Statistical innovations for estimating shape characteristics of biological macromolecules in solution using small-angle x-ray scattering data

2016 Spring.Includes bibliographical references.Small-angle X-ray scattering (SAXS) is a technique that yields low-resolution images of biological macromolecules by exposing a solution containing the molecule to a powerful X-ray beam. The beam scatters when it interacts with the molecule. The intensity of the scattered beam is recorded on a detector plate at various scattering angles, and contains information on structural characteristics of the molecule in solution. In particular, the radius of gyration (Rg) for a molecule, which is a measure of the spread of its mass, can be estimated from the lowest scattering angles of SAXS data using a regression technique known as Guinier analysis. The analysis requires specification of a range or “window” of scattering angles over which the regression relationship holds. We have thus developed 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. The theory and methodology are developed using a local polynomial model with autoregressive errors. Simulation studies confirm the quality of the asymptotic approximations and the superior performance of the proposed methodology relative to the accepted standard. We show that the algorithm is applicable to data acquired from proteins, nucleic acids and their complexes, and we demonstrate with examples that the algorithm improves the ability to test biological hypotheses. The radius of gyration is a normalized second moment of the pairwise distance distribution p(r), which describes the relative frequency of inter-atomic distances in the structure of the molecule. By extending the theory to fourth moments, we show that a new parameter ψ can be calculated theoretically from p(r) and estimated from experimental SAXS data, using a method that extends Guinier's Rg estimation procedure. This new parameter yields an enhanced ability to use intensity data to distinguish between two molecules with different but similar Rg values. Analysis of existing structures in the protein data bank (PDB) shows that the theoretical ψ values relate closely to the aspect ratio of a molecular structure. The combined values for Rg and ψ acquired from experimental data provide estimates for the dimensions and associated uncertainties for a standard geometric shape, representing the particle in solution. We have chosen the cylinder as the standard shape and show that a simple, automated procedure gives a cylindrical estimate of a particle of interest. The cylindrical estimate in turn yields a good first approximation to the maximum inter-atomic distance in a molecule, Dmax, an important parameter in shape reconstruction. As with estimation of Rg, estimation of ψ requires specification of a window of angles over which to conduct the higher-order Guinier analysis. We again employ a local polynomial model with autoregressive errors to derive methodology and supporting asymptotic theory for selection of an optimal window, minimum mean square error estimation of the aspect ratio, and estimation of its variance. Recent advances in SAXS data collection and more comprehensive data comparisons have resulted in a great need for automated scripts that analyze SAXS data. Our procedures to estimate Rg and ψ can be automated easily and can thus be used for large suites of SAXS data under various experimental conditions, in an objective and reproducible manner. The new methods are applied to 357 SAXS intensity curves arising from a study on the wild type nucleosome core particle and its mutants and their behavior under different experimental conditions. The resulting Rg2 values constitute a dataset which is then analyzed to account for the complex dependence structure induced by the experimental protocols. The analysis yields powerful scientific inferences and insight into better design of SAXS experiments. Finally, we consider a measurement error problem relevant to the estimation of the radius of gyration. In a SAXS experiment, it is standard to obtain intensity curves at different concentrations of the molecule in solution. Concentration-by-angle interactions may be present in such data, and analysis is complicated by the fact that actual concentration levels are unknown, but are measured with some error. We therefore propose a model and estimation procedure that allows estimation of true concentration ratios and concentration-by-angle interactions, without requiring any information about concentration other than that contained in the SAXS data

Climate and Soil Characteristics Determine Where No-Till Management Can Store Carbon in Soils and Mitigate Greenhouse Gas Emissions

Article number: 11665 (2019)201

Climate and soil characteristics determine where no-till management can store carbon in soils and mitigate greenhouse gas emissions

Adoption of no-till management on croplands has become a controversial approach for storing carbon in soil due to conflicting findings. Yet, no-till is still promoted as a management practice to stabilize the global climate system from additional change due to anthropogenic greenhouse gas emissions, including the 4 per mille initiative promoted through the UN Framework Convention on Climate Change. We evaluated the body of literature surrounding this practice, and found that SOC storage can be higher under no-till management in some soil types and climatic conditions even with redistribution of SOC, and contribute to reducing net greenhouse gas emissions. However, uncertainties tend to be large, which may make this approach less attractive as a contributor to stabilize the climate system compared to other options. Consequently, no-till may be better viewed as a method for reducing soil erosion, adapting to climate change, and ensuring food security, while any increase in SOC storage is a co-benefit for society in terms of reducing greenhouse gas emissions.Facultad de Ciencias Agrarias y Forestale

Improved estimation of the radius of gyration from small-angle x-ray scattering data

Small-angle X-ray scattering (SAXS) is an experimentally simple technique that provides access to low-resolution information about biological macromolecules in solution. We here provide R code and example data sets for a new algorithm that produces accurate and precise values for the radius of gyration, Rg, of a particle. Theory states that the information derived from the lowest scattering angles can be used to estimate Rg. The value Rg is a fundamental structural parameter that is related to a molecule's size and shape. The original algorithm implemented with the R code estimates Rg with a reliable variance estimate and with higher precision than the classical method. A bias-variance criterion is minimized to determine the optimal number of data points to calculate Rg. After accounting for correlation in the data, least squares regression is used to estimate the radius of gyration and an accurate variance estimate. The software also supports the use of replicate data. Use of the code and examples is described in README.pdf