Comparing Alternative Corrections for Bias in the Bias-Corrected Bootstrap Test of Mediation.

Although the bias-corrected (BC) bootstrap is an often-recommended method for testing mediation due to its higher statistical power relative to other tests, it has also been found to have elevated Type I error rates with small sample sizes. Under limitations for participant recruitment, obtaining a larger sample size is not always feasible. Thus, this study examines whether using alternative corrections for bias in the BC bootstrap test of mediation for small sample sizes can achieve equal levels of statistical power without the associated increase in Type I error. A simulation study was conducted to compare Efron and Tibshirani's original correction for bias, z0, to six alternative corrections for bias: (a) mean, (b-e) Winsorized mean with 10%, 20%, 30%, and 40% trimming in each tail, and (f) medcouple (robust skewness measure). Most variation in Type I error (given a medium effect size of one regression slope and zero for the other slope) and power (small effect size in both regression slopes) was found with small sample sizes. Recommendations for applied researchers are made based on the results. An empirical example using data from the ATLAS drug prevention intervention study is presented to illustrate these results. Limitations and future directions are discussed.

Fast 19F Magic Angle Spinning NMR Crystallography for Structural Characterization of Fluorine-Containing Pharmaceutical Compounds.

Fluorine-containing compounds comprise 20 to 30 percent of all commercial drugs, and the proportion of fluorinated pharmaceuticals is rapidly growing. While magic angle spinning (MAS) NMR spectroscopy is a popular technique for analysis of solid pharmaceutical compounds, fluorine has been underutilized as a structural probe so far. Here, we report a fast (40-60 kHz) MAS 19F NMR approach for structural characterization of fluorine-containing crystalline pharmaceutical compounds at natural abundance, using the antimalarial fluorine-containing drug mefloquine as an example. We demonstrate the utility of 2D 19F-13C and 19F-19F dipolar-coupling-based correlation experiments for 19F and 13C resonance frequency assignment, which permit identification of crystallographically inequivalent sites. The efficiency of 19F-13C cross-polarization and the effect of 1H and 19F decoupling on spectral resolution and sensitivity were evaluated in a broad range of experimental conditions. We further demonstrate a protocol for measuring accurate interfluorine distances based on 1D DANTE-RFDR experiments combined with multispin numerical simulations.

Natural Product-Derived Chiral Pyrrolidine-2,5-diones, Their Molecular Structures and Conversion to Pharmacologically Important Skeletons.

The versatility of the natural products (2S,3S)- and (2S,3R)-3-hydroxy-5-oxotetrahydrofuran-2,3-dicarboxylic acids (1 and 2), isolated in large amounts from tropical plant sources, has been demonstrated by the construction of 3-substituted and 3,4-disubstituted chiral pyrrolidine-2,5-diones. The absolute configurations of chiral pyrrolidine-2,5-diones have been ascertained using chiroptical spectroscopic methods and/or single-crystal XRD data. A combination of different reaction strategies delivering a diverse matrix of fused heterocyclic ring systems is presented. The pyrrolo[2,1-a]isoquinoline alkaloid (+)-crispine A possesses a wide range of pharmacological activities including antidepressant, antiplatelet, antileukemic, and anticancer activities. The analogues of indolizino[8,7-b]indole alkaloids (+)- and (-)-harmicine show strong antileishmanial, antinociceptive, PDE5-inhibitory, antimalarial, and antiviral activities. The bicyclic furo[2,3-b]pyrrolo skeleton is present in many natural products. Thus, the uniqueness of relatively cheap, naturally occurring chiral 2-hydroxycitric acid lactones as chirons has been demonstrated by the construction of some important molecular skeletons that are otherwise difficult to synthesize.

Measurement of Accurate Interfluorine Distances in Crystalline Organic Solids: A High-Frequency Magic Angle Spinning NMR Approach.

Long-range interatomic distance restraints are critical for the determination of molecular structures by NMR spectroscopy, both in solution and in the solid state. Fluorine is a powerful NMR probe in a wide variety of contexts, owing to its favorable magnetic properties, ease of incorporation into biological molecules, and ubiquitous use in synthetic organic molecules designed for diverse applications. Because of the large gyromagnetic ratio of the 100% naturally abundant 19F isotope, interfluorine distances as long as 20 Å are accessible in magic-angle spinning (MAS) dipolar recoupling experiments. Herein, we present an approach for the determination of accurate interfluorine distances in multispin systems, using the finite pulse radio frequency driven recoupling (fpRFDR) at high MAS frequencies of 40-60 kHz. We use a series of crystalline "molecular ruler" solids, difluorobenzoic acids and 7F-L-tryptophan, for which the intra- and intermolecular interfluorine distances are known. We describe the optimal experimental conditions for accurate distance determinations, including the choice of a phase cycle, the relative advantages of selective inversion one-dimensional versus two-dimensional correlation experiments, and the appropriate numerical simulation protocols. An optimal strategy for the analysis of RFDR exchange curves in organic solids with extended spin interaction networks is presented, which, even in the absence of crystal structures, can be potentially incorporated into NMR structure determination.

Accuracy and precision of protein structures determined by magic angle spinning NMR spectroscopy: for some 'with a little help from a friend'.

We present a systematic investigation into the attainable accuracy and precision of protein structures determined by heteronuclear magic angle spinning solid-state NMR for a set of four proteins of varied size and secondary structure content. Structures were calculated using synthetically generated random sets of C-C distances up to 7 Å at different degrees of completeness. For single-domain proteins, 9-15 restraints per residue are sufficient to derive an accurate model structure, while maximum accuracy and precision are reached with over 15 restraints per residue. For multi-domain proteins and protein assemblies, additional information on domain orientations, quaternary structure and/or protein shape is needed. As demonstrated for the HIV-1 capsid protein assembly, this can be accomplished by integrating MAS NMR with cryoEM data. In all cases, inclusion of TALOS-derived backbone torsion angles improves the accuracy for small number of restraints, while no further increases are noted for restraint completeness above 40%. In contrast, inclusion of TALOS-derived torsion angle restraints consistently increases the precision of the structural ensemble at all degrees of distance restraint completeness.

Night-to-Night Variability in the Bedtime Routine Predicts Sleep in Toddlers.

The present study examined relations between nightly bedtime routines and sleep outcome measures in a sample of 185 toddlers aged 30 months. Parents reported on their toddler's sleep duration and the length and activities included in the bedtime routine each night for approximately 2 weeks. Toddlers wore actigraphs to track their sleep during the same time period. Correlation, mean difference, and regression analyses indicated that toddlers experienced different bedtime routines and exhibited differences in parent reported sleep duration between weeknights and weekends. Multi-level models revealed that variability in the bedtime routine on an individual night most consistently affected parent reported sleep duration on that night. Differences in the bedtime routines between weeknights and weekends also affected actigraph recorded sleep duration and sleep efficiency. Results suggest that keeping consistent bedtime routines between weeknights and weekends is important for optimal sleep outcomes.

Health beliefs as a key determinant of intent to use anabolic-androgenic steroids (AAS) among high-school football players: implications for prevention.

The use of anabolic-androgenic steroids (AAS) is problematic for youth because of negative effects such as reduced fertility, increased aggression and exposure to toxic chemicals. An effective programme for addressing this problem is Adolescents Training and Learning to Avoid Steroids (ATLAS). This secondary analysis expands prior research by identifying prominent mechanisms of change and highlighting key longitudinal processes that contributed to the success of ATLAS. The current sample consists of high-school football players (N = 1.068; M age = 15.25) who began ATLAS in grades nine through eleven and participated in booster sessions for two years post-baseline. Knowledge of AAS effects, belief in media ads, reasons not to use AAS, perceived severity of and susceptibility to AAS effects and ability to resist drug offers were critical mediators of the relations between ATLAS and outcomes. Modern applications of the ATLAS programme are also discussed.

Dynamic regulation of HIV-1 capsid interaction with the restriction factor TRIM5α identified by magic-angle spinning NMR and molecular dynamics simulations.

The host factor protein TRIM5α plays an important role in restricting the host range of HIV-1, interfering with the integrity of the HIV-1 capsid. TRIM5 triggers an antiviral innate immune response by functioning as a capsid pattern recognition receptor, although the precise mechanism by which the restriction is imposed is not completely understood. Here we used an integrated magic-angle spinning nuclear magnetic resonance and molecular dynamics simulations approach to characterize, at atomic resolution, the dynamics of the capsid's hexameric and pentameric building blocks, and the interactions with TRIM5α in the assembled capsid. Our data indicate that assemblies in the presence of the pentameric subunits are more rigid on the microsecond to millisecond timescales than tubes containing only hexamers. This feature may be of key importance for controlling the capsid's morphology and stability. In addition, we found that TRIM5α binding to capsid induces global rigidification and perturbs key intermolecular interfaces essential for higher-order capsid assembly, with structural and dynamic changes occurring throughout the entire CA polypeptide chain in the assembly, rather than being limited to a specific protein-protein interface. Taken together, our results suggest that TRIM5α uses several mechanisms to destabilize the capsid lattice, ultimately inducing its disassembly. Our findings add to a growing body of work indicating that dynamic allostery plays a pivotal role in capsid assembly and HIV-1 infectivity.

Fast Magic-Angle Spinning 19 F†NMR Spectroscopy of HIV-1 Capsid Protein Assemblies.

19 F NMR spectroscopy is an attractive and growing area of research with broad applications in biochemistry, chemical biology, medicinal chemistry, and materials science. We have explored fast magic angle spinning (MAS) 19 F solid-state NMR spectroscopy in assemblies of HIV-1 capsid protein. Tryptophan residues with fluorine substitution at the 5-position of the indole ring were used as the reporters. The 19 F chemical shifts for the five tryptophan residues are distinct, reflecting differences in their local environment. Spin-diffusion and radio-frequency-driven-recoupling experiments were performed at MAS frequencies of 35 kHz and 40-60 kHz, respectively. Fast MAS frequencies of 40-60 kHz are essential for consistently establishing 19 F-19 F correlations, yielding interatomic distances of the order of 20 Å. Our results demonstrate the potential of fast MAS 19 F NMR spectroscopy for structural analysis in large biological assemblies.

19F Magic Angle Spinning NMR Spectroscopy and Density Functional Theory Calculations of Fluorosubstituted Tryptophans: Integrating Experiment and Theory for Accurate Determination of Chemical Shift Tensors.

The 19F chemical shift is a sensitive NMR probe of structure and electronic environment in organic and biological molecules. In this report, we examine chemical shift parameters of 4F-, 5F-, 6F-, and 7F-substituted crystalline tryptophan by magic angle spinning (MAS) solid-state NMR spectroscopy and density functional theory. Significant narrowing of the 19F lines was observed under fast MAS conditions, at spinning frequencies above 50 kHz. The parameters characterizing the 19F chemical shift tensor are sensitive to the position of the fluorine in the aromatic ring and, to a lesser extent, the chirality of the molecule. Accurate calculations of 19F magnetic shielding tensors require the PBE0 functional with a 50% admixture of a Hartree-Fock exchange term, as well as taking account of the local crystal symmetry. The methodology developed will be beneficial for 19F-based MAS NMR structural analysis of proteins and protein assemblies.

Determination of accurate backbone chemical shift tensors in microcrystalline proteins by integrating MAS NMR and QM/MM.

Chemical shifts are highly sensitive probes of local conformation and overall structure. Both isotropic shifts and chemical shift tensors are readily accessible from NMR experiments but their quantum mechanical calculations remain challenging. In this work, we report and compare accurately measured and calculated 15NH and 13Cα chemical shift tensors in proteins, using the microcrystalline agglutinin from Oscillatoria agardhii (OAA). Experimental 13Cα and 15NH chemical tensors were obtained by solid-state NMR spectroscopy, employing tailored recoupling sequences, and for their quantum mechanics/molecular mechanics (QM/MM) calculations different sets of functionals were evaluated. We show that 13Cα chemical shift tensors are primarily determined by backbone dihedral angles and dynamics, while 15NH tensors mainly depend on local electrostatic contributions from solvation and hydrogen bonding. In addition, the influence of including crystallographic waters, the molecular mechanics geometry optimization protocol, and the level of theory on the accuracy of the calculated chemical shift tensors is discussed. Specifically, the power of QM/MM calculations in accurately predicting the unusually upfield shifted 1HN G26 and G93 resonances is highlighted. Our integrated approach is expected to benefit structure refinement of proteins and protein assemblies.

Toward Closing the Gap: Quantum Mechanical Calculations and Experimentally Measured Chemical Shifts of a Microcrystalline Lectin.

NMR chemical shifts are exquisitely sensitive probes for conformation and dynamics in molecules and supramolecular assemblies. Although isotropic chemical shifts are easily measured with high accuracy and precision in conventional NMR experiments, they remain challenging to calculate quantum mechanically, particularly in inherently dynamic biological systems. Using a model benchmark protein, the 133-residue agglutinin from Oscillatoria agardhii (OAA), which has been extensively characterized by us previously, we have explored the integration of X-ray crystallography, solution NMR, MAS NMR, and quantum mechanics/molecular mechanics (QM/MM) calculations for analysis of 13Cα and 15NH isotropic chemical shifts. The influence of local interactions, quaternary contacts, and dynamics on the accuracy of calculated chemical shifts is analyzed. Our approach is broadly applicable and expected to be beneficial in chemical shift analysis and chemical-shift-based structure refinement for proteins and protein assemblies.

The Combined Effects of Measurement Error and Omitting Confounders in the Single-Mediator Model.

Mediation analysis requires a number of strong assumptions be met in order to make valid causal inferences. Failing to account for violations of these assumptions, such as not modeling measurement error or omitting a common cause of the effects in the model, can bias the parameter estimates of the mediated effect. When the independent variable is perfectly reliable, for example when participants are randomly assigned to levels of treatment, measurement error in the mediator tends to underestimate the mediated effect, while the omission of a confounding variable of the mediator-to-outcome relation tends to overestimate the mediated effect. Violations of these two assumptions often co-occur, however, in which case the mediated effect could be overestimated, underestimated, or even, in very rare circumstances, unbiased. To explore the combined effect of measurement error and omitted confounders in the same model, the effect of each violation on the single-mediator model is first examined individually. Then the combined effect of having measurement error and omitted confounders in the same model is discussed. Throughout, an empirical example is provided to illustrate the effect of violating these assumptions on the mediated effect.

The role of anger rumination and autism spectrum disorder-linked perseveration in the experience of aggression in the general population.

This study (a) examined the role of anger rumination as a mediator of the relation between social anxiety and the experience of anger, hostility, and aggression, in the general population, and (b) evaluated the degree to which the presence of autism spectrum disorder characteristics moderates the indirect influence of anger rumination. We then explored whether social cognition and perseveration characteristic of autism spectrum disorder uniquely accounted for the predicted moderation. In this survey study of young adults (n = 948), anger rumination mediated the relation between social anxiety and hostility, as well as verbal and physical aggression, as predicted. Greater autism spectrum disorder characteristics augmented the effect of social anxiety on hostility and physical aggression by increasing the effect of anger rumination, but not by increasing the effect of social anxiety on anger rumination. Implications for developing treatment approaches that target hostility and aggression among young adults who may not be formally diagnosed but have characteristics of autism spectrum disorder are discussed.

Increasing Statistical Power in Mediation Models Without Increasing Sample Size.

Inadequate statistical power to detect treatment effects in health research is a problem that is compounded when testing for mediation. In general, the preferred strategy for increasing power is to increase the sample size, but there are many situations where additional participants cannot be recruited, necessitating the use of other methods to increase statistical power. Many of these other strategies, commonly applied to analysis of variance and multiple regression models, can be applied to mediation models with similar results. Additional predictors or blocking variables will increase or decrease statistical power, however, depending on whether these variables are related to the mediator, the outcome, or both. The effect of these two methods on the power for tests of mediation is illustrated through the use of simulations. Implications for health researchers using these methods are discussed.

An exponential decay model for mediation.

Mediation analysis is often used to investigate mechanisms of change in prevention research. Results finding mediation are strengthened when longitudinal data are used because of the need for temporal precedence. Current longitudinal mediation models have focused mainly on linear change, but many variables in prevention change nonlinearly across time. The most common solution to nonlinearity is to add a quadratic term to the linear model, but this can lead to the use of the quadratic function to explain all nonlinearity, regardless of theory and the characteristics of the variables in the model. The current study describes the problems that arise when quadratic functions are used to describe all nonlinearity and how the use of nonlinear functions, such as exponential decay, address many of these problems. In addition, nonlinear models provide several advantages over polynomial models including usefulness of parameters, parsimony, and generalizability. The effects of using nonlinear functions for mediation analysis are then discussed and a nonlinear growth curve model for mediation is presented. An empirical example using data from a randomized intervention study is then provided to illustrate the estimation and interpretation of the model. Implications, limitations, and future directions are also discussed.

Explanation of Two Anomalous Results in Statistical Mediation Analysis.

Previous studies of different methods of testing mediation models have consistently found two anomalous results. The first result is elevated Type I error rates for the bias-corrected and accelerated bias-corrected bootstrap tests not found in nonresampling tests or in resampling tests that did not include a bias correction. This is of special concern as the bias-corrected bootstrap is often recommended and used due to its higher statistical power compared with other tests. The second result is statistical power reaching an asymptote far below 1.0 and in some conditions even declining slightly as the size of the relationship between X and M, a, increased. Two computer simulations were conducted to examine these findings in greater detail. Results from the first simulation found that the increased Type I error rates for the bias-corrected and accelerated bias-corrected bootstrap are a function of an interaction between the size of the individual paths making up the mediated effect and the sample size, such that elevated Type I error rates occur when the sample size is small and the effect size of the nonzero path is medium or larger. Results from the second simulation found that stagnation and decreases in statistical power as a function of the effect size of the a path occurred primarily when the path between M and Y, b, was small. Two empirical mediation examples are provided using data from a steroid prevention and health promotion program aimed at high school football players (Athletes Training and Learning to Avoid Steroids; Goldberg et al., 1996), one to illustrate a possible Type I error for the bias-corrected bootstrap test and a second to illustrate a loss in power related to the size of a. Implications of these findings are discussed.

A graphical representation of the mediated effect.

Mediation analysis is widely used in the social sciences. Despite the popularity of mediation models, few researchers have used graphical methods, other than structural path diagrams, to represent their models. Plots of the mediated effect can help a researcher better understand the results of the analysis and convey these results to others. This article presents a method for creating and interpreting plots of the mediated effect for a variety of mediation models, including models with (1) a dichotomous independent variable, (2) a continuous independent variable, and (3) an interaction between an independent variable and the mediating variable. An empirical example is then presented to illustrate these plots. Sample code for creating plots of the mediated effect in R and SAS is also included, and may be downloaded from www.psychonomic.org/archive.

Erroneous knowledge of results affects decision and memory processes on timing tasks.

On mental timing tasks, erroneous knowledge of results (KR) leads to incorrect performance accompanied by the subjective judgment of accurate performance. Using the start-stop technique (an analogue of the peak interval procedure) with both reproduction and production timing tasks, the authors analyze what processes erroneous KR alters. KR provides guidance (performance error information) that lowers decision thresholds. Erroneous KR also provides targeting information that alters response durations proportionately to the magnitude of the feedback error. On the production task, this shift results from changes in the reference memory, whereas on the reproduction task this shift results from changes in the decision threshold for responding. The idea that erroneous KR can alter different cognitive processes on related tasks is supported by the authors' demonstration that the learned strategies can transfer from the reproduction task to the production task but not visa versa. Thus effects of KR are both task and context dependent.

Distribution of the product confidence limits for the indirect effect: program PRODCLIN.

This article describes a program, PRODCLIN (distribution of the PRODuct Confidence Limits for INdirect effects), written for SAS, SPSS, and R, that computes confidence limits for the product of two normal random variables. The program is important because it can be used to obtain more accurate confidence limits for the indirect effect, as demonstrated in several recent articles (MacKinnon, Lockwood, & Williams, 2004; Pituch, Whittaker, & Stapleton, 2005). Tests of the significance of and confidence limits for indirect effects based on the distribution of the product method have more accurate Type I error rates and more power than other, more commonly used tests. Values for the two paths involved in the indirect effect and their standard errors are entered in the PRODCLIN program, and distribution of the product confidence limits are computed. Several examples are used to illustrate the PRODCLIN program. The PRODCLIN programs in rich text format may be downloaded from www.psychonomic.org/archive.