included in development of PSSPs and other approaches such as de novo approaches.

Engineering a thermostable version of D-allulose 3-epimerase from Rhodopirellula baltica via site-directed mutagenesis based on B-factors analysis.

D-allulose has received increasing attention due to its excellent physiological properties and commercial potential. The D-allulose 3-epimerase from Rhodopirellula baltica (RbDAEase) catalyzes the conversion of D-fructose to D-allulose. However, its poor thermostability has hampered its industrial application. Site-directed mutagenesis based on homologous structures in which the residuals on high flexible regions were substituted according to B-factors analysis, is an effective way to improve the thermostability and robustness of an enzyme. RbDAEase showed substrate specificity toward D-allulose with a Km of 58.57 mM and kcat of 1849.43 min-1. It showed a melting temperature (Tm) of 45.7 °C and half-life (t1/2) of 52.3 min at pH 8.0, 60 °C with 1 mM Mn2+. The Site-directed mutation L144 F strengthened the thermostability to a Δt1/2 of 50.4 min, ΔTm of 12.6 °C, and ΔT5060 of 22 °C. It also improved the conversion rate to 28.6%. Structural analysis reveals that a new hydrophobic interaction was formed by the mutation. Thus, site-directed mutagenesis based on B-factors analysis would be an efficient strategy to enhance the thermostability of designed ketose 3-epimerases.

Analyzing Fluctuation Properties in Protein Elastic Networks with Sequence-Specific and Distance-Dependent Interactions.

Simple protein elastic networks which neglect amino-acid information often yield reasonable predictions of conformational dynamics and are broadly used. Recently, model variants which incorporate sequence-specific and distance-dependent interactions of residue pairs have been constructed and demonstrated to improve agreement with experimental data. We have applied the new variants in a systematic study of protein fluctuation properties and compared their predictions with those of conventional anisotropic network models. We find that the quality of predictions is frequently linked to poor estimations in highly flexible protein regions. An analysis of a large set of protein structures shows that fluctuations of very weakly connected network residues are intrinsically prone to be significantly overestimated by all models. This problem persists in the new models and is not resolved by taking into account sequence information. The effect becomes even enhanced in the model variant which takes into account very soft long-ranged residue interactions. Beyond these shortcomings, we find that model predictions are largely insensitive to the integration of chemical information, at least regarding the fluctuation properties of individual residues. One can furthermore conclude that the inherent drawbacks may present a serious hindrance when improvement of elastic network models are attempted.

Sequence-specific dynamic information in proteins.

We examine the local and global properties of the average B-factor, 〈B〉, as a residue-specific indicator of protein dynamic characteristics. It has been shown that values of 〈B〉 for the 20 amino acids differ in a statistically significant manner, and that, while strongly determined by the static physical properties of amino acids, they also encode averaged information about the influence of global fold on single-residue dynamics. Therefore, complete sequences of amino acids also encode fold-related global dynamic information, in addition to the local information that arises from static physical properties. We show that the relative magnitudes of these two contributions can be determined using Fourier methods, which represent the global properties of the sequences. It has also been shown that the behavior of Fourier components of 〈B〉 differs, with very high statistical significance, between structural groups, and that this information is not available from a comparable analysis of static amino acid properties.

An in vitro study of NF-κB factors cooperatively in regulation of Drosophila melanogaster antimicrobial peptide genes.

An important innate immune response in Drosophila melanogaster is the production of antimicrobial peptides (AMPs). Expression of AMP genes is mediated by the Toll and immune deficiency (IMD) pathways via NF-κB transcription factors Dorsal, DIF and Relish. Dorsal and DIF act downstream of the Toll pathway, whereas Relish acts in the IMD pathway. Dorsal and DIF are held inactive in the cytoplasm by the IκB protein Cactus, while Relish contains an IκB-like inhibitory domain at the C-terminus. NF-κB factors normally form homodimers and heterodimers to regulate gene expression, but formation of heterodimers between Relish and DIF or Dorsal and the specificity and activity of the three NF-κB homodimers and heterodimers are not well understood. In this study, we compared the activity of Rel homology domains (RHDs) of Dorsal, DIF and Relish in activation of Drosophila AMP gene promoters, demonstrated that Relish-RHD (Rel-RHD) interacted with both Dorsal-RHD and DIF-RHD, Relish-N interacted with DIF and Dorsal, and overexpression of individual RHD and co-expression of any two RHDs activated the activity of AMP gene promoters to various levels, suggesting formation of homodimers and heterodimers among Dorsal, DIF and Relish. Rel-RHD homodimers were stronger activators than heterodimers of Rel-RHD with either DIF-RHD or Dorsal-RHD, while DIF-RHD-Dorsal-RHD heterodimers were stronger activators than either DIF-RHD or Dorsal-RHD homodimers in activation of AMP gene promoters. We also identified the nucleotides at the 6th and 8th positions of the 3' half-sites of the κB motifs that are important for the specificity and activity of NF-κB transcription factors.

Simulated Protein Thermal Detection (SPTD) for Enzyme Thermostability Study and an Application Example for Pullulanase from Bacillus deramificans.

BACKGROUND: The relationship between protein structure and its bioactivity is one of the fundamental problems for protein engineering and pharmaceutical design. METHOD: A new method, called SPTD (Simulated Protein Thermal Detection), was proposed for studying and improving the thermal stability of enzymes. The method was based on the evidence observed by conducting the MD (Molecular Dynamics) simulation for all the atoms of an enzyme vibrating from the velocity at a room temperature (e.g., 25°C) to the desired working temperature (e.g., 65°C). According to the recorded MD trajectories and the coordinate deviations of the constituent residues under the two different temperatures, some new strategies have been found that are useful for both drug delivery and starch industry. CONCLUSION: The SPTD technique presented in this paper may become a very useful tool for pharmaceutical design and protein engineering.

RABDAM: quantifying specific radiation damage in individual protein crystal structures.

Radiation damage remains one of the major limitations to accurate structure determination in protein crystallography (PX). Despite the use of cryo-cooling techniques, it is highly probable that a number of the structures deposited in the Protein Data Bank (PDB) have suffered substantial radiation damage as a result of the high flux densities of third generation synchrotron X-ray sources. Whereas the effects of global damage upon diffraction pattern reflection intensities are readily detectable, traditionally the (earlier onset) site-specific structural changes induced by radiation damage have proven difficult to identify within individual PX structures. More recently, however, development of the BDamage metric has helped to address this problem. BDamage is a quantitative, per-atom metric identifies potential sites of specific damage by comparing the atomic B-factor values of atoms that occupy a similar local packing density environment in the structure. Building upon this past work, this article presents a program, RABDAM, to calculate the BDamage metric for all selected atoms within any standard-format PDB or mmCIF file. RABDAM provides several useful outputs to assess the extent of damage suffered by an input PX structure. This free and open-source software will allow assessment and improvement of the quality of PX structures both previously and newly deposited in the PDB.

Enhancement of Heat Stability and Kinetic Parameters of the Maize Endosperm ADP-Glucose Pyrophosphorylase by Mutagenesis of Amino Acids in the Small Subunit With High B Factors.

ADP-glucose pyrophosphorylase (AGPase) is an important enzyme in starch synthesis and previous studies showed that the heat lability of this enzyme is a determinant to starch synthesis in the maize endosperm and, in turn, seed yield. Here, amino acids in the AGPase endosperm small subunit with high B-factors were mutagenized and individual changes enhancing heat stability and/or kinetic parameters in an Escherichia coli expression system were chosen. Individual mutations were combined and analyzed. One triple mutant, here termed Bt2-BF, was chosen for further study. Combinations of this heat stable, 3-PGA-independent small subunit variant with large subunits also heat stable yielded complex patterns of heat stability and kinetic and allosteric properties. Interestingly, two of the three changes reside in a protein motif found only in AGPases that exhibit high sensitivity to 3-PGA. While not the 3-PGA binding site, amino acid substitutions in this region significantly alter 3-PGA activation kinetics.

Activity inhibition and crystal polymorphism induced by active-site metal swapping.

The Arenaviridae family is one of the two RNA viral families that encode a 3'-5' exonuclease in their genome. An exonuclease domain is found in the Arenaviridae nucleoprotein and targets dsRNA specifically. This domain is directly involved in suppression of innate immunity in the host cell. Like most phosphate-processing enzymes, it requires a divalent metal ion such as Mg2+ (or Mn2+) as a cofactor to catalyse nucleotide-cleavage and nucleotide-transfer reactions. On the other hand, calcium (Ca2+) inhibits this enzymatic activity, in spite of the fact that Mg2+ and Ca2+ present comparable binding affinities and biological availabilities. Here, the molecular and structural effects of the replacement of magnesium by calcium and its inhibition mechanism for phosphodiester cleavage, an essential reaction in the viral process of innate immunity suppression, are studied. Biochemical data and high-resolution structures of the Mopeia virus exonuclease domain complexed with each ion are reported for the first time. The consequences of the ion swap for the stability of the protein, the catalytic site and the functional role of a specific metal ion in enabling the catalytic cleavage of a dsRNA substrate are outlined.

Molecular dynamics-based refinement and validation for sub-5 Å cryo-electron microscopy maps.

Two structure determination methods, based on the molecular dynamics flexible fitting (MDFF) paradigm, are presented that resolve sub-5 Å cryo-electron microscopy (EM) maps with either single structures or ensembles of such structures. The methods, denoted cascade MDFF and resolution exchange MDFF, sequentially re-refine a search model against a series of maps of progressively higher resolutions, which ends with the original experimental resolution. Application of sequential re-refinement enables MDFF to achieve a radius of convergence of ~25 Å demonstrated with the accurate modeling of ß-galactosidase and TRPV1 proteins at 3.2 Å and 3.4 Å resolution, respectively. The MDFF refinements uniquely offer map-model validation and B-factor determination criteria based on the inherent dynamics of the macromolecules studied, captured by means of local root mean square fluctuations. The MDFF tools described are available to researchers through an easy-to-use and cost-effective cloud computing resource on Amazon Web Services.

Criteria to Extract High-Quality Protein Data Bank Subsets for Structure Users.

It is often necessary to build subsets of the Protein Data Bank to extract structural trends and average values. For this purpose it is mandatory that the subsets are non-redundant and of high quality. The first problem can be solved relatively easily at the sequence level or at the structural level. The second, on the contrary, needs special attention. It is not sufficient, in fact, to consider the crystallographic resolution and other feature must be taken into account: the absence of strings of residues from the electron density maps and from the files deposited in the Protein Data Bank; the B-factor values; the appropriate validation of the structural models; the quality of the electron density maps, which is not uniform; and the temperature of the diffraction experiments. More stringent criteria produce smaller subsets, which can be enlarged with more tolerant selection criteria. The incessant growth of the Protein Data Bank and especially of the number of high-resolution structures is allowing the use of more stringent selection criteria, with a consequent improvement of the quality of the subsets of the Protein Data Bank.

Universal features of fluctuations in globular proteins.

Using data from 2000 non-homologous protein crystal structures, we show that the distribution of residue B factors of proteins collapses onto a single master curve. We show by maximum entropy arguments that this curve is a Gamma function whose order and dispersion are obtained from experimental data. The distribution for any given specific protein can be generated from the master curve by a linear transformation. Any perturbation of the B factor distribution of a protein, imposed at constant energy, causes a decrease in the entropy of the protein relative to that of the reference state. Proteins 2016; 84:721-725. © 2016 Wiley Periodicals, Inc.