Illuminating Solution Responses of a LOV Domain Protein with Photocoupled Small-Angle X-Ray Scattering

The PAS-LOV domain is a signal-transducing component found in a large variety of proteins that is responsible for sensing different stimuli such as light, oxygen, and voltage. The LOV protein VVD regulates blue light responses in the filamentous fungi Neurospora crassa. Using photocoupled, time-resolved small-angle X-ray scattering, we extract the solution protein structure in both dark-adapted and light-activated states. Two distinct dark-adapted conformations are detected in the wild-type protein: a compact structure that corresponds to the crystal structure of the dark-state monomer as well as an extended structure that is well modeled by introducing conformational disorder at the N-terminus of the protein. These conformations are accentuated in carefully selected variants, in which a key residue for propagating structural transitions, Cys71, has been mutated or oxidized. Despite different dark-state conformations, all proteins form a common dimer in response to illumination. Taken together, these data support a reaction scheme that describes the mechanism for light-induced dimerization of VVD. Envelope reconstructions of the transient light-state dimer reveal structures that are best described by a parallel arrangement of subunits that have significantly changed conformation compared to the crystal structure.     

Confidence Intervals for Microbial Density Using Serial Dilutions with MPN Estimates

An alteration to Woodward's methods is recommended for deriving a 1 — α confidence interval for microbial density using serial dilutions with most-probable-number (MPN) estimates. Outcomes of the serial dilution test are ordered by their MPNs. A lower limit for the confidence interval corresponding to an outcome y is the density for which y and all higher ordered outcomes have total probability α/2. An upper limit is derived in the analogous way. An alteration increases the lowest lower limits and decreases the highest upper limits. For comparison, a method that is optimal in the sense of null hypothesis rejection is described. This method ranks outcomes dependent upon the microbial density in question, using proportional first derivatives of the probabilities. These and currently used methods are compared. The recommended method is shown to be more desirable in certain respects, although resulting in slightly wider confidence intervals than De Man's (1983) method.     

Anomalous Small Angle X-Ray Scattering Simulations: Proof of Concept for Distance Measurements for Nanoparticle-Labelled Biomacromolecules in Solution

Anomalous small angle X-ray scattering can in principle be used to determine distances between metal label species on biological molecules. Previous experimental studies in the past were unable to distinguish the label-label scattering contribution from that of the molecule, because of the use of atomic labels; these labels contribute only a small proportion of the total scattering signal. However, with the development of nanocrystal labels (of 50–100 atoms) there is the possibility for a renewed attempt at applying anomalous small angle X-ray scattering for distance measurement. This is because the contribution to the scattered signal is necessarily considerably stronger than for atomic labels. Here we demonstrate through simulations, the feasibility of the technique to determine the end-to-end distances of labelled nucleic acid molecules as well as other internal distances mimicking a labelled DNA binding protein if the labels are dissimilar metal nanocrystals. Of crucial importance is the ratio of mass of the nanocrystals to that of the labelled macromolecule, as well as the level of statistical errors in the scattering intensity measurements. The mathematics behind the distance determination process is presented, along with a fitting routine than incorporates maximum entropy regularisation.     

Estimation and Confidence Intervals for Two-Stage Sample-Size-Flexible Design with LSW Likelihood Approach

Adaptive sample size methods have been a popular topic in the field of clinical trials. There are a few basic requirements for the adaptive methods to be acceptable from the international regulatory viewpoint. All valid methods need to control the overall type-I error rate at the pre-specified level. The rule of the interim and final decisions needs to be explicit and clearly documentable. It is extremely desirable that the method employed also provides estimation of the treatment effect in addition to the significance test. In this paper we describe the point and confidence interval estimation for the likelihood approach of sample-size adaptive design proposed by Li et al. (Biostatistics 3:277–287, 2002, J. Biopharm. Stat. 15:707–718, 2005). We use the median unbiased estimator (Cox and Hinkley, Theoretical Statistics, p. 273, 1974) for estimating the treatment effect and demonstrate that the estimator has small mean squared error compared to the naïve method, and that the confidence interval estimation has correct coverage probability.     

X-Ray Solution Scattering of Squid Heavy Meromyosin: Strengthening the Evidence for an Ancient Compact off State

The overall conformations of regulated myosins or heavy meromyosins from chicken/turkey, scallop, tarantula, limulus, and scorpion sources have been studied by a number of techniques, including electron microscopy, sedimentation, and pulsed electron paramagnetic resonance. These studies have indicated that the binding of regulatory ions changes the conformation of the molecule from a compact shape found in the “off” state of the muscle to extended relationships between the tail and independently mobile heads that predominate in the “on” state. Here we strengthen the argument for the generality of this conformational change by using small angle X-ray scattering on heavy meromyosin from squid. Small angle X-ray scattering allows the protein to be visualized in solution under mild and relatively physiological conditions, and squid differs from the other species studied by at least 500 million years of evolution. Analysis of the data indicates that upon addition of Ca²⁺ the radius of gyration increases. Differences in the squid “on” and “off” states are clearly distinguishable as bimodal and unimodal pair distance distribution functions respectively. These observations are consistent with a Ca²⁺-free squid heavy meromyosin that is compact, but which becomes extended when Ca²⁺ is bound. Further, the scattering profile derived from the current model of tarantula heavy meromyosin in the “off” state is in excellent agreement with the measured “off” state scattering profile for squid heavy meromyosin. The previous and current studies together provide significant evidence that regulated myosin''s compact off-state conformation is an ancient trait, inherited from a common ancestor during divergent evolution.     

Confidence Intervals for the Mean of a Poisson Distribution: A Review

The paper provides a comprehensive review of methodology for setting confidence intervals for the parameter of a Poisson distribution. The results are illustrated by a numerical example.     

Confidence Intervals for Morphology-Based Cladistic Trees: A Platyrrhine Phylogeny Test Case

I estimate confidence intervals for phylogenetic trees based on bootstrap resampling while calculating special coefficients of similarity. I treat each successive cladistic dichotomy as a null hypothesis for sampling from a universe of cranial and postcranial synapomorphically-based similarities that includes the next lower similarity. Successive dichotomies that are not at significantly different similarity levels are collapsed into polytomies. Following a trial application to equid cladistic traits employed in Felsenstein's introduction (Felsenstein, J. (1985). Evolution 39: 783–791), I apply the methods to New World monkey relationships using morphological character sets. Unresolvable polytomies among platyrrhine subfamilies are the rule when these methods are applied.     

AutoDockFR: Advances in Protein-Ligand Docking with Explicitly Specified Binding Site Flexibility

Automated docking of drug-like molecules into receptors is an essential tool in structure-based drug design. While modeling receptor flexibility is important for correctly predicting ligand binding, it still remains challenging. This work focuses on an approach in which receptor flexibility is modeled by explicitly specifying a set of receptor side-chains a-priori. The challenges of this approach include the: 1) exponential growth of the search space, demanding more efficient search methods; and 2) increased number of false positives, calling for scoring functions tailored for flexible receptor docking. We present AutoDockFR–AutoDock for Flexible Receptors (ADFR), a new docking engine based on the AutoDock4 scoring function, which addresses the aforementioned challenges with a new Genetic Algorithm (GA) and customized scoring function. We validate ADFR using the Astex Diverse Set, demonstrating an increase in efficiency and reliability of its GA over the one implemented in AutoDock4. We demonstrate greatly increased success rates when cross-docking ligands into apo receptors that require side-chain conformational changes for ligand binding. These cross-docking experiments are based on two datasets: 1) SEQ17 –a receptor diversity set containing 17 pairs of apo-holo structures; and 2) CDK2 –a ligand diversity set composed of one CDK2 apo structure and 52 known bound inhibitors. We show that, when cross-docking ligands into the apo conformation of the receptors with up to 14 flexible side-chains, ADFR reports more correctly cross-docked ligands than AutoDock Vina on both datasets with solutions found for 70.6% vs. 35.3% systems on SEQ17, and 76.9% vs. 61.5% on CDK2. ADFR also outperforms AutoDock Vina in number of top ranking solutions on both datasets. Furthermore, we show that correctly docked CDK2 complexes re-create on average 79.8% of all pairwise atomic interactions between the ligand and moving receptor atoms in the holo complexes. Finally, we show that down-weighting the receptor internal energy improves the ranking of correctly docked poses and that runtime for AutoDockFR scales linearly when side-chain flexibility is added.     

Resonant X-Ray Scattering and Absorption for the Global and Local Structures of Cu-modified Metallothioneins in Solution

With Cd and Zn metal ions removed from the native rabbit-liver metallothionein upon unfolding, Cu-modified metallothioneins (Cu-MTs) were obtained during refolding in solutions containing Cu^I or Cu^II ions. X-ray absorption near-edge spectroscopic results confirm the respectively assigned oxidation states of the copper ions in Cu^I-MT and Cu^II-MT. Global and local structures of the Cu-MTs were subsequently characterized by anomalous small-angle x-ray scattering (ASAXS) and extended x-ray absorption fine structure. Energy-dependent ASAXS results indicate that the morphology of Cu^II-MT resembles that of the native MT, whereas Cu^I-MT forms oligomers with a higher copper content. Both dummy-residue simulation and model-shape fitting of the ASAXS data reveal consistently rodlike morphology for Cu^II-MT. Clearly identified Cu-S, Cu-O, and Cu-Cu contributions in the extended x-ray absorption fine structure analysis indicate that both Cu^I and Cu^II ions are bonded with O and S atoms of nearby amino acids in a four-coordination environment, forming metal clusters smaller than metal thiolate clusters in the native MT. It is demonstrated that a combination of resonant x-ray scattering and x-ray absorption can be particularly useful in revealing complementary global and local structures of metalloproteins due to the atom specific characteristics of the two techniques.     

SCORE: A New Empirical Method for Estimating the Binding Affinity of a Protein-Ligand Complex

A new method is presented to estimate the binding affinity of a protein-ligand complex with known three-dimensional structure. The method, SCORE, uses an empirical scoring function to describe the binding free energy, which includes terms to account for van der Waals contact, metal-ligand bonding, hydrogen bonding, desolvation effect, and deformation penalty upon the binding process. The coefficients of each term are obtained by multivariate regressional analysis of a diverse training set of 170 protein-ligand complexes. The final scoring function reproduces the binding free energies of the whole training set with a cross-validated deviation of 6.3 kJ/mol. The predictive ability of the function is further tested by a set of 11 endothiapepsin complexes and the internal consistency of the function is demonstrated in a stepwise procedure named Evolutionary Test. A major innovation of this method is the introduction of an atomic binding score which allows the researcher to inspect and optimize the lead compound rationally in a structure-based drug design scheme.     

Auto-FACE: An NMR Based Binding Site Mapping Program for Fast Chemical Exchange Protein-Ligand Systems

Background

Nuclear Magnetic Resonance (NMR) spectroscopy offers a variety of experiments to study protein-ligand interactions at atomic resolution. Among these experiments, N Heteronuclear Single Quantum Correlation (HSQC) experiment is simple, less time consuming and highly informative in mapping the binding site of the ligand. The interpretation of N HSQC becomes ambiguous when the chemical shift perturbations are caused by non-specific interactions like allosteric changes and local structural rearrangement. Under such cases, detailed chemical exchange analysis based on chemical shift perturbation will assist in locating the binding site accurately.

Methodology/Principal Findings

We have automated the mapping of binding sites for fast chemical exchange systems using information obtained from N HSQC spectra of protein serially titrated with ligand of increasing concentrations. The automated program Auto-FACE (Auto-FAst Chemical Exchange analyzer) determines the parameters, e.g. rate of change of perturbation, binding equilibrium constant and magnitude of chemical shift perturbation to map the binding site residues. Interestingly, the rate of change of perturbation at lower ligand concentration is highly sensitive in differentiating the binding site residues from the non-binding site residues. To validate this program, the interaction between the protein and the ligand BH3I-1 was studied. Residues in the hydrophobic BH3 binding groove of were easily identified to be crucial for interaction with BH3I-1 from other residues that also exhibited perturbation. The geometrically averaged equilibrium constant () calculated for the residues present at the identified binding site is consistent with the values obtained by other techniques like isothermal calorimetry and fluorescence polarization assays (). Adjacent to the primary site, an additional binding site was identified which had an affinity of 3.8 times weaker than the former one. Further NMR based model fitting for individual residues suggest single site model for residues present at these binding sites and two site model for residues present between these sites. This implies that chemical shift perturbation can represent the local binding event much more accurately than the global binding event.

Conclusion/Significance

Detail NMR chemical shift perturbation analysis enabled binding site residues to be distinguished from non-binding site residues for accurate mapping of interaction site in complex fast exchange system between small molecule and protein. The methodology is automated and implemented in a program called “Auto-FACE”, which also allowed quantitative information of each interaction site and elucidation of binding mechanism.     

The Structure of High Molecular Weight Ribonucleic Acid in Solution: A Small-Angle X-Ray Scattering Study

Small-angle x-ray scattering studies on an absolute scale have been carried out on isotropic solutions of high molecular weight RNA obtained from ascites tumor cells, E. coli, and yeast. It was found that in all three cases the RNA is composed of short rigid rods (50 to 150Å in length) joined by small flexible regions. The rods account for almost the entire structure (at least 90 per cent); their radius of gyration about the axis and their mass per unit length are similar to those of DNA, suggesting a double-stranded helical structure. The rods are joined in an array forming the compact RNA molecule. On thermal degradation, the molecular superstructure disappears while the rods persist.     

SASCUBE: An Updated Method of Cubes for Calculation of the Intensity of X-Ray Scattering by Biopolymers in Solution

Biophysics - Abstract—This work describes an updated method of cubes, which allows calculation of the SAS curves for biopolymers in solution on the basis of the coordinates of their atoms...     

A Method for Helical RNA Global Structure Determination in Solution Using Small-Angle X-Ray Scattering and NMR Measurements

We report a “top-down” method that uses mainly duplexes' global orientations and overall molecular dimension and shape restraints, which were extracted from experimental NMR and small-angle X-ray scattering data, respectively, to determine global architectures of RNA molecules consisting of mostly A-form-like duplexes. The method is implemented in the G2G (from global measurement to global structure) toolkit of programs. We demonstrate the efficiency and accuracy of the method by determining the global structure of a 71-nt RNA using experimental data. The backbone root-mean-square deviation of the ensemble of the calculated global structures relative to the X-ray crystal structure is 3.0 ± 0.3 Å using the experimental data and is only 2.5 ± 0.2 Å for the three duplexes that were orientation restrained during the calculation. The global structure simplifies interpretation of multidimensional nuclear Overhauser spectra for high-resolution structure determination. The potential general application of the method for RNA structure determination is discussed.     

X-Ray Small Angle Scattering: A New Deconvolution Method for Evaluating Electron Density Distributions from Small Angle Scattering Diagrams

The direct determination of the electron density distributions of multilayered specimens with a small number of unit cells from X-ray small angle scattering experiments via the Q-function method of Hosemann and Bagchi includes the deconvolution of the so-called Q_o-function, the generalized Patterson function of one unit cell. In this paper a new and direct deconvolution method on the basis of Fourier series is presented which is suitable for one-dimensional centrosymmetrical (or antisymmetrical) density distributions. A FORTRAN-program has been written which has an execution time of ca. 20 s on an UNIVAC 1106-computer. The procedure has been successfully tested on some convolution functions generated by membrane-type electron density distributions.     

Using the Past to Predict the Present: Confidence Intervals for Regression Equations in Phylogenetic Comparative Methods

Two phylogenetic comparative methods, independent contrasts and generalized least squares models, can be used to determine the statistical relationship between two or more traits. We show that the two approaches are functionally identical and that either can be used to make statistical inferences about values at internal nodes of a phylogenetic tree (hypothetical ancestors), to estimate relationships between characters, and to predict values for unmeasured species. Regression equations derived from independent contrasts can be placed back onto the original data space, including computation of both confidence intervals and prediction intervals for new observations. Predictions for unmeasured species (including extinct forms) can be made increasingly accurate and precise as the specificity of their placement on a phylogenetic tree increases, which can greatly increase statistical power to detect, for example, deviation of a single species from an allometric prediction. We reexamine published data for basal metabolic rates (BMR) of birds and show that conventional and phylogenetic allometric equations differ significantly. In new results, we show that, as compared with nonpasserines, passerines exhibit a lower rate of evolution in both body mass and mass-corrected BMR; passerines also have significantly smaller body masses than their sister clade. These differences may justify separate, clade-specific allometric equations for prediction of avian basal metabolic rates.     

An Introduction to Phylogenetically Based Statistical Methods, with a New Method for Confidence Intervals on Ancestral Values

Interspecific comparisons have played a prominent role in evolutionarybiology at least since the time of Charles Darwin. Since 1985,the "comparative method" has been revitalized by new analyticaltechniques that use phylogenetic information and by increasedavailability of phytogenies (often from molecular data sets).Because species descend from common ancestors in a hierarchicalfashion, related species tend to resemble each other (elephantslook like elephants); therefore, cross-species data sets generallydo not comprise independent and identically distributed datapoints. Phylogenetically based statistical methods attempt toaccount for this fact. Phylogenetic methods allow traditionaltopics in comparative and ecological physiology to be addressedwith greater rigor, including the form of allometric relationshipsand whether physiological phenotypes vary predictably in relationto behavior, ecology or environmental characteristics, whichprovides evidence about adaptation. They can also address newtopics, such as whether rates of physiological evolution havediffered among lineages (clades), and where and when a phenotypefirst evolved. We present brief overviews of three phylogeneticallybased statistical methods: phylogenetically independent contrasts,Monte Carlo computer simulations to obtain null distributionsof test statistics, and phylogenetic autocorrelation. In a newresult, we show analytically how to use independent contraststo estimate ancestral values and confidence intervals aboutthem. These confidence intervals often exceed the range of variationobserved among extant species, which points out the relativelygreat uncertainty inherent in such inferences. The use of phytogeniesshould become as common as the use of body size and scalingrelationships in the analysis of physiological diversity.     

Confidence Intervals for Population Allele Frequencies: The General Case of Sampling from a Finite Diploid Population of Any Size

The estimation of population allele frequencies using sample data forms a central component of studies in population genetics. These estimates can be used to test hypotheses on the evolutionary processes governing changes in genetic variation among populations. However, existing studies frequently do not account for sampling uncertainty in these estimates, thus compromising their utility. Incorporation of this uncertainty has been hindered by the lack of a method for constructing confidence intervals containing the population allele frequencies, for the general case of sampling from a finite diploid population of any size. In this study, we address this important knowledge gap by presenting a rigorous mathematical method to construct such confidence intervals. For a range of scenarios, the method is used to demonstrate that for a particular allele, in order to obtain accurate estimates within 0.05 of the population allele frequency with high probability (%), a sample size of is often required. This analysis is augmented by an application of the method to empirical sample allele frequency data for two populations of the checkerspot butterfly (Melitaea cinxia L.), occupying meadows in Finland. For each population, the method is used to derive % confidence intervals for the population frequencies of three alleles. These intervals are then used to construct two joint % confidence regions, one for the set of three frequencies for each population. These regions are then used to derive a % confidence interval for Jost''s D, a measure of genetic differentiation between the two populations. Overall, the results demonstrate the practical utility of the method with respect to informing sampling design and accounting for sampling uncertainty in studies of population genetics, important for scientific hypothesis-testing and also for risk-based natural resource management.