Time- and ensemble-averaged direct NOE restraints

Summary NMR data are collected as time- and ensemble-averaged quantities. Yet, in commonly used methods for structure determination of biomolecules, structures are required to satisfy simultaneously a large number of constrainsts. Recently, however, methods have been developed that allow a better fit of the experimental data by the use of time- or ensemble-averaged restraints. Thus far, these methods have been applied to structure refinement using distance and J-coupling restraints. In this paper, time and ensemble averaging is extended to the direct refinement with experimental NOE data. The implementation of time- and ensemble-averaged NOE restraints in DINOSAUR is described and illustrated with experimental NMR data for crambin, a 46-residue protein. Structure refinement with both time- and ensemble-averaged NOE restraints results in lower R-factors, indicating a better fit of the experimental NOE data.     

SAR versus VAR, and the size and shape that provide the most appropriate RF exposure metric in the range of 0.5-6 GHz

Basic restrictions for protecting against localized tissue heating induced from exposure to radiofrequency (RF) fields are typically specified as the specific energy absorption rate (SAR), which is mass averaged in recognition of the thermal diffusion properties of tissues. This article seeks to determine the most appropriate averaging mass (1, 3, 5, 7, or 10 g) and averaging shape (cube or sphere). We also consider an alternative metric, volumetric energy absorption rate (VAR), which uses volume averaging (over 1, 3, 5, 7, and 10 cm³; cube and sphere). The SAR and VAR averaging approaches were compared by considering which was a better predictor of tissue temperature rise (ΔT) induced by near‐ and far‐field RF exposures (0.5–6 GHz), calculated in a detailed human body model. For the exposure scenarios that we examined, VAR is better correlated with ΔT than SAR, though not at a statistically significant level for most of the metric types we studied. However, as VAR offers substantive advantages in ease of assessment we recommend this metric over SAR. Averaging over a cube or a sphere provides equivalent levels of correlation with ΔT, and so we recommend choosing the averaging shape on the basis of which is easier to assess. The optimal averaging volume is 10 cm³ for VAR, and the optimal mass is 10 g for SAR. The correlation between VAR or SAR and ΔT diminishes substantially at 6 GHz, where incident power flux density may be a better exposure metric. Bioelectromagnetics 32:312–321, 2011. © 2010 Wiley‐Liss, Inc.     

Heating of tissues by microwaves: A model analysis

We consider the thermal response times for heating of tissue subject to nonionizing (microwave or infrared) radiation. The analysis is based on a dimensionless form of the bioheat equation. The thermal response is governed by two time constants: one(τ₁) pertains to heat convection by blood flow, and is of the order of 20–30 min for physiologically normal perfusion rates; the second (τ₂) characterizes heat conduction and varies as the square of a distance that characterizes the spatial extent of the heating. Two idealized cases are examined. The first is a tissue block with an insulated surface, subject to irradiation with an exponentially decreasing specific absorption rate, which models a large surface area of tissue exposed to microwaves. The second is a hemispherical region of tissue exposed at a spatially uniform specific absorption rate, which models localized exposure. In both cases, the steady-state temperature increase can be written as the product of the incident power density and an effective time constant τ_eff, which is defined for each geometry as an appropriate function of τ₁ and τ₂. In appropriate limits of the ratio of these time constants, the local temperature rise is dominated by conductive or convective heat transport. Predictions of the block model agree well with recent data for the thresholds for perception of warmth or pain from exposure to microwave energy. Using these concepts, we developed a thermal averaging time that might be used in standards for human exposure to microwave radiation, to limit the temperature rise in tissue from radiation by pulsed sources. We compare the ANSI exposure standards for microwaves and infrared laser radiation with respect to the maximal increase in tissue temperature that would be allowed at the maximal permissible exposures. A historical appendix presents the origin of the 6-min averaging time used in the microwave standard. Bioelectromagnetics 19:420–428, 1998. © 1998 Wiley-Liss, Inc.     

Preaveraging or Postaveraging of Data Measured in Chronobiology: Will the Mean Mouse Please Stand Up?

Chronological measures are often made on several subjects, or for a period of days, or both, to define cycles of 24 hr in order to obtain a variety of information which can be submitted to statistical tests to characterize the subjects. In this paper, a simple theoretical model for two subjects is presented to examine the consequences of preaveraging. Preaveraging is defined as the summing of those temporal values which define the phenomenon in question. This type of operation is in fact the equivalent of filtering with moving averages. This model is then extended to N subjects exhibiting randomly assigned shifts. The disadvantages of preaveraging are illustrated from data drawn from experimental studies on mouse activity in three inbred strains: DBA/2, BALB/B6 and C57BL/6. Different effects of preaveraging, both voluntary and involuntary, are described. It is shown that preaveraging masks features that in fact discriminate across strains whereas postaveraging, because it does not suppress information, makes it possible to define the parameters of an “average” subject.     

A genetic algorithm-based protocol for docking ensembles of small ligands using experimental restraints

Summary A genetic algorithm (GA) based method for docking ensembles of small, flexible ligands to receptor proteins using NMR-derived constraints is described. In this method, three translations and rotations of the ligand and the dihedral angles of the ligand are represented by binary strings and evolve under the genetic operators of cross-over, mutation, migration and selection. The fitness function for the selection process includes distance and dihedral restraints and a repulsive van der Waals term. The GA was applied to a three-atom model system as well as to the streptavidin-biotin complex using simulated intermolecular distance restraints. In both systems, the GA was able to obtain low-energy conformations when only a single binding site was simulated. Calculations were also performed using distance restraints from two distinct binding sites. In these simulations, the GA was able to obtain low-energy conformations corresponding to ligand molecules in each of the two sites. The inclusion of additional ligands in the ensemble did not result in an energetic benefit, confirming that only two ligand conformations were necessary to fulfill the distance restraints. This method allows for a direct investigation of the minimum number of ligand orientations necessary to fulfill experimental distance restraints, and simultaneously yields detailed structural information about each site.     

Quantitative relationships of invertebrates to pH in Norwegian river systems

The invertebrate fauna has been surveyed for twenty one unlimed generally acidic river systems in Norway. The data consist of 180 samples and 127 invertebrate taxa and associated water chemistry data (pH, calcium, acid neutralizing capacity, total aluminium, and conductivity). Multivariate numerical methods are used to quantify the relationships between aquatic invertebrates and water chemistry. Detrended canonical correspondence analysis (DCCA) shows one dominant axis of variation with high correlations for pH and aluminium. DCCA axis 2 is significantly correlated with calcium. The predictive abilities of invertebrates to pH are explored by means of weighted averaging (WA) regression and calibration and weighted averaging partial-least-squares regression (WA-PLS). The performance of the methods is reported in terms of the root mean square error of prediction (RMSEP) of (observed pH-inferred pH). Bootstrapping and leave-one-out jackknifing are used as cross-validation procedures. The predictive abilities of invertebrates are good (RMSEP_boot for WA = 0.309 pH units). Comparison of the invertebrates with diatom studies shows that invertebrates are as good predictors of modern pH as diatoms are. RMSEP_jack shows that WA-PLS improves the predictive abilities. Indicator taxa for pH are found by Gaussian regression. Anisoptera, Agrypnia obsoleta, Leptophlebia marginata, Sialis lutaria, and Zygoptera have significant sigmoidal curves where abundances increase with decreasing pH. Cyrnus flavidus shows a significant unimodal response and has an estimated optimum in the acid part of the gradient. Isoperla spp. and Ostracoda show significant sigmoidal responses where abundances increase with increasing pH. Amphinemura borealis, Diura nanseni, Isoperla grammatica, I. obscura, and Siphonoperla burmeisteri show significant unimodal responses and have high pH optima. Many taxa do not have statistically significant unimodal or sigmoidal curves, but are found by WA to be characteristic of either high pH or low pH. These results suggest that a combined use of Gaussian regression and direct gradient analysis is needed to get a full overview of potential indicator taxa.     

On the encoding of movement vectors by honeybees. Are distance and direction represented independently?

Honeybees flying repeatedly over the same trajectory link it to an associated visual stimulus such that on viewing the stimulus they perform a trajectory in the habitual direction. To test if trajectory length can also be linked to a visual stimulus, bees were trained to fly through a multi-comparmented maze. Bees flew through a multi-compartmented maze. In one compartment a short trajectory could be linked to a stripe pattern oriented at 45° to the horizontal. In another compartment a longer trajectory could be linked to 135° stripes. Bees made both associations: their trajectories were short when viewing 45° stripes and longer when viewing 135° stripes. 90° stripes evoked trajectories of intermediate length.To test if distance and direction are linked independently to stripe orientation, a bee's trajectory was linked to 135° stripes in one compartment and to 45° stripes in another. These trajectories were the same length but differed in their horizontal direction by 60° or by 120°. 90° stripes evoked trajectories of intermediate direction which were shorter than those elicited by either training pattern. Bees were also trained to generate one long and one short trajectory with directions 120° apart. The trajectories elicited by 90° stripes were then biased towards the direction of the long training vector. Length and direction are not treated separately. The rules for combining trajectories resemble those of vector averaging.     

The Biological Sediment Tolerance Index: Assessing fine sediments conditions in Oregon streams using macroinvertebrates

Fine sediments in excess of natural background conditions are one of most globally common causes of stream degradation, with well documented impacts on aquatic communities. The lack of agreement on methods for monitoring fine sediments makes it difficult to share data, limiting assessments of stream conditions across jurisdictions. We present a model that circumvents these limitations by inferring fine sediments in Oregon streams through sampling of macroinvertebrates. Tolerances to fine sediments (<0.06 mm diameter) were calculated for 240 macroinvertebrate taxa, from a calibration dataset of 446 sites across Oregon, as well as an independent validation dataset of 50 samples. Weighted averaging methods were used to infer fine sediment levels in streams by weighting the tolerances of modeled taxa observed in a sample by their abundances. The final model, the Biological Sediment Tolerance Index (BSTI), showed a strong relationship to measured fine sediments (calibration r² = 0.49, validation r² = 0.58). Root-mean-squared-error was small in the calibration dataset (2% fines), but larger in the validation dataset (14% fines). Repeatability was assessed by examining variability in BSTI at 14 sites across Oregon. Because field methods for sampling macroinvertebrates are standardized across resource agencies in Oregon and the responses of macroinvertebrates represent the actual effects of fine sediments on stream ecosystems, the BSTI may offer water resource managers’ a cost-effective method for assessing fine sediment conditions in their ongoing efforts to improve water quality across the state.     

Adjustment uncertainty in effect estimation

Often there is substantial uncertainty in the selection of confounderswhen estimating the association between an exposure and health.We define this type of uncertainty as `adjustment uncertainty'.We propose a general statistical framework for handling adjustmentuncertainty in exposure effect estimation for a large numberof confounders, we describe a specific implementation, and wedevelop associated visualization tools. Theoretical resultsand simulation studies show that the proposed method providesconsistent estimators of the exposure effect and its variance.We also show that, when the goal is to estimate an exposureeffect accounting for adjustment uncertainty, Bayesian modelaveraging with posterior model probabilities approximated usinginformation criteria can fail to estimate the exposure effectand can over- or underestimate its variance. We compare ourapproach to Bayesian model averaging using time series dataon levels of fine particulate matter and mortality.     

Uncertainty Evaluation of a Groundwater Conceptual Model by Using a Multimodel Averaging Method

ABSTRACT

A groundwater field is a complex and open system. Groundwater simulation and prediction often deviated from true values, which is attributed to the uncertainty of groundwater modeling. The conceptual model (model struture) is one of the main sources of groundwater modeling uncertianty. In this study, the mean Euclidean distance (MED) between model simulations and observations is proposed to assess the integrated likelihood value of a conceptual model in Bayesian model averaging (BMA). Moreover, this proposed BMA method is compared with the traditional generalized likelihood uncertainty estimation (GLUE) BMA method by a synthetical groundwater model, and the characteristics of these two BMA methods are summarized.     

Functional and structural analysis of acetylcholine receptor-rich membranes after negative staining

Phosphotungstate (pH 7.4) used for negative staining of membranes from Torpedo electric tissue rich in acetylcholine receptor does not affect binding properties and cation permeability of the receptor and its ion channel. Uranyl salts, frequently used for negative staining, precipitate the receptor-rich membranes making measurements of ligand binding and ion-permeability regulation impossible. The gross ultrastructure in the two stains is not significantly different, but for future high-resolution electron microscopy aiming at visualizing structural details of functional receptor molecules it is necessary to resort to a stain preserving native and active receptor. Uranyl salts are not applicable for this purpose. The electron micrographs obtained with phosphotungstate reveal two distinct structures in the receptor-rich membrane: a closed ring ('doughnut') and an open ring ('horseshoe'), with a ratio of abundance of about 3:2.     

Modeling vital rates improves estimation of population projection matrices

Population projection matrices are commonly used by ecologists and managers to analyze the dynamics of stage-structured populations. Building projection matrices from data requires estimating transition rates among stages, a task that often entails estimating many parameters with few data. Consequently, large sampling variability in the estimated transition rates increases the uncertainty in the estimated matrix and quantities derived from it, such as the population multiplication rate and sensitivities of matrix elements. Here, we propose a strategy to avoid overparameterized matrix models. This strategy involves fitting models to the vital rates that determine matrix elements, evaluating both these models and ones that estimate matrix elements individually with model selection via information criteria, and averaging competing models with multimodel averaging. We illustrate this idea with data from a population of Silene acaulis (Caryophyllaceae), and conduct a simulation to investigate the statistical properties of the matrices estimated in this way. The simulation shows that compared with estimating matrix elements individually, building population projection matrices by fitting and averaging models of vital-rate estimates can reduce the statistical error in the population projection matrix and quantities derived from it.     

Effective stomatal and boundary-layer resistances of heterogeneous surfaces

In nature surfaces are rarely uniform, so terms such as ‘surface’, ‘stomatal’ or ‘canopy’ resistance usually indicate some kind of average over a population of sub-areas, each with its own separate resistance. Questions then arise as to how gross measurements of these resistances should be interpreted in terms of the components, or how components should be aggregated into representative single values. Aggregation schemes have been published by Raupach (1991, Vegetatio 91, 105–120) and Lhomme (1992, Agriculture and Forest Meteorology 61, 11–21), but these are different for reasons that were not explained. This paper develops the idea that averaging schemes should be designed to serve particular purposes, and that they can be varied to suit these purposes. It is shown that the ‘effective’ resistances defined by Raupach and Lhomme preserve different quantities. A further averaging scheme is developed which preserves both correct transpiration rate and CO₂ flux when used in the Penman-Monteith equation and an equation describing assimilation. All of these schemes are fairly complex, so the work provides a warning against naive use of effective variables.     

Imputation and variable selection in linear regression models with missing covariates

Across multiply imputed data sets, variable selection methods such as stepwise regression and other criterion-based strategies that include or exclude particular variables typically result in models with different selected predictors, thus presenting a problem for combining the results from separate complete-data analyses. Here, drawing on a Bayesian framework, we propose two alternative strategies to address the problem of choosing among linear regression models when there are missing covariates. One approach, which we call "impute, then select" (ITS) involves initially performing multiple imputation and then applying Bayesian variable selection to the multiply imputed data sets. A second strategy is to conduct Bayesian variable selection and missing data imputation simultaneously within one Gibbs sampling process, which we call "simultaneously impute and select" (SIAS). The methods are implemented and evaluated using the Bayesian procedure known as stochastic search variable selection for multivariate normal data sets, but both strategies offer general frameworks within which different Bayesian variable selection algorithms could be used for other types of data sets. A study of mental health services utilization among children in foster care programs is used to illustrate the techniques. Simulation studies show that both ITS and SIAS outperform complete-case analysis with stepwise variable selection and that SIAS slightly outperforms ITS.     

Iteratio: calculating environmental indicator values for species and relevés

Question: Is it possible to translate vegetation maps into reliable thematic maps of site conditions? Method: This paper presents a new method, called Iteratio, by which a coherent spatial overview of specific environmental conditions can be obtained from a comprehensive vegetation survey of a specific area. Iteratio is a database application which calculates environmental indicator values for vegetation samples (relevés) on the basis of known indicator values of a limited number of plant species. The outcome is then linked to a digitalized vegetation map (map of plant communities) which results in a spatial overview of site conditions. Iteratio requires the indicator values of a minimum of 10–20% of the species occurring. The species are given a relative weight according to their amplitudes: species with a narrow range are weighted stronger, species with a broad range are weighted weaker. Conclusion: The method presented here enables a coherent assessment of site conditions on the basis of a vegetation survey and the indicator values of a limited number of plant species.     

The influence of stream invertebrate composition at neighbouring sites on local assemblage composition

1. The composition of freshwater invertebrate assemblages at a location is determined by a range of physico‐chemical and biotic factors in the local environment, as well as larger‐scale spatial factors such as sources of recruits. We assessed the relative importance of the species composition of local neighbourhoods and proximal environmental factors on the composition of invertebrate assemblages. 2. Macroinvertebrate assemblages were sampled at 188 running‐water sites in the catchment of the River Rede, north‐east England. A total of 176 species were recorded. 3. Environmental data, in the form of 13 biotic and abiotic measurements that described stream physical structure, aquatic vegetation and water characteristics, were recorded for each site. Detrended correspondence analysis was then used to simplify nine of these stream environmental variables to create an index of stream structure. 4. The species composition of the invertebrate assemblages was related to the environmental variables, using an information theoretic approach. The impact of the species composition of neighbouring sites on each site was determined using Moran's I and autoregressive modelling techniques. 5. Species composition was primarily associated with water pH and stream structure. The importance of the species composition of neighbouring sites in determining local species assemblages differed markedly between taxa. The autoregressive component was low for Coleoptera, intermediate for Trichoptera and Plecoptera, and high for Ephemeroptera. 6. We hypothesise that the observed differences in the autoregressive component amongst these orders reflects variation in their dispersal abilities from neighbouring sites.     

An asymptotic theory for model selection inference in general semiparametric problems

Hjort & Claeskens (2003) developed an asymptotic theoryfor model selection, model averaging and subsequent inferenceusing likelihood methods in parametric models, along with associatedconfidence statements. In this article, we consider a semiparametricversion of this problem, wherein the likelihood depends on parametersand an unknown function, and model selection/averaging is tobe applied to the parametric parts of the model. We show thatall the results of Hjort & Claeskens hold in the semiparametriccontext, if the Fisher information matrix for parametric modelsis replaced by the semiparametric information bound for semiparametricmodels, and if maximum likelihood estimators for parametricmodels are replaced by semiparametric efficient profile estimators.Our methods of proof employ Le Cam's contiguity lemmas, leadingto transparent results. The results also describe the behaviourof semiparametric model estimators when the parametric componentis misspecified, and also have implications for pointwise-consistentmodel selectors.